The Problem of Induction has often been considered to be one of the main challenges in the philosophy of science (see e.g., Noonan 1999: 11, Ladyman 2005: 39, Beebee 2006: 37). Even Maxwell (1972) highlighted the relevance of the problem as it might undermine the rationality of science (Maxwell 1972: 137-140). The present paper does not aim at providing a review of the entire debate but has a rather modest aim: Presenting one particular view of the Problem of Induction and evaluating in how far 3RSSHU¶V theory might be seen as a solution to this problem.
Our first point will be to define (one version of) the Problem of Induction. Having done so, the task will be to look at what Popper says with regard to this problem. It will turn out that there are three main lines of reasoning within Popper's work concerning the Problem of Induction, namely his falsificationist account, his anti-justificationist account, and his rationalist account. For each of those lines of argumentation, we will examine what Popper means by it, why he claims it, whether we are convinced by it and whether it might solve the Problem of Induction. This will take the main part of the essay followed only by some short concluding remarks.
2. Defining the Problem of Induction
In this essay, the term µProblem of Induction 1 is meant to describe the following nine-step scenario: 2
i. X thinks that science involves induction.
ii. X thinks that induction must be justified for science to be rational.
iii. X thinks that any justification of induction must be either inductive or deductive.
iv. X thinks that any inductive justification of induction must be viciously circular.
v. X thinks that any deductive justification of induction must depend on the premise that the future will resemble the past, or more generally, that unobserved cases resemble observed cases. vi. X thinks that any such premise could itself only be justified inductively.
vii. X thinks that because of (v.) and (vi.), any deductive justification of induction must fail.
viii. X no longer thinks that induction can be justified.
ix. X concludes that science cannot be rational.
Using this 34 formulation of the problem, we have to be aware of the following: Anything that makes X conclude that science can be rational could solve the problem at hand. µ$Q\WKLQJ¶ can, but does not have to consist of showing that there is a way to justify induction. This is something one has to bear in mind while evaluating whether and to what extent a theory solves the problem.
3. Considering Popper's theory as a possible solution to the problem
Let us now look at what Popper says in his three main works dealing with the Problem of Induction (Popper 2008 1934: The Logic of Scientific Discovery, Popper 2000 1983: Realism and the Aim of Science, Popper 1996 1994 The Myth of the Framework. In Defence of Rationality and Science). Considering the formulation of the Problem of Induction outlined above, Popper replies the following:
1) Science does not involve induction.
2) Scientific methods do not have to be justified for science to be rational.
3) Science is rational.
For each of those statements, we have to see«
a) why he claims it, i.e.:
i. what his background premises are
ii. what his line of reasoning is
b) whether we are convinced by his argumentation, i.e.:
i. whether we agree with his premises
ii. whether his line of reasoning is sound
c) whether it can be seen as solving the Problem of Induction, i.e.:
i. whether it is a necessary step towards solving the problem
ii. whether it is a sufficient step towards solving the problem.
3. Popper's first claim:'Science does not involve induction.'
Let us begin with considering his first, falsificationist, statement. As his premises, we can identify the following: There is a (and only one) objective reality (Popper 2000: 81). The aim of science is to come as close as possible to the truth (understood as correspondence with the facts) concerning this reality (Popper 2000: 24). Science is guided by (what Popper calls) the Rationality Principle (Popper 1996: 181, see below).
His line of reasoning goes as follows: Because scientists are guided by the µRationality Principle¶ VHH EHORZ , they do not aim at verifying hypotheses but at falsifying them (Popper 2008: 33). For falsifying a hypothesis, no induction is needed: The observation of one single occurrence being in contrast with theory's prediction is sufficient to constuct a logically valid deductive argument which shows that the theory is falsified (Popper 2008: 20). As an example, imagine that some theory T claims that all humans are male. Therefore, a proponent of T claims that the next human being that will enter this room must be male. We look at reality and see that the next human being who enters the room happens to be female. The logical conclusion to draw is that theory T is wrong in its claim that all humans are male. Drawing this conclusion is a purely deductive act. Science only involves falsification, falsification does not involve induction, therefore science does not involve induction (Popper 2008: 20f.).
We do not have to bother ± for the time being ± whether we agree with his realist premise or whether we agree with his premise concerning the aim of science. Whether we agree with Popper's third premise,though,is essential, as Popper's entire falsificationist argumentation is based on it. To be able to judge whether we agree with this premise, we have to see what Popper means by the term 'Rationality Principle'.
According to Popper, for person X to be rational, she has to acknowledge that her knowledge and beliefs are hypothetical (i.e. open to criticism and change) (Popper 1996: 180). Popper holds that science is guided by the Rationality Principle. This principle states that scientists have to put forward falsifiable, i.e. empirically refutable hypotheses and enter in critical discussion about them (Popper 1996: 160). Furthermore, the Rationality Principle implies that the decisions about whether or not to (tentatively) adopt a theory has to be based on the judgement of whether the theory seems to be closer to the truth (i.e. to have a higher degree of verisimilitude) than the known alternatives (Popper 2000: 33). In making this judgement, X has to take into account the results of observations (Popper 2000: 32), the theory's consistency,its agree of falsifiablity, its relevance, and its explanatory power (Popper 2000: 55).
I do not believe that this premise is adequate. It is impossible to investigate empirically whether all scientists do think and act like that. Still, using Popper's own methode, one can show that this claim cannot be true.There are many scholars who claim that they do not think and act this way (see Vickers 2011). Each single one of them is sufficient to deductively refute Popper's thesis.That is logically valid can easily be seen: Popper (2008) claims that all scholars are guided by the Rationality Principle.
1 Since Kant, the Problem of Induction has often been called µ+XPH¶V SUREOHP¶ (see e.g., Bird 2002: 165). Still, with Beebee (2006) I hold that attributing the Problem of Induction to Hume is inadequate. Hume will therefore play no role in this essay. For further information Hume's account of knowledge and causality see Ladyman 2005).
2 Let X denote some person who happens to be female.
3 The problem has been formulated like that because formulations that do not mention step (i.), (ii.) and (ix.) deprive the Problem of Induction of much of its relevancy for the philosophy of science.
4 This way of formulating the Problem of Induction is compatible with, but not identical with Popper's (2000:32f.,53) desciption of the problem