Comparing Religions X: Moral Depth

[It's hard to believe it's been nearly 3 years since the last post in this series; maybe writing about a "long delay" jinxed me.  Anyway I got pretty busy with academic stuff, but now I'm on sabbatical.  Like the rest of this series, the core of this post was written about 7-8 years ago, but I kept feeling like I needed to tinker around with it.  But it's past time to release it into the wild, so here it is.—AW]

10. What is the general moral character of the religious teaching?

This is relevant for two reasons.  First, a good person is more honest, and therefore less likely to try to deliberately trick other people into believing something false (see my previous section on fraud.) People who make up religions are hardly likely to be paragons of moral virtue in other respects.  As Jesus said:

Watch out for false prophets.  They come to you in sheep’s clothing, but inwardly they are ferocious wolves.  By their fruit you will recognize them.  Do people pick grapes from thornbushes, or figs from thistles?  Likewise, every good tree bears good fruit, but a bad tree bears bad fruit.  (Matt. 7:15-17)

By "fruit" Jesus means, not simply conversions or quantity of pious devotions (which any fanatical cult can produce), but rather the moral character of those who claim to be prophets of a true religion, which serve as a test of their claims to be supernaturally inspired.

Second, if God is good and holy—which is a core article of faith for all Abrahamic religions, and also Platonism—then presumably any religion he reveals must also be good and holy.  In fact, one might well expect it to be supernaturally good, since if the religion merely taught ordinary human ethics, we could just as easily come to it by natural reason alone.  This does not, of course, imply that the people God reveals his laws to will be morally perfect (if they had no flaws, they wouldn't need instruction) but the teaching itself should be morally good.

I. Making Moral Judgements

In comparing different religions for their degree of moral goodness, I am presupposing that moral virtue is not merely a matter of conformity to the arbitrary social conventions that one is brought up with, but rather that an open-minded person can recognize and appreciate goodness, even when it is embedded in a culture very different from their own.

In other words, I am assuming in this blog post that we will not allow ourselves to be bogged down by "Meno's paradox".  In a conversation with Socrates, Meno tried to argue that it was impossible for a person who didn't already know what virtue is, to ever find out about it:

How will you search for it, Socrates, when you have no idea what it is?  What kind of thing from among those you are ignorant of will you set before yourself to look for?  And even if you happened exactly upon it, how would you recognize that this is what you didn't know?  (Meno, 80d)

But as Socrates pointed out in reply, this argument is fallacious because (as he illustrates with an example from Geometry) we are sometimes capable of "recognizing" a truth, even when we are encountering it for the first time.  Put another way, we already have some sort of "germ of truth" inside of us, which helps us to recognize greater truth when we stumble across it.

Plato called this human ability ἀνάμνησις (recollection), and proposed that it was due to having known the truth in a previous existence.  But we don't need to take this Platonic myth too literally to recognize the essential point about learning.  As Socrates says in this same dialogue:

I wouldn't strongly insist on the other aspects of the argument [the stuff about reincarnation], but that we would become better men and braver and less lazy if we believe it is necessary to search for what one doesn't know, rather than if we think that we can't discover what we don't know and should not look for it, for this I will fight strongly, if I am able, in both word and deed.  (86d)

Thus, if we want to search for the true religion in a reasonable and open-minded way (rather than take religious disagreements as an excuse not to think for ourselves) then we need to avoid two opposite extremes:

  1. The first extreme would be if we make a list of all our opinions about highly controversial ethical topics (e.g. abortion, vegetarianism, alcohol, specific sexual taboos...) and demand that a religion can be true only if it agrees with us about each one of these particular issues.  But this approach would absolutely preclude ever using religion to progress in our understanding of morality.                                                                                                                                           .
    It would, after all, be a very limited deity who didn't know anything more about the conditions for human flourishing than we do.  And since people's views about morality evolve with time, it would be quite a coincidence if God's views happened to agree with e.g. early 21st century postmodern liberal mores in every single detail—even on points where we disagree with other places and times!  (And even, with many other people who live in the same country as us.)   Such an approach would only make sense, if I arrogantly assumed that I have nothing to learn from any being wiser than myself.                                                                                                                                           .                                                                                    .
  2. The opposite extreme—which is equally petrifying—would be to adopt a position of total moral helplessness, and take the attitude that we have no inherent knowledge of morality except for what we can learn through the dictates of some specific religion.  But such total deference would make it impossible to use morality as a measuring-rod to help us determine which religion is true.  After all, each religion will claim that its own moral system is right.  So this sort of helplessness, is no better than moral relativism!                                                                                                                                           .
    Even if we start out in a religion which was truly revealed by God, this particular type of fundamentalism would actually prevent us from ever truly internalizing a moral system—as this requires, not just blind obedience, but also learning to appreciate how a particular way of life is healthy and good, at least for human beings like ourselves.                                                                                                                                           . 
    A final and decisive objection is that it is simply incorrect!—in fact, human beings do have the ability to instinctively understand moral truths, in ways that are broadly similar; even if the details of how it expresses itself are modulated by our particular cultures and religious frameworks.

In summary, we should not expect our preconceptions to line up with every single teaching of a religion.  But taken as a whole, it should come across as something clearly better than what we would have on our own.

We can rationally take our agreement/disagreement on a particular moral topic to be evidence for/against a particular religion.  But, if we discover a religion which seems to have gotten many deep and important truths about humanity right, then we also need to take it seriously even when it makes claims that seem counterintuitive to us.  (A rational person can take such claims "on the credit of the system", as St. John Newman memorably put it.)

Who is the Judge?

A closely related question is this: Do we come to religion with some degree of humility, and in the posture of someone willing to learn something new?  Suppose we imagine assembling all of the `holy books' in the world, and looking through each one.  How will we pick the morally best one?

If we come in the posture of a cynic, then we will be looking for something in the book which morally offends us.  Once that happens, we will reject the book (unless somebody can convince us we were mistaken in doing so).  In other words, we are coming to the book with the intention of judging God.  Well, I cannot imagine any such person deciding to rank the Bible as the most moral of all religious books.  Yes, there is some good stuff in there, but there is a considerable amount of weird and violent stuff.  There are some inscrutable divine decrees, and several things which are foreign to modern sensibilities.

It is doubtful that such a person could be happy with any religion; but if they had to pick one, they'd probably be happier with some modernized religious community without much in the way of distinctive beliefs (like Unitarian Universalism, Reconstructionist Judaism, etc.)

On the other hand, we could also imagine somebody coming to a holy book as a penitent who needs spiritual healing, or as a confused person who wants wisdom.  If I take this attitude, then I (as a morally imperfect person) am looking for the holy book that is most able to judge me, to show the ways in which I fall short and can do better.  I want a book which can inspire me morally to a higher standard, and which illuminates the paradoxes and complexities which arise trying to live a spiritual life in the real world.  If you are looking to be judged in this way, then I am not aware of any book which is better for this purpose then the Bible.

(Note that this approach is quite different from "total moral helplessness", since it still requires us to engage our minds!  We still need to decide whether the holy book speaks to our condition; whether its moral critique is incisive or superficial; whether it is calling us to a higher stage of moral development, or a lower one which we have already superceded.)

In other words, your assessment of the Bible's ethics is going to depend in large part on what you are hoping to get out of it.  As the Bible itself says in multiple places, "God opposes the proud, but gives grace to the humble."

A Product of Its Time

What a true revealed religion should definitely not be, is simply a reflection of the prevailing ethics of the time and place in which the claimed prophet lived.  There are lots of examples of ancient religious leaders prescribing barbaric acts, that were common in their era of history.  But in some ways, this phenomenon is more hilariously obvious when the ethical system being hawked has only quite recently gone out of vogue.

As an example of this, consider the early 20th century internationalist modernism endorsed by Shoghi Effendi (the grandson and first successor to the main prophet of the Bahái religion):

The unity of the human race, as envisaged by Bahá’u’lláh, implies the establishment of a world commonwealth in which all nations, races, creeds and classes are closely and permanently united, and in which the autonomy of its state members and the personal freedom and initiative of the individuals that compose them are definitely and completely safeguarded.

This commonwealth must, as far as we can visualize it, consist of a world legislature, whose members will, as the trustees of the whole of mankind, ultimately control the entire resources of all the component nations, and will enact such laws as shall be required to regulate the life, satisfy the needs and adjust the relationships of all races and peoples.  A world executive, backed by an international Force, will carry out the decisions arrived at, and apply the laws enacted by, this world legislature, and will safeguard the organic unity of the whole commonwealth.  A world tribunal will adjudicate and deliver its compulsory and final verdict in all and any disputes that may arise between the various elements constituting this universal system.

A mechanism of world inter-communication will be devised, embracing the whole planet, freed from national hindrances and restrictions, and functioning with marvellous swiftness and perfect regularity.  A world metropolis will act as the nerve center of a world civilization, the focus towards which the unifying forces of life will converge and from which its energizing influences will radiate.  A world language will either be invented or chosen from among the existing languages and will be taught in the schools of all the federated nations as an auxiliary to their mother tongue.  A world script, a world literature, a uniform and universal system of currency, of weights and measures, will simplify and facilitate intercourse and understanding among the nations and races of mankind.

In such a world society, science and religion, the two most potent forces in human life, will be reconciled, will cöoperate, and will harmoniously develop.  The press will, under such a system, while giving full scope to the expression of the diversified views and convictions of mankind, cease to be mischievously manipulated by vested interests, whether private or public, and will be liberated from the influence of contending governments and peoples.  The economic resources of the world will be organized, its sources of raw materials will be tapped and fully utilized, its markets will be cöordinated and developed, and the distribution of its products will be equitably regulated.

("World Unity the Goal", The World Order of Bahá’u’lláh [paragraph breaks added by me])

These words were written in 1936, and they are quite obviously a product of the time and place in which they were written.  For anyone who has seen the rest of the 20th century, the idea of placing our spiritual hopes for the future in the hands of a more powerful version of the United Nations—which in turn imposes a monoculture on the rest of the world—is too absurd to contemplate as a potential divine revelation.

Obviously, no real divine revelation was needed to come up with this idea.  Effendi (and to a lesser extent Bahá’u’lláh) were simply taking up the "spirit of the age"—what the internationalists and socialists of that time were already striving for—and recasting it as a principle of their own religion.  But a universally valid moral system ought to transcend the prejudices of the particular time and place in which it was originally developed.

(The one somewhat prescient aspect of this passage is that humanity did indeed come up with a global "mechanism of world inter-communication": a.k.a. the Internet.  Kudos for that.  But the Internet is a highly de-centralized system, which allows for cultural diversity, and which certainly does not require a omnicompetent world-state in order to function.  And as we are all now acutely aware, the Internet doesn't actually solve our moral coordination problems, it just transfers them to a new sphere.)

If what you care about most is maximizing ethical niceness, but you also want a religion which is a few centuries old (and thus not simply a repackaged version of contemporary morals) you could always try Sikhism—about which I know relatively little, but it seems to be one of the ethically nicer religions out there (notwithstanding being the religion of a warrior caste).  However, I haven't been able to get much out of reading its holy book (the Guru Granth Sahib) at an intellectual level, as it mainly seems to repeat the same basic ideas over and over again.  Probably the point is not so much to be intellectually stimulated but to absorb the main idea by singing it over and over again.  But, I suppose that is the sort of benefit that one would only get by actually joining a religion...

II. Christianity

So is there a system of religious ethics which does transcend its particular time and place, sufficiently to be credible as having a transcendental origin?

Surprisingly, Jesus' moral teaching, as recorded in the Gospels, e.g. the Sermon on the Mount, actually passes this test.  [If you've never read it before, stop and read the whole thing right now, starting with "Blessed are the poor in spirit" in chapter 5 and ending at the statement of the crowds being astonished by his teaching at the end of chapter 7.]  It is still an impressive spiritual standard, still relevant even after 2,000 years of humanity's moral development, and it has inspired even non-Christian activists such as Gandhi to greater moral heights.

(The Sermon does contain a few minor cultural references to religious institutions of the time; for example Jesus mentions the practice of offering gifts to the Temple at Jerusalem, and also the Sanhedrin which was the supreme court for religious practice in Israel.  But it seems clear that all these references are inessential to the basic principles Jesus was preaching.)

Jesus cuts away the legalism common to many religious traditions, and puts the focus on integrity in the heart:

You have heard that it was said to the people long ago, `You shall not murder, and anyone who murders will be subject to judgment.'  But I tell you that anyone who is angry with a brother will be subject to judgment.  Again, anyone who calls his brother ‘Raqa’ [Empty-headed] is answerable to the Sanhedrin, but anyone who says, ‘fool!’ will be in danger of the fire of hell.

Therefore, if you are offering your gift at the altar and there remember that your brother or sister has something against you, leave your gift there in front of the altar. First go and be reconciled to them; then come and offer your gift.  (5:21-24)

In other words, if you want to be righteous, it's not sufficient to just not kill people.  Even somebody who doesn't express their hatred in words, may be murdering their brother in their hearts (many times over), and that contempt comes out in the words we use to speak about other people.  So if you want to cut to the root of the matter, you have to begin with the way you regard others in your mind.

The same sort of deepening applies to the other commandments as well:

You have heard that it was said, `You shall not commit adultery.'  But I tell you that anyone who looks at a woman lustfully has already committed adultery with her in his heart!...

It has been said, ‘Anyone who divorces his wife must give her a certificate of divorce.’  But I tell you that anyone who divorces his wife, except for sexual immorality, makes her the victim of adultery, and anyone who marries a divorced woman commits adultery.

Again you have heard that it was said to those of old, `You shall not swear falsely, but shall perform your oaths to the Lord.'  But I say to you, do not swear at all...  Let your ‘Yes’ be ‘Yes,’ and your ‘No,’ ‘No.’  For whatever is more than these is from the evil one.

(5:27-37, excerpts)

Jesus' radical new interpretation of the Torah shows us the real source of misdeeds—our own desire to get what we want, even at the price of manipulating others.  They show that no amount of following of technical justifications—"it's okay that I left my wife for another woman because I filled out the proper legal paperwork"; or "I don't have to keep this promise because I didn't swear I would do it"—can prevent us from doing wrong.  Instead, we need for our own internal motivations to be right.

Beyond Legalism: Children, not Slaves

Most religions tend to focus on regulating externals of behavior.  They are obsessed with figuring out the answer to the question "What is the minimum acceptable standard of behavior?"  This process tends to produce an elaborate law-code, often (as in the case of rabbinic Judaism) becoming more and more complex with time.

But Christianity says that God doesn't want slaves, who obey mindlessly out of fear, without knowing the reasons why.  It is true that his awe-inspiring glory deserves our worship and submission.  Yet the New Testament says he wants to treat us as his adult children (who can be trusted with freedom after learning what is good) and as his close friends (who know his plans and thoughts).  As far as I know, this attitude is unique among theistic religions.  It would be quite presumptuous, if God had not taken the initiative by drawing near to us, in order to share the mind of his Spirit with us.  Yet now that I have been granted these privileges, giving them up again in order to serve a more distant deity would be disappointing.  To draw back from this intimacy, from the thoughtful responsibility he has entrusted me with, seems more like immaturity than humility.

Love your Enemies

When Jesus goes on to say:

But I tell you, do not resist an evil person.  If anyone slaps you on the right cheek, turn to them the other cheek also.  And if anyone wants to sue you and take your shirt, hand over your coat as well.  If anyone forces you to go one mile, go with them two miles.  Give to the one who asks you, and do not turn away from the one who wants to borrow from you.

You have heard that it was said, ‘Love your neighbor and hate your enemy.’ But I tell you, love your enemies and pray for those who persecute you, that you may be children of your Father in heaven.  He causes his sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous.  (Matthew 5:39-45),

these sayings are far from trivial to implement, yet actually this is the only practical suggestion—the one that actually works in practice, e.g. in the Civil Rights movement in America—for creating peace between those who hate each other, other than wiping one of the groups out.

Christians have differed as to whether Jesus' words imply total Pacifism (I don't think so myself), but I do think that these words introduce us to a nonviolent form of power which, when applied intelligently, is far greater than the power of violence; because it has the power to move people to freely become better, in a way that no amount of external coercion can ever do.

America's greatest 20th century political activist, St. Martin Luther King Jr., explained the meaning of this passage as follows:

The ultimate weakness of violence is that it is a descending spiral begetting the very thing it seeks to destroy, instead of diminishing evil, it multiplies it. Through violence you may murder the liar, but you cannot murder the lie, nor establish the truth. Through violence you may murder the hater, but you do not murder hate. In fact, violence merely increases hate. Returning violence for violence multiplies violence, adding deeper darkness to a night already devoid of stars. Darkness cannot drive out darkness; only light can do that. Hate cannot drive out hate; only love can do that.

(Where do we go from here: Chaos or Community)

These words are not mere idealism, as in: wouldn't it be nice if people behaved this way, but we know they never will.  For King, these words described a highly practical strategy for social change.  He had hands-on experience using Jesus' method to reform the segregationist South.   Of course, King also paid the price for it.  It can be seen from this example that nonviolence does not imply submissively accepting the status quo; rather it is a creative way of seeking justice by appealing to people's better nature.

As far as I can see, Jesus' radical ethic of love, forgiveness and acceptance is morally better than anything else on offer.

I do not of course mean to imply that the ethical duty to love one's enemies was absolutely original in all respects when stated by Jesus.  It was anticipated by Plato, and certain parts of the Hebrew Bible, although Christ emphasized it more forcefully.   The point is not so much that it was utterly new, but that it was right, even though it was not a truth generally appreciated in Jesus' culture, nor indeed in any culture not influenced by Christianity.  (Sometimes I'm not too sure about Christians either!)

Two Potential Stumbling Blocks

Although it should be indisputable from the above that Jesus' ethical teaching calls his followers to an extremely high ethical standard, there are still a couple of ways in which his morality might still seem alienating or "bad" to many nonreligious readers.  It is worth highlighting these issues briefly, although each would really justify a long post of its own:

Road Bump #1: God the Father

The first point is that Christianity is unavoidably and distinctively theistic, through and through.  Without denying that there are some aspects of Jesus' teaching which could be applied with profit by non-religious people, much of what he says simply makes no sense, when separated from the idea of a God whose character we can count on.  Even when Jesus announces a moral rule that atheists might be able to get behind, he nearly always appeals to theological reasons—for example, imitating the character of God—to explain why the rule should be followed.

I have seen pastors who tried to put forward Jesus' teachings as a sort of "worldly wisdom" that can be appreciated and put into practice even by those who aren't yet religious.   But, apart from a few tidbits, I'm not sure this approach is a very coherent way of introducing seekers to Christianity.

The fact is, it makes no sense to give up your earthly life and goals for the sake of eternal happiness, if in fact there is no God to take care of us, and to keep his promises, and to be blessed by being in communion with him.  Anyone who wants to "try it out", will quickly see that Jesus' commands cannot be separated from Jesus' teaching about our generous and kind Father, whom we are urged to trust to provide for our needs:

“Ask and it will be given to you; seek and you will find; knock and the door will be opened to you.  For everyone who asks receives; the one who seeks finds; and to the one who knocks, the door will be opened.

Which of you, if your son asks for bread, will give him a stone?  Or if he asks for a fish, will give him a snake?  If you, then, though you are evil, know how to give good gifts to your children, how much more will your Father in heaven give good gifts to those who ask him!"  (Matthew 7:7-11)

This does not necessarily mean that an agnostic cannot begin to try to obey some of Jesus' teachings—but I do not see how they could possibly do so, without at least hoping or wishing that a God like this exists, and that following Jesus' teaching might put them in some kind of relationship with something like this deeper reality that Jesus called Father.

Given that we are currently evaluating different forms of religious ethics, this is only to be expected.  If you do not yet currently believe in a God, then understanding Jesus' teaching will require you to imaginatively "suspend your disbelief" on this point.  There is no point in taste-testing a religion for its ethical truth, if you aren't prepared to grant, at least hypothetically, its most essential premise.

Having granted this premise, what is most distinctive in Christianity is not just whether we believe in God, but rather than nature and character of the God being described, and the way in which his goodness can be taken as a model to transform our own lives.

The second potential road-block is this:

Road Bump #2: Final Judgement

A second, more sensitive issue, is the fact that Jesus repeatedly warns people about the fact that there is a final judgment coming at the end of history, and that even though God loves us, it is quite possible—in fact easy, if a person takes no care to avoid it—for that person to be condemned to Hell.  This is a feature which is bound to seem unpalatable to anyone who doesn't feel that their degree of guilt (or perhaps, anyone's guilt) would warrant such a stiff sentence.  And of course, the higher the moral standard we are expected to uphold, the scarier these threats are.

As Bertrand Russell argued:

There is one very serious defect to my mind in Christ’s moral character, and that is that He believed in hell. I do not myself feel that any person who is really profoundly humane can believe in everlasting punishment. Christ certainly as depicted in the Gospels did believe in everlasting punishment, and one does find repeatedly a vindictive fury against those people who would not listen to His preaching—an attitude which is not uncommon with preachers, but which does somewhat detract from superlative excellence. You do not, for instance, find that attitude in Socrates. You find him quite bland and urbane towards the people who would not listen to him; and it is, to my mind, far more worthy of a sage to take that line than to take the line of indignation.   (Why I am not a Christian)

Of course, belief in post-mortem punishment is far from unique to Christianity.  Any religion which believes in both human freedom and life after death, necessarily has to grapple with the question of what happens to people who sink into a self-chosen state of moral corruption.  Even most Buddhist sects believe in various hells (generally regarded as finite, but astronomically long, in duration).

