God exists.
FLAW: There are certain computational procedures governed by what logicians call recursive rules. A recursive rule is one that refers to itself, and hence it can be applied to its own output ad infinitum. For example, we can define a natural number recursively: 1 is a natural number, and if you add 1 to a natural number, the result is a natural number. We can apply this rule an indefinite number of times and thereby generate an infinite series of natural numbers. Recursive rules allow a finite system (a set of rules, a computer, a brain) to reason about an infinity of objects, refuting Premise 3.
COMMENT: In 1931 the young logician Kurt Godel published a paper proving The Incompleteness Theorem (actually there are two). Basically, what Godel demonstrated is that recursive rules cannot capture all of mathematics. For any mathematical system rich enough to express arithmetic, we can produce a true proposition that is expressible in that system but not provable within it. So even though the flaw discussed above is sufficient to invalidate Premise 3, it should not be understood as suggesting that all of our mathematical knowledge is reducible to recursive rules.
30. The Argument from Mathematical Reality Mathematical truths are necessarily true (there is no possible world in which 2 plus 2 does not equal 4).
The truths that describe our physical world are empirical, requiring observational evidence.
Truths that require empirical evidence are not necessary truths. (We require empirical evidence because there are possible worlds in which these are not truths, and we have to test that ours is not such a world.) The truths of our physical world are not necessary truths (from 2 and 3).
The truths of our physical world cannot explain mathematical truths (from 1 and 3).
Mathematical truths exist on a different plane of existence from physical truths (from 5).
Only something which itself exists on a different plane of existence from the physical can explain mathematical truths (from 6).
Only God can explain the necessary truths of mathematics (from 7).
God exists.
Mathematics is derived through pure reason-what the philosophers call a priori reason-which means that it cannot be refuted by any empirical observations. The fundamental question in the philosophy of mathematics is, how can mathematics be true but not empirical? Is it because mathematics describes some trans-empirical reality-as mathematical realists believe-or is it because mathematics has no content at all and is a purely formal game consisting of stipulated rules and their consequences? The Argument from Mathematical Reality assumes, in its third premise, the position of mathematical realism, which isn't a fallacy in itself; many mathematicians believe it, some of them arguing that it follows from Godel's incompleteness theorems (see the Comment in The Argument from Human Knowledge of Infinity, #29, above). This argument, however, goes further and tries to deduce God's existence from the trans-empirical existence of mathematical reality.
FLAW 1: Premise 5 presumes that something outside of mathematical reality must explain the existence of mathematical reality, but this presumption is non-obvious. Lurking within Premise 5 is the hidden premise: mathematics must be explained by reference to non-mathematical truths. But this hidden premise, when exposed, appears murky. If God can be self-explanatory, why, then, can't mathematical reality be self-explanatory-especially since the truths of mathematics are, as this argument asserts, necessarily true?
FLAW 2: Mathematical reality-if indeed it exists-is, admittedly, mysterious. Many people have trouble conceiving of where mathematical truths live, or exactly what they pertain to. But invoking God does not dispel this puzzlement; it is an instance of the Fallacy of Using One Mystery to Explain Another.
31. The Argument from Decision Theory (Pascal's Wager) Either God exists or God doesn't exist.
A person can either believe that God exists or believe that God doesn't exist (from 1).
If God exists and you believe, you receive eternal salvation.
If God exists and you don't believe, you receive eternal damnation.
If God doesn't exist and you believe, you've been duped, have wasted time in religious observance, and have missed out on decadent enjoyments.
If God doesn't exist and you don't believe, then you have avoided a false belief.
You have much more to gain by believing in God than by not believing in him, and much more to lose by not believing in God than by believing in him (from, 3, 4, 5, and 6).
It is more rational to believe that God exists than to believe that he doesn't exist (from 7).
This unusual argument does not justify the conclusion that "God exists." Rather, it argues that it is rational to believe that God exists, given that we don't know whether he exists.
FLAW 1: The "believe" option in Pascal's Wager can be interpreted in two ways.
One is that the wagerer genuinely has to believe, deep down, that God exists; in other words, it is not enough to mouth a creed, or merely act as if God exists. According to this interpretation, God, if he exists, can peer into a person's soul and discern the person's actual convictions. If so, the kind of "belief" that Pascal's Wager advises-a purely pragmatic strategy, chosen because the expected benefits exceed the expected costs-would not be enough. Indeed, it's not even clear that this option is coherent: if one chooses to believe something because of the consequences of holding that belief, rather than being genuinely convinced of it, is it really a belief, or just an empty vow?
