Reviving material theories of induction

The traditional problem of induction consists of seeking a formalism that will allow us to assess the support hypotheses receive from a body of evidence that is relevant but not conclusive. A major limitation of this project arises because new data and new ideas provide challenges that were not previously imagined. Since this is an ongoing process, it a mistake to think of the limitations of inductive support as a problem to be solved; instead we need a strategy for coping with a permanent feature of our epistemic life. In fact, the required strategy has already been developed and implemented in the practice of scientific research. It is a social strategy that consist of maintaining a multi-generational community of researchers with diverse skills and cognitive styles who are capable of making new discoveries, introducing new ideas, and evaluating new proposals.

Episteme, 2020

According to John D. Norton's Material Theory of Induction, all reasonable inductive inferences are justified in virtue of background knowledge about local uniformities in nature. These local uniformities indicate that our samples are likely to be representative of our target population in our inductions. However, a variety of critics have noted that there are many circumstances in which induction seems to be reasonable, yet such background knowledge is apparently absent. I call such an absence of circumstances 'the frontiers of science', where background scientific theories do not provide information about such local uniformities. I argue that the Material Theory of Induction can be reconciled with our intuitions in favour of these inductions. I adapt an attempted justification of induction in general, the Combinatoric Justification of Induction, into a more modest rationalisation at the less foundational level that the critics discuss. Subject to a number of conditions, we can extrapolate from large samples using our knowledge of facts about the minimum proportions of representative subsets of finite sets. I also discuss some of Norton's own criticisms of his theory and argue that he is overly pessimistic. I conclude that Norton's theory at least performs well at the frontiers of science.

I argue that if John D. Norton's "Material Theory of Induction" could be combined with a theory of direct inference, then several novel and outstanding issues for his theory could be addressed. Most strikingly, there might be a promising answer to Hume's Problem of Induction, often thought to be a major weakness of Norton's theory.

2005

In this survey on implicit induction I recollect some memories on the history of implicit induction as it is relevant for future research on computer-assisted theorem proving, esp. memories that significantly differ from the presentation in a recent handbook article on “inductionless induction”. Moreover, the important references excluded there are provided here. In order to clear the fog a little, there is a short introduction to inductive theorem proving and a discussion of connotations of implicit induction like “descente infinie”, “inductionless induction”, “proof by consistency”, implicit induction orderings (term orderings), and refutational completeness.

2003

2003

Philosophical Books, 1987

Inductive reasoning, initially identified with enumerative induction (inferring a universal claim from an incomplete list of particular cases) is nowadays commonly understood more widely as any reasoning based on only partial support that the premises give to the conclusion. This is a tad too sweeping, for this includes any inconclusive reasoning. A more moderate and perhaps more adequate characterization requires that inductive reasoning not only includes generalizations , but also any (ideally, rational) predictions or explanations obtained in absence of suitable deductive premises. Inductive logic is meant to provide guidance in choosing the most supported from a given assembly of conjectures. In this paper we survey selected approaches to inductive logic. Paper forthcoming in: INTRODUCTION TO FORMAL PHILOSOPHY S. O. Hansson, V. Hendrick, and K. Esther Michelsen (eds), Springer, 2018.

Springer eBooks, 2022

How induction was understood took a substantial turn during the Renaissance. At the beginning, induction was understood as it had been throughout the medieval period, as a kind of propositional inference that is stronger the more it approximates deduction. During the Renaissance, an older understanding, one prevalent in antiquity, was rediscovered and adopted. By this understanding, induction identifies defining characteristics using a process of comparing and contrasting. Important participants in the change were Jean Buridan, humanists such as Lorenzo Valla and Rudolph Agricola, Paduan Aristotelians such as Agostino Nifo, Jacopo Zabarella, and members of the medical faculty, writers on philosophy of mind such as the Englishman John Case, writers of reasoning handbooks, and Francis Bacon.

Synthese, 1990

In it, Stove produced four different proofs to refute Hume's sceptical thesis about induction. I show that Stove's attempts to vindicate induction are unsuccessful. Three of his proofs refute theses that are not the sceptical thesis about induction at all. Stove's fourth proof, which uses the sampling principle to justify one particular inductive inference, makes crucial use of an unstated assumption regarding randomness. Once this assumption is made explicit, Hume's thesis once more survives. The refutation of Stove's fourth proof leads to some observations which relate Goodman's 'grue' paradox with randomness of a sample. I formulate a generalized version of Goodman's grue paradox, and argue that whenever a sample, no matter how large, is drawn from a predetermined smaller interval of a population that is distributed over a larger interval, any conclusion drawn about the characteristics of the population based on the observed characteristics of the sample is fatally vulnerable to the generalized grue paradox. Finally, I argue that the problem of justification of induction can be addressed successfully only from a cognitive point of view, but not from a metaphysical one. That is, we may ask whether an inductive inference is justified or not within the 'theories' or 'cognitive structures' of a subject, but not outside them. With this realization, induction is seen as a cognitive process, not unlike vision, that is useful at times, and yet has its own illusions that may~ake it a serious obstacle to cognition at other times.