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#266 Atheistic Physicists’ Repudiation of Logic and Probability Theory

May 20, 2012

Hello Dr. Craig,

First of all let me say that you are my favorite 'philosopher-missionary' on the scene, and I am just overjoyed and excited everytime I hear that you went somewhere new in the world! I recently watched your debate with the physicist from Finland named Kari . Kari's continued assertion that observations on the sub-atomic level have shown us that classical logic doesn't model the quantum realm is something that is beginning to appear more and more in the blogosphere. I was hoping to get a deeper explanation from you about each of the responses you gave in the debate:

1) Quantum logic is held by a tiny minority of physicists.
2) You seemed to imply that if we adopt a Bohmeian interpretation of quantum mechanics, then classical logic applies to the quantum level (does this also imply that quantum logic presupposes the Copenhagen interpretation of quantum mechanics).
3) I think you said that classical logic is distinct from the 9 rules of 'formal' logic (i.e. modus ponens, modus tollens, etc.) and your arguments don't rely on things like the law of excluded middle; but can you really separate these in this manner?
4) You also said that your arguments rely on observational evidence at macro-level where classical logic clearly does apply and not on any quantum observations. But didn't the universe began in some sort of quantum state which might imply that classical logic cannot guide us in our thinking about the origin of the universe (i.e. maybe something can come from nothing)?
5) It is self-defeating to use formal logic to deny applicability of formal logic at the quantum level.

Thank you,

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Dr. craig’s response


Kevin, I have been scratching my head about this seemingly crazy repudiation of classical logic and probability theory on the part of certain atheistic physicists ever since my debate with Lawrence Krauss, who took the same line as Kari Enqvist. Krauss even seemed to call into question the truth of theorems of elementary arithmetic like 2+2=4! What could they be thinking?

Since their repudiation of logic and probability theory was put forward as a response to my theistic arguments, it appeared that they are rejecting the rules of inference of formal sentential logic like modus ponens, modus tollens, disjunctive syllogism, etc. My conclusions are alleged, it seems, not to follow because quantum mechanics has overthrown the rules of logic. But that can’t be their contention, for there is nothing in quantum mechanics that would lead one to deny the logical rules of inference, and such a position would be hopeless in any case, since one has then rejected any means of rationally drawing conclusions—including those of the quantum physicist!

So are they rejecting Aristotelian syllogistic logic? That can’t be right, since my arguments don’t depend upon any peculiarities of Aristotelian logic (like the ability to draw existential conclusions from universally quantified statements) that are not part of modern sentential logic.

So maybe they’re repudiating the classical Law of Excluded Middle, the principle which states that for any proposition p, either p is true or not-p is true. A tiny minority of physicists and philosophers, as I mentioned, have sought to develop a quantum logic according to which, due to indeterminacy, certain statements about quantum entities or events are neither true nor false. But Enqvist denied that that was his claim, and, as I said, the program of quantum logic wouldn’t affect any of my arguments anyway, since there’s no ground for thinking that the premises of my arguments, which are not about quantum entities or events, are neither true or false.

It sometimes sounded as if Krauss and Enqvist were rejecting the probability calculus. But Bayes’ Theorem is a rock-solid formula for how probabilities are to be computed. And in my debate with Krauss I wasn’t even using the Theorem as a whole but just talking about certain factors in it, like the probability of God’s existence given our background information and certain specific evidence (like the beginning of the universe, fine-tuning, etc.).

So what in the world are these men talking about?

Well, fortunately, after our debate Enqvist and I went out to lunch together, and I was able to ask him directly what he meant. You can imagine my shock when he replied that what he was talking about was the violation of the Bell Inequalities by quantum mechanics! My mind shot back to my debate with Krauss, and it suddenly dawned on me that that is what he also must have been talking about! When Enqvist said this, I replied that the experimental results on Bell’s Theorem exposed a failure of physics but surely not of probability theory itself. But he was adamant, maintaining that the results exposed a deficiency in probability theory, which had predicted the wrong results.

Now this is completely wrong-headed. What John Bell did was use classical probability theory to show that any physical theory which affirms what is called locality (i.e., there is no action at a distance; all effects are local) will predict certain statistical results that are at odds with the predictions of quantum theory. The experimental evidence vindicated the predictions of quantum theory. The evidence therefore strongly suggests that the physical world is non-local. (Interestingly, the easiest way to have a non-local physical theory is to abandon Einsteinian special relativity and adopt instead Lorentz’s theory of relativity, which permits causal influences to be propagated at super-luminal velocities and therefore has no problem with the experimental results violating the Bell Inequalities. In fact, Bell’s own personal recommendation was precisely that we take this Lorentzian route. Bohm’s interpretation of quantum mechanics, though fully deterministic, is also a non-local theory featuring absolute simultaneity. For an account of the implications of the experimental results on Bell’s Theorem for relativity theory see my Time and the Metaphysics of Relativity, pp. 221-35. But I digress!)

The point is that what the experimental results should lead us to reject is locality, not probability theory! Indeed, if you reject probability theory, then locality and quantum theory are NOT incompatible after all! You could happily embrace both quantum mechanics and local, so-called hidden variable theories by just blowing off probability theory! So what if the Bell Inequalities are violated by quantum mechanics? Those inequalities were computed using probability theory, so who cares? Ironically, then, the experimental results to which these physicists appeal to reject probability theory actually presuppose probability theory!

I hope you can see how perverse this attack on probability theory is. The problem exposed by experimental science is not probability theory but the assumption of locality. Faulting probability theory rather than a particular physical theory is like rejecting mathematics because your checkbook fails to balance—but then Krauss did say 2+2=5, didn’t he?

There are some sobering lessons in all this. First, it shows once again what a gross abuse of science some philosophically naïve physicists are guilty of. (If I have misunderstood these gentlemen, then I am eager to be corrected and to hear an explanation of what they mean.) Second, even to suggest a rejection of logic and probability theory in order to avoid theistic conclusions is a sign of desperation. Can you imagine how ridiculed religious people would be if, in order to maintain our view, we had to renounce logic and probability theory? Finally, the tack taken by these thinkers is ultimately counter-productive for them and helpful to theists, for it just is to admit that theism is more logical and more probable than atheism.

- William Lane Craig