A complete discussion of the topics of Heaven and Hell goes well beyond the subject of this blog post, the purpose of which is not to share my own personal ideas about how this theology could be justified.  One could note however that the possibility of damnation would seem to be logically inherent in any theological system which satisfies the following criteria:

  1. All humans will live forever;
  2. It is impossible for humans to be happy forever without loving God;
  3. God does not force humans to love him, if they choose not to.

On these premises, if anyone would prefer to be immoral (and thus unhappy) rather than to love God, then there does not seem to be any obvious alternative to a system of indefinite incarceration, for those who reject Heaven.

The Offer of Grace

What is unique to Jesus' teaching, is the extent to which these warnings are side-by-side with the most forceful declarations of God's mercy and grace towards sinners:

What do you think?  If a man owns a hundred sheep, and one of them wanders away, will he not leave the ninety-nine on the hills and go to look for the one that wandered off?  And if he finds it, truly I tell you, he is happier about that one sheep than about the ninety-nine that did not wander off.  In the same way your Father in heaven is not willing that any of these little ones should perish.  (Matthew 18:10-24)

We do not have to be saved by our own efforts; instead the Good Shepherd comes looking for his lost sheep in order to save it.  Jesus welcomed the prostitutes and the dishonest tax collectors, because God is a loving Father whose heart goes out to all his children, no matter what they have done.  God doesn't want anyone to perish, but for everyone to come to him and be saved.

If anyone is outside the scope of God's forgiveness, it is not because God runs out of patience and kindness, but rather because that person is trapped in their own hatred and failure to forgive others.  In other words, the only unforgivable sin is to reject the Holy Spirit, even when he makes his goodness clear to you.  All who repent and turn to Christ can be saved, no matter what they have done.

Not "Meek and Mild"

Jesus' own ways of reaching out to people were highly controverisial.  Shockingly for the time, he took women on as close disciples.  He was criticized for going to parties with notorious sinners, for healing people on the Sabbath, and for telling religious people that their hypocrisy was an abomination in God's eyes.  As he himself noted, a life of real virtue leads to persecution.

They also accused him of blasphemy, for saying things which sounded as if he was claiming some sort of equality or association with God himself.  (This is also something which we have to come to terms with in deciding what Jesus really was, since as many people have pointed out, if he was wrong that would make him a delusional megalomaniac.)

I remember reading the Gospel of Matthew for the first time as a child and being surprised by the continual extremeness of Christ's teachings.  My parents are devoted Christians and I was very pious, so you would think I would already have known what to expect, but still—the words of Jesus were shocking.  It seemed appropriate that Christ's words were typed in red ink in my mother's Bible, as if they were going to burn through the page like acid.  As St. Chesterton wrote in The Everlasting Man (a rethinking of comparative religion from a Christian perspective):

A man reading the Gospel sayings would not find platitudes.  If he had read even in the most respectful spirit the majority of ancient philosophers and of modern moralists, he would appreciate the unique importance of saying that he did not find platitudes.  It is more than can be said even of Plato.  It is much more than can be said of Epictetus or Seneca or Marcus Aurelius or Apollonius of Tyana.  And it is immeasurably more than can be said of most of the agnostic moralists and the preachers of the ethical societies; with their songs of service and their religion of brotherhood.  The morality of most moralists ancient and modern, has been one solid and polished cataract of platitudes flowing for ever and ever.  That would certainly not be the impression of the imaginary independent outsider studying the New Testament.  He would be conscious of nothing so commonplace and in a sense of nothing so continuous as that stream.

He would find a number of strange claims that might sound like the claim to be the brother of the sun and moon; a number of very startling pieces of advice; a number of stunning rebukes; a number of strangely beautiful stories.  He would see some very gigantesque figures of speech about the impossibility of threading a needle with a camel or the possibility of throwing a mountain into the sea.  He would see a number of very daring simplifications of the difficulties of life; like the advice to shine upon everybody indifferently as does the sunshine or not to worry about the future any more than the birds.  He would find on the other hand some passages of almost impenetrable darkness, so far as he is concerned, such as the moral of the parable of the Unjust Steward.  Some of these things might strike him as fables and some as truths; but none as truisms.  For instance, he would not find the ordinary platitudes in favour of peace.  He would find several paradoxes in favour of peace. He would find several ideals of non-resistance, which taken as they stand would be rather too pacific for any pacifist.  He would be told in one passage to treat a robber not with passive resistance, but rather with positive and enthusiastic encouragement, if the terms be taken literally; heaping up gifts upon the man who had stolen goods....

The statement that the meek shall inherit the earth is very far from being a meek statement.  I mean it is not meek in the ordinary sense of mild and moderate and inoffensive.  To justify it, it would be necessary to go very deep into history and anticipate things undreamed of then and by many unrealised even now; such as the way in which the mystical monks reclaimed the lands which the practical kings had lost.  If it was a truth at all, it was because it was a prophecy.  But certainly it was not a truth in the sense of a truism.  The blessing upon the meek would seem to be a very violent statement; in the sense of doing violence to reason and probability....

Something of the same thing may be said about the incident of Martha and Mary; which has been interpreted in retrospect and from the inside by the mystics of the Christian contemplative life.  But it was not at all an obvious view of it; and most moralists, ancient and modern, could be trusted to make a rush for the obvious.  What torrents of effortless eloquence would have flowed from them to swell any slight superiority on the part of Martha; what splendid sermons about the Joy of Service and the Gospel of Work and the World Left Better Than We Found It, and generally all the ten thousand platitudes that can be uttered in favour of taking trouble—by people who need take no trouble to utter them.

("The Riddles of the Gospel", in The Everlasting Man)

But if Christ really came down from Heaven, you might expect him to teach a morality which is of a different nature than any Earthly cultural code.  Just as if you were sent back in time thousands of years to the ancient world, you would inevitably react with dismay at many atrocities which the ancients took for granted; so too Jesus preached just as if he came from another world, where life operates on completely different lines than what we Earthlings are used to.

Humble Service

Another of these paradoxes was Jesus' idea about the nature of leadership.  To the first leaders of his Church, he says:

“You know that the rulers of the Gentiles lord it over them, and their high officials exercise authority over them.  Not so with you!  Instead, whoever wants to become great among you must be your servant, and whoever wants to be first must be your slave—just as the Son of Man did not come to be served, but to serve, and to give his life as a ransom for many.”  (Matthew 20:20-28)

And here the Theology of Christianity—that God sent his Son to forgive his enemies and save us from destruction—is in perfect consonance with the Ethics.  Jesus' actions were not hypocritical; he lived a life (and died a death) of self-sacrifice and forgiveness.  Healing the sick and crazy, welcoming social outcasts and telling them their sins were forgiven, feeding the hungry, raising the dead, preaching the good news to the poor.  Jesus' character makes the commonplace seem miraculous and the miraculous commonplace.

It is certainly true that the doctrine of the Atonement—that Jesus' innocent victimization on the Cross is the method by which God forgives our sins—can be perplexing and disconcerting, when considered from the point of view of ordinary human justice, especially if it is explained using inapt metaphors.

If your notion of the divine does not allow for elements of mysterious depth, if you insist that nothing can transcend your own understanding, then I have no way of getting you past this third potential stumbling block.  All I can say is that a supposed divine revelation would be quite impoverished indeed if it contained nothing strange or difficult.  When we study subatomic matter, out of which we ourselves are made, we find the bizarre mind-bending paradoxes of Quantum Mechanics, which can be described mathematically but nobody can agree on what's going on metaphysically.  It would be strange indeed if our interactions with God—a being coming in from outside our physical world entirely—did not have a comparable degree of weirdness!

A Spiritual Kingdom

Finally, Christianity says that Jesus conquered death itself at his Resurrection from the grave.  He did not meet the Jewish expectations of a world revolution, but he did something greater, triumphing over all the strong things in the world with his tender weakness.  That is why he proclaimed that the kingdom of heaven was very near, and would be a revolution in the hearts and minds of anyone willing to be born anew, in order to enter it with humility, like a small child.

If this did not happen and—as some believe—the Messiah is yet to come, can he possibly be greater than this?  After Jesus, anyone else would be an anticlimax.  Even if you were to write a fictional story to try to imagine a superior Messiah, the only way you could make your fictional Messiah morally satisfying is by including enough elements of Jesus' character, that the story would really owe its emotional and moral depth to him.  (Or one could simply accept the moral retrogression back to the military leader trope, as is largely the case in e.g. the Dune mythos.  This leads to a satisfying story for a novel, but if it happened in reality, it would not answer the deepest spiritual needs of the human race.)

Christians believe that Jesus' teaching is the Way (the Tao) which comes down from Heaven.  Unlike the Torah or the Quran, the New Testament contains no instructions for setting up an earthly theocratic government; instead it is a spiritual kingdom:

Jesus said, "My kingdom is not of this world.  If it were, my servants would fight to prevent my arrest by the Jewish leaders.  But now my kingdom is from another place."  (John 18:36)

Therefore, his followers have no excuse for engaging in religious persecution on Earth.

Jesus and Hypocrisy

Although many have tried.  Let me say right away that I do not consider any religion to be refuted merely by the hypocrisy of those who come in later generations.  I am asking how glorious the original teachings are, not how well they have been followed.  Christians, like others, are frequently hypocrites.  In fact, one might well expect the religion with the highest ethical standards to provide the greatest temptation to hypocrisy, since those are the standards which are hardest to live up to.  So when people complain about how the Church is full of hypocrites, they thereby testify that they know that the Christian standards are (at least in certain respects) good and right.  We don't usually complain when people fall short of a religious standard which we don't approve of!

And if you hate hypocrisy, bear in mind that you probably owe this very insight to Jesus' teaching.  Just as the weekend comes from the Judaeo-Christian practice of Sabbath keeping, so the modern Westerner's sensitive conscience on this point comes, directly or indirectly, from the New Testament.  There is no religious text which speaks more forcefully against hypocrisy.  Jesus' denunciations of this sin were spectacularly harsh.  And yet his severity was clearly needed, given the later conduct of many of his own followers.

Because these warnings are in the DNA of the Christian Church, it can never remain permanently fossilized in legalism and spiritual decay.  There will always be a revival.  If you are sincerely worried about becoming a hypocrite yourself, and if you want to pick the religious teacher most likely to prevent you, if you follow him sincerely—surely, Jesus is the one.

(Although, I can't help but notice that the people who complain about religious people being hypocrites, seldom seem all that worried that they might be hypocritical in other respects.  Shall we coin a term and call that "meta-hypocrisy"?)

Of course, hypocrisy is not at all the same as simply not living up to one's own moral standards.  Otherwise there would be no difference between the self-righteous Pharisee and the repentant tax-collector!  We all fail to live up to what morality requires, but some people sincerely repent of it, while others don't care or try to pretend everything is okay.  If you ever find a religious group which succeeds in keeping their own moral standard, you should run away from them as fast as you can!  Because if they can meet it, it must be abysmally low.  At least if people fall short of the standard they set by their preaching, they leave open the possibility of repenting and doing better in the future.

Other Religions

The moral teachings of other religions, might indeed have been improvements on what went before, but are limited and defective in comparison with Christianity.  I don't mean of course to imply that there's nothing ethically good in other religions.  But they don't impress and amaze me, to the same degree that Christianity does.

III.  Judaism

Although Christians believe the Torah to be genuinely revealed by God, even this must be regarded as "limited", since according to Christianity it is  incomplete in nature, and its ceremonies pointed the way to something better, to come later.  Since Christianity came from Judaism, a Christian cannot consistently say that the core ideas of Jewish ethics were mistaken.  But, we can point to the place where Jewish ethics has reached its highest point of fulfilment, which is in the teachings of Jesus.

But first, what is the most distinctive feature of Jewish ethics?  One of the main innovations of Judaism was the unification of religion and morality.  God is believed to be both righteous himself, and the one who demands righteousness on Earth.

In paganism, the concepts of sin (that which offends God) and moral wrongdoing (injustice) can come apart; an act may please one god and yet offend another.  But in Jewish theology, sin and wrongdoing are coextensive: one can never offend God by a righteous act nor please him by a wicked one.  To be sure, the implication goes in both directions, meaning that a Jew might sometimes need to submit to a difficult divine command, the reasons for which are obscure.  But it is always implied that when this is so, the moral limitation lies with us humans, rather than with God.  Hence, obedience is itself a righteous act, and is never merely a craven submission to a more powerful being, as in much of paganism.

Before anyone marches in with a Dawkins-esque caricature of the "God of the Old Testament", let me say right away that there is simply no comparison here to the moral universe of pagan mythology.  Not even the most hardened blasphemer would deny that the God of the Bible is at least moralistic in his character.  He is always portrayed as actively defending moral norms, with acts of justice or mercy.  When a reader objects to one of the Old Testament God's verdicts, they usually do so for one of three reasons [not all of which are applicable to each case]: (1) because the punishment seems too harsh, or (2) involves collective justice on groups, or (3) involves offenses against archaic codes of conduct which we no longer accept.  In a certain Nietzschean sense, one might say that the biblical God is more frequently accused of an excess of morality (at least in the sense of punishing sins), rather than a deficit of morality.  But the God of the Old Testament does not ever simply disregard morality to gain personal advantage; nor does he, like Zeus, commit adultery with his neighbor's wife and then turn her into a animal to cover up his hijinks.  In this sense the Hebrew tradition, even at its most distressing, can be objectively seen to reside on a higher moral and metaphysical plane than pagan polytheism.

And it should be noted that the Israelites themselves, comparing their beliefs to others, did not view their own God as being especially implacable in wrath.  Rather, they characterized him as a "gracious and merciful God, slow to anger and abounding in love, a God who relents from sending calamity" (Jonah 4:2).

A critic might say that, simply by asking the question which religion is morally good, we are already begging the question massively in favor of Judaism and its offshoots, since it was Judaism that popularized this idea in the first place.

And yet none of us can completely transcend our roots.  When Western skeptics critique the moral sensibilities of Jewish scriptures, they are usually doing so on the basis of moral assumptions which they learned, indirectly, from Christianity.  Since Christianity is deeply rooted in Judaism, this really means that their ammunition against Judaism comes indirectly from sources within Judaism itself.  Had Judaism and Christianity never existed, it is quite probable that most modern "civilized" people would have no concept of universal human rights.  Hence: less emphasis on protection of the weak and victimized, more tolerance for barbaric practices like slavery, torture, and gladiator fights, etc.  There have been plenty of civilized pagan cultures (Greeks, Romans, Chinese, Japanese) in which these concepts have not played a major role.

(This does not mean that there were no ways that e.g. Greco-Roman pagan religion intersected with morality.  There were a few specific moral violations that were viewed as likely to be punished by the gods, such as violations of hospitality or oaths, or violence against parents.  And of course, Egyptian polytheism eventually developed some very precise notions of divine judgement in the afterlife.  But for the most part, appeasing the gods was regarded more as a practical necessity, than a moral one.  For a good overview of the way that most pagans in the Roman Empire viewed their religious rituals—which had very little in common with what most modern people would regard as "spiritual"—see this excellent blog series by a very entertaining historian.)

Proceeding to more specific observances, there are indeed many parts of the Torah which are still very morally inspirational today, such as the Ten Commandments, or the laws about ensuring justice and mercy for widows, orphans, and strangers:

Do not deprive the foreigner or the fatherless of justice, or take the cloak of the widow as a pledge.  Remember that you were slaves in Egypt and the Lord your God redeemed you from there.  That is why I command you to do this.

When you are harvesting in your field and you overlook a sheaf, do not go back to get it.  Leave it for the foreigner, the fatherless and the widow, so that the Lord your God may bless you in all the work of your hands.  When you beat the olives from your trees, do not go over the branches a second time.  Leave what remains for the foreigner, the fatherless and the widow.  When you harvest the grapes in your vineyard, do not go over the vines again.  Leave what remains for the foreigner, the fatherless and the widow.  Remember that you were slaves in Egypt. That is why I command you to do this.  (Deut 24:17-22)

When looking at passages like this, we can indeed agree with the Psalmist that:

The judgments of the LORD are true, being altogether righteous.  They are more precious than gold, than much pure gold; they are sweeter than honey, than honey from the comb.  (Psalm 19:9-10)

Yet, although much in the Torah is splendid and righteous, and many of its ceremonies seem beautifully significant, other provisions are difficult to justify except as concessions to the prevailing culture—as in the case of divorce, where Jesus justified his own teaching on the subject by saying that "Moses permitted you to divorce your wives because your hearts were hard.  But it was not this way from the beginning" (Matt. 19:8).

It is then, an option for a Christian to critique other morally repugnant provisions in the Torah, as making similar allowances to the barbaric conditions of the time, rather than being perpetually prescriptive norms.  Such provisions might include e.g. the rules allowing warfare to be waged against civilians (Deut. 20:10-15), the rules allowing Israelites to buy non-Israelite slaves (Lev. 25:44-46, but cf. Deut 23:15-16 for a contrasting rule concerning refugees), and indeed the subordinate position of women in a patriarchal society (not that this is a major topic of legislation in the Torah, it's more that it's taken for granted).

Of course this raises questions for Christians (like myself) who believe that these commandments were revealed by God to Moses.  It might be possible to justify these legal provisions as "perfect" in the limited sense that it these were the best set of laws that could be given to the Israelites at the time God gave them.  However, there's been considerable moral progress since then.  Thus—although it remains in the Christian Bible as a perpetual record of God's past guidance to his people—in its literal application, the Torah is simply no longer a contender for the best moral code for humanity.

(Given Christian ethics, the hardest commandment in the Torah to defend is probably the order to wipe out the Canaanite tribes.  Now defending genocide is one of those things that is no longer quite so respectable as it used to be, and rightly so!  Nevertheless, I tried my hand here at explaining several ways in which this divine command is meaningfully different than what e.g. Hitler did.)

Turning to Judaism in its modern rabbinic form, it is still somewhat racially narrow, and often more concerned with technical legalistic observances than with the heart.  After the destruction of the Temple, the Pharisees—the spiritual ancestors of modern day Rabbinic Judaism—reformed and modernized their religion, but also took many liberties of interpretation, some of which are staggering in their perverseness.  For example, the Pharisees interpreted Exodus 23:2:

Do not follow the crowd in doing wrong.  When you give testimony in a lawsuit, do not pervert justice by siding with the crowd.

as implying the right of a majority of rabbis to effectively (re)interpret Scripture, even though the literal meaning of the text specifically says not to follow the majority in doing wrong.

Of course, this rabbinic flexibility does allow for religious mores to be progressively updated in response to social changes, but it also tends to produce a game in which each new rule spins off an increasingly complex chain of further legislation via interpretation.  Since this process has been going on for thousands of years, the results can get very strange.

For example, the rabbinic prohibition on mixing milk with meat somehow emerged from the Torah commandment: "Do not cook a baby goat its mother's milk" (a better generalization might be: Don't be a jerk to beings that are totally in your power).  This in turn spun off the additional rule to keep separate dishware for meat and dairy, and so on.  Then one identifies various loopholes, allowing you to get around certain rabbinic rules when they become too onerous, and so on.  All of this seems like a major distraction from actual ethics and spirituality.

Although, taking a more positive point of view, there is a certain attractiveness (at least in an outsider's view) of an Orthodox Jewish piety; in which minute decisions are continually referred back to the Talmud and to divine law; so as to dedicate the smallest mundane details of family life to the service of a Name that is too sacred to even be spoken out loud.  From the Christian perspective, this is indeed very instructive as an image of what the word "holiness" means, total dedication to God.  But to take such a lifestyle as a matter of obligation differs from the Christian relationship to God which is based more on the guiding presence of the Holy Spirit than in following a particular code of laws.

Another positive effect of all these rabbinic disputations, which should probably be mentioned, was to produce a culture of vibrant intellectual debate.  Even separated from its original religious matrix, this culture of questioning seems to persist in the case of secular Jews.  This is one possible explanation for the enormous Jewish impact on philosophy, science, and culture (far exceeding what one would expect from the total Jewish world population).

IV.  Zoroastrianism

In Zoroastrianism, the commandments seem to be more concerned with ritual purity than with ethics, to a far greater extent than in Judaism.  Yes, honesty and fair-dealing are considered important, but the most important rules concern things like burial practices and hygiene codes.

While I don't think these punishments are enforced in modern times: in the Venidad (part of traditional Zoroastrian scripture), many purely ceremonial offenses are considered worse than murder, and are punishable by being flogged with hundreds or even thousands of lashes of the whip.  Unforgivable sins (those which cannot be expiated with any amount of punishment) include: burying the corpse of a man or dog, homosexuality, and voluntarily committing "the unnatural sin" [masturbation, according to some translators].  For these acts there can be no atonement whatsoever!  (At least for those who are already members of the religion.  Those who converted, back when that was a thing that happened, apparently got a pass, as long as they promised never to do it again.  Though nowadays, I imagine that most of these rules about punishments aren't seriously practiced.)

Zoroastrians are Dualists: they believe the world was made by two gods, one of them good and the other evil.  Unlike the Judaeo-Christian worldview, which affirms the essential goodness of creation, Zoroastrianism teaches that certain aspects of Nature were created by the Devil, and are inherently evil and impure.  For example they believe that cats were created by the Evil God, while dogs were created by the Good God.  Therefore it is considered is a righteous deed to kill cats, but a grievous sin to kill a dog.  Speaking as a cat person, I think this is pretty clearly drawing the line between good and evil in the wrong place!  It is simply not ecologically or ethically sound to simplistically divide animal species into "good" and "evil", as if we lived in a children's animal fable.  Even if there is a good case to be made for fewer bloodsucking mosquitoes!

