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I'm curious whether the following proposed solution to the problem of induction has ever been discussed in the literature:

Either the future resembles the past or it does not resemble the past. If it does not resemble the past, then all predictions about the future are equally reasonable. If the future does resemble the past, then it is logical to make predictions based on the assumption that the future resembles the past. Hence, the most reasonable prediction always assumes that the future resembles the past, since this prediction is optimal in both situations.

Are there any good critiques of this proposed solution?

Added: Notice that this solution does not claim that the future resembles the past. It only claims that the optimal procedure for predicting the future is based on the assumption that the future resembles the past.

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    I've come across similar ideas a number of times, but I wouldn't say that it's a solution to the problem of induction because the problematic part of induction is that it depends on an assumption that can never be proven. We observe that there is a predictable orderliness, but science cannot tell us that it must be that way or that it is always that way without exception. – user3017 Dec 7 '16 at 9:00
  • Then it is reasonable to assume that every time you flip a coin, you should get the same side, by choosing a single point in the past on which to base your predictions of the future... Or you can apply something like Laplace's "rule of succession". But statistically this is not very stable: it implies an ever-decreasing, but nonzero chance the sun will just not come up tomorrow, and that the overall temperature of the planet should not change when that happens (because it has not changed before). Basically, yes, if it were that easy, we would not still consider it an open question. – jobermark Dec 7 '16 at 17:29
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Not all inductive inferences are temporal, so the future "resembling" the past can be moot, a more general idea would be that various parts of nature are "uniform", "resemble" each other. But it is not logical to assume that the future will "resemble" the past, or that the nature is "uniform" in this or that aspect. In many cases such assumptions are blatantly unreasonable and contrary to fact, and much better predictions can be made by assuming the opposite, change and non-uniformity. The trick is to tell which is when, that is the real problem of induction. As outlined by Hume and elaborated by Mill the problem is basically that there is no justification for performing inductions: deductive justifications upend the "inductiveness", and inductive justifications are either circular (if there are finitely many types of induction) or lead to infinite regress (if there are infinitely many). Norton's Material Theory of Induction has a nice review of the current state of the issue.

A famous example discussed by Mill concerned the contrast between inductive validity of "some samples of bismuth melt at 271°C, therefore all of them do" and invalidity of "some samples of wax melt at 91°C, therefore all of them do". Mill was so impressed by it that he wrote in his System of Logic:"Whoever can answer this question knows more of the philosophy of logic than the wisest of the ancients and has solved the problem of induction". It was Mill, who replaced Hume's "custom" with the oft-quoted "axiom of the uniformity of the course of nature", but the melting example demonstrates how "uniformity of nature" is not a solution, but part of the problem. Because the "uniformity" is itself "non-uniform". Norton explains:

"For example, we might require that enumerative induction can only be carried out on A’s that belong to a uniform totality. But without being able to mention particular facts about bismuth and wax, how are we to state a general condition that gives a viable, independent meaning to ‘‘uniform’’? We are reduced to the circularity of making them synonyms for ‘‘properties for which the enumerative induction schema works’’.

[...] All these efforts fall to the problem already seen, an irresolvable tension between universality and successful functioning... if they are general enough to be universal and still true, the axioms or principles become vague, vacuous, or circular. A principle of uniformity must limit the extent of the uniformity posited. For the world is simply not uniform in all but a few specially selected aspects and those uniformities are generally distinguished as laws of nature.

We can argue in broad generalities that "if the nature is not uniform we are in trouble anyway so we might as well optimistically assume it uniform", and even throw in the anthropic principle for good measure ("in universes with non-uniform natures no intelligent creatures can exist"), but it does not provide what a justification must: when it is supposed to work. So at best it is a vague methodological maxim.


P.S. There are many proposals to solve the problem of induction (abductive, Bayesian, Norton's own material one, etc.), but perhaps the best known is Popper's "dissolution" of it. Induction, what induction? Popper's solution to the problem of induction is that there is no induction. What is attributed to induction, according to him, is really a guess followed by a hypothetic deduction of consequences and their corroboration or falsification. Often the guessing is so instinctive and the deduction so trivial (as in say "all crows are black") that we collapse it into undivided "induction". While Popper may have "solved" the problem to his satisfaction, his critics, Norton included, contend that he merely pushed it elsewhere. Because it is unclear what would "justify" entertaining and testing these hypotheses as opposed to infinite others, other than... induction:

"Popper’s account simply fails to bear close enough resemblance to scientific practice if corroboration does not contain a license for belief, with better corroboration yielding a stronger license (see Salmon 1981). Popper does not give much account of the details of the method. The process of conceiving the new hypothesis is explicitly relegated to psychology and the inclination to take any philosophical interest in it disavowed as ‘‘psychologism’’ (31– 32). So we have only our confidence in the scientist’s creative powers to assure us that the new hypothesis does not introduce more problems than it solves."

Norton himself looks for solution by localizing induction schemas to specific material domains, where they are licensed by "material facts". This resolves the universality vs functioning dilemma in favor of functioning, but he himself admits that it still creates a regress of "material facts" with unclear prospects of termination. It looks like the problem of induction will remain with us for the foreseeable future.

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Either the future resembles the past or it does not resemble the past. If it does not resemble the past, then all predictions about the future are equally reasonable. If the future does resemble the past, then it is logical to make predictions based on the assumption that the future resembles the past. Hence, the most reasonable prediction always assumes that the future resembles the past, since this prediction is optimal in both situations.

