Editing Problem of induction (section)

==Notable interpretations==

===Hume===
{{See also|David Hume#Induction and causation}}
Although induction is not made by reason, Hume observes that we nonetheless perform it and improve from it. He proposes a descriptive explanation for the nature of induction in §5 of the ''Enquiry'', titled "Skeptical solution of these doubts". It is by custom or habit that one draws the inductive connection described above, and "without the influence of custom we would be entirely ignorant of every matter of fact beyond what is immediately present to the memory and senses".<ref>''Enquiry'', §5.1.</ref> The result of custom is belief, which is instinctual and much stronger than imagination alone.<ref>''Enquiry'', §5.2.</ref>

===John Maynard Keynes===
In his ''[[A Treatise on Probability|Treatise on Probability]]'', [[John Maynard Keynes]] notes:
<blockquote>An inductive argument affirms, not that a certain matter of fact is so, but that relative to certain evidence there is a probability in its favour. The validity of the induction, relative to the original evidence, is not upset, therefore, if, as a fact, the truth turns out to be otherwise.<ref>{{cite book |last1=Keynes |first1=John Maynard |title=A Treatise on Probability |date=1921 |publisher=Macmillan |location=London |url=https://archive.org/details/treatiseonprobab007528mbp/page/n9/mode/2up?view=theater |access-date=2 December 2023}}</ref></blockquote>
This approach was endorsed by [[Bertrand Russell]].<ref>{{cite book |last1=Russell |first1=Bertrand |title=Human Knowledge: Its Scope and Limits |date=1948 |publisher=George Allen and Unwin |location=London |pages=397}}</ref>

===David Stove and Donald Williams===
[[David Stove]]'s argument for induction, based on the [[statistical syllogism]], was presented in the ''Rationality of Induction'' and was developed from an argument put forward by one of Stove's heroes, the late [[Donald Cary Williams]] (formerly Professor at Harvard) in his book ''The Ground of Induction''.<ref>{{cite book | author=Donald Cary Williams | title=The Ground of Induction | location=New York | publisher=Russell and Russell | year=1947 }}, {{cite encyclopedia |url=https://plato.stanford.edu/entries/williams-dc/ |title=Donald Cary Williams |date=2015 |encyclopedia=Stanford Encyclopedia of Philosophy |access-date=4 March 2017}}
</ref> Stove argued that it is a statistical truth that the great majority of the possible subsets of specified size (as long as this size is not too small) are similar to the larger population to which they belong. For example, the majority of the subsets which contain 3000 ravens which you can form from the raven population are similar to the population itself (and this applies no matter how large the raven population is, as long as it is not infinite). Consequently, Stove argued that if you find yourself with such a subset then the chances are that this subset is one of the ones that are similar to the population, and so you are justified in concluding that it is likely that this subset "matches" the population reasonably closely. The situation would be analogous to drawing a ball out of a barrel of balls, 99% of which are red. In such a case you have a 99% chance of drawing a red ball. Similarly, when getting a sample of ravens the probability is very high that the sample is one of the matching or "representative" ones. So as long as you have no reason to think that your sample is an unrepresentative one, you are justified in thinking that probably (although not certainly) that it is.<ref>D. Stove, ''The Rationality of Induction'', Clarendon Press, Oxford, 1986, ch. 6.</ref>

===Biting the bullet: Keith Campbell and Claudio Costa===
An intuitive answer to Hume would be to say that a world inaccessible to any inductive procedure would simply not be conceivable. This intuition was taken into account by [[Keith Campbell (philosopher)|Keith Campbell]] by considering that, to be built, a concept must be reapplied, which demands a certain continuity in its object of application and consequently some openness to induction.<ref>"One form of Skepticism about Induction", in Richard Swinburne (ed.) ''The Justification of the Induction''. Oxford, Oxford University Press, 1974.</ref> [[Claudio Costa (philosopher)|Claudio Costa]] has noted that a future can only be a future of its own past if it holds some identity with it. Moreover, the nearer a future is to the point of junction with its past, the greater are the similarities tendentially involved. Consequently – ''contra'' Hume – some form of principle of homogeneity (causal or structural) between future and past must be warranted, which would make some inductive procedure always possible.<ref>Claudio Costa: ''Philosophical Semantics: Reintegrating Theoretical Philosophy'', Appendix to Ch. V, CSP, 2018.</ref>

