What Are the Drivers of Induction? Towards a Material Theoryþ
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Studies in History and Philosophy of Science 83 (2020) 8–16 Contents lists available at ScienceDirect Studies in History and Philosophy of Science journal homepage: http://www.elsevier.com/locate/shpsa What are the drivers of induction? Towards a Material Theoryþ Julian Reiss Institute for Philosophy and Scientifc Method, Johannes Kepler University Linz, Altenberger Str. 69, 4040, Linz, Austria ABSTRACT John Norton’s Material Theory of Induction (Norton, 2003, 2005, 2008, forthcoming) has a two-fold, negative and positive, goal. The negative goal is to establish that formal logics of induction fail if they are understood as universally applicable schemas of induction. The positive goal is to establish that it is material facts that enable and justify inductive inferences. I argue in this paper that Norton is more successful with his negative than with his positive ambition. While I do not deny that facts constitute an important type of enabler and justifer of inductions, they are by no means the only type. This paper suggests that there are no less than six other types of background information scientists need and use to fuel and warrant inductions. The discussion of additional enablers and justifers of inductions will further show there are practically important and intellectually challenging methodological issues Norton’s theory prevents us from seeing because it leaves out this or that type of enabler and justifer. 1. Introduction None of these arguments establishes the material theory on its own, and even jointly. They are at best suggestive. That no formal theory of John Norton’s Material Theory of Induction (Norton, 2003, 2005, induction has succeeded so far does not mean that no formal theory ever 2008, forthcoming) has a two-fold, negative and positive, goal. The will succeed. More importantly, taking the failure of past formal theories negative goal is to establish that formal logics of induction fail if they are as evidence that no ‘universally applicable formal theory’ will succeed understood as universally applicable schemas of induction. The positive does not unequivocally speak in favour of Norton’s material theory. It goal is to establish that it is material facts that enable and justify only speaks in favour of some theory that is not universally applicable inductive inferences. I argue in this paper that Norton is more successful and formal. That the material theory is able to explain the successes of with his negative than with his positive ambition. While I do not deny, many instances of good inductive inferences, again, provides evidence of and don’t know anyone who does, that facts constitute an important its truth but leaves open the possibility that alternative theories explain type of enabler and justifer of inductions, they are by no means the only instances of inductive success equally well or better. That inductive type. Below I will suggest that there are no less than six other types of inference is ‘powered by facts’ allows the possibility of it not being background information scientists need and use to fuel and warrant powered by facts alone. inductions. The discussion of additional enablers and justifers of in- It is therefore possible to be largely in agreement with Norton’s ar- ductions will show there are practically important and intellectually guments and yet hold a different theory. The paper proceeds as follows. challenging methodological issues Norton’s theory prevents us from To pave the ground, I will describe the negative aspect of Norton’s seeing because it leaves out this or that type of enabler and justifer. theory, largely approvingly, in the next section. In Section 3 will discuss Norton provides three arguments in favour of the material theory of his positive case for material facts as drivers of inductions. Section 4 will induction (Norton, forthcoming: Ch. 2, 1–2; emphasis original): introduce a number of material elements Norton has left out in the Material Theory. Section 5 will add a number of normative enablers and (i) Failure of universal schema: [… ] no attempt to produce a uni- justifers of induction. Section 5 concludes. versally applicable formal theory of induction has succeeded. Norton remains ambiguous between a normative and a descriptive (ii) Accommodation of standard inferences: […] the successes of many reading of his theory. He certainly wants his theory to be descriptively exemplars of good inductive inferences can be explained by the accurate and maintains that in scientifc practice, material facts play the material theory of induction. role of enabling inductive inferences. But at times, he seems to be (iii) Inductive inference is powered by facts: The ampliative character of claiming more, viz. that material facts in fact warrant or justify in- inductive inference precludes universal schemas. ductions, quite