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

January 11th, 2009

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A standard Wittgensteinian response to philosophical problems is that they are reducible to mere linguistic puzzles. Since the origins of the so-called problem of induction lie in David Hume’s Treatise of Human Nature (1740), we might naively expect an inimical view to Hume from a Wittgensteinian standpoint. However, given Hume’s general spirit of philosophy elsewhere, Hume’s empiricism, from the Wittgensteinian standpoint, is at least very robust and sensible. So much ground is shared between these two grand thinkers, that to criticize Hume for his shortcomings is to be unfairly anachronistic toward the first philosopher to truly shatter the grandiose illusions of traditional philosophy. Further, these illusions were the very same ones which Wittgenstein would later come and elegantly but almost perplexingly smash further. Yet, not only must we afford Hume respect and credit for his ideas relative his place in time, as we often do with other philosophical giants, but we must still contend with his ideas in a very real sense in the present. In fact, the ground we will share here with Hume is indeed so great that an effective critique of Hume on any epistemic issue—like problem of induction—does not come easily, and we can only accomplish it with careful precision. –more–>The problem of induction can be characterized as having two sides: the epistemological problem, which is how to distinguish between good and bad inductive methods, and the metaphysical problem, which is how to altogether distinguish between good and bad inductions. [1] On the Wittgensteinian view put forward here, we will offer agreement with Hume’s response to the epistemological problem. However, the epistemological response is only possible when predicated upon some idea of a good induction—before we can determine reliability, which is a tabulation of frequency of “successes,” we must first determine what we mean by “success. ” Fundamentally, the question of good and bad inductions is what underlies the real crux of an attack on induction: in most cases, how we might traditionally define truth (particularly in a realist fashion) is going to lead to a susceptibility of our inductions to skeptical objection. Indeed, some have been inclined to, in accepting Hume’s arguments on induction, concede that the metaphysical problem of induction is insoluble. [2] Given their criteria for truth and falsehood, this is not surprising.

First, by investigating the terms used in Hume’s argument—particularly “necessity”—we will show how the argument against induction must presuppose induction to succeed. Then, by clarifying our picture of truth, we will argue that the metaphysical problem is in one sense irrelevant to our own position, but show a sense in which we do account for how good inductions are separated from bad inductions. Before proceeding into our arguments, however, we must explain Hume’s arguments against induction.

Hume on the Problem of Induction[3]

In Book I, Part III of the Treatise of Human Nature (1740), Hume formulated what would come to be known as the problem of induction so commandingly—especially for his time—that the problem is also accordingly named “Hume’s Problem. ” While the contemporary terminology of induction does not enter his discussion, Hume’s primary concern in Part III was with notions of causality and causal inference.

Because we have no impression of the relation of causation, Hume seeks to alternatively couch causation in terms of human thought, and hence defines a “cause” like so: “An object precedent and contiguous to another, and where all the objects resembling the former are plac’d in like relations of precedency and contiguity to those objects that resemble the latter. ” He provides several definitions in the course of his work, but this adequately characterizes his general notion of causation.

Hume distinguishes causal belief from causal inference, the latter of which is only the anticipation of similar conjunctions between a precedent and some state from past conjunctions when the precedent is observed. Causal beliefs, on the other hand, are of the form “[Precedent] X causes Y,” which comes about from reflection on causal inferences. Hume’s framing of the problem of induction, implicitly through his discussion about causation, then, is as follows: in trying to find an account for good or reliable inductions, if we take the statement “all past experiences of X have also been Y” to be a statement of causation, then adding “t is X” to it should yield the good induction “t, not yet observed, is also Y. ” However, since causality is not an objective feature of the world, this is not a possibility. The Humean problem, then, is to adjudicate among inductive habits in the absence of any objective distinction like causality, broken down into the epistemological and metaphysical parts described in the introduction. Broadly speaking, Hume’s point is that judgments about future or otherwise unknown instances are problematic, because such judgments are neither a report of an experience, nor a logical consequence of prior experience. This leaves an uncertain space in which we have multiple means of making those judgments that yield different results, but must find a way of choosing the best one (the epistemological problem). Further, we must define “best” in this context (the metaphysical problem).

Some have suggested that Hume has set induction up for failure by making induction far too stringent in suggesting that it proceeds from the premises “All observed Fs have also been Gs” and “a is an F” to the conclusion “a, not yet observed, is also a G. ” Instead, they contend that the proper conclusion is “it is therefore probable that a, not yet observed, is also a G. ”[4] Hume’s response is simple enough: probabilistic connections are no different from causal connections in that they are not to be found in our experience of the world, but they depend on habits of the mind. Thus, while we can complicate matters more by incorporating probability, the same problem remains.

Generally, Hume puts forward the following dilemma to demonstrate the impossibility of justifying any sort of induction. Given that any justification must be either deductive or inductive, deductive conclusions (which are necessarily true) can not justify inductive conclusions (which are never necessarily true). On the other horn of the dilemma, inductive justification of induction would be circular, since it uses the very principle it sets out to defend. Thus, it is clear that by this reasoning, induction is unjustifiable.

Hume qualifies this conclusion by saying that we may review our inferences and reflect upon their reliability, forming a hierarchy of meta-level inductions—specifically, a chain of inductions about inductions about inductions and so on. Reflecting on these inductions in sequence progressively increases our uncertainty ad infinitum, leading Hume to ask how we “retain a degree of belief, which is sufficient for our purpose, either in philosophy or in common life? [5] Hume’s answer, in short, is to propose two general epistemic rule types: those that lead us to singular predictive inferences (in other words, our basic inductive methodology), and those that we apply as corrective or qualificatory measures toward the products of rules of the first type. The former could be described as some system of sorting out confirming and disconfirming instances, and the establishment of a threshold of evidence at which we accept or reject an inference.

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