===Karl Popper===
[[Karl Popper]], a [[philosophy of science|philosopher of science]], sought to solve the problem of induction.<ref>{{cite book
| title = The Logic of Scientific Discovery
| author = Karl Popper
| year = 1959
| pages = Ch. 1
| quote = ...&nbsp;the theory to be developed in the following pages stands directly opposed to all attempts to operate with the ideas of inductive logic.
| isbn = 978-84-309-0711-3
| title-link = The Logic of Scientific Discovery
| publisher = Marban
| author-link = Karl Popper
}}</ref><ref>{{cite news
| url = http://www.abc.net.au/rn/science/ss/stories/s75303.htm
| title = A Portrait of Sir Karl Popper
| author = Alan Saunders
| work = The Science Show
| publisher = [[Radio National]]
| date = 15 January 2000
| access-date = 27 December 2007
}}</ref> He argued that science does not use induction, and induction is in fact a myth.<ref>{{cite book
| title = Conjectures and Refutations
| author = Karl Popper
| year = 1963
| page = 53
| quote = 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.
| isbn = 978-0-06-131376-9
| title-link = Conjectures and Refutations
| publisher = Harper & Row
| author-link = Karl Popper
}}</ref> Instead, knowledge is created by [[conjecture]] and criticism.<ref>{{cite book |author=Karl Popper |title=Conjectures and Refutations |title-link=Conjectures and Refutations |year=1963 |isbn=978-0-06-131376-9 |page=53 |publisher=Harper & Row |quote=The actual procedure of science is to operate with conjectures: to jump to conclusions – often after one single observation. |author-link=Karl Popper}}</ref> The main role of observations and experiments in science, he argued, is in attempts to criticize and refute existing theories.<ref>{{cite book |author=Karl Popper |title=Conjectures and Refutations |title-link=Conjectures and Refutations |year=1963 |isbn=978-0-06-131376-9 |page=128 |publisher=Harper & Row |quote=Tests proceed partly by way of observation, and observation is thus very important; but its function is not that of producing theories. It plays its role in rejecting, eliminating, and criticizing theories. |author-link=Karl Popper}}</ref>

According to Popper, the problem of induction as usually conceived is asking the wrong question: it is asking how to justify theories given they cannot be justified by induction. Popper argued that justification is not needed at all, and seeking justification "begs for an authoritarian answer". Instead, Popper said, what should be done is to look to find and correct errors.<ref>{{cite book
| title = Conjectures and Refutations
| author = Karl Popper
| year = 1963
| page = 25
| quote = I propose to replace&nbsp;... the question of the sources of our knowledge by the entirely different question: 'How can we hope to detect and eliminate error?'
| isbn = 978-0-06-131376-9
| title-link = Conjectures and Refutations
| publisher = Harper & Row
| author-link = Karl Popper
}}</ref> Popper regarded theories that have survived criticism as better corroborated in proportion to the amount and stringency of the criticism, but, in sharp contrast to the inductivist theories of knowledge, emphatically as less likely to be true.{{clarify|date=October 2018|reason=This misrepresents totally Popper's view.}}<ref>''Logic of Scientific Discovery'', section 43.</ref> Popper held that seeking for theories with a high probability of being true was a false goal that is in conflict with the search for knowledge. Science should seek for theories that are most probably false on the one hand (which is the same as saying that they are highly falsifiable and so there are many ways that they could turn out to be wrong), but still all actual attempts to falsify them have failed so far (that they are highly corroborated).

[[Wesley C. Salmon]] criticizes Popper on the grounds that predictions need to be made both for practical purposes and in order to test theories. That means Popperians need to make a selection from the number of unfalsified theories available to them, which is generally more than one. Popperians would wish to choose well-corroborated theories, in their sense of corroboration, but face a dilemma: either they are making the essentially inductive claim that a theory's having survived criticism in the past means it will be a reliable predictor in the future; or Popperian corroboration is no indicator of predictive power at all, so there is no rational motivation for their preferred selection principle.<ref>{{cite book
| title = The Foundations of Scientific Inference
| url = https://archive.org/details/foundationsscien00salm
| url-access = limited
| author = Wesley C. Salmon
| year = 1967
| pages = [https://archive.org/details/foundationsscien00salm/page/n35 26]
| publisher = [Pittsburgh] University of Pittsburgh Press
| isbn = 9780822951186
| author-link = Wesley C. Salmon
}}</ref>

[[David Miller (philosopher)|David Miller]] has criticized this kind of criticism by Salmon and others because it makes inductivist assumptions.<ref>{{cite book |last1=Miller |first1=David |title=Critical rationalism: A restatement and defense |date=1994 |publisher=Open Court |location=Chicago}}</ref> Popper does not say that corroboration is an indicator of predictive power. The predictive power{{according to whom|date=October 2016}} is in the theory itself, not in its corroboration. The rational motivation for choosing a well-corroborated theory is that it is simply easier to falsify: Well-corroborated means that at least one kind of experiment (already conducted at least once) could have falsified (but did not actually falsify) the one theory, while the same kind of experiment, regardless of its outcome, could not have falsified the other. So it is rational to choose the well-corroborated theory: It may not be more likely to be true, but if it is actually false, it is easier to get rid of when confronted with the conflicting evidence that will eventually turn up. Accordingly, it is wrong to consider corroboration as a reason, a [[justificationism|justification]] for believing in a theory or as an argument in favor of a theory to convince someone who objects to it.<ref>Thomas Bullemore, [https://www.academia.edu/4154895/Some_Remarks_on_the_Pragmatic_Problem_of_Induction "Some Remarks on the Pragmatic Problem of Induction"], Academia.edu.</ref>