The other interpretation is that it is enough to act in the way that traditional believers act: say prayers, go to services, recite the appropriate creed, and go through the other motions of religion.
The problem is that Pascal's Wager offers no guidance as to which prayers, which services, which creed to live by. Say I chose to believe in the Zoroastrian cosmic war between Ahura Mazda and Angra Mainyu to avoid the wrath of the former, but the real fact of the matter is that God gave the Torah to the Jews, and I am thereby inviting the wrath of Yahweh (or vice versa). Given all the things I could "believe" in, I am in constant danger of incurring the negative consequences of disbelief even though I choose the "belief" option. The fact that Blaise Pascal stated his wager as two stark choices, putting the outcomes in blatantly Christian terms-eternal salvation and eternal damnation-reveals more about his own upbringing than it does about the logic of belief. The wager simply codifies his particular "live options," to use William James's term for the only choices that seem possible to a given believer.
FLAW 2: Pascal's Wager assumes a petty, egotistical, and vindictive God who punishes anyone who does not believe in him. But the great monotheistic religions all declare that "mercy" is one of God's essential traits. A merciful God would surely have some understanding of why a person may not believe in him (if the evidence for God were obvious, the fancy reasoning of Pascal's Wager would not be necessary), and so would extend compassion to a non-believer. (Bertrand Russell, when asked what he would have to say to God, if, despite his reasoned atheism, he were to die and face his Creator, responded, "O Lord, why did you not provide more evidence?") The non-believer therefore should have nothing to worry about-falsifying the negative payoff in the lower-left-hand cell of the matrix.
FLAW 3: The calculations of expected value in Pascal's Wager omit a crucial part of the mathematics: the probabilities of each of the two columns, which have to be multiplied with the payoff in each cell to determine the expected value of each cell. If the probability of God's existence (ascertained by other means) is infinitesimal, then even if the cost of not believing in him is high, the overall expectation may not make it worthwhile to choose the "believe" row (after all, we take many other risks in life with severe possible costs but low probabilities, such as boarding an airplane). One can see how this invalidates Pascal's Wager by considering similar wagers. Say I told you that a fire-breathing dragon has moved into the next apartment, and that unless you set out a bowl of marshmallows for him every night he will force his way into your apartment and roast you to a crisp. According to Pascal's Wager, you should leave out the marsh-mallows. Of course you don't, even though you are taking a terrible risk in choosing not to believe in the dragon, because you don't assign a high enough probability to the dragon's existence to justify even the small inconvenience.
32. The Argument from Pragmatism (William James's Leap of Faith) The consequences for the believer's life of believing should be considered as part of the evidence for the truth of the belief (just as the effectiveness of a scientific theory in its practical applications is considered evidence for the truth of the theory). Call this the pragmatic evidence for the belief.
Certain beliefs effect a change for the better in the believer's life- the necessary condition being that they are believed.
The belief in God is a belief that effects a change for the better in a person's life.
If one tries to decide whether or not to believe in God based on the evidence available, one will never get the chance to evaluate the pragmatic evidence for the beneficial consequences of believing in God (from 2 and 3).
One ought to make "the leap of faith" (the term is James's) and believe in God, and only then evaluate the evidence (from 1 and 4).
This argument can be read out of William James's classic essay "The Will to Believe." The first premise, as presented here, is a little less radical than James's pragmatic definition of truth according to which a proposition is true if believing that it is true has a cumulative beneficial effect on the believer's life. The pragmatic definition of truth has severe problems, including possible incoherence: in evaluating the effects of the belief on the believer, we have to know the truth about what those effects are, which forces us to fall back on the old-fashioned notion of truth. To make the best case for The Argument from Pragmatism, therefore, the first premise is to be interpreted as claiming only that the pragmatic consequences of belief are a relevant source of evidence in ascertaining the truth, not that they can actually be equated with the truth.
FLAW 1: What exactly does effecting "a change for the better in the believer's life" mean? For an antebellum Southerner, there was more to be gained in believing that slavery was morally permissible than in believing it heinous. It often doesn't pay to be an iconoclast or a revolutionary thinker, no matter how much truer your ideas are than the ideas opposing you. It didn't improve Galileo's life to believe that the earth moved around the sun rather than that the sun and the heavens revolve around the earth. (Of course, you could say that it's always intrinsically better to believe something true rather than something false, but then you're just using the language of pragmatism to mask a non-pragmatic notion of truth.