(Islam has a completely different take on this, as Mohammad seems to have also been a cat person.)

However, Zoroastrians also strongly emphasize the importance of free will, and the ability of rational creatures (even the gods!) to choose between good or evil.  There is even an amusing Zoroastrian legend that the Devil created the Peacock just to prove that he could make something good, if he wanted to.

(Oddly, this is not the only Devil-Peacock connection one comes across in comparative religion.  The Yazidi venerate the "Peacock angel" Melek Taus, whom they identify with Iblis—an Arab word for the Devil.  In the Quran, Iblis refuses God's command to prostrate himself before the newly created Adam, and as a result loses his position as chief over the angels.  But in Yazidi mythology, Iblis refuses to venerate Adam out of a misguided loyalty to God, and he is eventually restored to his former position as the most exalted manifestation of God's glory.  Needless to say this belief, easily confused with a more malign Satanism, has led to considerable misunderstandings with the surrounding Muslim cultures, and the Yazidis have suffered many severe persecutions, most recently under ISIS.)

So, if you want to think of yourself as a participant in an epic battle between good and evil, Zoroastrianism is a pretty cool religion.  But the lines between good and evil are drawn in some pretty arbitrary seeming places.  I don't really see much ethical wisdom here which can't be obtained more easily from Judaism (plus Judaism actually accepts converts if you ask persistently enough).

V.  Islam

The Islamic religion preaches racial harmony, generosity to the poor, and sincere piety.  In the tradition of Ethical Monotheism, the Quran proclaims that God is firmly on the side of moral behavior and fair conduct:

God commands justice, doing good, and generosity towards relatives and He forbids what is shameful, blameworthy, and oppressive.  He teaches you, that you may take heed.  Fulfil any pledge you make in God's name and do not break oaths after you have sworn them, for you have made God your surety: God knows everything you do.  Do not use your oaths to deceive one another—like a woman who unravels the thread she has firmly spun—just because one party may be more numerous than the other.  God tests you with this, and on the Day of Resurrection He will make clear to you the things you differed about.  (Haleem translationSura 16:90-92)

On the other hand, the Quran does not pass modern standards for the treatment of women.  It permits the sexual exploitation of women through slavery, polygamy, and easy divorce; and in several cases its laws discriminate explicitly against females, e.g. Sura 2:282, which considers the testimony of two women equivalent to one man.  (Although Mohammad must be given credit for banning infanticide against female babies.)

In the Hadith, Mohammad legislated the death penalty for apostates (those who stop believing in Islam).  And in numerous passages, the Quran encourages warfare and violence against pagans and those viewed as enemies of Islam, sanctioned by reward and punishment in the afterlife:

God has purchased the persons and possessions of the believers in exchange for the Garden [i.e. Paradise]—they fight in God's way; they kill and are killed—this is a true promise given by him in the Torah, the Gospel, and the Quran.  Who could be more faithful to his promise than God?  So be happy with the bargain you have made, that is the supreme triumph.  Those who turn to God in repentance; who worship and praise Him; who fast, bow down and prostrate themselves; who order what is good, forbid what is wrong and observe God's limits.  Give glad news to such believers.  It is not fitting for the Prophet and the believers to ask forgiveness for the idolaters—even if they are related to them—after being shown that they are the inhabitants of the Blaze [i.e. Hell].  (HaleemSura 9:111-113, brackets are my own added interpretation)

It is certainly possible to exaggerate the extent to which the Quran commands religious warfare.  There are also some passages which advocate for peace (although many of these were from the early stages of Mohammad's ministry, leading some Muslim scholars to argue they were abrogated by later revelations).  But no one can deny that warfare is a frequently recurrent theme; even if the applicability of these verses to the modern day is, of course, a matter on which different Muslims have many different opinions.

The time has long passed when I last had the experience of finding a new book in my Bible.  If the voice that spoke in the Quran, had been the same voice that speaks to me in the Bible; if it had wooed me with divine paradoxes that call out to the depths of the spirit, cutting through all my excuses like a sword, and dazzling me with the promises of hidden glory; then I think I would have gladly listened to it, even if the price it asked me to pay (leaving behind my own family's religious convictions, and joining a new community) was high.

But as I see it, the Quran is not even trying to reveal a paradoxical reality or an awe-inspiring ethical code; it is really just a kind of civilization-building compromise; a simplification which attempts to combine the universalism of the Christian message with some of the ritualism of the Jewish system.  Despite the intense focus of the Quran on the rewards and punishments of the afterlife, Mohammad's kingdom was very much of this world; therefore his followers do fight.

Despite being later in time, Islam does not uphold nearly as bracing a moral standard as Christianity, and it is arguable whether it is even a moral improvement on the Torah.  In this respect it appears to be a moral retrogression—which might be justifiable if it had been intended for a limited cultural setting, but it is a severe problem in a supposedly final revelation for all humanity until the Day of Judgement.

Even Muslims can see that much of the legislation in the Quran is merely concerned with being good enough, setting a minimum standard of decency for what had previously been a barbaric time and place.  As one thoughtful Persian argued in a medieval debate with a Christian:

I have said, I say and I will say that good and beautiful is the Law of Christ and much better than the earlier Law, but that mine [the Quran] is superior to both.  Therefore consider what I am going to say, you may hear something that you do not condemn altogether.  Your law, I say, is beautiful and good, but it is very hard and very burdensome and can not easily be useful.  These remedies are too bitter to taste.  So there is no error in believing it is not completely perfect.  The Law of Mohammed follows the middle path and proclaims ordinances which are bearable and in sum gentler and more humane.  Hence it is moderate in all respects and takes precedence over other laws.  Indeed, the shortcomings of the old Law it fills by the supplements which it brings; on the other hand it reduces the exaggerations of the Law of Christ.  There is also what it prunes visibly from both Laws, and suddenly it quite prevails over them.

It also avoids, I think, the mediocrity and the imperfection of the Law of the Jews on the one hand, and on the other hand, the elevation and height of the precepts of Christ, their harshness, that they are excessive and impractical so far for men, because they force, so to speak, our terrestrial nature to mount up to Heaven.  It thus avoids both faults and strives for moderation in everything.  Thereby it appears better than all the Laws that have preceded it.

The virtues, you know, consist of avoiding excesses and keeping exactly to a happy medium.  That’s what we call virtue, and what virtue is.  What is virtue is a happy medium, and what is not such is not virtue.  This is the doctrine of all the ancients, and you yourself have said the same earlier.

But tell me, is it to stay in the happy medium—'to love one's enemies, to pray for them', to provide them with food when they are hungry;—And what is amusing—allow me this freedom—to 'hate his parents and brothers and even his own soul;—'to he who took your shirt, to give him also your coat';—'to give without distinction to he who asks' until you appear more naked than a stick and ridiculous in the eyes of those who would then make your property the loot of the Mysians, by pretending to be in need;—to he who strikes 'on one cheek, to turn the other; to never stand up to evil';—to have 'no stick, no bag, no money, nor two tunics';—‘to not worry about tomorrow’?  "Who is the man of iron, diamond, more insensible than stone, who will bear all these things,—who will bear the offence and cherish the insulter;—who will do good to he who is ill-disposed towards him;—who by his extra bounty will invite the people of this species to gorge on him like vultures on the corpses of the dead?

[We should probably make allowances for the fact that this debate was hosted by Christians, and recorded by them, so that the Persian scholar might not have felt free to attack Christianity in the strongest possible terms.  Nevertheless, the viewpoint being argued seems plausible enough as an honest statement of opinion by a real Muslim.]

From a Christian perspective, the basic mistake here is thinking of the law of Christ as if its main purpose was to be a terrestrial law code.  From this perspective, a law could deviate from perfection either by being "too strict" or by being "too lax", given the realities of human nature.  Yet Christianity is not primarily meant to be a new code of laws, but rather it is a means of experiencing supernatural grace.  From that perspective it is an attraction, that the law of Christ cuts deeper than anything we could obey by our own efforts.  Suppose that our "terrestrial nature" is indeed destined "to mount up to Heaven"; not indeed by our own efforts, but rather by the grace of God redeeming sinful people, and conforming us to the supernatural standard of goodness set by Jesus?  Then we need to know what truly heavenly people would look like, and Jesus provides that picture.

Muslims admire Islam for the reasonableness of its requirements.  For example, if you are physically unable to prostrate or to go on pilgrimage, then God understands that, and you can just do whatever you can do.  On the other hand, while Christians certainly believe God makes allowances for our weakness, we admire the Gospel message more for its unreasonableness by human standards.  God demands that which exceeds our abilities; but then gives us the grace to fulfil his commands.

Islam and Prophets

This issue is closely connected to the Islamic theology concerning prophets.  Most Muslims believe that all prophets are sinless, which would blatantly contradict the Bible in numerous places.  However, I have come to conclude that this doctrine was never taught by Mohammad; in particular it seems to explicitly contradict the Quran, which contains multiple examples of prophets sinning (e.g. there is a story of Jonah similar to the Bible, Mohammad is rebuked by God for doing certain things, etc).

Nevertheless, there is still a significant difference when it comes to the overall tone of respect which the Quran has for prophets, as compared to the Bible which consistently emphasizes the flaws and sins of nearly all of its major protagonists, except for Jesus.  Leave aside the villains; let's look at the saints: Noah gets drunk; Abraham lies about his wife; Isaac plays favorites; Jacob tries to trick everyone; Joseph's brothers sell him into slavery; Judah visits a prostitute; Aaron makes a golden calf; Moses loses his temper; Jephthah swears a rash vow; Samson is a violent hothead; David commits adultery with Bathsheba; Solomon is led astray to idolatry; Hezekiah boasts to the Babylonian envoys; Zechariah doubts the angel; Peter repeatedly wavers in his faith; Paul is quarrelsome.  Even Mary, the Blessed Mother of the Lord, comes to try to take Jesus home to cool off, after the rest of his family decides he's gone nuts!  This is all rather astonishing, especially given the tendency of other religious literature (including later Christian chronicles and legends) to succumb to pious hagiography.  To my mind this moral realism is one of the most striking effects of divine inspiration, in the narrative parts of the Bible.

(Conversely, one of the most striking aspects of those parts of the Bible in which humans talk to God—like the Psalms and Job—is the brutal honesty with which the saints are allowed to express their feelings to their Lord.  Here too, I know of no real parallel outside the Judaeo-Christian tradition.  It is certainly not a common practice in Islam.)

The Muslim attitude is, how can you trust a prophet if he's a sinner?  Which makes perfect sense if you think that sin is just a matter of disobeying some reasonable code of conduct which any decent person is capable of following.  But the Bible provides the more bracing truth that everyone is a sinner who needs salvation (Christ alone excepted).  Even heroes of nonviolence, like Mahatma Gandhi and Martin Luther King Jr., can commit quite serious sins (as a close look at their biographies will reveal).

The Gospel passes judgement even on its own messengers, "so that every mouth may be silenced and the whole world held accountable to God" (Romans 3:20).  The Christian doctrine of original sin is much maligned, but as St. Chesterton pointed out, its actual effects are to promote sympathy and solidarity between human beings.  We are all in the same leaky boat, and we all need rescuing!  Righteousness is something which we cannot achieve by merely human efforts, even if those efforts take the form of religious rituals (praying X times a day, going on pilgrimage, donating to charity etc.)

What is Grace?

Another way of putting this: Islam is inherently Pelagian in its theology of human nature.  (St?) Pelagius—despite the fact that he was himself a very devout and pious man—was condemned for his heretical and destructive teachings by the Catholic Church.  The problem was that he taught that human beings are morally capable of obeying the law without needing to undergo a radical spiritual transformation.  On a Pelagian (or Islamic) view of salvation, the main spiritual need of humanity is to be educated and informed about what it is that God commands.  Having learned the correct way to live, our task is choosing to submit to God's commands and obey them, which we have the power to do.  But orthodox Christianity teaches, that what humans need is not primarily instruction, but rather an infusion of new life which comes from on high.

What kind of grace do we need?  The Quran portrays God as merciful to believers, but he does not show extravagant love to sinners as he does in the Bible.  Indeed the Quran seems more frequently to relish in the damnation of evildoers, rather than mourning them.  Compare this to the biblical tradition: "As surely as I live, declares the Lord God, I take no pleasure in the death of the wicked, but rather that they turn from their ways and live!" (Ezekiel 33:11).

In my experience, it can be a bit difficult for Christians to communicate our theology of grace to Muslims, since it is easy to overstate the difference between the two religions, when in fact there is a lot of common ground.

If you try to tell your Muslim friend that it is impossible to be good without divine help, they will almost certainly agree with you!  This is just common sense, in any tradition of ethical monotheism.  Pelagius himself would never have said that God doesn't help us to do good works, or that it is wrong to pray for his assistance in being good.  After all, God created us, and nothing in the world can even continue to exist without his active sustenance.  (Even the most hard-core Calvinist ideas about divine predestination have parallels in Islamic theology.)

If you try to talk about God's mercy—well it is also very important to Muslims that God is merciful.  In all five of their prescribed daily prayers, they invoke "the Name of Allah—the Most Compassionate, Most Merciful" (Sura 1:1).  If you ask them whether it is always possible for even the most sinful person to repent and be forgiven by God, again your Muslim friend will probably agree.  Assuming the sinner is sincere in their repentance, and they earnestly desire to live a righteous life going forwards, why wouldn't God accept them?

But as we have seen, what the Bible means by grace goes deeper than this.  In the New Testament, God pours out his love and grace even to those who are currently his enemies.  There is no analogue in the Quran to divine "love" in the sense of: "For God so loved the world that he gave his one and only Son" (John 3:16), nor to "sacrifice" in the sense of: "While we were still sinners, Christ died for us" (Rom 5:8).  In fact, there can't be any parallel, because it would be considered blasphemous to say that God has a Son, or that anything which God does, can be compared to being a crucifixion victim.  (As discussed previously, Islam does not even seem comfortable with the idea of purely human prophet experiencing such a fate.)

And as for the human response to God's grace... suppose we consider the most law-oriented book of the New Testament: the epistle by Jesus' brother James.  This letter considers its most essential task, to be convincing Christians to obey Christ's "perfect law of freedom" (1:25), and it says that "faith without works is dead" (2:26).  If a Muslim scholar wanted to identify the stratum of early Christian teaching which is most compatible with Islam, they would probably pick this letter.  And yet, even in this book, St. James strikes a note totally incompatible with Islamic (or Pelagian) theology:

Every good and perfect gift is from above, coming down from the Father of the lights, with whom there is no variation or shadow of change.  By his own choice, he gave us birth by the word of truth" (1:17-18).

Or as Jesus said to a Jewish religious leader, "You must be born again" (John 3:7).  This refers not to our natural birth, but to a spiritual birth into a new life which comes from God!  Receiving this new life from God, makes us truly children of God.

While obviously this does not refer to literal procreation in an earthly sense, Jesus' use of a biological metaphor here still communicates something deeply important.  When Christians call God "Father", we do so not as a mere title of respect (though he is worthy of all respect, nor do we call him "Father" simply because he looks after our needs as a parent does (though he certainly does that as well).  Neither of these would require any notion of "new birth".  Rather, we call God Father because he has enabled us to participate in his own spiritual life, which we receive from Christ.  This divine life cannot be replicated simply by human effort.  (This would be just as impossible, as for a woman to get pregnant by looking at pictures of babies.)  This is why, throughout the Gospels, Jesus continually talks about receiving the word of God using agricultural metaphors: seeds growing into plants, vines nourishing branches, etc.

We come to Christ because we have had the experience of being unable to live up to even our own moral standards; and we find forgiveness and hope there, and a grace that seems to touch our point of need.  To say: "the problem is you were trying to follow moral rules that were too hard, just do these other rituals instead, and remember that God is merciful" seems like it is missing the point.  My own spiritual needs cry out for something deeper than that.

And then Christianity offers something far greater than we had any right to expect.  We believe that those who are in Christ, become spiritual sons and daughters of God, living by the power of God's own life.  Even though we are human and not divine—and however inadequate our current strivings may be—the purpose and goal of our sainthood is nevertheless to become, in some inconceivable manner, spiritually united to divinity.  As closely as a husband is united to a wife, or as a mother to her unborn child, or the soul to the body.  This is a relation to God that Islam does not offer, and cannot offer, given its other theological commitments.

Hence, from the perspective of someone who believes this central Christian gospel (the good news about Jesus), the Islamic religion simply doesn't come across as a mere extension or addition of new material.  Rather, it is a denial of what Christians consider to be the good news: that God did for us, and will do in us, a work of righteousness which goes beyond human capabilities.  In the moral realm, we need somebody who can say to us, what Jesus said to the crippled man: "Pick up your mat and walk!" (John 5:8).

VI.  Hinduism

To find a religion which competes with Christianity in its desire for mystical union with the divine, we now turn to the East, to the religions of India.  In this section we will look "Hinduism", although in fact this is a pretty broad target, containing a very eclectic group of different philosophical traditions, which are really only regarded as "one thing" as a result of being grouped together by British Imperialists.  As these traditions are practiced by different groups of people, there is no obligation for these ideas to all be compatible with each other, so it is very difficult to discuss Hinduism in any sort of unified way.  There is a lot going on here.  Some of it good, and some of it bad.

Traditional Hinduism is fairly closely bound up with a system of racial subordination, which it grew up around.  It's hard for me to get too worked up about this at the personal level, not being Indian, and I don't want to overstep when judging a culture different from my own.  But if there were a hypothetical American religion which taught that black people shouldn't necessary aspire to the same religious goals as white people, but should follow the duties of their own traditional station in life, in hopes of being reincarnated as a white person... then I think that religion would strike me as being pretty evil!

By contrast, the popular Bhakti (devotion) movement in Hinduism teaches that one can gain salvation through devotion to a particular deity (or set of deities), and that this devotion transcends caste divisions.  These reform movements became very popular in India, starting in the 15th century.  Perhaps this was in part due to influence from Western religious concepts.  Different religions do not actually exist in watertight compartments; they influence each other in various ways.

The mythology associated with Hinduism, like other pagan mythologies, often does not portray its deities as holy and righteous, but rather as petty, selfish and sensual.  This shows that these gods are only idols, made in the image of our own flaws in order to tell a good story.  Even if they were real, they would have no moral authority, because they behave no better than the powerful and rich rulers of our own species.

My friend Sudipta is an agnostic from India; he doesn't consider himself Hindu, but he is from a Hindu cultural background.  Although not a Christian, he says "I have no problem calling Christ divine, because he forgave those who crucified him."  We've had several conversations in which he minimized the differences between religions, saying they're all equally good, no way to know who is really right, etc.  On one occasion, after I invited him to my church in Maryland, we were walking back to the Metro station, and he was telling me about a religious festival (I think Diwali) involving one of the Hindu goddesses.  Suddenly he started coughing and sputtering as if he had something in his throat (we looked for a drinking fountain but none was available).  "Maybe I said something about the goddess she didn't like," he said. "They aren't merciful, like your god is!"

As St. E. Stanley Jones (a Christian missionary to India who was close friends with Gandhi) wrote:

Moreover, in Hinduism the moral law is not rooted in God, God is not the basis of morals.  It is to be found in the law of Karma which operates independently of God.  God is lifted above the law of Karma, and has nothing to do with it.  If God is lifted above morals, the devotee gets to the place where he, too, transcends morals.  He is not affected by good or evil.  Both for God and man morality has no eternal significance.

In the Gospel the moral life is founded in the very nature of God.  Both God and man are bound by the same moral attitudes.  "Follow me as I follow God," Paul could say, and when he said this he was saying the highest thing he could say.

By all that God requires of me
I know that He Himself must be.

This makes the moral universe a universe and not a multiverse.  Morality has permanent meaning and does not vary from age to age and from circumstance to circumstance.  What we have seen of God in Christ becomes the standard for God or man.  To be Christlike is the highest attainable or even imaginable goodness.  Our morality then is firm—fixed in the nature of God and in historic fact the nature of Christ.

But this is not true of Hinduism.  You are not supposed to follow the Incarnations in their moral actions.  I asked a priest at a temple on which was depicted the escapades of Krishna, "Can you follow this as your own example?"  "No," he said very thoughtfully, "unless you are very strong when you come here you will go off and do the same things."  The devotee's safety must lie in the fact that he is strong enough not to do what his Incarnation did.

Of course, the more philosophical side of Hinduism does not concentrate on these mythological indiscretions; it tries to get to a more transcendent concept of the Divine which is beyond both gods and men.  But here again, its morality continually founders on the rock of Pantheism, the idea that God is in everything, and is therefore indifferent to good and evil.  How can it be considered "good" to try to conform your own life to a reality which is indifferent to goodness?

(Here I am speaking to the majority Hindu position of "Non-Dualism"; however you can find Hindu schools of thought which have almost any set of views on the divine, including that God and the world are totally distinct e.g. the Dvaita school founded by Madhvacharya, who claimed to be an avatar of the wind god, but did not identify himself with the ultimate reality, Brahman.)

For example, the Bhagavad Gita was clearly written by a poet with a strong intuition concerning the grandeur and majesty of the One who is above all, and in that respect it is a spiritually insightful work.  But it continually waffles on this important issue, of whether God really is benevolent and loving, and whether creation is to be regarded with joy or suspicion.  Krishna sometimes speaks as if he were to be identified with the best and most noblest of things, but in other parts he claims to be identical with everything, both high and low.