The assumption "If it does not resemble the past, then all predictions about the future are equally reasonable" seems shaky. Consider the following alternative, which may be termed reverse induction.

Either the future is the opposite of the past or it is not the opposite of the past. If it is not the opposite of the past, then all predictions about the future are equally reasonable. If the future is the opposite of the past, then it is logical to make predictions based on the assumption that the future is the opposite of the past. Hence, the most reasonable prediction always assumes that the future is the opposite of the past, since this prediction is optimal in both situations.

Hence the same logic that is supposed to justify induction, would justify reverse induction just as well: always assume that the future is the opposite of the past.

  • That's exactly the type of critique I was looking for. Now a question: What does it mean when you said the future is opposite of the past? – Craig Feinstein Dec 8 '16 at 19:25
  • For instance, if X happens in the past and the future is always opposite of the past, then not X must happen in the future. But then after not X happens, it is the past, so its opposite X must happen again. Thus, we get a pattern, X, not X, X, not X,... which means that the future will resemble the past, a contradiction. So "future is always opposite the past" is problematic. – Craig Feinstein Dec 8 '16 at 21:00
  • @CraigFeinstein You're right, it has to given more specific formulations to be univocal. For example, considering a series of coin flips, one can suggest that it is optimal to assume that the next coin flip result will always be the opposite from the last coin flip. – Ram Tobolski Dec 8 '16 at 21:26
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    But then the future would resemble the past, since it would always be heads, tails, heads, tails, etc. – Craig Feinstein Dec 9 '16 at 3:32
  • @CraigFeinstein So what? The future will resemble the past in some aspects, and not resemble it in other aspects. The word "resemble" is too ambiguous. – Ram Tobolski Dec 9 '16 at 9:38
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Either the future resembles the past or it does not resemble the past. If it does not resemble the past, then all predictions about the future are equally reasonable. If the future does resemble the past, then it is logical to make predictions based on the assumption that the future resembles the past. Hence, the most reasonable prediction always assumes that the future resembles the past, since this prediction is optimal in both situations.

The idea that the future resembles the past doesn't entail anything specific about the future because it doesn't say in what respects the future resembles the past. As such, this idea is irrelevant to the actions you should take to discover anything about how the world works.

The problem of induction was solved by Karl Popper, who recognised that induction is impossible and is unnecessary for making progress. You create knowledge by noticing problems with your current theories, guessing solutions to the problem and criticising the guesses until only one is left. Then you move on a new problem. See "Objective Knowledge" by Popper, Chapter 1, "Realism and the Aim of Science" by Popper Introduction and Chapter I, "The Fabric of Reality" by David Deutsch Chapters 3 and 7 and "The Beginning of Infinity" by David Deutsch Chapter 1,2,4,10,13,15,16.

  • Is there a relationship between "doesn't say what aspects..." and the under determination of scientific theories? – Dave Dec 7 '16 at 15:33
  • Experimental results don't determine what scientific theories should be invented to explain them: that's under determination. The future resembles the past doesn't entail anything specific is one of the reasons for under determination. But this alone lets induction off too lightly since scientific theories are accounts of how the world works, not just instruments for making predictions, so predictions are not all of the useful content of a scientific theory. For example, a person thinking about a theory may find new problems that can lead to more progress. – alanf Dec 7 '16 at 16:26
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    I don't understand how this answers my question. The idea that the future resembles the past was called by Hume the "uniformity of nature", according to Wikipedia. The fact that this idea doesn't say anything specific about the future doesn't mean that it is "irrelevant to the actions that one should take to discover anything about how the world works". – Craig Feinstein Dec 7 '16 at 16:37
  • The idea that the future resembles the past is irrelevant. For example, I could say the future resembles the past in the sense that we won't understand any more in the future than we did in the past, so we shouldn't try to understand anything and all scientific research should be banned as a useless waste of time and resources. – alanf Dec 8 '16 at 9:26
  • The future resembles the past is also far more limited than what we can understand from physics. There are universal laws of physics that apply at all times and places. It is possible to construct universal computers that can simulate any finite physical object: the Turing principle. But none of this is remotely useful for saving inductivism since inductivism requires starting with data and proving stuff.Popper's epistemology doesn't have that defect. – alanf Dec 8 '16 at 9:43
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The philosopher Hans Reichenbach came up with this idea, which is called the "pragmatic justification for induction".

Numerous criticisms can be levelled at Reichenbach’s answer to the problem. The fatal weakness with a pragmatic justification of induction, however, is just that it is a pragmatic justification and not an epistemic justification. That is, while it may motivate us to employ a certain strategy (to reason inductively), it gives us no indication of the actual likelihood of its success (i.e., whether the inductive principle is true). In this respect, it suffers from the same ailment as Pascal’s Wager (which may offer motivation for believing in God, but leaves us none the wiser as to whether He actually exists). A true solution to the problem of induction requires an epistemic justification — a reason for believing that induction is reliable — yet Reichenbach’s solution, for all its ingenuity, offers no such thing.

Laurence BonJour, In Defense of Pure Reason (Cambridge: Cambridge University Press, 1998), pp 192-6.

  • Thanks for elaborating your answer! Perhaps you know this already, but you can click the check mark next to an answer to mark it as accepted. – Keelan Jan 26 '17 at 16:54

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