FLAW 2: The Argument from Pragmatism implies an extreme relativism regarding the truth, because the effects of belief differ for different believers. A profligate, impulsive drunkard may have to believe in a primitive retributive God who will send him to hell if he doesn't stay out of barroom fights, whereas a contemplative mensch may be better off with an abstract deistic presence who completes his deepest existential world-view. But either there is a vengeful God who sends sinners to hell or there isn't. If one allows pragmatic consequences to determine truth, then truth becomes relative to the believer, which is incoherent.
FLAW 3: Why should we only consider the pragmatic effects on the believer's life? What about the effects on everyone else? The history of religious intolerance, such as inquisitions, fatwas, and suicide bombers, suggests that the effects on one person's life of another person's believing in God can be pretty grim.
FLAW 4: The Argument from Pragmatism suffers from the first flaw of The Argument from Decision Theory (#31, above)-namely, the assumption that the belief in God is like a faucet that one can turn on and off as the need arises. If I make the leap of faith in order to evaluate the pragmatic consequences of belief then, if those consequences are not so good, can I leap back to disbelief? Isn't a leap of faith a one-way maneuver? "The will to believe" is an oxymoron: beliefs are forced on a person (ideally, by logic and evidence); they are not chosen for their consequences.
33. The Argument from the Unreasonableness of Reason Our belief in reason cannot be justified by reason, since that would be circular.
Our belief in reason must be accepted on faith (from 1).
Every time we exercise reason, we are exercising faith (from 2).
Faith provides good rational grounds for beliefs (since it is, in the final analysis, necessary even for the belief in reason-from 3).
We are justified in using faith for any belief that is so important to our lives that not believing it would render us incoherent (from 4).
We cannot avoid faith in God if we are to live coherent moral and purposeful lives.
We are justified in believing that God exists (from 5 and 6).
God exists.
Reason is a faculty of thinking, the very faculty of giving grounds for our beliefs. To justify reason would be to try to give grounds for the belief: "We ought to accept the conclusions of sound arguments." Let's say we produce a sound argument for the conclusion that "we ought to accept the conclusions of sound arguments." How could we legitimately accept the conclusion of that sound argument without independently knowing the conclusion? Any attempt to justify the very propositions that we must use in order to justify propositions is going to land us in circularity.
FLAW 1: This argument tries to generalize the inability of reason to justify itself to an abdication of reason when it comes to justifying God's existence. But the inability of reason to justify reason is a unique case in epistemology, not an illustration of a flaw of reason that can be generalized to some other kind of belief-and certainly not a belief in the existence of some entity with specific properties such as creating the world or defining morality.
Indeed, one could argue that the attempt to justify reason with reason is not circular, but, rather, unnecessary. One already is, and always will be, committed to reason by the very process one is already engaged in- namely, reasoning. Reason is non-negotiable; all sides concede it. It needs no justification, because it is justification. A belief in God is not like that at all.
FLAW 2: If one really took the unreasonability of reason as a license to believe things on faith, then which things should one believe in? If it is a license to believe in a single God who gave his son for our sins, why isn't it just as much a license to believe in Zeus and all the other Greek gods, or the three major gods of Hinduism, or the Angel Moroni? For that matter, why not Santa Claus and the Tooth Fairy? If one says that there are good reasons to accept some entities on faith, while rejecting others, then one is saying that it is ultimately reason, not faith, that must be invoked to justify a belief.
FLAW 3: Premise 6, which claims that a belief in God is necessary in order to have a purpose in one's life, or to be moral, has already been challenged in the discussions of The Argument from Moral Truth (#16, above) and The Argument from Personal Purpose (#19, above).
34. The Argument from Sublimity There are experiences that are windows into the wholeness of existence-its grandeur, beauty, symmetry, harmony, unity, even its goodness.
We glimpse a benign transcendence in these moments.
Only God could provide us with a glimpse of benign transcendence.
God exists.
FLAW: An experience of sublimity is an aesthetic experience. Aesthetic experience can indeed be intense and blissful, absorbing our attention so completely, while exciting our pleasure, as to seem to lift us right out of our surroundings. Aesthetic experiences vary in their strength, and when they are overwhelming, we grope for terms like "transcendence" to describe the overwhelmingness. Yet, for all that, aesthetic experiences are still responses of the brain, as we see from the fact that ingesting recreational drugs can bring on even more intense experiences of transcendence. And the particular triggers for natural aesthetic experiences are readily explicable from the evolutionary pressures that have shaped the perceptual systems of human beings. An eye for sweeping vistas, dramatic skies, bodies of water, large animals, flowering and fruiting plants, and strong geometric patterns with repetition and symmetry was necessary to orient attention to aspects of the environment that were matters of life and death to the species as it evolved in its natural environment. The identification of a blissfully aesthetic experience with a glimpse into benign transcendence is an example of the Projection Fallacy, dramatic demonstrations of our spreading ourselves onto the world. This is most obvious when the experience gets fleshed out into the religious terms that come most naturally to the particular believer, such as a frozen waterfall being seen by a Christian as evidence for the Christian Trinity.