The book certainly makes a distinction between those who cultivate good desires and rise in their next life, and those who act ignorantly and fall in their next life.  But the best and noblest thing is to be indifferent to any such rewards, and so to transcend the system altogether, going straight to love of Krishna alone.  At one point, the text gets within striking distance of Christian morality:

A person is said to be still further advanced when he regards all—the honest well-wisher, friends and enemies, the envious, the pious, the sinner and those who are indifferent and impartial—with an equal mind.  (Gita 6:9)

But reading the context makes it clear that this is more about indifference than benevolence:

For such persons heat and cold, happiness and distress and honor and dishonor are all the same.  (Gita 6:7)

Yes, one is to regard enemies as equal to friends, but only as one is to regard pain as equal to pleasure—the point is not to regard them at all!

Thus, at the end of the day, Arjuna still ends up killing his friends and family in battle.  He is to do so without any concern for them, because it is really God who is swallowing them up with his many mouths; Arjuna is merely fulfilling his duty in life.

VII. Buddhism

I suppose that Buddhism has the most noble type of ethical system (the Stoic type) that could possibly be expected from a wise philosopher without the benefit of divine revelation.  Like Christianity, it is concerned primarily with the heart, not with external regulations.  (In theory, if not always in practice.)  As Buddha said to an inquirer:

"What do you think, Kalamas?  When non-greed, non-hatred, non-delusion arise in a person, is it for his welfare or for his harm?" — "For his welfare, venerable sir."  "Kalamas, a person without greed, hatred, delusion not overcome by them, his mind not obsessed by them, does not destroy life, take what is not given, transgress with another's wife, or speak falsehood; nor does he encourage others to do likewise.  Will that lead to his welfare and happiness for a long time?" — "Yes, venerable sir."  (Discourse with Kalamas)

The structure of this idea is very similar to the Christian doctrine of the unity of ethics:

The commandments, “You shall not commit adultery,” “You shall not murder,” “You shall not steal,” “You shall not covet,” and whatever other command there may be, are summed up in this one command: “Love your neighbor as yourself.”  Love does no harm to a neighbor.  Therefore love is the fulfillment of the law.  (Romans 13:9-10),

yet in another respect it is the exact opposite since Buddha posited dispassion (negative) rather than love (positive) as the root of moral conduct.

These quotations illustrate the fact that religions do not differ very much in their account of the most basic ethical obligations to other humans—the behaviors prohibited by Buddha are basically identical to the second half of the Ten Commandments—but they do differ essentially in their account of how and why we are to be ethical, and indeed what a supremely ethical person would look like.  They differ at the heart, but more or less agree on the basic outward observances.

Having said that, it is noteworthy that most sects of Buddhism (like many Hindus) take the rule against killing much further, by requiring vegetarianism; which Christianity generally regards as an optional practice.  There is certainly an obvious ethical case to be made for vegetarianism, given that most animals raised as livestock seem to be capable of experiencing affection and suffering, and are therefore appropriate objects of empathy.  On the other hand, many animals in Nature are naturally carnivorous, and our own human teeth imply that we evolved to be an omnivorous species, so that is some evidence we are "meant" to eat meat.  It seems to me this ethical difference may come down partly to different beliefs about facts—if you happen to believe that people can reincarnate as animals, then the case for not eating meat is a lot stronger.

(Please note, that I am talking about vegetarianism in the abstract, as the issue would have been presented in the ancient world.  We are not currently discussing modern industrial "factory farms", which were created only about 100 years ago.  These seem like an obvious moral abomination, which I assume would have horrified most ancient religious leaders in the West as well as the East.  Anyway, I am not denying that the suffering of factory farmed animals is a grave evil, despite the fact that I have only made the most pathetically minimal attempts to modify my own diet in response—mostly I only try to reduce the amount of chicken I eat.)

Buddha also rejected the caste system of Hinduism, observing wryly that:

Whoever from a noble, priestly or royal family, bringing an upper piece of fire-stick of teak or sāl or of a sweet-scented tree or of sandal or lotus, lights a fire and gets it to give out heat — this fire has flame and hue and brightness and is able to serve the purposes of a fire.

And too, whoever from a despised family, a trapper family, a bamboo-plaiter family, a cartwright family, a scavenger family, bringing an upper piece of fire-stick from a dog's trough or a pig's trough or a trough for dyeing or dry sticks from a castor-oil shrub, lights a fire and gets it to give out heat — this fire too has flame and hue and brightness and is able to serve the purposes of a fire.  (Discourse with Asalayana)

And yet, Buddhist texts do not contain the same denunciations of social injustice that you find in Abrahamic religious scriptures.  (Indeed they could not, given their views about avoiding attachment to worldly goals.)  Indeed, I may be giving a false impression by selecting out a few Scriptures that touch on what Westerners would recognize as ethical themes.  In general, ethics are discussed much less frequently than questions about how to organize monastic communities, and the techniques for attaining enlightenment.

This brings us to the key point.  Buddhism correctly recognizes—from observation—that there is a serious flaw or mistake in human nature which needs to be rectified by extreme measures.  People cannot be happy because, regardless of what we have already attained or experienced, we are left unsatisfied and desire more.

From the Christian point of view, its main fault is that it proposes a type of despair; it assumes that the human condition is essentially bad, and that we need to escape from our desires, cravings, attachments, and illusions, into something more closely akin to apathy.  Benevolence is a virtue, but all forms of emotional attachment (including love for family and friends) are to be rejected.

Please understand that I am here talking about real Buddhism, not the vaguely exotic Eastern ambiance which Westerners use as a foil to project their ideas of what a non-Christian wisdom tradition ought to look like.  According to David Chapman (himself a rather eccentric modernizing Tantric Buddhist), much of what passes for Buddhist ethics was simply reimported from the West.  Chapman writes:

By the Victorian era, Christianity’s beliefs had become obviously false...

Rationally-inclined liberal Victorians developed secular moral philosophy, trying to find new, rational foundations for more-or-less the same morals.  (Current secular morality, both left and right, derives primarily from Christian morality.)

Romantically-inclined Victorians hoped for an-alternative spiritual foundation for ethics.  Rejecting rationality, they were sure Truth lay in the mystical connection of the True Self with the Absolute Principle of the Universe.  Some great civilization, in a land less barbarous than the ancient Middle East, must have discovered a correct system of ethics, and must have based it on this mystical unity.  Surveying the world’s religions, Buddhism looked most promising. (Buddhist morality is surprisingly un-bad compared with pre-modern alternatives.)  Ah, the ancient wisdom of the exotic East!

Unfortunately, traditional Buddhist morality is plainly inferior to liberal Victorian morality.  And, Buddhism does not use mysticism to justify its morals.  But, these are mere details! Buddhism must have the correct ethics—so we need to look harder to find it.

In fact, since it is not there, the Victorians wrote the ethics they wanted onto Buddhism, creatively hallucinating the object of their desire.

But this was not just a European project.  Asian Buddhist modernizers had their own reasons for inventing “Buddhist ethics,” and they collaborated vigorously in the project.

First, educated Asians recognized that European morality was, in fact, superior.  It was at minimum a stage 4 ethical system: a rational structure of justifications that eliminates arbitrary rules and assigns sensible weights to different moral considerations.  Traditional Buddhist morality goes no further than stage 3, which aims only at communal harmony, not justice.  Although Asian intellectuals disagreed with some specifics, they could see the value of a justifiable structure; so the idea of a Buddhist version was compelling.

Second, Asian rulers constructed modern Buddhism as a defense against colonialism.  Europe’s moral justification for colonialism was “bringing the benefits of civilization to the benighted savages.”  Demonstrating that an Asian country was fully civilized successfully prevented the colonization of Thailand and Japan.  One of the greatest benefits of civilization was a just system of ethics, for which Christianity was the standard.  Christianity was an instrument of colonialism, so it was urgent for Asians to invent an alternative system of ethics that would compare favorably with Christianity on Europe’s own terms

(How Asian Buddhism Imported Western Ethics, some formatting changes)

At a later state of the same process, we get the wishy-washy American Buddhism, which is really just therapeutic moralism with a side of meditation.  It is easy enough to find some hippie teacher who says that Buddhism is just about getting rid of unhealthy attachments while living the life you always wanted, but this is completely foreign to the complete renunciation of all pleasures demanded by most of the historical forms of Buddhism.

In particular, Buddha's "Middle Way" does not refer to a comfortable middle class existence; rather it refers to Buddha's conclusion that severe ascetic practices intended to torment the body are just as distracting and unhelpful as pleasure-seeking.

If you are looking for a sex-positive religion, Buddhism isn't it!  When an early disciple named Sudinna had intercourse with his wife, solely because his family wanted an heir, the Buddha rebuked him severely:

Worthless man, haven't I taught the Dhamma in many ways for the fading of passion, the sobering of intoxication, the subduing of thirst, the destruction of attachment, the severing of the round, the ending of craving, dispassion, cessation, unbinding?  Haven't I in many ways advocated abandoning sensual pleasures, comprehending sensual perceptions, subduing sensual thirst, destroying sensual thoughts, calming sensual fevers?

Worthless man, it would be better that your penis be stuck into the mouth of a poisonous snake than into a woman's vagina.  It would be better that your penis be stuck into the mouth of a black viper than into a woman's vagina.  It would be better that your penis be stuck into a pit of burning embers, blazing and glowing, than into a woman's vagina.  Why is that? For that reason you would undergo death or death-like suffering, but you would not on that account, at the break-up of the body, after death, fall into deprivation, the bad destination, the abyss, hell.  But for this reason you would, at the break-up of the body, after death, fall into deprivation, the bad destination, the abyss, hell.  (from the Vinaya Pitaka, quoted here)

[Note that as discussed previously, my quotations are from the Theravadan Pali canon, to keep them as close as possible to the historical Buddha's teaching.]

To a monk who questioned whether it is really necessary to give up all sensual acts (perhaps thinking he would do them without becoming attached to them) the Buddha replied:

For a person to indulge in sensual pleasures without sensual passion, without sensual perception, without sensual thinking: That isn't possible.  (Discourse on the Water Snake Simile)

Of course this is extremely difficult to do if you aren't a monk; so it was understood (even in the Theravada traditions) that most laypeople would still eat nice food, and have sex with their spouses, and love their kids—but that just means they are currently failing to become enlightened in this life.  Hopefully, by being decent and moral people (ideally by taking vows to abstain from killing, sexual immorality, stealing, lying, and drinking alcohol), they can improve their chances to succeed in the next reincarnation!  (Hence Buddhist texts like the Advice to Sigala, encouraging householders to adhere to a sort of conventional-bourgeoisie work ethic.)  But it was generally understood that actual enlightenment was not really compatible with fulfilling such social roles.  In this respect, Buddhist monasticism is not like ordination in other religions, where you can be e.g. a fully practicing Jew without becoming a rabbi, or a fully practicing Catholic without becoming a priest, monk, or nun.

(A lot of later schools of thought in Buddhism can be understood as reacting to the difficulty of this Theravada teaching by adding mitigating features—for example Mahayana adds to Buddhism the idea that bodhisattvas (Buddhist saints) can intercede on behalf of ordinary people to make Enlightenment easier for them; while Tantric Buddhism allows for the indulgence of sensuality and for breaking traditional Buddhist vows as an alternative path towards enlightenment.  But as far as I can tell, both of these are departures from Buddha's original teaching.)

Seeing that the human condition is full of suffering, Buddhism looks around for the door marked Exit.  (In a system with reincarnation, you can't just top yourself.)  The goal is to permanently escape from the cycle of births into cessation of suffering, returning (if at all) only to help other people also escape from life.

I take it that Nirvana (literally "blowing out" or "quenching") is not necessarily regarded as quite the same thing as nonexistence, but it would at least seem to involve the ceasing of all that makes us uniquely human.  No Christian would ever use the word "extinguished" to refer to the state of heavenly glory, let alone the state of the resurrected saints reigning with Christ in the New Heaven and Earth.  By contrast, Buddha himself refused to say whether the enlightened person persisted after death, holding that any possible viewpoint on the issue would keep one entangled in suffering:

[Note: the repetitiveness of many Buddhist sutras was designed to make them easier to recite by memory.  In the following quote I retain this feature, despite its awkwardness in written text.]

Vaccha, the position that "after death a Tathagata exists" is a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views.  It is accompanied by suffering, distress, despair, & fever, and it does not lead to disenchantment, dispassion, cessation; to calm, direct knowledge, full Awakening, Unbinding.

Vaccha, the position that ''after death a Tathagata does not exist'' is a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views.  It is accompanied by suffering, distress, despair, & fever, and it does not lead to disenchantment, dispassion, cessation; to calm, direct knowledge, full Awakening, Unbinding.

Vaccha, the position that ''after death a Tathagata both exists & does not exist'' is a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views.  It is accompanied by suffering, distress, despair, & fever, and it does not lead to disenchantment, dispassion, cessation; to calm, direct knowledge, full Awakening, Unbinding.

Vaccha, the position that ''after death a Tathagata neither exists nor does not exist'' is a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views.  It is accompanied by suffering, distress, despair, & fever, and it does not lead to disenchantment, dispassion, cessation; to calm, direct knowledge, full Awakening, Unbinding.

(To Vacchagotta on Fire)

Thus, while Buddhism encourages many noble virtues, its core goal is what some Christians might refer to as a "mortal sin", which (unless it is repented of) is inconsistent with salvation.  By this I do not mean that it is a vice for which God arbitrarily withholds salvation.  Rather, I mean that, if any Buddhist in fact succeeded in their quest to unmake themselves, it would be a logical contradiction for them to also receive the Kingdom of God, as Christians understand it.  (The sins of the flesh, like sexual immorality, are quite trivial in comparison to the existential despair that causes a person to seek spiritual suicide.)

But I don't want to be misunderstood as making a judgment about the final state of salvation of Buddhists, since not all of them will succeed in damning themselves.  I would not be very surprised to find out that a great many Buddhists (perhaps even Buddha himself) were sincerely trying to follow the best they knew, and will be rewarded with a fuller knowledge of the truth in the age to come.  But this will necessarily require them to stop chasing after annihilation, and instead go through the gate of life.

The Goodness of Creation, and Suffering

Christianity believes that physical existence is good; because it was created by a God who is good.  Redemption is not about escaping from physicality, instead it is about God assuming human nature in Christ and healing it from within.  It is true that we are called to die to our selfishness, and to be willing to sacrifice anything else if it conflicts with our relationship to Christ, but only so that we may become the holy people who God truly created us to be, more human than ever before!  Unlike Buddhism—and most sects of Hinduism—it does not preach the destruction of our essential individuality.  We are not to be merely absorbed into something impersonal.  The Christian message is called the gospel (good news) for a reason.  Our good news is better than their "good news"!

To be fair, I should probably note that in the past, many Christian monastics came very close to a "Buddhist" interpretation of Christianity, where the ideal monk is supposed to renounce every sort of earthly pleasure or desire, for the sake of seeking Christ alone.  Many early church fathers spoke out against "passions" in general.  And there are passages in Roman Catholic spiritual classics such as  The Imitation of Christ (by St. Thomas à Kempis) or the Ascent of Mount Carmel (by St. John of the Cross) which seem to advocate a total renunciation of everything that is not God.  It must be remembered that Christianity developed in a world which was—partly due to cultural influence from the East—far more sympathetic to asceticism than most moderns are comfortable with.

But this was only one strand of Christian tradition.  At least in theory, Christianity has always affirmed the goodness of the physical creation, including marriage and procreation.  The emotions expressed by St. David in the Psalms, crying out to be delivered from earthly troubles, are representative of a much older view: that you can put God first without having stoic indifference towards the world.

(On the other hand, modern Christians, especially Protestants, are far more likely to fall into the opposite mistake, thinking that the point of worshipping God is to live a fulfilling earthly life; while ignoring all the scriptural passages cautioning us not to set our hopes on this world, but to store up treasures in heaven.)

Zooming out more broadly, it is actually kind of surprising to me how many religions teach that suffering is, in one way or another, basically our own fault.  Pagans look to propitiate the gods whenever something goes wrong; Buddhists say it is our own desires that cause suffering; the doctrine of karma implies that we deserve whatever we get.  Even the medieval Rabbis, somehow overlooking or misreading the Book of Job, taught that all misfortune is a punishment for sin (although I gather that the Holocaust has led most modern Jews to reconsider this idea).

But Christianity has always allowed for the existence of unjust suffering.  It follows a Messiah who was not ashamed to be seen weeping, who felt the full range of human experiences, who went to the Cross in order to suffer on behalf of others.  Instead of karma, it offers grace, undeserved favor.  We get something unimaginably better than what we deserve, including the privilege of suffering with Christ, alongside the needy and oppressed.  And if we share in his sufferings, we will also share in his joy.

Next: Spiritual Experiences

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Curvature II: Spacetime

By Scott Church – Guest Blogger

In the first installment of this series, we explored the nature of curved spaces and introduced ourselves to some of the mathematical tools needed to describe how length, breadth, and height can be curved without higher dimensions to “curve into.” In the interest of keeping our exploration as intuitive as possible, we began with the Euclidean geometry we learned in high school and explored curvature from the vantage point of time as we experience it—a universal history that is the same for all of us and independent of the spatial stage on which our lives unfold. Today we will explore the nature of time and its relationship to space and discover (spoiler alert!) that in fact, it is neither separate from space nor absolute—not only can length, breadth, and height be curved, duration can be as well. The universe we inhabit is one of curved spacetime.

Special Relativity

The Newtonian physics we learned in high school presumes absolute three-dimensional space and time. In the low gravity and velocity world we live in, that is how we experience them. But intuitive as this may seem to us, there are hints that something is amiss. That physics also taught us that the speed of light c is a universal constant that can be derived from Maxwell’s equations. And as we saw in Part I, the laws of physics, including c, must be invariant for all observers stationary or moving. Pause for a moment and reflect on what this implies. If I am standing beside a highway and you drive by at 50 mph, that is the speed I will observe. In the car, you will see yourself as stationary and the world passing you at 50 mph in the opposite direction, including me. Another driver doing 70 mph in the fast lane will pass me at that speed and you at 20 mph. But Maxwell’s equations will remain true and invariant for all observers, so if a beam of light is shined in the same direction, it will pass all three of us at the same speed. How is this possible?

Imagine that you are now the one who is stationary, and I fly past you in a fighter jet at a speed v of 3600 mph, (or one mile/sec for round numbers) carrying a clock that is in sync with an identical clock of yours. As I pass you, it emits a pulse of light in your direction at time t_1 which reaches your eye after travelling a distance d_{t1} (Figure 1). One second later at t_2, a second pulse is emitted, but I will have flown one mile further so that pulse must travel a distance d_{t2} before it reaches your eye. My clock will be ticking at the same rate in my reference frame as yours is for you, but the seconds you observe on my clock will be longer because the second pulse you receive from it must travel further at the same speed c to reach your eye than the first one did. Your experience will be that my time runs slower for you than it does for me. And for the same reason, your clock will be running slower for me than it is for you.

 

Figure 1

As for distances, the length of my jet will be measured by the time it takes a pulse of light to travel from the nose (A) to the tail (B) at speed c (Figure 2). In my reference frame that will be given by,

L = c\Delta t_{ba}                    [Eqn. 1]

 where t_{ba} is my proper time (that is, the time measured by a clock at rest in my reference frame).

Figure 2

In your reference frame, the pulse of light will take a time \Delta t^{'}_{ba} to travel the length of my jet. However, while the pulse is in transit, point B will have moved forward a distance v \Delta t{'}_{ba} so the pulse will arrive at point B_2 instead (Figure 3),

Figure 3

And you will observe the length of my jet to be the distance between A and B_2, or,

L^{'} = (c - v)\Delta t^{'}_{ba}                    [Eqn. 2]

Not only will you see the pulse travelling a shorter distance that me, the time \Delta t^{'}_{ba} will also be less than the \Delta t_{ba} I observe because time is running slower for you than for me. The length L^{'} you observe for my jet will be smaller than the length L I observe, and you will see me and my jet as though we were compressed in the direction of travel.

Thus, we arrive at one of the foundational principles of special relativity; Space and time are neither absolute nor independent of each other. They’re united in a single spacetime manifold whose metric contains an underlying symmetry that preserves Maxwell’s equations and c for all observers. And this manifold is not simply a map of locations and distances—it’s a frame-independent history of events for every location within it.

In Part I we saw that in the flat Newtonian universe of our experience, time is absolute and independent of space. All observers experience it the same, and spatial geometry is Euclidean with the interval between any two points is given by the Pythagorean Theorem,

 ds^{2} = dx^{2} + dy^{2} + dz^{2}                    [Eqn. 3]

In spacetime, however, this is no longer the case. Now we have a collection not of points, but events that reflect the histories of each spatial point within it. The interval no longer defines the distance from here to there; It defines here and now, to there and then. Accounting for this in our metric tensor won’t be as simple as it may sound. As we’ve seen, the speed of light must remain the same for all observers whether stationary or moving in any reference frame. And the relative motion slows time down and compresses space until both reach zero at the speed of light. From our vantage point, a photon’s reference frame is a single event with a zero-length interval, so our interval must include time with a sign opposite to that of space. After multiplying time by c to convert it to equivalent distance units, this gives,

ds^{2} = dx^{2} + dy^{2} + dz^{2} - (ct)^{2}                    [Eqn. 4]

Which adopting the usual (though not strictly necessary) convention of making time the first, or zero component, results in the spacetime metric tensor,

                              [Eqn. 5]

The diagonal terms expressed as a tuple, [-1, 1, 1, 1], is known as the metric’s signature. In differential geometry (the branch of mathematics that generalizes the geometry we learned in high school to all types of curves spaces), a continuous N-dimensional manifold that has a well-defined and positive-definite metric tensor at all points (not all mathematically possible ones do) is referred to as Riemannian. That is, a flat 4-D Riemannian metric is one that for every point on it, infinitesimal displacements in the locally flat tangent plane have a metric signature of [1, 1, 1, 1]. A universe with Euclidean geometry and absolute time would have this metric everywhere. But in a universe constrained by special-relativity the interval can be zero as well as positive, so the metric is non-degenerate rather than positive-definite. Manifolds of this type are referred to as pseudo-Riemannian.

