Editing Problem of induction (section)

===Ancient and early modern origins===

====Pyrrhonism====
{{Pyrrhonism sidebar}} 
The works of the [[Pyrrhonism|Pyrrhonist]] philosopher [[Sextus Empiricus]] contain the oldest surviving questioning of the validity of inductive reasoning. He wrote:<ref>Sextus Empiricus. ''Outlines of Pyrrhonism'', Book II, Chapter 15 Section 204 trans. Robert Gregg Bury (Loeb ed.) (London: W. Heinemann, 1933), p. 283.</ref>
{{quote|It is also easy, I consider, to set aside the method of induction. 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.}}

The focus upon the gap between the premises and conclusion present in the above passage appears different from Hume's focus upon the [[circular reasoning]] of induction. However, Weintraub claims in ''[[The Philosophical Quarterly]]''<ref>Weintraub, R. (1995). What was Hume's Contribution to the Problem of Induction? The Philosophical Quarterly 45(181):460–470.</ref> that although Sextus's approach to the problem appears different, Hume's approach was actually an application of another argument raised by Sextus:<ref>Sextus Empiricus. ''Against the Logicians'', trans. Robert Gregg Bury (Loeb ed.) (London: W. Heinemann, 1935), p. 179.</ref>
{{quote|Those who claim for themselves to judge the truth are bound to possess a [[criterion of truth]]. This criterion, then, either is without a judge's approval or has been approved. But if it is without approval, whence comes it that it is truthworthy? For no matter of dispute is to be trusted without judging. And, if it has been approved, that which approves it, in turn, either has been approved or has not been approved, and so on ''[[Regress argument|ad infinitum]]''.}}

Although the [[regress argument|criterion argument]] applies to both deduction and induction, Weintraub believes that Sextus's argument "is precisely the strategy Hume invokes against induction: it cannot be justified, because the purported justification, being inductive, is circular." She concludes that "Hume's most important legacy is the supposition that the justification of induction is not analogous to that of deduction." She ends with a discussion of Hume's implicit sanction of the validity of deduction, which Hume describes as intuitive in a manner analogous to modern [[foundationalism]].

====Indian philosophy====
The [[Cārvāka]], a materialist and skeptic school of Indian philosophy, used the problem of induction to point out the flaws in using inference as a way to gain valid knowledge. They held that since inference needed an invariable connection between the middle term and the predicate, and further, that since there was no way to establish this invariable connection, that the efficacy of inference as a means of valid knowledge could never be stated.<ref>Dr. S. Radhakrishnan, ''Indian Philosophy'' Vol I, p. 279.</ref><ref>S. Dasgupta, ''A history of Indian philosophy'', Vol III. p. 533.</ref>

The 9th century Indian skeptic, [[Jayarāśi Bhaṭṭa|Jayarasi Bhatta]], also made an attack on inference, along with all means of knowledge, and showed by a type of reductio argument that there was no way to conclude universal relations from the observation of particular instances.<ref>Piotr Balcerowicz, [http://plato.stanford.edu/entries/jayaraasi/ "Jayarāśi"].</ref><ref>Franco, Eli, 1987, ''Perception, Knowledge and Disbelief: A Study of Jayarāśi's Scepticism.''</ref>

====Medieval philosophy====
Medieval writers such as [[al-Ghazali]] and [[William of Ockham]] connected the problem with God's absolute power, asking how we can be certain that the world will continue behaving as expected when God could at any moment miraculously cause the opposite.<ref>Franklin, J. (2001), ''The Science of Conjecture: Evidence and Probability Before Pascal'' (Baltimore: Johns Hopkins University Press), 232–233, 241.</ref> [[Duns Scotus]], however, argued that inductive inference from a finite number of particulars to a universal generalization was justified by "a proposition reposing in the soul, 'Whatever occurs in a great many instances by a cause that is not free, is the natural effect of that cause.{{'"}}<ref>''Duns Scotus: Philosophical Writings'', trans. A. Wolter (Edinburgh: 1962), 109–110; Franklin, ''Science of Conjecture'', 206.</ref> Some 17th-century [[Jesuits]] argued that although God could create the end of the world at any moment, it was necessarily a rare event and hence our confidence that it would not happen very soon was largely justified.<ref>Franklin, ''Science of Conjecture'', 223–224.</ref>