"Crazy" Notes as MH Props

Does Inductive Reasoning Originate in a Deductive Fallacy?

Hume in the Enquiry shows that the idea of causal relation as a hidden force behind events is vacuous, since this is an idea with no actual content beyond the temporal-spatial conjunction of the events in question. But if this idea is really empty, how did we end up with it as the central mechanism of our reasoning about the world?

In section VII, Hume suggests some possible answers to this question-- including the conjecture that the idea of causal power being behind things derives from our own power over our bodies, or from some notion of divine power-- but he dismisses each of these answers as circular or inadequate. Instead, Hume proposes that “it is not reasoning” that produces the idea of causal relation, but some more primitive tendency, one that is present even in children. On this view, the problem of induction would be solved through a kind of utility theory that admits inductive inference has no rational basis but points out that the benefit we have gotten from it already, throughout our formation as a species, has shaped us so as to rely on it as a guide to future benefit.

However, another thought is that inductive reasoning in itself may be a product of a common mistake involving deductive implication. The advantage of this view is that it posits induction as prior to and independent of notions of causation and the uniformity of nature-- instead, these notions would follow from it, after it is adopted. More is explained by having these complex ideas be the product of a simple reasoning mechanism than vice versa. The disadvantage is that it leaves induction in an even worse state than Hume's theory, since it claims that induction as such is not only unsupported but fallacious.

Suppose some people start with the experiential data of always encountering two terms together, e.g. red apples and sweetness. They have collected a data set of all the times the terms have occurred together and found that there was no case when the first occurred but not the second. So this makes them wonder: "is there an implication here, such that we can know for sure that 'if red apples, then sweetness' is always true?" Suppose also that the deductive inferential principle of modus ponens is already known, whether instinctively or explicitly, i.e. (1) if p, then q; (2) p; (C) therefore, q. Now, again, they want to know if there is in general such an implication relation (1) between the two phenomena. 

Some pairs of phenomena necessarily have this relation by definition or by a part-whole relation. For instance, because we know that bachelors are by definition unwed males, it is necessarily the case that if someone is an unwed male, then he is a bachelor. Likewise, because a red apple must be a thing that is red, it is necessarily the case that if something is a red apple, then that thing is red. Notice in these cases that we can also always infer the conjunction of the two terms from the antecedent, given the implication (if and only if the implication), i.e. (p → q) ≡ (p → (p & q)). Then, again, suppose people want to know if they can infer that if a thing (t) is a red apple (A), then that thing is sweet (S). Naively, they might note that for all things that are red apples that they have ever encountered, those things have been sweet, i.e. (A(t) & S(t)). This might lead them to mistakenly affirm the consequent, such that A(t) → (A(t) & S(t)). Because this has the same form as (p → (p & q)), they can then conclude A(t) → S(t), that is, if something is a red apple, it is sweet. The problem of course is the deductively fallacious step of affirming the consequent.

But isn't this exactly what goes on with inductive reasoning? We note that two empirical things have always appeared together, in conjunction, and that if the first of the two occurs, it has never been the case that the second did not occur, and from this we infer that the first is the cause of the second, that is, the first implies the second. This is all that is needed to get the basic form of inductive reasoning. But if this is so, then inductive reasoning is just a product of a mistake in deductive reasoning.

This really is not in disagreement with Hume at all, though. It just fleshes out an intermediary step between an even more primitive origin in instinct, which I think is right, and the conception of ideas of cause and uniformity. I think it could be helpful because it shows that there really is no difference between an analytic implication and a law of nature other than the fact that the law of nature is not actually necessary. What it shows is that we don't need the cause and uniformity ideas at all.

Another reason why I see this intermediary step as likely is that affirming the consequent is such a widespread, often automatic mistake elsewhere among humans. The way I state it here, making each step explicit, might suggest that I mean it is actually an explicit, deliberate process, but I am really referring to a more unconscious, instinctual process. We see this same process in all kinds of prejudices and magical thinking. An all too common, but usually implicit, line of thought goes: (1) If all people in a group have a trait, then some people in that group have that trait. (2) Some people in a group have a trait. (3) Therefore all people in that group have that trait. Maybe we can even say animals make this mistake. Take Pavlov's dogs: (1) If there is a bell sound and food, then there is a bell sound. (2) There is a bell sound. (3) Therefore there is a bell sound and food (so I should excitedly bark for the latter).

If this affirming the consequent based thinking is both common and prior to the conscious development of valid deductive reason, meaning that formal, explicit deductive reason is actually the newer innovation, the advent of deductive reason calls into question the validity of the type of thinking one has come to rely on in order to function. This is where the introduction of causal powers and uniformity come into play, as justifications for upholding our everyday inductive practices despite the challenge presented to them by deduction.