Philpropsophy – Philosophy Articles and Article Summaries

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.

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. 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. So, given that, we have actually gone ahead and strengthened Hume’s justificatory dilemma by turning it into just a lemma: the option of justifying induction deductively is nonsensical for reasons that prevent us from even admitting it into our discussion. To justify using deduction, we must first justify induction.

Hence, the conclusion of the argument that constitutes the problem of induction, that we are not “justified” in believing the conclusion of inductive arguments, is itself dependent on an inductive argument. Here, we have reached the skeptical error of externalizing logic, which creates arguments more paradoxical than unimportant on this account. If the logical possibility that things could be some other way than we believe them is used to undermine all of our beliefs, then no beliefs undermined in this way can be believed while constructing logical possibilities. But the construction of logical possibilities is only possible given the inductive process that creates our idea of necessity. Further, we cannot sensibly falsify (or take any other action standing outside of) logic, since we can not describe what a non-logical world would look like.[7] Yet this is precisely what, by implication, skepticism requires by questioning our foundations for logic, which are the very experiences and thus inferences from experience that they challenge.

Because Hume does not want to make extra-sensory assertions at all, he is then also committed to holding to this account for the very logical principles he uses to criticize inductive statements. Thus, we have established that the argument attempting to establish that induction is problematic implicitly must assert what it intends to disprove. By showing how we can not use deductive necessity as a criteria for justification (at the epistemic level), we have eliminated the standard by which induction is considered to be problematic. More generally, we have implied that some coordination of repeat sense impressions is the only means we have of generating any criteria of justification. And we can properly call such coordination “induction,” as it is indeed in what “the problem of induction” purports to show defect. By this, we have shown how the general argument against induction fails.

More clarification of the unproblematic nature of induction is still worthwhile, nonetheless. For one, we are still pressed with the question of importance of skeptical arguments such as the argument against induction, as suggested earlier. If the lack of necessity of inductive conclusions prevents us from attaining omniscience—an immunity of our theories to subsequent falsifying events—and can validly offer no prescriptive changes in our behavior, there seems to be no value in pointing it out. It is part of the unavoidable limits of our world. We can label this state as our being “unjustified” in believing inductive conclusions, but what have we changed by doing so? We could easily say a belief is unjustifiable when it does not reduce its conclusions to the properties of cheese. We must ask, “Unjustified relative to what?” The word must be put in some context to have any implications. Saying that we are “unjustified” because we can not look beyond the limits of our world—a precise lack of context—can not have any condemning epistemic implications, for the simple reason that there is no prescription that could ever conceivably change it! To speak meaningfully about “justification,” then, we must affix it to some sensory phenomena to which we can appeal to differentiate among the justified and the unjustified. In this regard, there is still a sense in which we have “justification”; in Humean terms, that sense is predicated on the notion that some inductions are more reliable than others.

Finding out how to distinguish the reliability of different inductive methods is the epistemological component of the problem of induction. More or less, Hume’s response to this part of the problem works quite well: Hume’s intuition that induction about induction begins to yield how we separate good inductive habits from bad ones is straightforward enough. We look at different inductive methods applied over time, and see how often each method produced a good induction. From this, we discern the reliability of different methods.

It is in reference to the so-called metaphysical problem of induction that we can offer more clarity regarding the validity of induction. Certainly, the metaphysical problem, if unanswered, leaves the epistemological problem insoluble as well: after all, we do need some account for what is a “good” versus “bad” induction in order to determine which inductive methods are more reliable than others. Yet, having tossed out criteria for “good” and “bad” such as “corresponding with the external world,” the answer is quite simple: there is no metaphysical problem because there is no metaphysics (at least in the relevant sense).

One posing the metaphysical problem might ask: if we only have sense experiences, what is there that could possibly provide objectivity? Indeed, what reason do we have to sort and organize different experiences to form theories? Without constraints, our sense experiences are simply floating variables from which we could construct an infinite amount of different theories with no difference in consequence. Thus, just as a 2-variable equation has infinite solutions until another equation constrains it, so too does what is “true” have infinite solutions until we affix some constraint to our interpretations. In short, our interpretation of sensory phenomena only has implications when those phenomena arise to some degree outside of our will, and we have particular goals for those phenomena. We have particular desires to bring about certain things in our sense experiences, but we can not simply will these things to come about. We wish to taste something sweet, but no amount of willing a taste of sweetness into our mouths gets us that. Ultimately, this lies against a background of what we understand to be necessary for accomplishing our goals (life) and what we understand to be the end of all accomplishment (death). Simply put, our “metaphysics” is one of life versus death.