35. The Argument from the Intelligibility of the Universe (Spinoza's God) All facts must have explanations.
The fact that there is a universe at all-and that it is this universe, with just these laws of nature-has an explanation (from 1).
There must, in principle, be a Theory of Everything that explains why just this universe, with these laws of nature, exists. (From 2. Note that this should not be interpreted as requiring that we have the capacity to come up with a Theory of Everything; it may elude the cognitive abilities we have.) If the Theory of Everything explains everything, it explains why it is the Theory of Everything.
The only way that the Theory of Everything could explain why it is the Theory of Everything is if it is itself necessarily true (i.e., true in all possible worlds).
The Theory of Everything is necessarily true (from 4 and 5).
The universe, understood in terms of the Theory of Everything, exists necessarily and explains itself (from 6).
That which exists necessarily and explains itself is God (a definition of "God").
The universe is God (from 7 and 8).
God exists.
Whenever Einstein was asked whether he believed in God, he responded that he believed in "Spinoza's God." This argument presents Spinoza's God. It is one of the most elegant and subtle arguments for God's existence, demonstrating where one ends up if one rigorously eschews the Fallacy of Invoking One Mystery to Explain Another: one ends up with the universe and nothing but the universe, which itself provides all the answers to all the questions one can pose about it. A major problem with the argument, however, in addition to the flaws discussed below, is that it is not at all clear that it is God whose existence is being proved. Spinoza's conclusion is that the universe that itself provides all the answers about itself simply is God. Perhaps the conclusion should, rather, be that the universe is different from what it appears to be-no matter how arbitrary and chaotic it may appear, it is in fact perfectly lawful and necessary, and therefore worthy of our awe. But is its awe-inspiring lawfulness reason enough to regard it as God? Spinoza's God is sharply at variance with all other divine conceptions.
The argument has only one substantive premise, its first one, which, though unprovable, is not unreasonable; it is, in fact, the claim that the universe itself is thoroughly reasonable. Though this first premise can't be proved, it is the guiding faith of many physicists (including Einstein). It is the claim that everything must have an explanation; even the laws of nature, in terms of which processes are explained, must have an explanation. In other words, there has to be an explanation for why it is these laws of nature rather than some other, which is another way of asking for why it is this world rather than some other.
FLAW: The first premise cannot be proved. Our world could conceivably be one in which randomness and contingency have free reign, no matter what the intuitions of some scientists are. Maybe some things just are ("stuff happens"), including the fundamental laws of nature. Philosophers sometimes call this just-is-ness "contingency," and if the fundamental laws of nature are contingent, then, even if everything that happens in the world is explainable by those laws, the laws themselves couldn't be explained. There is a sense in which this argument recalls The Argument from the Improbable Self. Both demand explanations for just this-ness, whether of just this universe or just this me.
The Argument from the Intelligibility of the Universe fleshes out the consequences of the powerful first premise, but some might regard the argument as a reductio ad absurdum of that premise.
COMMENT: Spinoza's argument, if sound, invalidates all the other arguments, the ones that try to establish the existence of a more traditional God-that is, a God who stands distinct from the world described by the laws of nature, as well as distinct from the world of human meaning, purpose, and morality. Spinoza's argument claims that any transcendent God, standing outside of that for which he is invoked as explanation, is invalidated by the first powerful premise, that all things are part of the same explanatory fabric. The mere coherence of The Argument from the Intelligibility of the Universe, therefore, is sufficient to reveal the invalidity of the other theistic arguments. This is why Spinoza, although he offered a proof of what he called "God," is often regarded as the most effective of all atheists.
36. The Argument from the Abundance of Arguments The more arguments there are for a proposition, the more confidence we should have in it, even if every argument is imperfect. (Science itself proceeds by accumulating evidence, each piece by itself being inconclusive.) There is not just one argument for the existence of God, but many- thirty-five (with additional variations) so far, in this list alone.
The arguments, though not flawless, are persuasive enough that they have convinced billions of people, and for millennia have been taken seriously by history's greatest minds.
The probability that each one is true must be significantly greater than zero (from 3).
