Problem of induction

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The problem of induction is the philosophical issue involved in deciding the place of induction in determining empirical truth. The problem of induction is whether inductive reason works. That is, what is the justification for either:

generalizing about the properties of a class of objects based on some number of observations of particular instances of that class of objects (for example, "All swans we have seen are white, and therefore all swans are white", Hume's Problem of Induction, 18th century, before the discovery of Cygnus atratus in Australia); or
presupposing that a sequence of events in the future will occur as it always has in the past (for example, the attractive force described by Isaac Newton's law of universal gravitation, or Albert Einstein's revision in general relativity).

A problem with the above statement describing the Problem of Induction is that it incorporates the term 'inductive reason'. Aristotle was first to establish the mental process of induction as a class of reasoning. If inductive concept formation is not a type of reasoning, but a distinct mental process, then asking if it is rational is a slightly different question.

[edit] Statements of the problem

A better way to state the problem is "is it rational to form inductive concepts", or, does it make sense to generalize from limited experience. See further discussion/proposed solution.

Francis Bacon, Isaac Newton, and numerous others up until at least the late 19th century have considered inductive reasoning the basis of scientific method—indeed inductive reasoning is used today, though in a more balanced interaction with deductive reasoning and abductive reasoning. By the inductive approach to scientific method, one makes a series of observations and forms a universal generalization. If correct and stated in a sufficiently accurate way, an inductively arrived-at statement relieves others of the need for making so many observations and allows them to instead use the generalization to predict what will happen in specific circumstances in the future. So, for instance, from any series of observations that water freezes at 0°C at sea-level it is valid to infer that the next sample of water will do the same--but only if induction works. That such a prediction comes true when tried merely adds to the series; it does not establish the reliability of induction, except inductively. The problem is, then, what justification can there be for making such an inference?

David Hume framed the problem in An Enquiry Concerning Human Understanding, §§4.1.20-27, §§4.2.28-33^[1]. Among his arguments, Hume asserted there is no logical necessity that the future will resemble the past. Justifying induction on the grounds that it has worked in the past, then, begs the question. It is using inductive reasoning to justify induction, and as such is a circular argument. This logical positivist formulation of the problem would prove to be a tenacious counterargument to the use of inductive propositions. Further, even the largest series of observations consistent with a universal generalization can be logically negated by just one observation in which it is false. By Hume's arguments, there also is no strictly logical basis for belief in the Principle of the Uniformity of Nature. Notably, Hume's stated position on the issue was that instead of unproductive radical skepticism about everything, he actually was advocating a practical skepticism based on common sense, where the inevitability of induction is accepted (but not explained). Hume noted that someone who insisted on sound deductive justifications for everything would starve to death, in that they would not, for example, assume that based on previous observations of, e.g., what time of year to plant seeds, or who has bread for sale, even that bread previously nourished them and others, that these inductions would likely continue to hold true. Hume nonetheless left a lasting legacy by showing that there is no absolute certainty to any induction, even those inductions for which a contrary has never been observed. Bertrand Russell elaborated and confirmed Hume's analysis in his 1912 work, The Problems of Philosophy, chapter 6.^[2] (see also: logical positivism)

Karl Popper, an influential philosopher of science, sought to resolve the problem in the context of the scientific method, in part by arguing that science does not primarily rely on induction, but rather primarily upon deduction, in effect making modus tollens the centerpiece of his theory. On this account, when assessing a theory, one should pay greater heed to data which is in disagreement with the theory than to data which is in agreement with it. Popper went further and stated that a hypothesis which does not allow for experimental tests of falsity is outside the bounds of science. However, critics of Popper's approach to solving the problem, such as the famous utilitarian and animal rights advocate Peter Singer, argue that Popper is merely obscuring the role induction plays in science by concealing it in the step of falsification. In that, they mean that the proposition of something having been falsified is in and of itself a scientific theory and can only be assumed to be definitive through induction; no matter how many times a proposition is demonstrated to be accurate, when taken as a strict matter of logic it cannot necessarily be assumed that the proposition will always be accurate under the same circumstances. For this reason, among others, contemporary scientific research tends to regard hypotheses and theories as tentative, validated in terms of degrees of confidence rather than true/false propositions.

Nelson Goodman presented a different description of the problem of induction in the article "The New Problem of Induction" (1966). Goodman proposed a new predicate, "grue". Something is grue if it has been observed to be green before a given time t, or if it is has been observed to be blue thereafter. The "new" problem of induction is, since all emeralds we have ever seen are both green and grue, why do we suppose that after time t we will find green but not grue emeralds? The standard scientific response is to invoke Occam's razor.

Goodman, however, points out that the predicate "grue" only appears more complex than the predicate "green" because we have defined grue in terms of blue and green. If we had always been brought up to think in terms of "grue" and "bleen" (where bleen is blue before time t, or green thereafter), we would intuitively consider "green" to be a crazy and complicated predicate. Goodman believed that which scientific hypotheses we favour depend on which predicates are "entrenched" in our language.

W.V.O. Quine offers the most practicable solution to the problem by making the metaphysical claim that only predicates which identify a "natural kind" (i.e. a real property of real things) can be legitimately used in a scientific hypothesis.

[edit] Proposed solutions

When using induction, we modify our expectations of the future by noting how we have been wrong in the past. Thus, induction is not circular but regressive or hierarchical: induction converges on good solutions.

To induce facts from the past is part of what we mean when we talk about "reason" (we also are refering to deduction, a distinct mental process). It's meaningless to discuss whether we should "reasonably" trust induction: induction is part of what reason is all about.