In Part I, we conducted a geometric thought experiment in which we traversed a closed triangular path through the flat space of an observer named Freddy, and another through the curved space of an observer named Cathy along geodesics (paths that reflect the shortest distance between any two points). In each, we carried one vector with us while leaving an identical parallel copy of it behind and upon returning to point A. When we did this in Freddy’s flat space we found, not surprisingly, that after completing the journey the two vectors were still parallel to each other. But after the same journey through Cathy’s curved space, we discovered that the vector we carried with us was no longer parallel to the one we left behind even though both were still pointing in the same direction (globally south), and we had travelled a shorter distance that still encompassed a larger area. We introduced some mathematical concepts that allowed us to define a covariant derivative 1 to describe the rate of change of the vector we carried with us along our path s^{\sigma},

\nabla_{\mu}s^{\sigma} = \partial_{\mu}s^{\sigma} + \Gamma^{\sigma}_{\mu\nu}s^{\nu}                    [Eqn. 6]

The first term on the right is the usual vector calculus gradient along the direction of travel. The second term, however, introduced a new object, the Christoffel symbol, that allowed us to map changes in the underlying tangent plane containing s^{\sigma}, itself onto local coordinate systems within it as we traversed the path. Integrating this derivative along our path would then fully capture the changes in our mobile vector with respect to its stationary twin we left behind.

That exercise, however, traversed a path through Cathy’s curved two-dimensional space, so equation 6 described distances and directions only. Had we included time in her curved universe, the path we walked would have been a trajectory of motion with history, and upon arriving back at A we would have found that our mobile vector was now older or younger than its stationary copy as well. In curved space, geodesics are the shortest distance between points—here and there. But in spacetime they are histories that reflect the shortest path, stationary or moving, between here and now, and there and then. As such, they define an equation of motion for the trajectory an object will follow when no forces are acting on it.

In a flat spacetime like Freddy’s, an object left to itself will remain stationary or move at constant velocity, so its geodesic will be a straight line whose slope will be the constant speed it is moving at. If one or more forces act on the object it will accelerate, and its history will follow a curved path whose velocity changes from moment to moment. We can derive the equation of motion for this by using equation 5 to derive the second order time derivative along ds^{\sigma}, to equate the acceleration produced by a force it to its strength divided by the object’s mass. In his flat spacetime, a single unvarying tangent plane spans the entire universe, so the Christoffel term will vanish, leaving us with,

\frac{\partial^2 s^{\sigma}}{\partial t^2} = \frac{F}{m} = 0                    [Eqn. 7]

Which we will recognize as a geodesic equation of motion for Newton’s second law that we learned in high school.

In Cathy’s universe things are different. There, geodesics are curved so the Christoffel term will generally be non-zero, and her equation of motion will be given by,

\frac{\partial^2 s^{\sigma}}{\partial t^2} + \Gamma^{\sigma}_{\mu\nu}\frac{\partial s^{\mu}}{\partial t^2}\frac{\partial s^{\nu}}{\partial t^2} = 0                    [Eqn. 8]

Notice that in curved spacetimes like hers, the second term on the left will be non-zero even in the absence of forces, so the first term will be as well. Left to themselves, objects in a curved spacetime will experience freefall along accelerating trajectories.

Which brings us to the next topic…

General Relativity

The other hallmark of our high-school physics lessons was Newtonian gravity. In a universe of flat space and absolute time like Freddy’s, gravity is an attractive force between objects whose strength is a function of their masses and the distance separating them. Specifically, the gravitational force F_g between two objects with masses m_1 and m_2 is given by,

F_g = g_c\frac{m_1m_2}{r^2}                    [Eqn. 9]

Where r is the distance between their centers of mass and g_c is the universal gravitational constant we also learned in our high-school physics classes.

For centuries this understanding of gravity has served us well in regions of low mass, velocity, and distance, and still does. I spent twenty years as an aerospace engineer designing commercial jet aircraft structures, and the aircraft my colleagues and I applied these principles to still have exemplary safety and performance records. But even so, physicists have long been troubled by the idea of “spooky action at a distance” forces. How can objects interact with each other invisibly over large distances? On the other hand, we can put it differently by saying that gravity causes objects with mass to accelerate toward each other at a rate given by their masses and the distance separating them, and as we saw above, freefall acceleration is a consequence of spacetime curvature. Jumping the gun, we also know that mass and energy are equivalent (hence Einstein’s celebrated E = mc^2) and moving objects with mass have a kinetic energy that is a function of their momentum and mass (K = p^2/2m). This raises an interesting question…

What if gravity isn’t a force at all, but simply a local manifestation of spacetime curvature due to mass, energy, and momentum?

If this is true, then we would expect that two objects of differing mass in the field of a third object of much larger mass (like the earth, for instance) would experience the same freefall acceleration toward it—essentially, that the “force” F_g the gravitational field exerts on their differing small masses would result in the same acceleration for both,

\frac{F_{g1}}{m_1} = \frac{F_{g2}}{m_2}                    [Eqn. 10]

And this would be the same acceleration that would result from an equal but non-gravitational force (e.g. - the thrust produced by a rocket engine). As you’ve probably guessed by now, this is the case. Gravitational mass and inertial mass are indistinguishable from each other, and freefall accelerations induced by the former are a consequence not of any “spooky action at a distance” force, but of the local spacetime curvature created by its presence. This identity, known as the equivalence principle, is the heart and soul of general relativity. Throw a pebble into a pond and watch it arc through the summer sky before splashing down, and you are literally seeing the curvature of length, height, breadth, and duration where you’re standing because of the mass of the earth beneath your feet! 2

And once again, if spacetime curvature is caused by mass, energy, and momentum, we can ask ourselves how this could be captured mathematically. As in Part I, a formal derivation of the relationship between the two is beyond the scope of an introduction to the topic, but we can introduce the types of mathematical objects needed and how they relate to each other. The first thing we need is an object that describes curvature. Like the terms introduced so far, it will need to capture the change in angles over infinitesimal displacements from any reference frame we view it from, so it will need to be a covariant or contravariant tensor. And since we want it to describe curvature specifically rather than displacements, it will be a function of the Christoffel symbols that describe how they change when we walk a parallel transport path (or more properly, a function of their first derivatives, or rates of change). To unambiguously capture this, we will have to carry a four-vector ds (that is, a vector in three spatial dimensions plus time) around an enclosed path for which all the interior angles are orthogonal to each other (locally 90 degrees). Previously, we were able to do this with a triangular path in Cathy’s space because for clarity of the underlying principles we presumed it to be spherically curved, but that won’t be true of curved spacetime in general. So, now we must carry our four-vector along a four-legged parallel transport path (presumed to be infinitesimally small for a local curvature description), again preserving its local orientation at every point, as shown in Figure 4 (Wikimedia, 2015).

Figure 4

Upon returning to our starting point, we will have a function that describes how each of the four components of ds changed with respect to the others for each of the four legs of the journey. As such it will be a tensor with four indices (rank 4) each of which covers four dimensions, so it will have 4^4, or 256 components. This tensor, known as the Riemannian curvature tensor R^{\mu}_{\nu\rho\sigma}, fully describes the actual curvature of spacetime at every point on the manifold. It can be specified in covariant or contravariant terms, but since it captures how a contravariant vector is affected by local covariant curvature, it’s customary to express it with one “upstairs” index and three “downstairs” ones, as shown here.

Before going any further, there are two related tensors we’re going to need (why will become apparent shortly). In Part I we discussed how a tensor object defined by N indices can be “contracted” to fewer indices by projecting one or more of the index’s components onto the others—in essence, “averaging” it into the remaining ones. For a tensor expressed in covariant form for all indices, we do this by multiplying it by the contravariant metric tensor in one or more of its indices. Contracting the Riemann tensor in this manner for two of its four indices gives,

 g^{\rho\sigma}R_{\mu\nu\rho\sigma} = R_{\mu\nu}                    [Eqn. 11]

The resulting tensor, R_{\mu\nu}, is known as the Ricci tensor. Contracting it again on both of its indices yields the Ricci scalar, R. These have different physical interpretations. The Ricci tensor describes the rate of change of an infinitesimal element of spacetime volume along ds due to tidal forces. That is, as we move through spacetime along a group of infinitesimally separated parallel geodesics, it describes how an element of volume between them changes in each direction. The Ricci scalar, on the other hand, gives a non-dimensional measure of how the overall enclosed volume itself changes.

Next, we need a tensor object that describes the mass, energy, and momentum we suspect to be curvature’s source. That tensor (which we won’t make any attempt to formally derive here), is known as the stress energy momentum tensor, T^{\mu\nu}. Its components are defined in a manner similar to those of the metric tensor, g_{\mu\nu}, but using momentum density four-vectors (momentum density in three spatial dimensions plus energy density, which can be thought of as “momentum” in time for a stationary object). Because its momentum density components are vectors, it is customary to express it in contravariant form (indices “upstairs”). The first index (\mu) gives the four-momentum components being considered, and the second (\nu) gives the direction it is being compared to. The physical significance of its components is as shown in Figure 2 (Wikimedia, 2013).

 

Figure 5 – The Stress Energy Momentum Tensor

With these tools in hand, we can proceed with our investigation of how mass, energy, and momentum curve space and time, but there are still a few constraints we need to account for.

First, the stress energy momentum tensor is rank 2 but the Riemann curvature tensor is rank 4 (that is, the former has two indices with 16 components, whereas the latter has 4 indices and 256 components), so we can’t just equate them to each other. Whatever effect T^{\mu\nu} has on curvature will have to manifest itself as a rank 2 curvature object as well—that is, it will have to be a contraction of the Riemann tensor that reflects the behavior we observe in gravity, so we want to know what sort of contraction will give us that.

We saw earlier that in the absence of forces, spacetime curvature manifests as acceleration. Strictly speaking, this applies only to point masses in the gravitational field of a much larger mass. For objects that have size and shape, the story changes. In Newtonian physics, the gravitational force between two masses varies inversely as the square of the distance between them (equation 9). So, if you are falling toward the earth feet first, your feet are being pulled harder than your head because they are closer to the earth’s center of gravity. Inasmuch as this is the low mass/energy/momentum limit of GR, the same will be true in curved spacetime as well. Likewise, your freefall into the earth’s gravitational well will be along a geodesic, and the deeper you go, the closer adjacent geodesics to your sides will be. Figure 3 (Wikimedia, 2008) shows what a gravitational well created by a mass as the bottom of the “pocket” looks like.3 The longitudinal lines are freefall geodesics with their steepness at each node being the strength of gravity there, and the squares enclosed by the grid can be thought of as shapes.

 

Figure 6 – Gravitational Well

Notice how falling into the well squeezes the latitudinal rectangles into increasingly longitudinal ones. In the earth’s relatively weak gravitational field compared to your size, the effect is too small to notice. But as you fall toward it, feet-first, you are being stretched and squeezed. This stretching and squeezing of large objects are tidal forces, and in the limit of a point mass, they reduce to simple freefall acceleration. Since in the most general terms, tidal forces are how curvature manifests, we would expect the stress energy momentum tensor to equate to a rank 2 tensor that describes them. And as we’ve seen, we have one… the Ricci tensor!

But we’re not out of the woods yet. There is one more constraint we need to honor; Another of the fundamental ones we learned in our high school physics, conservation of energy and momentum. Although neither is well-defined nor self-evidently conserved for the whole universe (or large regions of it), for locally flat inertial reference frames in the tangent planes of every point in it, both need to be conserved. This means that for every point on the manifold the divergence of the stress energy momentum tensor must be zero. That is,

\nabla_{\mu}T^{\mu\nu} = 0                   [Eqn. 12]

And here we have a problem… Tidal forces do not vanish in locally flat regions, and neither does the divergence of the Ricci tensor. If they did, falling through a black hole event horizon would be a lot less traumatic! So, our contracted curvature tensor object is going to need some tweaking.

Fortunately, the full Riemann curvature tensor itself gives us a way out. As it happens, its own internal consistency does require it to vanish locally; When curvature vanishes (as it must in local tangent planes) so does the curvature tensor. One consequence of this is that the sum of its divergences with respect to any three of its four indices must add to zero. That is,

\nabla_{\mu}R^{\mu }_{ \nu\rho\sigma} + \nabla_{\nu}R^{\nu}_{\mu\rho\sigma} + \nabla_{\rho }R^{\rho}_{\mu\nu \sigma} = 0                   [Eqn. 13]

This relationship is known as the second Bianchi identity (of which there are several). Again, we needn’t worry about its formal derivation here. But for our purposes, what matters is that with some mathematical gymnastics we can derive from it the contracted Bianchi identity,

\nabla_{\mu}R^{\mu\nu} = \frac{1}{2}\nabla_{\mu}g^{\mu\nu}R                   [Eqn. 14]

 Gathering terms gives,

\nabla_{\mu}\left ( R^{\mu\nu} - \frac{1}{2}g^{\mu\nu}R \right ) = 0                   [Eqn. 15]

And finally, by combining the Ricci tensor for tidal forces and the Ricci scalar for volumetric curvature, we have a tensor object we can equate to the stress energy momentum tensor that captures the spacetime curvature it induces while sharing with it a zero divergence that locally preserves conservation of energy and momentum. It’s customary to refer to the term in brackets as the Einstein tensor G^{\mu\nu}, from which we have,

G^{\mu\nu} = R^{\mu\nu} - \frac{1}{2}g^{\mu\nu}R = \kappa T^{\mu\nu}                   [Eqn. 16]

Where \kappa is a proportionality constant which again, we won’t derive here, but turns out to be,

\kappa = \frac{8\pi g_c}{c^4}                   [Eqn. 17]

And there you have it, Ladies and Gentlemen… an equation that relates mass, energy, and momentum to spacetime curvature, and therefore gravitation!

One final question remains. Technically, equation 16 is arbitrary to within an additive constant as well. When Einstein first derived this relationship, he realized that it predicted a universe that was necessarily expanding or contracting, and thus impermanent. The idea of a universe that wasn’t eternal was philosophically abhorrent to him, so he included a constant term on the left (typically denoted with the Greek letter \Lambda), multiplied by the metric tensor for consistency and sized to offset the expansion, thereby preserving a curved, but static and eternal universe. Later, when it was independently confirmed that the universe is in fact, expanding (a fascinating story in its own right!), Einstein retracted the constant calling it “the greatest mistake of my life.” But as it turns out, it wasn’t. It has since been discovered that the cosmological constant is not only real, but positive and causing the expansion of the universe to accelerate! The discovery was so striking that the leaders of the team who discovered it, Saul Perlmutter, Brian Paul Schmidt, and Adam Guy Riess were jointly awarded the 2011 Nobel Prize in physics.

So… combining equations 16 and 17 with all terms expressed as covariant (which is customary), and restoring the cosmological constant to its rightful place we have,

G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi g_c}{c^4} T_{\mu\nu}                   [Eqn. 18]

These are the celebrated Einstein Field equations that are the hallmark of general relativity. The terms on the left fully describe the geometry of spacetime for all observers at every point in the universe, and the term on the right describes the mass, energy, and momentum that produces that geometry.

This was meant to be an introduction to spacetime curvature, so we’ve arrived at them with some big leaps and little in the way of formality. Though at first blush they may seem daunting and difficult to wrap your mind around, the important thing for today is an understanding of what the terms in these equations mean, and why they must have the general forms they do to describe how length, height, breadth, and duration can be curved. For those who want to explore further, there any number of good introductions to general relativity for the layperson. One that I found particularly readable and informative was Clifford Will’s book Was Einstein Right – Putting General Relativity to the Test (1993), first published in 1986 when I was in grad school. If you feel ready to make the deep dive into the full formalism of general relativity, there are many textbooks on the subject. But if there is one that has stood for many years as the Bible of general relativity, it’s Misner, Thorne, and Wheeler's Gravitation (2017). It’s rigorous and will take some time to wade through, but it’s the best, and most thorough general relativity course I am personally aware of and has been since it was first published in 1973.

The psalmist tells us,

“The heavens are telling the glory of God; and the firmament[a] proclaims his handiwork. Day to day pours forth speech, and night to night declares knowledge. There is no speech, nor are there words; their voice is not heard; yet their voice goes out through all the earth, and their words to the end of the world.” – Psalm 19:1-4

When I gaze up at the nighttime sky, I see stars that are hundreds of light years away, many of which are surrounded by worlds, possibly even worlds not unlike my home. And I realize that I’m gazing upon those stars and worlds not as they are now in my reference frame, but as they were centuries ago. If I were to turn a large enough telescope on that sky I would see galaxies, quasars, nebulae, and a bewildering spectacle of other wonders, some of which are billions of years old and revealing themselves to me from a time long before humans or even our solar system existed. And if I filter their light through a spectrometer, I will see the fingerprints of their chemical constituents shifted increasingly toward the red the more distant they were, and I would realize that I was watching the universe grow—not as an expansion of matter into a pre-existing void, but literally the expansion of space and time themselves from a cataclysmic birth 13.73 billion years ago. I would see in that the glory of God and his handiwork…

And I would suspect, as J.B.S. Haldane did a century ago, the handiwork of God, where length, breadth, height, and duration are themselves clay in His artistic hands, is not only queerer than I suppose, but queerer than I can suppose.

Footnotes

1)  In Part I we introduced the nabla symbol on the left (\nabla_{\mu}), which in mathematics is known as the Laplace operator. It is a shorthand reference for the gradient (first derivative) in the direction of a vector defining the \mu coordinate system. That is, \nabla_{\mu} = \frac{\partial }{\partial x_0} + \frac{\partial }{\partial x_1} + \frac{\partial }{\partial x_2} + \frac{\partial }{\partial x_3} where the index \mu = 0, 1, 2, 3. This representation of a gradient in a particular direction is also referred to as the divergence.

2)  Interestingly, this isn’t just theoretical. Google and Apple map apps leverage first-order corrections for spacetime curvature near the earth’s surface to refine the accuracy of your location from raw GPS triangulated signals. General relativity is literally why your phone knows your location to within a couple hundred feet or so rather than one or two city blocks!

3)  Strictly speaking, this is a 2-D gravitational well with absolute time rather than a true 4-D gravitational which would include time. But for the current purpose, it suffices to illustrate the point.

References

Misner, C.W., Thorne, K.S. & J.A. Wheeler. 2017. Gravitation. Princeton University Press (Oct. 24, 2017). ISBN-10: 9780691177793, ISBN-13: ‎978-0691177793. Online at https://www.amazon.com/Gravitation-Charles-W-Misner/dp/0691177791/ref=sr_1_1?crid=1OKXLNQA5YVAR&keywords=gravitation&qid=1694219167&sprefix=gravitation%2Caps%2C253&sr=8-1&ufe=app_do%3Aamzn1.fos.18630bbb-fcbb-42f8-9767-857e17e03685.  Accessed Oct. 9, 2023.

Wikimedia. 2008. Image courtesy of AllenMcC. Based on the work of Bamse, and Melchoir, CC BY-SA 4.0, Mar. 2, 2013. Online at https://commons.wikimedia.org/wiki/File:GravityPotential.jpg. Accessed Oct. 9, 2023.

Wikimedia. 2013. Image courtesy of Maschen. Based on the work of Bamse, and Melchoir, CC BY-SA 4.0, Mar. 2, 2013. Online at https://commons.wikimedia.org/w/index.php?curid=24940142. Accessed Oct. 9, 2023.

Wikimedia. 2015. Image courtesy of IkamusumeFan, CC BY-SA 4.0, Jan. 1, 2015. Online at https://commons.wikimedia.org/w/index.php?curid=2615879. Accessed Oct. 9, 2023.

Will, C.N. 1993. Was Einstein Right? - Putting General Relativity to the Test. Basic Books; 2nd edition (June 2, 1993). ISBN-10: ‎0465090869; ISBN-13: ‎978-0465090860. Online at https://www.amazon.com/Was-Einstein-Right-Putting-Relativity/dp/0465090869/ref=sr_1_1?crid=TOG1ZAWGPF20&keywords=was+einstein+right&qid=1696883510&sprefix=was+einstein+right%2Caps%2C171&sr=8-1. Accessed Oct. 9, 2023.

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Curvature I: Space

My own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose. – J.B.S. Haldane (Possible Worlds and Other Papers, 1927)

I was born hopelessly curious and under the tutelage of a nurturing teacher and parents who surrounded me with books, I fell in love with physics in the 2nd grade—when all my friends were enthralled with Batman, jets, and G.I. Joe. What drew me to it was the wonder of mysteries I couldn’t wrap my budding mind around, and chief among these was the notion that space, and time could be curved. I remember pouring over my parent’s Time-Life encyclopedia set which among other things, contained a full-color plate titled “Three kinds of space” featuring gridded surfaces shaped like a sphere, a pancake, and a saddle labeled +1, 0, and -1 respectively (the Friedmann constants, although of course, I didn’t know that then). I remember gazing at them struggling to understand… How can length, breadth, height, and duration be bent…? What does that even mean…? The question became even more mind-numbing when I later discovered that there can be spaces with more than three or four dimensions—indeed, an infinite number of dimensions—and these can all be curved as well. It wasn’t until well into graduate school that I started to get a shaky footing in that recondite landscape.

