The Problem with Probabilistic Arguments

One of the perennial problems of philosophy is the question of the existence of God. This question has traditionally revolved around the so-called “theistic proofs” and has a philosophical tradition going back at least to Plato. Some philosophers think there are successful theistic proofs (Swinburne or Craig, for example), others – probably the majority – think there are no successful proofs at all. Still others think the issue of proof is an interesting philosophical sideshow at best but is either irrelevant with respect to the rational justification of belief in God or has little, if any, positive religious value.

My own view – very briefly stated is:

There is a God, and there are arguments which lend some not insubstantial weight to theism. However, very few people – myself included – believe in God because of such arguments. Theistic beliefs seem to rest upon very different grounds.

In this article I want to say why I think the project of theistic (or atheistic) proofs is not a promising one.

Types of Proof

Theistic proofs typically come in two forms: a priori and a posteriori. A posteriori proofs are those which rely on some premise or other derived from experience. For example, the fine tuning argument or the Kalam cosmological argument both rely on certain things which we can only learn from experience: that the laws or constants of the universe are fine-tuned for life, or that the universe began to exist. An a priori proof, on the other hand, is an argument which is logically prior to and independent of experience. I can only think of one such argument: the ontological argument.

Sadly, whilst ontological arguments are very interesting it’s far from clear that any such arguments are successful. A posteriori arguments are therefore much more common. These types of arguments also come in two general forms: deductive demonstrations or some form of probabilistic argument.

Take the strictly logical deductions first. What would it mean for arguments of this type to prove the existence of God? Well, first of all we must be clear what “prove” means in this context. We aren’t thinking of proof in terms of mere logical validity or even arguments which have true premises but which no-one knows are true. To prove something means fundamentally to prove it to some specific person. So, the conclusion must follow from the premises, the premises must be true, and the premises must be acknowledged to be true by those we hope to convince.

It seems to me that we hit something of a snag here. Whilst I disagree with John Hick who reckons all such strict a posterior proofs necessarily beg the question, he’s almost certainly correct that anyone who accepts the premises of such arguments almost certainly already accepts the conclusion that God exists. Purely from my own experience I would hazard a guess that the vast majority who think the Kalam cosmological argument is a persuasive argument for the existence of God already believed in God prior to entertaining the argument. That’s no coincidence.

But perhaps even though such arguments do not succeed as strict demonstrative proofs they could be taken as providing pointers, clues or indications; in short they could be presented as probability arguments for the existence of God which appeal to a more informal kind of rationality. Are these any more successful?

Arguments such as the various design arguments or arguments from religious experience are amongst those which seek to establish the existence of God to some degree of high probability rather than logical certainty. The general form of such arguments is that “in view of some characteristic or other of the world it is more probable that there is a God than not; or, such features are better explained (or “to be expected”) on theism rather than naturalism.”

Now, quite clearly the probability at work here is not the sort of strict mathematical notion we come across in the physical sciences. The concept of probability that operates in various theistic (and atheistic) arguments must be nonmathematical, something along the lines of more reasonable or less reasonable acts of assent on the basis of the relative antecedent/intrinsic probabilities of theism or naturalism. The claim that is typically made is that it is more reasonable to interpret the universe in theistic terms than naturalistic terms (or vice versa).

But can this nonmathematical concept of probability be usefully applied to the question of God’s existence? It is of course a matter of fact that human beings have experienced things within the world from which they conclude that God exists or, more likely, on the basis of which their already existing conviction concerning the existence of God is strengthened or reaffirmed. Such conclusions are often couched in probabilistic language: “it seems more probable than not that…” or “it is overwhelmingly more probable that…” However, is it not the case that when used in this way the notion of probability is simply an expression of subjective judgments, a hunch, a feeling or a “how it just seems to me?”

The problem, as I see it, is that there is a huge number and variety of relevant considerations. Some seem to clearly point towards theism; others clearly to naturalism. For example, even theists would agree that the problem of evil counts to some degree against theism, for why else would they seek to answer it? On the theist side at least some of the following provide some weight in favour of theism: fine-tuning, objective moral values, consciousness, contingency, certain other human traits such as free will and rationality, and even the phenomena of religious experiences. Atheists of course try to present interpretations of such things so as to fit them into their own worldview, whatever that is (typically materialism/naturalism). Likewise with the atheist, he presents arguments from evil or hiddenness and the theist tries to give these an understanding which helps them to sit within their overall theistic way of seeing the world. None of the many factors that we could consider seem to point so unequivocally in one direction such that only one explanation or interpretation is possible; despite the fact that in isolation they point one way or the other, each can be fitted into a theistic or naturalistic worldview. Put simply: there is no single piece of evidence for either view which cannot be incorporated into the contrary view by the mind of a person operating with different presuppositions.

So, can acceptance of one interpretation or the other be said to be more reasonable in the face of the total evidence? Someone may be convinced of Christian theism after reading a Lee Strobel book, but of course Strobel doesn’t entertain contrary arguments. All he achieves is the rather jejune conclusion that the existence of God is more probable on X, Y or Z, a conclusion an atheist could easily grant. Often when apologists (theist or atheistic) claim the evidence as a whole points clearly one way rather than the other it’s not unreasonable to conclude that his research has been infected with confirmation bias. We must treat theism and naturalism as comprehensive wholes, each with their own particular strengths and weaknesses. But which of the various hypotheses squares best with our whole experience of the universe?

How can we say one is more probable than the other? Can we count points in favour of each? So, consciousness and morality in favour of theism gives us a score of 2-0? Add in the problem of evil: 2-1? If 10 items go in favour of theism and only 8 in favour of atheism does theism win by 2 points? That method hardly seems promising. Some factors will be clearer evidence one way than other factors. Some considerations will carry weight – even substantially greater weight – than others. Moreover, there will be no agreed objective way of weighing the various items. It all starts getting rather vague and subjective. Judgments on these matters are personal and intuitive: each of us simply makes a judgment call, and if we seek to apply the notion of probability here we can only legitimately do so on the understanding that it no longer has any objective meaning.

On the methods typically adopted by theistic and atheistic apologists alike there seems no objective sense in which one worldview rather than the other can be described as “more probable.” It’s fairly uninteresting to point out that to theists theism seems more likely, whilst to naturalists naturalism seems more adequate. The reason for this lies, I think, in that they are judging from very different standpoints, with different criteria and presuppositions. We aren’t the wholly rational impartial observers we might like to paint ourselves as. Each of us, for better or worse, is a complex of many factors and influences: our upbringing, our background experiences, our cultural milieu, our peers, our education, our innate temperament and dispositions, and much else besides. These things provide the spectacles through which we view our world. It is largely for these reasons that I find, say, Swinburne’s attempt to convince us that the existence of God is 97% probable, or a naturalist’s attempt to tell me that the immensity of the universe is more probable or more expected on naturalism rather than theism, to be borderline laughable. Of course, great minds make such claims; the claims are no less risible for that.

In the final analysis I can see very little grounds to think the dispute can be settled by appeal to some agreed procedure or by referring to some alleged objectively ascertainable probabilities.

Can my opponents convince me otherwise? Probably not…

Stephen J Graham


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Filed under Philosophy, Probability

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