independently of whether or not scientists are aware of E-mail address: [email protected]. URL: https://www.jreiss.org. https://doi.org/10.1016/j.shpsa.2020.02.003 Received 3 May 2019; Received in revised form 31 October 2019; Accepted 23 February 2020 Available online 6 March 2020 0039-3681/© 2020 Published by Elsevier Ltd. J. Reiss Studies in History and Philosophy of Science 83 (2020) 8–16 this. I want to remain neutral on this issue and will, in what follows, refer is a valid inference (even though, of course, from false premisses to a to material facts as the drivers of inductions. Using this term, I hope to false conclusion in this case). convey a dual descriptive and normative meaning: that which does in When Norton denies that all formal schemas of induction fail, he is in fact enable inductive inferences and that which justifes or warrants it. fact saying that induction does not work this way. In case of inductive inferences, the reliability of an inference is not invariant to substitutions 1 2. Formal theories of induction are unsuccessful of alternative premisses of the same form. Let us take the simplest case of enumerative induction or inductive generalisation. That has the form: Induction is a type of inference, the act of passing from one set of Some As are B. propositions, statements, or judgements taken to be true — the pre- misses — to another — the conclusion — the truth of which is believed Therefore, all As are B. to follow in one way or another from the truth of the premisses. Para- digm cases of good inferences are deductive inferences, which are such This inference is reliable, for instance, if we substitute ‘electron’ for ‘A and ‘has a mass of 9.10938356 10 31 kg for ‘are B , but not if we that the truth of the premisses guarantees the truth of the conclusion. ’ Â – ’ ’ Some basic examples of deductive inferences include: substitute ‘gold coin’ and ‘has a mass of one ounce’. Sometimes weak- ening the conclusion helps to make an inference more reliable. Thus, A. Modus Ponens ‘Some ravens are black, therefore all ravens are black’ is subject to ex- ceptions due to the (rare) existence of albino ravens. Thus, weakening If it rains, then it pours. the conclusion to ‘Almost all ravens are black’ improves the inference. This won’t work, however, when the As are cats rather than ravens. It rains. The same point — that inductive inferences are not reliable merely in Therefore, it pours. virtue of their form — can be made with respect to all theories or models of induction. An additional problem for simple enumerative induction is that it is very narrow in its applications. Plainly, many inductions are not inferences from ‘some’ to ‘all’ but rather inferences from effects to B Disjunctive Syllogism causes (e.g., when a disease is inferred from symptoms or a perpetrator Either the gardener was the murderer, or the stable boy. from fngerprints and other clues) or from a collections of facts to a unifying hypothesis (e.g., when a hypothesis about dietary trends is The stable boy wasn’t the murderer. inferred from facts about people’s weights and other aspects of their health). Norton calls these cases of ‘hypothetical induction’ (e.g., Nor- Therefore, the gardener was the murderer. ton, 2003, 2005). The hypothetico-deductive account (e.g., Hempel, 1966), for example, models inductive inferences as follows: C Dilemma Hypothesis H deductively entails evidence E. If Antigone follows King Creon’s order not to bury her brother, she’ll E. betray her love for him and most deeply held values. Therefore, H. If Antigone does secure a respectable burial for her brother, she’ll be stoned to death. Formally, this is an instance of an inference called the ‘fallacy of affrming the consequent’. The reason the inference is a fallacy in Therefore, Antigone will either betray the love for her brother and deductive logic is that the fact that H deductively entails E does not most deeply held values or be stoned to death. preclude the existence of one or more alternative hypotheses H0, H00 etc. Though I have used specifc statements concerning concrete exam- that equally entail the evidence E. Thus, many diseases produce similar ples in each case, what makes deductive inferences special is that their symptoms, the same set of clues may have been left by many different validity derives fully from the logical form of the statement and is suspects, many dietary behaviours may be responsible for the same therefore independent of the statements’ content. Modus Ponens, for patterns in health outcomes. To be reliable, hypothetico-deductivism instance, has the general form: must therefore be supplemented by mechanisms for selecting among the competing hypotheses. If A, then B. Proponents of inference to the best explanation (IBE) maintain, un- A surprisingly, that the hypothesis which best explains the evidence, is to be selected. One immediate problem for applying the model is that there Therefore, B.