That we can not merely will certain things to occur is a basis for objectivity in interpreting our sense experiences; our acceptance of mortality is what gives us the motive to take one interpretation over all and call it “truth,” even if only by the actions we take. 14^th-century explorers had two competing views of the earth, one saying it was flat, one saying it was round. Without fear of death or fear of a voyage done for nothing (both objective constraints), this debate would have been meaningless. After all, there are infinite logical possibilities as to why a flat-earth theory might still prevail over a round-earth. But that explorers found new lands and, after sailing in one direction long enough, wound up in the same place, and have acted on the principle of “circumnavigation” successfully up until the present, has compelled people to accept a round-earth theory over a flat one. People who have acted on this principle, other things equal, have achieved the goals they set out, and they and others will continue to act on that principle. In this sense, people have accepted the round-earth theory as truth; it was a “good” induction.

Thus, good inductions are separated from bad ones on the basis of how successfully they inform our goal-directed actions, where success is measured by the presence of a desired sense experience. By our having thrown out realism, the only case of error that can even be meaningfully considered is where some theory posited based on sense experiences is later falsified by a subsequent sense experience. On our view, this is no longer a problem with induction, of course. It is merely a case in which a particular induction has been identified as “bad” through induction.

Undoubtedly, we can be continually pressed to justify each successive answer we have given. Why shouldn’t we doubt mortality, or anything else foundational to the above discussion? Certainly, there is a point at which we can no longer give any justification, yet it is the very point from which we get our notion of justification. We do superficially agree with the skeptic that such foundational propositions lie beyond any empirical verification, but this is only because our notion of empirical verification is solely derived from these kinds of propositions. At some point, we must reach bedrock: certain beliefs “underlie all questions and thinking.”[8] Even if we imagined the most hard-core doubter telling us that we have “no reason” to believe the “biological myth” of death, he could not be using anything but human-contextual concepts in, say, appealing to our self-interest through telling us that what we believe is false and that we ought to change it. In that way, doubt is only possible with knowledge, so an all-encompassing, ‘hyperbolic’ doubt is clearly nonsensical; in even thinking of that doubt, much more communicating that doubt, we are invariably asserting things that we know.

In addition to questioning the logical feasibility of Hume’s general argument against induction, we have now also supplemented it with an answer to the fundamental question of how we separate good inductions from bad inductions. Most importantly, we have shown how a careful examination of the terms at play in the argument against induction demonstrates how it relies on a contrived sense of necessity as a criterion for justification and improperly treats this idea of necessity as standing independently of induction. In this, we showed how induction is, in fact, the basis of all criteria in evaluating the justification of our beliefs. Then, in addressing the metaphysical problem, we showed how meaningful criteria are generated against a back-drop of goal-oriented action.

With this answer to the supposed problem of induction in hand, we have a kind of argument which, when generalized, defeats skeptical arguments against empiricism. By reducing our criteria for the truth or falsehood of a proposition to its relation to strictly sensory phenomena, we have removed the possibility of skeptical error, and brought the concept of error within the boundaries of the senses: we can only be mistaken in a sense that is relative to other sense experiences. Hume, imaginably, would have appreciated this, as he did not desire to be a thoroughgoing skeptic; he only wished to fight off philosophical phantoms, much like Wittgenstein did. Again, like Wittgenstein, he sought a rational basis for our norms of speech and action, but found the answers of philosophers to be mystical and woefully deficient. Indeed, he did not see a convincing means of showing how we could justifiably believe in induction, and retreated to a seemingly resigned position of “custom and habit.” Our goal here, as was Wittgenstein’s goal, was to show how we are justified in believing in our senses, and thus induction—without resignation.

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[1] Vickers, John, “The Problem of Induction”, The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), Edward N. Zalta (ed.), forthcoming URL = <http://plato.stanford.edu/archives/win2008/entries/induction-problem/>.

[2] Ibid.

[3] Ibid. This exposition of Hume’s account of the problem is paraphrased from this source.

[4] Ibid., section 2: “Hume”

[5] Ibid., section 7: “Hume’s Dilemma Revisited”

[6] The Wikipedia entry on Philosophical Investigations explains Wittgenstein’s approach well, at http://en.wikipedia.org/wiki/Philosophical_Investigations#Method_and_presentation

[7] Tractatus, 3.031

[8] On Certainty pp. 415.