As three-dimensional beings, most of us grasp curvature visually. We can see curved lines and sheets against the backdrop of three dimensions because they bend into the other dimension/s. But how can three-dimensional space (or more properly four-dimensional space-time) bend when there are no other dimensions to bend into? The key to understanding this is to approach the question not by trying to visualize higher-dimensional spaces, but by exploring them with a mathematically based thought experiment physicists and mathematicians refer to as parallel transport. Let’s introduce two explorers: Flat Freddy who lives in a two-dimensional flat universe, and his sister Curved Cathy who lives in a curved one. For them, there is no third dimension much less any higher ones.

Parallel Transport

Let’s start with Freddy, placing him at the vertex of a triangle with two parallel vectors oriented along his direction of travel, one red and one green (Figure 1).

Figure 1

Now, let him go for a walk around the triangle’s perimeter in the direction the vectors are pointing, leaving the green vector behind, and taking the red one with him while ensuring that for the entire journey it remains oriented in the same direction (as we will soon see, this matters). Completing the first leg of the journey, he arrives at point B (Figure 2) with his red vector still parallel to the green one, and unchanged from its original orientation (light red).

 

Figure 2

Then, let’s have him journey an equal distance to the right at a 90-degree angle. When he arrives at point C, his red vector is still parallel to the green one and its previous orientations (Figure 3).

 

Figure 3

Finally, let’s take Freddy back home and reunite his two vectors. When Freddy checks his compass, he sees that point A is to his left and back at a 45-degree angle to the BC leg he just covered. When he arrives home again, he finds that his red and green triangles are still parallel to each other, exactly as they were when he began, and remained throughout his trek (Figure 4).

 

Figure 4

Getting his map out, Freddy sees that his journey traversed a right triangle with two 45-degree angles, the final leg of which covered a distance given by the Pythagorean Theorem,

\overline{AC} = \sqrt{({\overline{AB})^{2}} + ({\overline{BC})^{2})            [Eqn. 1]

And enclosed an area given by,

A = \frac{X^{2}}{2}           [Eqn. 2]

Where X is the length of \overline{AB} (or \overline{BC}). No surprises here. This is exactly what earth-bound three-dimensional creatures like us would expect.

Parallel Transport in Curved Space

Now, let’s have Cathy take the same journey in her universe. For clarity’s sake, let’s assume her universe is spherical with a “radius” that will better illustrate the outcome (more on why that word is in quotes soon). Like Freddy, we’re going to have her walk a triangular path beginning at point A with parallel red and green vectors, both tangent to the straightest path from point A to point B (Figure 5). As before, she will leave the green vector behind while carrying the red one with her, keeping it oriented in the same direction throughout. This time however, things are going to be a little more subtle. In Freddy’s universe the meaning of “straight” is clear enough. But as we will soon see, in Cathy’s this term will require a more precise definition.

 

Figure 5

When she completes the first leg of her journey at point B, her red vector hasn’t changed orientation. It is still pointing straight ahead, tangent to her path of travel (Figure 6).

Figure 6

Following in Freddy’s footsteps, she then journeys an equal distance to the right at a 90-degree angle, arriving at point C with her red vector still unchanged in direction (Figure 7).

 

Figure 7

Cathy has now travelled the same route from point A to point C that Freddy did in his universe and covered the same distance getting there. But now, something is amiss. When she checks her compass, she finds that point A isn’t to the left of her BC leg and 45 degrees back. Home is now 90 degrees to her left. Even more strangely, upon arriving home (Figure 8) she sees that her red vector is no longer parallel to the green one as it was when she started (light red). Now it is oriented at 90 degrees to it, even though it remained pointed in the same direction for the entire trip!

Figure 8

Furthermore, when she gets her map out, she sees that unlike her brother, she has traversed an equilateral triangle whose inner angles add up to 270 degrees rather than 180 degrees. And even though the final leg of her journey was noticeably shorter than Freddy’s, she traversed a larger region. Having studied higher mathematics at Flatland University, she is familiar with higher-dimensional spaces than the two dimensional one she knows, and an equilateral triangle with three 90-degree interior angles sounds suspiciously like a higher-dimensional sphere. Sure enough, when she measures the area enclosed by her journey, she finds that it is given by,

A = \frac{\pi R^{2}}{2}           [Eqn. 3]

Where R is a parameter that behaves mathematically like the radius of a three-dimensional sphere even though in her universe, there is no third dimension to contain one.

Note that Cathy’s conclusions were based only on measurements of distance and area, and the orientation of a vector she carried with her around a closed two-dimensional path. At no time did she step “outside” of her space into a third dimension from which the radius of a 3-D sphere could be observed. What she measured is simply a parameter that behaves like one in area calculations. Of course, Figures 5-8 are shown in 3-D perspective for heuristic purposes, but beyond that, there is no need for Cathy to postulate any higher dimensions to explain what she sees. As far as she knows, in her universe only two dimensions exist. How could Cathy’s two-dimensional universe be “spherical” when the sphere of our experience is a three-dimensional shape?

Straight vs. Geodesic

To answer this question, let’s go back to the turn of the 3rd Century B.C. when the Greek Mathematician Euclid published his Elements. In it, he laid the foundation of geometry in our three-dimensional space and Freddy’s two-dimensional one with five axioms, or postulates. Of these, four are interdependent in that each one can be formally derived from the remaining three. The remaining one, his fifth postulate, he stated as follows,

If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles. – (Heath, 1956)

It follows from this that if the two interior angles formed are equal to two right angles, those lines will never meet. Though Euclid doesn’t specifically say so, this would make the two lines parallel, which led 19th Century Scottish mathematician John Playfair to restate it in what today is perhaps its most popular version,

There is at most one line that can be drawn parallel to another given one through an external point.

For centuries, the fifth postulate troubled mathematicians because reasonable as it may seem, it’s entirely ad hoc. It has no interdependence with the other four and is superfluous to a complete formalism of Euclidean geometry. It was only a matter of time until people began to wonder what geometric doors would be opened if it were discarded.

The first step in that direction is a reexamination what we mean by straight and parallel. Like Freddy, most of us think of a line as straight if it is one-dimensional in the sense of having no curvature—or more formally perhaps, if all points on it share a common tangent vector in one direction. Likewise, we think of two lines as parallel if they lie within a common two-dimensional plane and are aligned in the same direction with no intersection point. Indeed, this is how mathematicians defined both terms for many centuries, and to this day Euclid’s fifth postulate is often referred to as his parallel postulate. But if it proves to be superfluous to the formalism of Euclidean geometry then non-Euclidean geometry becomes possible and these definitions will need to be revisited.

Without the fifth postulate, on an N-dimensional manifold (or space), a curve connecting any two points A(x_1, x_2, ..., x_N) and B(x_1, x_2, ..., x_N) is said to be straight if, and only if it is the shortest distance between them on the manifold. In a flat space like Freddy’s (or ours), this reduces to our intuitive definition above, but that definition alone does not constrain manifolds to be flat. This suggests that if we want to quantify how paths between events are traversed in universes like Cathy’s, our mathematical descriptions need to be revised, and our parallel transport thought experiment gives us a clue as to how.

Modeling Curved Geometry

A full mathematical treatment of general relativity is beyond our scope today, but we can get our feet wet with an overview of the tools it will require. To model any N-dimensional space, be it flat or curved, there are two fundamental requirements we must meet.

First, we need a way to describe not only distances, but angles. To do that we will need to define at least two vectors at every point on it, r^{\mu} and r^{\nu}, where the indices \mu and \nu denote the N coordinates of each. Strictly speaking, they can be specified in any coordinate system of our choosing, and oriented in any non-parallel direction we like, but ideally, we want them to be orthogonal to each other (as shown in Figure 9) so that they define a coordinate system/s themselves. With these, we can then use a vector inner product, or dot product of them to define a matrix function  g_{\mu\nu} whose squared diagonal terms can be summed to give the squared distance along any interval, and whose off-diagonal terms are the dot product projections of each vector’s components onto those of the other. This function, which is referred to as the metric tensor,1 contains within its N^{2} components a description of all lengths and trigonometric relationships between the two vectors.2  [Aron discusses this at length in his 2012 post All points look the same.]

Figure 9

Neglecting time for simplicity (we’ll get to this later), in a flat 2-D space like Freddy’s, the two vectors will not have components that lie along each other so the off-diagonal terms will be zero, and the vectors are chosen so that their lengths define units in our chosen coordinate system,3  the diagonal terms will be 1 and the sum of their squares defines the Pythagorean theorem. Thus,

            [Eqn. 4]

Second, we need to ensure that our models preserve one of the most sacred principles in physics—namely, that the universe exists independent of us, so its behavior should be independent of how we choose to describe it. If the most fundamental laws of physics are different here and now in this coordinate system and units than it is there and then in those coordinates and units, that would imply that we have an unreasonably unique status in it. In our hearts, we know that isn’t the case, so our descriptions of it should look the same in all frames of reference and units. In physics this is referred to as the principle of general covariance.

To do this we need to account for the fact that some quantities behave differently under a change of scale in coordinate system units. For instance, if the vector r^{\mu} is one meter long, it will have a length of 1 in a coordinate system specified in meters. But if the scale is changed to centimeters, its length will be 100. The same will apply to angles. The vector itself remains the same—what has changed is its representation in a rescaled coordinate system. Quantities that behave this way are said to be contravariant because their size will vary counter to variations in the scale of units they’re represented with.

On the other hand, there are quantities such as gradients for which this isn’t the case. A 6% grade is a 6% grade whether we specify it in meters/meter or cm’s/cm, so rescaling coordinate systems will vary length specifications along any coordinate axis, but not the gradient in that direction. The metric tensor g_{\mu\nu} is such an object. As we’ve seen, it’s effectively a generalized dot product between local coordinate system axes. Since its components give their projections onto each other, it behaves like a gradient under coordinate system transformations. Quantities like this are said to be covariant because they retain their values regardless of how their coordinate system scale is varied. The difference is shown in Figure 10 (Wikimedia, 2018).

Figure 10

This may seem like hair-splitting, but when we move from the realm of absolute flat spaces to that of curved geometries, the difference matters. Some quantities like vectors, lend themselves to a contravariant description whereas others, like gradients, lend themselves to a covariant one. In the parlance of general relativity, it’s customary to specify the indices of the former with superscripts (“upstairs”) and the latter with subscripts (“downstairs”). Each type of tensor can be converted into the other by multiplying with an appropriately dimensioned factor (which is referred to as “raising or lowering indices”), but things are a lot clearer when we stick to representing each in the form that is most natural to them. As such, objects like vectors whose specifications vary under a rescaling multiple coordinate axes are typically specified with “upstairs” indices and those like the metric that behave more like gradients use “downstairs” ones.

With these qualifications, let’s revisit our earlier parallel transport experiments and put some flesh on the bones. In Figure 9 we saw that in Freddy’s universe, r^{\mu} and r^{\nu} will be the same everywhere and so will g_{\mu\nu}. It makes no difference where (or when) we place any coordinate system. But what about Cathy’s universe? At point A, a small surrounding region will be approximately flat and represented by a tangent plane containing r^{\mu}, r^{\nu} centered on it (Figure 11). Now, let’s define a third tangent vector s^{\sigma} along our parallel transport path from A to B.

Figure 11

Once again, we walk the path from A to B in the direction ds^{\sigma} as in Figures 5 and 6, carrying the tangent plane and r^{\mu} and r^{\nu} with us (Figure 12).

 

Figure 12

At each point in the path, r^{\mu}, r^{\nu}, and s^{\sigma} are still oriented in the same directions with respect to any local coordinate system, and the latter remains parallel to the path we’re travelling. When we arrive at B, we see that things still look the same to us as they did when we started. But this time the local tangent plane and coordinate systems we carried with us have twisted with respect to where they were at A and no longer looks the same to an observer who stayed behind.

In Freddy’s universe, one tangent plane uniquely spans the entire space. All distances and angles look the same from any reference frame within it, and carrying vectors such as r^{\mu} and r^{\nu} from one point to another is just a matter of summing displacements along any given path between them. But in a curved space like Cathy’s, we need a mathematical object that not only describes displacements along a path, but also one that maps that path onto the local tangent planeas it rolls across the curved surface as shown in Figure 13 (Wikimedia, 2023).

Figure 13

This object, which mathematicians refer to as an affine connection, allows us to describe vectors along any path through a larger curved space in terms of a fixed coordinate system within the local tangent plane at any point. An infinite number of such connections are possible but there is one, known as the Levi-Civita connection, that is a natural choice for spaces that have a well-defined metric tensor at every point because it allows us to define a derivative (or rate of change) along a curved space path that generalizes the usual mathematical rules of vector calculus in locally flat tangent plane regions to the larger curved space. This covariant derivative (which we denote with the nabla symbol 4) will need to have two parts and is given by,

\nabla_{\mu} = \partial_{\mu} + \Gamma^{\sigma}_{\mu\nu}           [Eqn. 5]

For an infinitesimal displacement along any path, the first term on the right is the gradient with respect to the local tangent plane as defined in the usual flat space manner. The second term is the rate at which the tangent plane itself (and the covariant metric tensor embedded in it) is changing in the direction of a contravariant displacement ds^{\sigma} in the direction of a tangent vector to the path. As such, it will be matrix function with three indices, two of which are best represented as covariant and a third contravariant one which we will denote with the index \sigma. This function, which per convention we designate with a capital Greek Gamma, is known as a Christoffel symbol. Since it requires three indices to fully capture the evolution of the metric tensor, in Cathy’s space it will have 23, or 8 components to her metric tensor’s 4. We refer to Christoffels as “symbols” because they aren’t true tensors in that they aren’t globally frame-independent until multiplied by an infinitesimal displacement in at least one direction. And as shown, equation 5 doesn’t make sense because the indices on the right and left sides don’t agree with each other. More properly, it defines a mathematical operator that must act on something to produce a meaningful equation. Applying it to ds^{\sigma} gives,

\nabla_{\mu}s^{\sigma} = \partial_{\mu}s^{\sigma} + \Gamma^{\sigma}_{\mu\nu}s^{\nu}           [Eqn. 6]

With the upstairs and downstairs \nu in the second term cancelling, this equation is now consistent across indices and the Christoffel term behaves like a tensor. This path derivative will look the same from every coordinate system in Cathy’s curved space. In flat spaces like Freddy’s, the tangent plane is the same everywhere and unchanging so the Christoffel term will vanish leaving us with the usual Euclidean directional derivative we learned in first-year vector calculus.

 

For today’s purposes we needn’t worry about how these equations were derived. The important thing is to understand why curved spaces require these kinds of mathematical tools rather than the familiar ones of Euclidean geometry, and how they reflect curvature in multiple dimensions without additional dimensions to “curve into.” If you’re like me, the latter point is the biggest stumbling block. It’s one thing to know that curved spaces are mathematically possible without additional background dimensions. But it’s another thing altogether for three-dimensional Euclidean space beings to visualize them. Space (or spacetime) can be curved in one of two ways: positive, or negative.5 Positively curved space is spherical and, if extended far enough, finite and closed. In our previous example, Cathy’s universe is a spherical one. And as we saw, the interior angles of a triangle in such a space add to greater than 180 degrees. Her space is finite in size, and travelling in a straight line in any direction will eventually return you to where you started from. Negatively curved space is saddle-shaped and has hyperbolic geometry. The interior angles of a triangle in it would add to less than 180 degrees, and like flat Euclidean space, it extends to infinity in all directions. Figure 14 shows both as compared to flat space.

Figure 14

It’s easy to visualize two-dimensional curved spaces like these in isometric views that show their contours in an additional dimension. But what would they look like where there was none?

In the case of a positively curved space, we can’t do this because there is no way to represent a path that returns to where it started in the same number of dimensions.6 But for negatively curved spaces that extend to infinity, we have a visual example in the art of 20th Century Dutch graphic artist M.C. Escher. Among other things, Escher was known for artistic renderings of mathematical concepts including symmetries and tessellation. His Circle Limit collection of wood carvings depict repeating image patterns whose changing shapes from the center outward are a tessellation of hyperbolic geometry on a disc into right triangles. His 1959 work Circle Limit III (Figure 15), widely regarded as the best in the series, does this with patterns of fish.

 

Figure 15

There are many ways to tessellate geometric spaces and none are perfect, including this one. But if Cathy’s two-dimensional space was negatively rather than positively curved, this would be a reasonable representation of how it would look to her. If she walked a parallel transport path through it as in figures 5-8 taking the size and orientation of the fish as indicative of distances and angles, upon returning to where she started, she would find that the distances and interior angles she traced would be like those in the negatively curved saddle in figure 14. And if she travelled a straight geodesic path in any direction indefinitely, she would asymptotically reach infinity as she approached the rim. The disc is two-dimensional, but the geometry embedded in it behaves as though it were a saddle-shaped sheet in three dimensions even though the third dimension isn’t there. The underlying mathematics of its hyperbolic (saddle) geometry are embodied in Equation 6. And while we have until now restricted ourselves to two-dimensional spaces for ease of illustration, notice that the indices in its terms can assume any number of values, not just two. As such, it generalizes to any number of curved dimensions, none of which need any “higher” dimension/s to curve into.

There is, however, one dimension that we’ve conspicuously ignored until now… time. We live in a universe where not only length, breadth, and height can be curved, but duration can be as well, and curved spacetime ups the ante in several important respects that we’ll dive into in Part II. So, stay tuned!
 
Curvature II: Spacetime
 

Footnotes

1)   In mathematics, tensors are matrix functions that define a multilinear relationship between sets of objects in a vector space that preserve their identity in any coordinate system or transformation. Vectors can be thought of as a one-dimensional tensor (that is, a tensor with only one column or row). The dimensionality of a tensor’s matrix array (as specified in the number of indices it requires) is referred to as its rank R, and the number of components it will have in an N-dimensional space is given by N^{R}. Thus, g_{\mu\nu} is a rank 2 tensor that in Freddy’s 2-D space will have four components, and in our 4-dimensional spacetime has 16.

2)   Strictly speaking, the metric tensor isn’t really a true dot product. Rather, it is a generalization of the familiar dot product of Euclidean geometry to the pseudo-Riemannian geometry constrained by special relativity, where time behaves differently than space (more on this in Part II). But for our current exploration of 2-D spatial curvature, this needn’t concern us.

3)   Mathematicians refer to this as an orthonormal basis that spans the space.

4)   In mathematics, the nabla symbol (\nabla_{\mu}) is known as the Laplace operator. It is a shorthand reference for the gradient (first derivative) in the direction of a vector defining the \mu coordinate system; That is, \nabla_{\mu} = \frac{\partial }{\partial x_0} + \frac{\partial }{\partial x_1} + \frac{\partial }{\partial x_2} + \frac{\partial }{\partial x_3} where the index \mu = 0, 1, 2, 3. This representation of a gradient in a particular direction is also referred to as the vector’s divergence.

5)   The reasons for this are mathematical and beyond the scope of this discussion.

6)   This is because spherically curved space has a different topology than flat and negatively curved spaces. In mathematics, topology is the study of a manifold’s geometric properties that are preserved when it is stretched or deformed without cutting or sewing, opening or closing holes, or passing it through itself. Negatively curved space has the same topology as flat space because a flat rubber sheet can be stretched to form a saddle. By contrast, a positively curved space cannot be flattened or deformed into a saddle without cutting and forming edges (e.g. – a Mercator projection). There is no way to create a flat representation of it that preserves great circle paths that end where they began without encountering an edge. Likewise, a toroid (donut) cannot be deformed into a sphere or a saddle without cutting and sewing edges, so it has a higher-level topology than negatively or positively curved spaces.

 

References

Heath, T.L. ed., 1956. The thirteen books of Euclid's Elements. Courier Corporation. Online at https://books.google.com/books?hl=en&lr=&id=mvBIAwAAQBAJ&oi=fnd&pg=PP1&dq=euclid+elements&ots=ed2L7zetPz&sig=wPKfMQ22SZvf4gF_83USfDwb0oY#v=onepage&q=euclid%20elements&f=false. Accessed Sept. 28, 2023.

Wikimedia. 2018. Image courtesy of Jacob Bertolotti. Online at https://commons.wikimedia.org/wiki/File:Covariantcomponents.gif. Accessed Sept. 28, 2023.

Wikimedia. 2023. Image courtesy of Silly rabbit, CC BY-SA 3.0. Online at https://commons.wikimedia.org/w/index.php?curid=2615879. Accessed Sept. 28, 2023.

Posted in Physics | 2 Comments

Book by St. Tom Rudelius (and me, a bit)

So my friend St. Tom Rudelius is a physicist who works on string theory, QFT, and early universe cosmology (e.g. the theory of inflation).  He is also a brother in Christ who I have had the privilege to both mentor, and learn from.

He has just written a book about his conversion to Christ (it's a pretty interesting story, involving rather more "polygraph tests" than this sort of story usually involves) and also his experiences as a Christian in academia.  The book, which was just released today, is called:

 

 

 

 

 

 

 

 

 

 

 

I was asked by the publisher to include an excerpt from the book to help promote it.  Completely disregarding their proposed selections, I have chosen one of the later chapters of the book, after he's already become a Christian:

People often ask me what it’s like to be a person of faith in the field of science. It’s a hard question to answer, because my experiences have varied widely.

