Monday, September 28, 2009

A hypothesis about inductive reasoning

It is normal to talk of "inductive logic", as if non-deductive reasoning formed a branch of logic, with discoverable rules. But what if it is not so? What if the rules of inductive reasoning, unlike the rules of deductive logic, are merely "subjectively necessary", to use Kant's phrase? It is perhaps simply the case that our minds are hard-wired to think in certain ways inductively. This hard-wiring is truth-conducive, not for any deep logical reason (as in the case of deductive logic, where the validity of modus ponens, and the truth of excluded middle, etc. are all necessary truths), but simply because God created us with minds hard-wired to reason inductively in ways that match the arrangement of large segments of the world that he has created.

One can say some of this with natural selection in place of God, but natural selection will only yield the result that our minds' functioning matches the structure of the world in those respects that are relevant to the fitness of our evolutionary forebears—it will give us little or no reason to think that things will work out when we do cosmology or quantum mechanics.

If this is right, then we should not be surprised if one particular formalization of inductive logic—say, the Bayes-Kolmogorov probabilistic account—yields doxastic rules that some of our doxastic practices break, and are right to break. (See the previous several days' posts.) For the theistic story gives us reason to think that our inductive reasoning will get us to the truth, but does not give us much reason to think that our inductive reasoning can be formalized. If this is right, then working scientists may very well do better than ideal Bayesian epistemic agents, say, and be unable to explain their successes.

Probably, the epistemology that would go along with a view like that would have to be some sort of proper-function epistemology. But I am happy to leave that to the epistemologists—I am just a probability theorist.

[Edited. -ARP]


Christopher Cloos said...

Interesting hypothesis Alexander. What kind of evidence would support your hypothesis? You mention that natural selection could not account for the subjective necessity of the rules of inductive reasoning. Natural selection can only yield a fit between mind and world in relation to things relevant to evolutionary fitness, but when it comes to cosmology or QM evolutionary theory is unable to explain (predict) truth-conducive results. Would an evolutionary theorist regard cosmology or QM as outside the predictive success of evolutionary theory? What about the idea that our minds evolved in such a way as to be able to accurately make predictions about the formation of the universe or reach conclusions about quantum uncertainty from specific facts about the universe or sub-atomic descriptions? What additional evidence would there be for your hypothesis about God?

Perhaps another direction to take your hypothesis is in the direction of faith. Our minds might be hard-wired to think inductively because knowing God ultimately involves possessing confidence in that which is unseen. There is no lab experiment that can be done to prove the existence of God. So, to some degree, faith in God involves confidence (belief, conviction) in things unseen. This faith can be rational when it is based on evidence. The world is organized in such a way that it reveals evidence of the existence of God (though not the kind of evidence that could produce deductive certainty), and our minds are hard-wired in such a way to reason from the evidence to the true prediction that God exists or that he is who he says he is as revealed in scripture. The degree of confirmation of the hypothesis (h) on the evidence (e) is (r). The weight of the prediction that God exists must be based on empirical knowledge, testimony, personal religious experience and the statistical likelihood of the relevant historical evidence. If believer X knows (e) on the basis of the things just mentioned, then he has good reasons for expecting the unknown facts described by (h) to be true. Faith involves this kind of leap from what is known, seen or revealed to what is unknown, unseen and (to some degree) yet to be fully revealed. The problem, of course, with any probabilistic argument is that it must make sense of countervailing evidence (e.g., evil, alternate descriptions of the same evidence, etc.). This, however, is a worthwhile endeavor.

Alexander R Pruss said...

Thanks for these thought-provoking remarks.

I hadn't thought about the evidential issue. I wasn't, for instance, trying to come up with an argument for theism.

Consider the Level Uniformity Hypothesis (LUH): the way regularities are arranged on different levels (say, the quantum or cosmological level, and the medium-sized realm) has structural similarities of a sort sufficient to ensure that general reasoning methods developed for one level are likely to work for others.

Naturalistic Evolution (NE) + ~LUH predicts that we will be scientifically unsuccessful outside of the medium-sized realm. Moreover, it is likely that the lack of success will be not just of the subtle "can never tell that we're wrong" but will be of the much more obvious sort--our electronic circuits won't work, etc.

NE + LUH predicts some scientific success outside of the medium-sized realm.

NE + ~LUH has, I take it, been strongly disconfirmed.

Thus, if NE is true, probably so is LUH. And if Naturalism is true, probably so is NE and hence LUH. This is all a matter of posterior probability.

Now, apart from theism, I think we would have little reason to expect LUH to be true. We have good reason to think that the behavior of stuff at the micro and cosmological levels is very different from what we are used to seeing at the medium-sized level. People do initially--and maybe not just initially--find QM and relativity counterintuitive, precisely for this reason. Yet LUH says that despite these differences, there are deep similarities. This is surprising, unless there is a designer.

Thus, as a matter of prior probabilities:
P(LUH | Theism) = moderate
P(LUH | Naturalism) = quite low

So LUH confirms Theism against Naturalism. And I think it does so pretty strongly.

The standard criticisms of EAAN do not apply here.

So we do have an argument for Theism here.

Christopher Cloos said...

Interesting argument. My first worry would be in the neighborhood of ontological vagueness. The argument assumes an ability to locate determinate objects with structural similarities at different levels of reality. My worry finds sharp expression at the quantum level. In QM one cannot completely specify the location and velocity of a subatomic particle with certainty. So, on a ‘de re’ reading, “The referent of t [a subatomic particle] is such that it is indeterminate whether certain chucks of reality lie within its boundaries” (Varzi 2001). The boundaries of quantum particles are not just fuzzy, the entire object itself is fuzzy because there is no determinate fact of the matter about where the object is located or its velocity.

Another worry I have is in the neighborhood of question begging. The argument for a designer is that it would be a shock to find out that LHU is true unless there is a way to explain deep structural regularities in nature despite apparent differences. Naturalistic evolution (NE) is unable to account for these similarities, yet for NE to be true LHU must be true, so something else must explain the truth of LHU and that something must be a designer capable of hard-wiring those similarities into different levels of reality. I’m wondering whether or not LHU presupposes a designer--what you are trying to prove or provide probabilistic support for. LHU is really about reasoning (like inductive reasoning) being able to work at different levels of reality. This reasoning works because the way regularities are organized on different levels generates structural similarities between the levels. Inductive reasoning works by employing something like the uniformity of nature (UN) principle (i.e., that if a regularity holds in my experience, then it holds in nature in general or in the future). Inductive reasoning presupposes the uniformity of nature. So, there must be something capable of explaining that uniformity. By definition, that something cannot be NE because NE is mainly concerned with medium-sized objects and cannot predict success in quantum or cosmological domains. However, by definition, a designer is capable of generating deep structural regularities so that induction can work at different levels of reality. Thus, a designer must exist in order for LHU to work as defined.