The principle of induction, the capacity for knowledge of the universal based on knowledge of the particular, was identified as a major philosophical impasse since Antiquity (Sextus Empiricus). Its significance was reaffirmed, most notably, by David Hume (1739), but later rejected by Karl Popper (1979) as not a genuine epistemological concern. In this article I argue that induction is a valid epistemological procedure and is indispensable to practical reasoning.
“For, when they propose to establish the universal from the particulars by means of induction, they will effect this by a review either of all or of some of the particular instances. But if they review some, the induction will be insecure, since some of the particulars omitted in the induction may contravene the universal; while if they are to review all, they will be toiling at the impossible, since the particulars are infinite and indefinite. Thus on both grounds, as I think, the consequence is that induction is invalidated.” (Empiricus 1990, Book II Chapter XV) “Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure.” (Popper 1965, 53)
The problem of induction is usually expressed as follows: ‘Considering that the Sun had risen every morning for as long as anyone can remember, is it possible to prove that it will rise again tomorrow?’ Hume argued that despite apparent obviousness of the expected outcome a proof is not possible, because no finite number of evidentiary cases can give a non-zero probability of prediction if there is an infinite number of cases yet possible, but that does not mean that in this particular case a rational proof does not obtain. The Sun must rise tomorrow, because that is what tomorrow means: the concept of tomorrow is defined by the Sun rising and then setting, and if the Sun would not rise, there would be no tomorrow. The Sun rising tomorrow is a definitional certainty, an implicit tautology, but a tautology is not a valid epistemological theorem. The concepts of sunrise, morning and tomorrow are definitionally entangled and therefore not meaningful as isolated events. The example is indeed unfalsifiable and therefore not epistemological in the sense examined by Popper (1979).
Tye (2006) engages in a similar argument: “Suppose a certain rock R is dropped. Will it fall to the earth? Of course, it will.” The definitional relationship between the terms ‘drop’ and ‘fall’ is logically circular: it would be logically fallacious to entertain the possibility of something being dropped but not falling, because the meaning of dropping (not just releasing) already implies (or is synonymous with) the consequence of falling. Tye then argues that “even though it is nomologically necessary that if R is dropped, then it falls, still it is conceptually possible that it does not do so. (…) After all (…) we can imagine the rock, R, floating in the air or moving away from the earth.” But now Tye conflates the conceptual necessity associated with the former definitional context with a conceptual possibility in an augmented definitional context. It is certainly both conceptually and physically possible for the rock to be released and then float or move away from the earth if it is subject to forces other than the Earth’s gravity, but in the latter definitional context the initial exclamation that ‘the rock must fall if dropped’ is false. The original conclusion, in its own definitional context, remains both nomologically and conceptually necessary.
Inductive reasoning can be both nomologically and conceptually true iff the implied ontological commitments are consistent and existentially indispensable: X is always true, because if X was ever untrue, the world as we know it would not be. In that context the problem is not strictly epistemological but instead gains validity as an ontological constant. It could be objected that perhaps the real world is not ‘as we know it’, but this begs the question how could we possibly act in a world without acting on the grounds of what we think the world is like: “If you say these are not grounds, then you must surely be able to state what must be the case for us to have the right to say that there are grounds for our assumption…” (Wittgenstein 1953, 481)
While some cases of induction can be defended on the basis of nomological or conceptual necessity, my primary analytical target is induction about possibilities that are not existentially indispensable. Whenever we act on a reason we do so in consideration of what we know about the effects of past actions and the observed interactions between objects. We can plan how to get what we want out of action only by assuming that some kind of action that has worked in the past will work the same way in the same circumstances in the future. Induction is therefore indispensable to practical reasoning and, by implication, to agency: we must reason inductively to function in the world. The fact that provability is unachievable for future phenomena is a moot point since what we get at the experiential level is not re-occurrence of the same phenomena but new occurrences of something similar. The phenomenological relation of similarity is retrospective as well as prospective; it is an idealisation that admits of both repetition and induction but only in the realm of categories.
“The repetition is in fact a mental construction, which eliminates from each occurrence everything belonging to it that is peculiar to itself, in order to preserve only what it shares with all the others of the same class, which is an abstraction: the sun, the morning, to rise.” (Genette 1980, 113)
In other words, repetition is not a phenomenon in its own right but presupposition of abstract categories within which all elements or instances are only qualitatively the same. “Imaginary repetition is not a false repetition which stands in for the absent true repetition: true repetition takes place in imagination.” (Deleuze 1994, 76. Cf. Hume 1739, 1.3.6.12) Consequently, the problem of induction is both ontological, about the conditions of being similar or of-the-same-kind, and transcendental – induction is indispensable to practical reasoning even if it fails to accurately predict future phenomena. When consistent inductive reasoning fails, it changes the nomological structure of the world as we know it. This constitutes a genuine epistemological problem whose object is not phenomena but the laws according to which phenomena are related. It is indispensable to practical reasoning to assume that the laws that appeared to hold in the past will hold in the future, or they are not laws. Inductive reasoning need not be limited to (ideal) repetition but may follow any set of rules according to which different phenomena are causally, constitutively or temporally related.
- Deleuze, Gilles. Difference & Repetition. New York: Columbia University Press, 1994.
- Empiricus, Sextus. Outlines of Pyrrhonism. New York: Prometheus Books, 1990.
- Genette, Gerard. Narrative Discourse. Ithaca: Cornell University Press, 1980.
- Hume, David. A Treatise of Human Nature. Oxford: Oxford University Press, 1739.
- Hume, David. An Enquiry Concerning Human Understanding. Oxford: Oxford University Press, 1748.
- Popper, Karl R. Conjectures and Refutations. Oxford: Oxford University Press, 1979.
- Popper, Karl R. Objective Knowledge. London: Routeledge & Kegan Paul, 1965.
- Tye, Michael. “Absent Qualia and the Mind-Body Problem.” The Philosophical Review, 2006.
- Wittgenstein, Ludwig. Philosophical Investigation. New Jersey: Prentice Hall, 1953.
“Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure.”
This seems jarringly wrong. I am curious to know Popper’s line of reasoning.