Sometimes, physicists will ridicule religion. Once, while visiting the University of Texas to give a talk on my research, I went to lunch with a number of physicists, including the late Nobel laureate (and outspoken atheist) Steven Weinberg. Unaware of my religious leanings, Weinberg began the lunch with a pointed question toward the antievolution movement: “Do all these people who reject evolution also reject cosmology?”

I thought about explaining the difference between young earth creationists and old earth creationists, but ultimately held my tongue.

Sometimes, physicists simply steer clear of religious topics. One day when I was a postdoc at the Institute for Advanced Study in Princeton, the man whose donations to the Institute helped pay my salary came to have lunch with Ed Witten—quite possibly the greatest living theoretical physicist, if not the smartest man on earth—and me. A quick online search had made the donor aware of my religious views, so he spent the entire lunch asking me (very respectfully) about my opinions on religion and politics. It was probably the most stressful conversation I’ve ever had—talking about Jesus and Donald Trump with the smartest man alive and the man who paid my salary.

During the entire conversation, Ed Witten was surprisingly quiet. His only remark came when we were discussing God’s miraculous intervention. “I think a lot of people wish God would intervene more often,” he said.

Sometimes, physicists respect religion. Several of my colleagues have expressed admiration for my religious faith, or religious faith in general, though they themselves do not have any religious convictions.

Sometimes, physicists embrace religion. I don’t know very many Christians in my field, but whenever I meet one, I feel an immediate kinship. Our scientific drive for knowledge pushes us to learn as much as we can about the physical universe, and as Christians that same drive pushes us to learn as much as we can about God. The result is a common language of science, theology, and philosophy not so different from the “twin telepathy” my brother and I have shared since childhood. Though sometimes it is discouraging that so few of my colleagues embrace religious faith, it is encouraging—perhaps even more so—that the ones who do are so strong in their faith and so capable of defending it intellectually.

In much of the world, there is intense animosity, and sometimes even violence, between people of differing religious faiths. Perhaps it’s because we religious physicists represent a minority in our world, but I’ve certainly never felt anything like that from my Jewish, Muslim, and Hindu colleagues. And I hope they’ve never felt anything like that from me. Rather, there seems to be a sense of solidarity among religious scientists. Though there are important differences between our faiths, there’s an even deeper sense of mutual respect among us: I’ve probably received more comments of admiration regarding my faith from Jewish colleagues than I have from Christian ones, and a Muslim colleague once told me that my public interviews and articles on science and God had strengthened his own faith.

On the whole, though, I can say with certainty that I have never felt persecuted or personally attacked for my faith. There are places in the world where Christians are suffering for their faith. But America is not one of those places. I can go to church, pray, read my Bible, and even write books like this one without fear of losing my job. Some of my colleagues may not agree with my faith, but fortunately my success in physics depends on my ability to do physics, not on how I worship in my free time.

Though science and faith are often viewed as enemies, I can also say I have felt less hostility toward religious faith in the upper echelons of physics than at the lower levels, or in the soft sciences or humanities. Anthropology, history, and religious studies departments are famously dismissive of Christianity—a trend many of my Christian friends and I experienced during the course of our university studies.

One of my friends who studied chemistry at Princeton had a high school science teacher who forced the class to learn the definition of a so-called scientific theory—an explanation for some natural phenomenon supported by a vast body of evidence—to refute the common creationist retort that “evolution is only a theory.” But when he got to college, my friend soon realized that such definitions are nonsense: In practice, scientists use the term theory to describe many different things. Some theories, like quantum field theory, are among the best tested phenomena in all of science. Other theories, like string theory, lack any experimental verification whatsoever.

My high school physics teacher—who was one the best and most important teachers I ever had—occasionally made snide remarks about religion. Yet at Cornell, Harvard, and Princeton, I met several religious physics professors. One professor even suggested to his class that God might be the best explanation after all for the fine-tuning of the universe for intelligent life—and he wasn’t even a theist.

Now, it’s also true that most of my extraordinarily brilliant colleagues do not embrace religion. But I’ve found that their reasons are generally quite ordinary. If you ask the average atheist why he or she doesn’t believe in God, you’ll probably get some version of the problem of evil: “If God is all-powerful, all-knowing, and all-loving, why do evil and suffering exist?” If you ask one of the world’s most brilliant scientists why they don’t believe in God, you’ll probably hear the exact same thing.

That’s not to say that the problems of evil and suffering are easy for theists to deal with. It’s simply that the most brilliant minds don’t have a huge advantage over others when it comes to questions of faith. We all have basically the same questions, objections, and doubts. In my experience, the ones who find answers to these questions are typically those who need answers the most. Personally, before Steve’s conversion and subsequent conversations with me, I never felt much need for religion, as I was generally able to get by on my intelligence alone. Perhaps other scientists feel similarly.

Finally, I have found that most scientists—even nonreligious ones—believe in some sort of power greater than ourselves. It’s very common to hear physicists refer to Nature as a sort of placeholder god. For example, Ed Witten once said in an interview, “If I knew how Nature has done supersymmetry breaking, then I could tell you why humans had such trouble figuring it out.” There is a widespread acknowledgment that Nature has chosen a particular way for our universe to be, and it could have chosen something different.

What’s the difference between this Nature and the God (capital G) I believe in? I think the biggest difference is simply that Nature doesn’t really care much about the affairs of humanity, whereas God does. Most everyone would agree that Nature has a preference for order, simplicity, and beauty, but many balk at the suggestion that it would concern itself with the affairs of one particular species on one little insignificant planet. We humans are, to quote astronomer Carl Sagan, nothing but “a mote of dust in the morning sky.” [1] Why would God care about us?  

[1] Carl Sagan, Cosmos (New York: Random House, 1980).

To this, I like to point out that size is not a very good measure of value. I care more about the life of a baby than I do about most galaxies. I care more about the ten-nanometer transistors that make my computer work than I do about distant stars. And even as someone who studies black holes and the big bang for a living, I find nothing more incredible about the cosmos than the fact that it somehow birthed intelligent, conscious beings like us.

Ultimately, one can choose to view the size of our universe as a sign of our insignificance, or one can choose to view it as a sign of the great significance of its creator—a creator whose attention is not divided, who built and sustains the intricate workings of the cosmos, yet who simultaneously cares enough about humanity to become a human himself, to experience pain, suffering, and death so that we could have life.

Perhaps you noticed that my name is also on the front of the book, in much tinier yellow letters at the bottom.  (Or more likely, you didn't and are even now scrolling back to see if my claim is true.)  This is because I was asked by St. Tom to write a foreword to his book.  (And not only that, I did.)  My foreword begins as follows:

Foreword

(from this formative experience with the publishing world, I have learned that the word has an "e" in it) but after that it goes on to say:

The book you are holding is a remarkable one. There are lots of books out there promoting Christianity, by a type of person you might call salesmen. The goal of a salesman is to produce a watertight and squeaky-clean argument, to convince you that only one position is intellectually respectable, and fully capable of servicing your needs. He is afraid to admit any weakness in his arguments. He is afraid that if he talks honestly about his own doubts and struggles, his audience will take it as a reason to reject the product he is promoting. If you want a book like that, I suggest you look elsewhere. My friend Tom is not a salesman. But he is a person who cares deeply about what is real, both in scientific and religious contexts. And because of this, he is also unafraid to share his spiritual doubts and struggles, both before and after he became convinced that Christianity is objectively true.

After that, the foreword includes eleven more juicy paragraphs, and importantly the only way to read them (if you don't know about libraries) is by buying the book.  You can do this by clicking on one of the following links:

Amazon

ChristianBook

Tyndale

Target

That's right, you can now buy the equivalent of one of my blog posts, at the same store you can get detergent and kid's T-shirts from!  But, you should probably also buy the book to read an interesting and sincere account from Tom, about his obstacles coming to Christ and his emotional struggles with faith afterwards.

Now, you are going to buy the book at any time in the future, it would probably be helpful to Tom if you would buy it ASAP, for example TODAY, so it can go into the early sales figures that make the industry decide whether this book is hot stuff or not.  Sorry, I don't make the rules of worldly success in the publishing industry, that's just how it goes.

Having said that, some of you may be tempted to write comments asking, well when are you (Aron Wall, PhD) going to write your own book about Sciencey-and-Religiony stuff, and not just a foreword or backewards glued onto somebody else's book?

Well, as you can probably tell from my recent blog performance: I'm just way too busy (with mentoring PhD students and postdocs, parenting my 2 & 4 year olds, quantizing gravity, and doing faculty busywork) to get any useful writing done, for the most part.  Nevertheless, you should expect some book about the Fine Tuning Argument for God and/or the Multiverse to appear under my name (as well as that of my coauthors, philosophers John Hawthorne and Yoaav Isaacs), some time in the next oh 1-50 years from now.  Just thought I'd give you a heads-up about that since a file looking deceptively like a rough draft basically already exists, more or less.  Mostly less.

(If any skeptical promotion committees are reading this post, I promise I spent very few of my months working on the Fine Tuning book, and any deficit of actual physics papers is explained by the other stuff in my life...)

Anyway, life is short so don't save your money for a book that might or might not come out in the next couple of years.  Instead BUY TOM'S BOOK NOW (if you feel led to do that) and trust that you'll have the spare change to buy mine later.

[Disclaimer: I understand that I will be receiving a free copy of Tom's book in the mail.  But it will come too late to change my opinion of the book—I will always think of Tom's manuscript primarily as a Word file.  I'm sure the publishers put a lot of effort into making it look like a real book; but I'm sorry, that's just the way it is.]

Posted in Links, Reviews | 15 Comments

Followup on the Moral Argument for Theism

A commenter named Nikki argued against my post Fundamental Reality XII: The Good, and the Not.

Nikki writes:

I don't think the post's argument works - I'd argue that non-theistic morality can be objective and well-grounded, or at least be no worse off in those regards than theistic morality is.

So the first part of this post that really jumped out at me is the claim that if morality is objective, it must be like a mind. Frankly, to me this seems not only false, but a category error. Morality is things like systems, principles, rules, etc. - I'm not sure what the exact best word choice is. The point, though, is it is a thing that minds use, but not in and of itself a mind. You describe morality as approving or disapproving certain things, but this seems to be conflating things like "this abstract system contains claims that X is good/bad," which could validly be said about morality, and "this abstract system itself consciously judges that X is good/bad," which could not. It is us who use morality to consciously make those judgements.

As an analogy, personality traits are part of minds, but not minds themselves - to speak of them, by themselves, being conscious, thinking, willing, etc. would be a fundamental mistake. (Though Inside Out was a pretty fun movie). I'll admit though, I don't actually think that's the best analogy. I'd argue the set of laws of logic or mathematics are an even better example of something that is a feature of minds - but is not, and could not possibly be, a mind in itself. However, you've said in an above comment that logic is also a description of God's character.

(Perhaps a bit of a sidetrack here, but I don't think this could be true either. I believe that you've stated elsewhere that while you believe God is metaphysically necessary, he is not logically necessary - but of course, it is logically necessary that the laws of logic or mathematics are true. I don't think the dependence you're arguing for could work, even if God exists in some sense. That said, as one might guess, I don't think God is metaphysically necessary in the first place.

In fact, I have doubts that there is even a "metaphysical necessity" distinct from logical necessity at all. I find Chalmers' arguments in his paper "Does Conceivability Entail Possibility?" fairly convincing in this regard. I do think there are some weak points, but it seems to me that at least it shows that even if there is a metaphysical modality separate from logical modality, we don't currently have a good reason to believe in it. I know there are several relevant arguments on this blog, but well, I can't discuss every single reason for and against the existence of God in this post, so here I'm trying to stick with things related to the original topic/what's been mentioned in previous comments on it. I might debate the other arguments later.

As a note, Chalmers' arguments there are important for the case he makes that consciousness is not physical, because they counter the reply of some materialists that consciousness is metaphysically the same as a physical property, even if it cannot logically be derived from other physical facts. Others have argued that this causes problems for theists who both defend the metaphysical necessity of God and the non-physicality of consciousness. I suppose this may not apply to you because you've said you can't rule out that consciousness is physical in some sense, as in what Chalmers calls "Type-B Materialism," but I did think it was interesting).

Alright, back to the main topic. Does an objective morality depend on God? The whole field of moral philosophy is certainly not something I can fully describe in one post, but I'll start with something interesting you said in your own previous post in this series:
"Even people who say there's no such thing as ethical truth suddenly sound quite different when somebody treats them unfairly."

I suspect that in that statement is at least a hint at what the basis for a nontheistic objective morality might be like. If there is an objective morality, I think it has something to do with the symmetry between you and others - if you don't treat others well, what's to prevent them from doing things to you that you don't want? Even if evil may sometimes have short-term rewards, people committing acts like theft or murder or terrorism ultimately make things worse for everyone, including themselves. Note that these statements do not depend on God to make them true. And I think several strands of thought, such the Golden Rule, Kantian morality, Rawls' veil of ignorance, and even some game-theoretic analyses, among others, all point towards something like this in a sense.

Now, this may not be very compelling - I'm being vague and have not spelled out a fully detailed nontheistic system. Furthermore, many of the systems I've cited actually contradict each other. Nevertheless, I think that there are important shared elements that don't depend on a belief in God to be convincing (well, Kant's morality was theistic and the Golden Rule is a part of many religions, but I don't think everything along the lines that I've mentioned is). So it seems that the claim that no secular account of morality can possibly succeed isn't very certain. I'll note that you linked in your previous article to the SEP's article on Moral Naturalism, but merely said those systems were "problematic" without really discussing the individual ideas presented there, although there are many important nonreligious thinkers whose ideas on morality are much more detailed than mine. (I won't complain about that too much though - after all, I'm not discussing every form of theistic morality in this post myself).

Some more notes: 1. Speaking of moral naturalism, even on atheism, that isn't the only option available for an objective morality. While I agree naturalism and atheism are often found together in practice, it is still possible for an atheist to be a non-naturalist, including about morality. So even if morality cannot be justified on naturalism, you would have to show that God specifically is the only one who can ground morality, not some other non-natural element.

2. Above, Scott Church argues that on naturalism, the universe does not care about us and we are fundamentally unimportant, so it cannot ground objective morality. But the universe itself does not have to care about us/be a moral agent for morality to be objective! I'd argue that if morality, say, applies to all rational beings, it is objective, and the universe not obeying it does not matter because the universe is not a rational agent. The laws of rationality themselves are a good analogy for this - the universe, itself, does not reason, and it requires minds to use reason, yet the standards of rationality are fully objective (and not derivable from physical equations, by the way). And even on theism, it is agreed that some things, like inanimate objects, are not and cannot be moral, yet again, that does not prevent morality from being objective. Related, while pure pleasure-maximization/pain-minimization has several well-known problems, so I doubt that's the full objective morality, I do think there are non-arbitrary reasons why those are at least important. They are necessarily important to us by their very nature - no one can truly be indifferent to them even if they claim to be. And even if the universe does not care about them, I take the anti-nihilistic view that it is precisely the fact we care that matters - it's not as if the universe has any rule against that!

3. I've seen this part stated before in some other comments on the blog, but I think it's important enough that I'll state it again (especially since unless I'm missing it, I don't think I've seen a response). Escaping the Euthyphro dilemma by saying that God is identical to goodness can only work if we have good reasons to believe that the two could possibly be identical. I don't think we have those (unlike for the triangle case, in which we do have reasons to believe that "having three sides" and "having three angles" are the same, even though those are logically necessary), but we do, in fact, have reasons to believe the opposite. As I wrote at the beginning of my post, if God is to be viewed as even like a mind, he cannot possibly be identical to morality even if he is an (ultimately) moral agent. For instance, one of the important reasons to consider God like a mind is that he is supposed to be able to take actions, but morality cannot, by itself, take actions. (Also, I'll admit I don't know whether your analysis of Plato is accurate, but even if it is, it's generally fine to take inspiration from an argument and adapt it to your own views. After all, in the original article, you said you used "Hume's Is-Ought dictum in a manner which he would have thoroughly disapproved of!")

As a final statement, I don't think theism is actually better at convincing people of being moral than secularism. There's some evidence that nonreligious people are even more moral than very religious people, but interpretations are controversial and I'm focusing more on purely philosophical points here. (I do suspect nonreligious people being more moral than the religious, if true, would be a particularly big problem for theism and theistic morality. I think the evidence at least shows that the nonreligious are generally not less moral than the religious, but you've agreed in another article that for some senses of "good," religion is not strictly necessary for it, so that may not be a big problem for you). But anyway, you've agreed that not all rational people might be convinced by theistic arguments, and it's been pointed out above that you can always ask questions like "Why should you follow God's commands?" so that seems to be an issue. Of course, you might very well always be able to ask similar questions about any nontheistic system, and rational people might not find it convincing. But my point was that secular morality is at least equal to theistic morality in this regard, and while this is a bit speculative, perhaps some of the reasons above might make the former even more convincing than the latter.

My reply got pretty long, so I'm turning it into a blog post.

Dear Nikki,
Welcome to my blog, and thanks for your interesting comment. However, I am not sure that your arguments are actually directed against the specific argument I am making. Here are some replies (not in the order of your points):

I. Objective Morality is a Premise in the Moral Argument

You make a good case defending this proposition: It is possible for a non-theist to rationally come to believe in the existence of an objective ethical system, without thereby coming to believe in God. However, I also believe that this is the case!

In fact, if this were not true, there would be little rhetorical point in presenting a Moral Argument for God's existence.  In order for an argument for God's existence to be capable of being convincing, there have to be some people out there who agree with the premises of the argument, but have not yet realized that the conclusion follows (or at least, is made more probable) by the premises.  I obviously do not deny the existence of non-theistic moral realists, because they are the target audience for my post!  (That is why I presented an argument for ethical realism in part XI before describing how  I think Theism grounds ethics in part XII.)

Now obviously, if the a nontheistic argument for objective ethics happened to take the form of an entirely satisfactory reduction of concepts like ethical obligation into naturalistically acceptable terms—e.g. in terms of physical facts of the sort that even Sean Carroll would accept—then the Moral Arguments for Theism would fail, since there would be no additional work for God to do in terms of grounding ethics.  (There might still be a need to ground the laws of physics in some way, but no additional and separate need to ground ethical truths.)  But of course, if you could show that this were true, you would have just solved a very famous and important problem in philosophy!  So I sort of doubt you really think that we can know this to be the case.  And if we cannot know it to be the case, then there is room for discussing non-naturalistic groundings of ethics, in a probabilistic argument for Theism.

You sketch some ways in which you think an non-theistic grounding for objective ethics might work (which fall into the rough family category of what I called "Kantian approaches'' to ethics in part X).  As I explicitly stated in that post, Kantianism is not as friendly to the Moral Argument, as Platonism or Aristotelianism is; although I don't think it is utterly hopeless on that front.  (Kant himself made a sort of pragmatic argument for Theism from Morality, but he didn't agree with metaphysical arguments of the sort I'm discussing.)   The only conclusion I explicitly drew from Kantianism was:

If Ethics can be deduced rationally as in the Kantian system, then one can at least deduce that if the Universe originates from something like a mind, that mind should also be able to appreciate ethical truths.

So the point you are making was to some extent already acknowledged in this series.  (Of course, on classical forms of Theism, where God is something like the ultimate Reason or Logos behind the Universe, this would still end up identifying God with moral goodness in some deep sense; but such classical views are necessarily bordering on Platonism anyways...)

B. Moral Naturalism and Non-Naturalism

By the way, I revisited the SEP article, and found to my dismay that it had been edited in a way that removed (without refutation) some of the critiques of Moral Naturalist positions. Here is the original version of the article.  If you look, for example, at the original article's section 4.3, you can see what appears to me to be a pretty desperate attempt by Jackson to make naturalistic ethics work, together with (what appears to me to be) a pretty strong refutation in terms of the permutation problem.  But the main point is not the refutation of that particular idea, but that I don't see any way forward mentioned in the article which doesn't seem to have serious problems.

You write:

Speaking of moral naturalism, even on atheism, that isn't the only option available for an objective morality. While I agree naturalism and atheism are often found together in practice, it is still possible for an atheist to be a non-naturalist, including about morality.

Yes, obviously.  Such views exist (which is why I mentioned them in part X of this series). In fact, individuals with such views (e.g. Moral Platonists) are closer to being the target audience of this post, then perhaps you are.

So even if morality cannot be justified on naturalism, you would have to show that God specifically is the only one who can ground morality, not some other non-natural element.

No, because as I tried to make it clear at the beginning of this series that I wasn't trying to present a deductive, logically watertight argument for Theism.  As I said in Part I:

Even if there are no strictly deductive arguments (from indisputable premises), there are still going to be plausibility arguments pointing in various directions.  It's irrational to put too much faith in plausibility arguments, but it's also irrational to be completely insensible to them.

So the mere existence of logically possible positions, besides the one I argue for, doesn't bother me.  The question is which positions are most credible.

On the plausibility front, it seems to me that once you start modifying your metaphysics in order to accommodate objective ethics, it would be irrational not to take that into account when assessing the probability of other metaphysical hypotheses.  Ethical Monotheism is, among other things, the belief that a fundamentally good being exists.  The plausibility of this statement depends in part on what we think moral goodness is.  For example, on the view that:

1. "Morality is a emergent and subjective set of feelings found in some of the higher apes, conducive to their evolutionary survival, but having no basis in any metaphysical reality"

then the idea that there exists a fundamentally good being outside the physical universe—which did not evolve—is totally absurd.  On the other hand, if:

2. "moral facts are necessary truths, which tell us something substantive about the structure of non-physical realities",

then the idea of a fundamentally good being is, though not logically compulsory, at the very least far more plausible than on viewpoint (1) than (2).  Do you agree with that?  If so, then you are necessarily agreeing with me that the Moral Argument for Theism has significant probabilistic force.

