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A Wittgensteinian Answer to the “Problem” of Induction: Why the Scare Quotes are Merited (Part 2)

January 11th, 2009

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This could also be framed probabilistically (e. g. Bayesian induction). The latter type of rule would form some system of delimiting the precise significance of an inference given its evidence; for example, it might show us in what ways an inference may be falsified, and thus the level of certainty with which we should treat a particular proposition.

The Non-Problem of Induction

A Wittgensteinian response to any philosophical “problem” can be described as a reduction of the problem to a linguistic puzzle, and a subsequent resolution of that puzzle. In short, a linguistic puzzle is a seemingly insoluble contradiction that can be successfully rectified by clarifying the definitions of the terms in use. Once the definitions have been clarified, the next stage is to determine whether the conclusion (whose terms have also been clarified) still follows from the premises, and whether the premises are true. Once this has been done, a problem should have been shown to be merely confusion. This methodology is most strongly associated with Wittgenstein’s most significant work, Philosophical Investigations. [6]

Given this background, we can now freely address the problem of induction. To show how the problem of induction can be reduced to a linguistic puzzle, we will first return to a simplified formulation of it: no inductive conclusions necessarily follow from their premises, because we have no justification for believing that the unobserved will be like the observed once we observe it (a generalization of “the future will be like the past. ”) The justificatory problem of induction, put in simple terms by Hume, states it similarly: the definite outcomes of deduction can not justify the indefinite outcomes of induction, and induction can not justify induction without circularity. Thus, we are not justified in believing the conclusion of an inductive argument.

Now, to prove that this is merely a linguistic puzzle, we have to show how clarifying our terms in this argument will dissipate the problem, whether in showing some self-contradictory aspect of the argument, showing that the conclusion that follows from those definitions is unimportant to us, showing that the desired conclusion of the argument does not follow from the premises, etc. By an “unimportant conclusion,” we only mean that all further implications of that conclusion do not constitute anything that merits addressing or reparation. In other words, the conclusion made to have followed from the premises is not a philosophical problem requiring a solution on our part, but just some proposition that conforms to its premises. Our criteria for importance is not simply soundness, as there are many sound arguments that are not of philosophical concern to us. Thus, it is certainly the case that if we define “justification for a belief” as “immunity to the logical possibility of subsequent falsifying events,” we could easily concoct an argument from skeptical premises that (properly) concludes that we are not “justified” in believing any proposition because we have not immunized it from subsequent falsifying events. But, as we will see, this conclusion sounds important because it uses a word which is usually of epistemic importance (justification), but is in fact unimportant because it fails to have any implications worth considering.

We can apply this method to the problem of induction by first investigating the employment of the idea of necessity in the argument against induction. Asserting that there is no necessary connection between matters of fact is not incorrect, given a particular meaning of the word “necessary”—namely, where “necessity” implies conformity to the rules of deductive reasoning. Given that induction has been identified as non-deductive because of the “unfounded” assumption that the future will be like the past, then we can conclude that there is no “necessary” connection between inductive arguments and their conclusions. Asserting that this poses some sort of epistemic problem is a mistake, however. In other words, clarifying the definitions as we have, this conclusion follows from the premises, but it does not tell us anything important. The sense in which we mean “necessary” to establish this conclusion is much connected to the sense in which we used “justified” above: it produces a conclusion that sounds scary because of what we associate with the words in it, but can only establish its conclusion by redefining those words in a way that makes the conclusion ineffective.

Naturally, a defender of induction would be impelled to ask “why is the assumption that the future will be like the past unfounded? ”; but note that we are returning to the justificatory dilemma once again. In the dilemma, Hume has ruled out induction justifying induction, on the basis that it is a circular argument. But Hume must find circular arguments unacceptable for some reason: specifically, because of deductive logic. We know from this that the only way to “justify” anything, as the word is used in the argument, is to find a deductive argument for it. So it is evident that understanding the exact implications of accepting the notion of necessity as it arises in deductive logic as our standard for justifiability will help us understand why the conclusion that there is no “necessary” connection between inductive arguments and their conclusions is not important. In fact, we will now show how using deductive logic as a standard of justifiability (in this context) renders the argument against induction useless.

Much like the concept of infinitude, the concept of necessity has no direct referent in our sense experience. Because we have implicitly rejected an a priori account for it, we can only say that the notion of necessity is an effect of our repeat experiences and interactions with the world which represents an effective certitude with which we expect some association to hold. We say that by necessity, the sun rising in the east is associated with morning, but this is an expression of an effective certainty than a certainty so as to assert our omniscience; we simply have little incentive to mention the remaining logical possibility that the sun might not rise in the east. Hume’s account of necessity is the same:

Upon this head I repeat what I have often had occasion to observe, that as we have no idea, that is not deriv’d from an impression, we must find some impression, that gives rise to this idea of necessity, if we assert we have really such an idea. In order to this I consider, in what objects necessity is commonly suppos’d to lie; and finding that it is always ascrib’d to causes and effects, I turn my eye to two objects suppos’d to be plac’d in that relation; and examine them in all the situations, of which they are susceptible. I immediately perceive, that they are contiguous in time and place, and that the object we call cause precedes the other we call effect. In no one instance can I go any farther, nor is it possible for me to discover any third relation betwixt these objects. I therefore enlarge my view to comprehend several instances; where I find like objects always existing in like relations of contiguity and succession.

Clearly, Hume adheres to our view that the epistemic origins of an idea must reside in sense-experiences (“impressions”). Though he was speaking about causal necessity in this passage, his reasoning ensures that he accepts that our idea of deductive logic is also the consequence of a series of impressions.

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