For God not to exist, every one of the arguments for his existence must be false, which is extremely unlikely (from 4). Imagine, for the sake of argument, that each argument has an average probability of only .2 of being true, which means that it has a probability of .8 of being false. Then the probability that all thirty-five are false is (1 .835) = .004, an extremely low probability.
It is extremely probable that God exists (from 5).
FLAW 1: Premise 3 is vulnerable to the same criticisms as The Argument from the Consensus of Humanity. The flaws that accompany each argument may be extremely damaging, even fatal, notwithstanding the fact that they have been taken seriously by many people throughout history. In other words, the average probability of any of the arguments' being true may be far less than .2, in which case the probability that all of them are false could be high.
FLAW 2: This argument treats all the other arguments as being on an equal footing, distributing equal probabilities to them all, and rewarding all of them, too, with the commendation of being taken seriously by history's greatest minds. Many of the arguments on this list have been completely demolished by such minds as David Hume and Baruch Spinoza: their probability is zero.
COMMENT: The Argument from the Abundance of Arguments may be the most psychologically important of the thirty-six. Few people rest their belief in God on a single, decisive logical argument. Instead, people are swept away by the sheer number of reasons that make God's existence seem plausible-holding out an explanation as to why the universe went to the bother of existing, and why it is this particular universe, with its sublime improbabilities, including us humans; and, even more particularly, explaining the existence of each one of us who know ourselves as unique conscious individuals, who make free and moral choices that grant meaning and purpose to our lives; and, even more personally, giving hope that desperate prayers may not go unheard and unanswered, and that the terrors of death can be subdued in immortality. Religions, too, do not justify themselves with a single logical argument, but minister to all of these spiritual needs and provide a space in our lives where the largest questions with which we grapple all come together, which is a space that can become among the most expansive and loving of which we are capable, or the most constricted and hating of which we are capable-in other words, a space as contradictory as human nature itself.
ACKNOWLEDGMENTS.
I wish to shout out my gratitude to both the Guggenheim Foundation and the Radcliffe Institute, Harvard University, for supporting the writing of this novel. Among the wonderful fellows at the Radcliffe Institute during the year of my residence was Megan Marshall, who was one of the first of my readers. I thank her for her comments and her friendship.
Gabriel Love was another early reader who provided me with essential feedback. Elaine Pfefferblit's comments were, as always, illuminating.
I am grateful to the following people for being, I'd wager, the only ones in the world who would not respond "huh?" when sent my bizarre questions but answered them with precision and playfulness: Douglas Hofstadter, Martin Seligman, and, pivotally, Doron Zeilberger.
Readers may be surprised to learn that I did not make up the Kabbalistic musings on such Jewish delicacies as potato kugel, but learned of them from the article "Holy Kugel: The Sanctification of Ashkenazic Ethnic Foods in Hasidism," by Allan Nadler, reprinted in Food & Judaism, edited by Leonard Greenspoon, Creighton University Press, 2005.
It is a gift for me to be able to avail myself of the wealth of smarts, from the most practical to the most literary, that Tina Bennett provides. Stephanie Koven has been wonderful in her efforts on behalf of this book. I thank the stars to have been able to place my work in the hands of Dan Frank, an editor with whom I have long dreamed of working.
The gratitude and love that I owe my partner, Steve Pinker, are too deep and too many for the telling. Suffice it to say that, among all the profusion of his talents, is his perfect knowledge of love.
I selfishly raised my two daughters, Yael Goldstein Love and Danielle Blau, to be astute critics, and they have never let me down. Each has become a consummate artist in her own right. This book is dedicated to Danielle, who helped me, through all the years, not to lose Azarya. It is often her voice and her purity of vision that I hear and see in him.
About the Author.
Rebecca Newberger Goldstein, a novelist and philosopher, was awarded a MacArthur "Genius" prize for her ability to "dramatize the concerns of philosophy without sacrificing the demands of imaginative storytelling." Her first novel was the critically acclaimed best seller The Mind-Body Problem. She has received numerous prizes for her five other works of fiction, including National Jewish Book Awards for Strange Attractors and Mazel and the Whiting Writers' Award for The Dark Sister. Her two most recent books are Incompleteness: The Proof and Paradox of Kurt Godel and Betraying Spinoza: The Renegade Jew Who Gave Us Modernity, winner of the Koret Prize. She has been awarded two honorary doctorates, Guggenheim and Radcliffe fellowships, and is a Humanist Laureate and a fellow of the American Academy of Arts and Sciences. She lives in Boston and Truro, Massachusetts.
ALSO BY REBECCA NEW BERGER GOLDSTEIN.
Betraying Spinoza: The Renegade Jew Who Gave Us Modernity.