[Notes: I am not saying these are the only possible views.  Also, hypothesis (2) does not necessarily deny biological evolution, as it is possible for evolved systems to recognize necessary truths such as mathematical theorems.]

C. The Role of Analogies

Let me remind you a bit of the context of my argument in the Fundamental Reality series.  In parts II-VI, I argued that it is plausible that there exists some fundamental reality which explains everything else, I discussed some properties this entity should have, and after reviewing various candidates I suggested that (based on the mathematical character of the laws of physics) the two most plausible metaphors for understanding this fundamental reality are:

* something like an equation
* something like a mathematician

Now it is important to remember that both of these ideas involve metaphors!  Obviously, if a Naturalist says that some equation provides the deepest truth about the Universe, that doesn't mean this assertion is being made about a set of chalk lines on a blackboard.

Similarly, if a Theist says that God is like a mind, that doesn't mean that this Mind is like our mind in every respect.  In particular, Classical Theism proposes a mind for whom there is no distinction between its subjective beliefs and objective reality, and also no distinction between its subjective preferences and objective morality.  This is obviously very different from evolved primate minds like our own!

You wrote:

So the first part of this post that really jumped out at me is the claim that if morality is objective, it must be like a mind. Frankly, to me this seems not only false, but a category error. Morality is things like systems, principles, rules, etc. - I'm not sure what the exact best word choice is. The point, though, is it is a thing that minds use, but not in and of itself a mind. You describe morality as approving or disapproving certain things, but this seems to be conflating things like "this abstract system contains claims that X is good/bad," which could validly be said about morality, and "this abstract system itself consciously judges that X is good/bad," which could not. It is us who use morality to consciously make those judgements.

and

As I wrote at the beginning of my post, if God is to be viewed as even like a mind, he cannot possibly be identical to morality even if he is an (ultimately) moral agent. For instance, one of the important reasons to consider God like a mind is that he is supposed to be able to take actions, but morality cannot, by itself, take actions.

I think perhaps you missed the amount of qualifying words I put into my reasoning.  What I wrote was (emphasis added):

But now observe that morality is at least a little bit like a mind, insofar as it approves or favors certain things, and disapproves or disfavors other things. So a fundamental morality would have something analogous to will or desire, and in that respect it would be more like a mind than like an equation, as in Theism.

The point here is not that an objective morality is exactly like a mind, but that it in certain respects more similar to a mind than (say) the equations of the Standard Model are, namely that the Standard Model does not encode any judgements that certain states of affairs are desirable or undesirable (as opposed to probable vs. improbable).

Now, obviously, when we say that God is personal, and can do things like forgive or create, we are adding more to our concept of God then is implied by the mere abstract notion of a metaphysical objective morality.  In my understanding of God, we are adding more to our idea of divinity than the idea of a Platonic form of the Good, but we are not necessarily taking anything away.

In other words, in my conception of God, God is such that he is good, not in an accidental (happenstance) way, but in an essential way, because all goodness in the universe in some sense participates in his goodness, just as all existence participates in his existence.  (The latter claim, of course, obtains for any fundamental reality which is taken to explain all other things.)

D. God Transcends the Abstract/Concrete Divide

Another commenter, St. David Madison, replied to your comment by saying (in part):

"You draw an analogy between morality and personality traits and then point out that personality traits are not conscious and do not themselves think. However, personality traits cannot exist without a personality that possesses those traits."

This is certainly a reasonable distinction to draw in general; and we could indeed escape from the supposed category error by simply replacing the words "objective ethics" with "that which grounds objective ethics, whatever it is."  But I think I am instead going to double down on this idea, and say that this supposed category distinction between abstractions and concrete objects breaks down when one is speaking about divinity, just as the distinction between particles and waves breaks down at the subatomic scale.  If God is the source of all else that exists, he must unify within himself the perfections of both abstractions (necessary, eternal, unchanging) and concrete realities (which are causally active, definite, individual etc).

This is indeed, already implied by certain sorts of religious language, in which God is portrayed not as some good or beautiful thing, but as the Supreme Goodness or Truth or Beauty or Life etc.  For example, in the Gospel of John, Jesus asserts his divinity by saying that he is the Way, the Truth, and the Life, which is not the sort of thing that a Positivist philosopher would consider a well-formed statement (a person cannot be an abstract quality).  But I am not convinced we can restrict our language in the way the Positivists wanted to do (I don't think Positivism even satisfies its own criteria of meaningfulness).  What this religious language points to, is an insight into the nature of divinity as a necessary being, in which all other realities are grounded.  A proposition about a created being can be true, but only the ultimate reality can be the Truth.  In other words, denying the applicability of the concrete/abstract distinction is not something I am doing merely to avoid a logical puzzle, but is already implied by standard religious language about God.

This sort of language about God makes Classical Theism radically different from traditional forms of polytheism, in which the gods are simply regarded as more powerful individuals than us, who still can be born/killed, have conflicts with each other, make mistakes etc.  Yeah, obviously the preferences of finite beings like ourselves can't possibly ground objective ethics, which was the whole reason why Plato went in a platonic direction instead.

Furthermore, I don't think we can avoid postulating this sort of concrete/abstract unification, simply by rejecting Classical Theism, as Naturalism seems to me to imply exactly the same thing.  For example, if the fundamental reality is something like a mathematical equation, then we are asserting that it is both an abstract piece of mathematics—which can in principle be understood by humans—AND ALSO the governing principle controlling the universe.  In other words, when a Naturalist does physics, they are still are postulating that the fundamental reality is a λογος, i.e. a rational principle.

Of course, I'm not saying that the equations we write on the blackboard, or in our minds, are strictly identical to the actual laws of physics, which obviously exist whether or not we ever discover them.  But if we asked, "what are the fundamental laws of physics like" we can't point to anything other than to our abstract human formulation of the equations, and then lamely add "except that it also exists as an actual concrete reality, in a way which transcends our human abstractions".

In the same way, objective morality exists even apart from human processes to reason about what is or is not moral—So I'm not saying, that this latter, social process of reasoning is equal to God.  Rather it is goodness as it actually exists (which our human reasoning is a mere approximation of) that is rooted in God's nature, as the ultimate Goodness that other things participate in.

E. Implications for Euthyphro

Escaping the Euthyphro dilemma by saying that God is identical to goodness can only work if we have good reasons to believe that the two could possibly be identical.

This is a strange way to discuss this subject, given that the (modern) Euthyphro dilemma is typically phrased, not in the form of a deductive argument, but in the form of a challenge to Theists to explain their beliefs more clearly.  It's phrased in the form: "Do you believe A, or B?" (both of which have unpalatable consequences).  But if A and B are not, in fact, exhaustive possibilities, because some other option C is conceivable—and if in fact C was the belief of most ethical monotheists historically, as well as myself—then merely pointing this out is sufficient to defuse the dilemma.

That being said, there is a good reason to think that, if God exists at all, he can ground morality.  Recall that God is, by definition, the explanation for all entities other than himself.  (That's the whole point of Mono-theism, to have only one ultimate entity.)  So if God exists at all, he either grounds or creates all other realities.  Now if there is objective ethics, then ethics counts as one of these realities.  Since it doesn't make sense to create ethics (since at least some ethical principles are non-arbitrary, necessary truths) then he must ground it.  (The same argument would hold for logic or mathematics.)

Now, to be clear, this is an argument that God grounds ethics.  It is not an argument which explains how God grounds ethics.  To understand how God grounds ethics we would have to first have direct perception of the divine essence, which we don't possess.  Instead, we only know the things which proceed from the divine essence, and we have to learn about what God is like, as best we can, from that.

If you like, you can take "a concrete reality which grounds ethics" as a defining property of God, and then ask questions like i) what other properties would such a being need to have, and ii) is there good reason to believe that such a being exists?

If you will allow me to make a more meta-level argument.  It seems to me that giving the Euthyphro dilemma as an objection to Classical Theism is historically obtuse.  It's like proposing the Equivalence Principle as an objection to General Relativity, when the Equivalence Principle was in fact the motivating thought experiment that led to GR in the first place.  In the same way, the question of what the gods (or really God) has to be like in order to justify treating piety as a virtue, was the underlying question motivating the Euthyphro dilemma.  But somehow atheists never say to themselves, "Geez, the fact that this famous philosophical argument was introduced in a Platonic dialogue, by a theist whose ideas laid the groundwork for the most mainstream philosophical formulation of Monotheism, maybe is a reason to think I've missed something and the argument isn't actually a knock-down in favor of Atheism."

(To be sure, arguments aren't "owned" by philosophers and there is no reason in principle why an argument by a philosopher P can't sometimes be turned against P's own worldview.  So sure, maybe there is some very subtle reason why GR is still inconsistent with the best formulation of the Equivalence Principle.  But if somebody sends me and email about why they think GR is inconsistent with the EP, and it shows no awareness of why some people have historically thought that GR satisfies the EP, then it's unlikely that their "gotcha" question about how the EP refutes GR has much merit.  Ditto for Classical Theism and Euthyprho.)

F. Metaphysical vs Logical Necessity

Now to be fair, you did explain why you don't believe in scenario C.  In addition to your "category error" assertion, you add this:

In fact, I have doubts that there is even a "metaphysical necessity" distinct from logical necessity at all. I find Chalmers' arguments in his paper "Does Conceivability Entail Possibility?" fairly convincing in this regard.

So on your recommendation, I read through this Chalmers article and I found it pretty unconvincing.  Why should reality be fundamentally scrutable to us?  Or said another way, why can't there be propositions P which are necessary, but only a mind fundamentally more powerful than the human mind could see why they are necessary?  It seems hubristic to think that human reasoning has access to every possible necessary truth.

Ironically, the reason I don't believe in Chalmers' thesis here, is actually very similar to the reasons why I side with Chalmers over Dennett when it comes to Consciousness.  While Dennett makes an interesting philosophical case for the reducibility of conscious experience to neurological facts, ultimately I concluded that Dennettism can only work if Dennettism is true by logical necessity.  In other words, that once you've specified all the physical facts then Dennett's views on consciousness follow automatically.  And it seems to me that this is simply not the case.

Similarly, Chalmers' idea that if we specify all the physical nonmodal facts, then a single set of views about modal necessity must logically follow (to idealized human reasoners) seems plainly false to me.

(Assuming it even makes sense to distinguish between "modal" and "nonmodal" facts in this way.  This is an important distinction between analytic philosophy and traditional medieval philosophy.  Analytic philosophy sees modality as primarily a feature of certain propositions, and only secondarily as a property of things.  While Aristotelian/scholastic philosophy sees modality as primarily as a property of things, while only secondarily as an attribute of propositions.  A scholastic might argue that the analytic habit of immediately jump to always reasoning about maximal "possible worlds" obscures the role that modal concepts play in causal reasoning, which involves specific concrete entities.)

Anyway, since you hold to something like Chalmers' view, here's a dilemma for you: Is the proposition expressing this view itself a logically necessary truth?

(P) There are no metaphysically necessary truths, other than logically necessary truths.

If you say that P is logically necessary, then there must be a proof that it is true which follows deductively from the definitions of the words.  What is that proof?  As far as I can tell, none exists.  Certainly Chalmers doesn't give a logically conclusive proof in that article, he just gives some reasons why he considers belief in P to be plausible, which is not the same thing.

On the other hand, if is not logically necessary, then either it is contingent (which is inconsistent with the usual S5 rules for modal logic) or else it is an example of a metaphysically necessary (but not logically necessary) truth, in which case it refutes itself.

One could make a similar, superficially less "meta" argument for the same conclusion by considering the proposition:

(N) A necessary being exists.

A standard analytic argument from S5 modal logic implies that either: i) N is necessarily true, or ii) N is necessarily false.  So which of these is logically necessary?  I say neither, but if you disagree then what do you think the proof of N or its negation would look like?

G. Can God be the grounds of Logic?

I believe that you've stated elsewhere that while you believe God is metaphysically necessary, he is not logically necessary - but of course, it is logically necessary that the laws of logic or mathematics are true. I don't think the dependence you're arguing for could work, even if God exists in some sense.

This is a little compact, but I'm guessing your argument is something like the following:

1. A contingent truth cannot ground a necessary truth.*
2. God's existence is logically contingent.
3. But logic itself is logically necessary,
4. Therefore, God cannot ground logic.

[*I suppose there is some sense in which, if a Cat walks onto a Mat, this arguably grounds the necessary proposition: "Either the Cat is on the Mat or the Cat is Not on the Mat" by virtue of being a truthmaker for one of its disjunctives.  But I won't pursue this possible counterexample further, since I don't think it is relevant to the sense in which God grounds logic.]

But this argument is fallacious, because when I say that God grounds logic, I am making a metaphysical statement rather than a logical one.  From the perspective of metaphysics, both logic and God are (in my view) metaphysically necessary, and it is not at all impossible for a necessary statement to ground another necessary statement.  In other words, we have to distinguish between:

1a: A logically contingent truth cannot logically ground a logically necessary truth.

which is true, and:

1b: A logically contingent truth cannot metaphysically ground a logically necessary truth.

which does not in any way follow from 1a, and I would say it is false.

H. What Metaphysical Necessity Means

Actually, there is a better way to put this which makes the concept of "metaphysical necessity" somewhat less mysterious.  The right way to talk about this is to make Aristotle's distinction between that which is necessary to us (axioms of human thought) and that which is necessary in itself (propositions which could not have been otherwise).

When we say that a proposition is metaphysically necessary, we merely mean it falls into the latter category.  The adjective is misleading since, unlike the cases of "logical necessity" or "nomic necessity" (which mean necessary given certain specific principles), the phrase "metaphysically necessary" simply means whatever is necessary simpliciter, i.e. that which (without adding any qualifications) could not have been otherwise (whether or not the reason for its necessity is known to human beings.)

On the other hand, logical necessity is an example of what is necessary to human beings, i.e. an axiom of human reasoning, or a particular technique L used to prove the impossibility of certain propositions.

So, the proposition P from earlier boils down to:

(Equivalent to P): If a proposition cannot be proven to be impossible by technique L, then it really is possible.

while I see no reason to believe that technique L is sufficient to uncover all possible cases of necessity.  Especially since technique L does not even seem to be powerful enough to refute the statement that no concrete entity whatsoever exists.

This relates of course to cosmological considerations as well.  As is well-known, if P is true, then the basic principles of existence are just contingent "brute facts" which means they are not true for any reason at all.  So there is an obvious reason to postulate a necessary concrete entity, which is that it serves as a starting point to explain why anything else exists at all.

This reason to want a necessary being, does not seem to depend on us being able to know why the being is necessary.  This is the Thomistic viewpoint on the Cosmological Argument, and it seems to me to be the only possible middle ground between Anslemian positions (there is a valid Ontological Argument for a necessary being from pure logic) and explanatory nihilism (there is no good reason why the universe exists, it just does).

(Now you could just double down and say, I have no idea what you mean by the phrase: ``could not be otherwise'', please explain it to me; and then refuse to accept any answer I give other than one which reduces it to logical implication.  But the same technique could be done to motivate skepticism towards practically any other concept, including the other concepts in this discussion like "mind" or "good" or "abstract" or "grounds".   (It is not even clear that logical necessity can be fully explained without an infinite regress, as  St. Lewis Carroll pointed out in his Achilles and the Tortoise dialogue.)  I don't claim to have a definition of metaphysical necessity that would satisfy Socrates, but if we make that the standard, there aren't going to be very many philosophical terms left!)

I. An Irrelevant Topic

As a final statement, I don't think theism is actually better at convincing people of being moral than secularism.

This is just so totally irrelevant to the metaphysical questions behind the Moral Argument for Theism, that perhaps I should simply refuse to respond to this entirely.  It's really just a complete change of topic.

God could be the metaphysical grounds for morality, even if every single human being on Earth were an atheist, or even if every single theist were morally worse than every single atheist.  These motivational questions really have nothing whatsoever to do with the question about what metaphysical theses are made more plausible, if we subscribe to moral realism.  I wrote my blog post Is it Possible to be Good without God? precisely because I was annoyed by how regularly people seem to conflate these totally unrelated questions.

(I'm not saying that the degree of goodness of religious people can't potentially be used as an evidential argument for or against the existence of God.  What I am saying is that it is a mistake to allow such sociological questions to contaminate our interpretation of the thesis that God grounds ethics.)

That being said, I''ll take the bait and say I do think there is some pretty serious question begging required for a non-circular argument that atheism is fully compatible with moral behavior.  For one thing, if a being such as is described by Classical Theism in fact exists (a perfectly wise and holy and good being, who created us and is the source of all our goodness), then we have the moral obligation to worship and obey that being, and to reflect God's holiness through a life of prayer and repentance, dedicating our earthly activities to the glory of God.  It is difficult to see how an atheist can satisfy that obligation, because for the atheist these activities are just distractions from a different, more secular understanding of what the good life consists of.

(To be sure, if the atheist has some intellectually honest reasons why they think God does not exist, then this may well be a mitigating circumstance that reduces—or even eliminates entirely—their culpability for this omission.  But if we are discussing the question of which beliefs make it easier to be moral, then usually mitigating circumstances are considered mitigating precisely because they make it harder to be moral.  Furthermore, a lack of culpability does not remove all of the causal consequences of trying to place our ultimate happiness in things other than God—what Christians call idolatry.)

I do suspect nonreligious people being more moral than the religious, if true, would be a particularly big problem for theism and theistic morality.

From the standpoint of Christian doctrine, it is not actually clear why this should be.  Merely having knowledge of God's existence does not necessarily translate into obedience, and in some cases knowledge can make people morally worse since they ought to behave better but don't.  As Jesus' brother St. James said:

You believe that there is one God. You do well. Even the demons believe—and tremble!  (James 2:19)

and as Jesus himself said:

“Not everyone who says to me, ‘Lord, Lord!’ will enter the kingdom of heaven, but only the one who does the will of my Father in heaven.  On that day many will say to me, ‘Lord, Lord, didn’t we prophesy in Your name, drive out demons in Your name, and do many miracles in your name?’  Then I will announce to them, ‘I never knew you! Depart from me, you lawbreakers!’ ”  (Matthew 7:21-23)

The Pharisees were among the most "religious" people in Jesus' day, and many of their leaders handed Jesus over to Pilate to be crucified.  See also St. Paul's observations of religious people in Romans 2.

According to Christianity, what people need to be transformed morally, is not so much knowledge as grace.  Knowledge is good if it helps us acknowledge our need for grace, but not so much if it makes us look down on other people.

I think the evidence at least shows that the nonreligious are generally not less moral than the religious...

I'm not sure what evidence you are referring to here, or how you could actually know this to be the case.  If your claim is just that religious people can be morally weak and inadequate, well I already knew that from my own life, without looking at anybody else's.

If it refers to survey data, you have the problem that what many polls of religious affiliation captures a lot of individuals who only identify as religious in a nominal sense.  Polling nominally religious people, and asking about their rates of divorce, adultery etc. is sort of like asking whether watching the Olympics on TV makes people more physically fit!  It's the wrong question to study.

If you are referring to personal experience, I can only say that while I know good and bad seeming people (emphasis on "seeming", it's not my place to judge them) who are both religious and non-religious, the most loving and self-sacrificial people I know seem to be religious.  And religion also often plays a significant role when very bad seeming people repent and turn their lives around.  Furthermore I have very often heard people refer explicitly to God when they explain why they did something morally difficult, while I cannot ever recall in my personal experience ever hearing somebody say that they did something morally difficult because atheism is true.  (I mean, I could imagine such a motivation: e.g. God isn't going to save this person, so I have to.  But I don't think I've ever heard anyone explicitly say this "in the wild" so to speak.)

By comparison, studying secular ethics seems to itself have little observable consequences in terms of making people better.  This could be taken as a critique of secular ethics, but it might be better taken as a critique specifically of what modern analytic philosophers mean by ethics as a discipline (as opposed to ancient philosophies, which were typically viewed as a way of life that had to be put into practice, in order to be understood).  I mean, why should studying little numbered arguments about whether ethics is objective, or arguing about what to do in some controversial edge case involving trolleys, actually help one to build habits of life that make one treat your fellow human beings better, and a community which helps support you in doing so?  Religion is one of the few ways of getting such support in the modern era.  (There are some others, but they are getting sparser in an increasingly disconnected age.)  While this isn't necessarily an argument for God's existence, it does make your thesis that serious religious practice is totally orthogonal to ethical accomplishment seem pretty implausible.

I called this an "irrelevant topic" because it isn't terribly relevant to the validity of the Moral Argument.  But of course, from the perspective of what ultimately matters, it is this section that is most important, and the rest which are of lesser relevance.  If Christianity is true, then what will matter the most in the end is not whether you are persuaded by this or that specific argument for Theism, but more whether your heart is open or closed to God at a deeper level than that.  Jesus has promised that those who truly seek God will find him.

If you take it as a goal to be as moral of a person as you can possibly be, then that is at least a start along that road—even if the final destination is going to be, in some ways, quite different than what you expected when starting out on that journey.  But somewhere along the way comes the recognition that you can't actually be good, and need help to do better, and that is where concepts like grace and salvation start to make more sense...

Blessings,
Aron

Posted in Ethics, Metaphysics, Theological Method | 40 Comments