What a Theory of Induction Could Be

Abstract

Providing a theory of inductive inference is a challenge for philosophy. David Hume purports to show, with his famous Problem of Induction, that no inductive inference can be justified. Any potential justification must assume, without justification, some principle of the Uniformity of Nature. Nelson Goodman adds his famous New Riddle of Induction. On one interpretation, this argument purports to show that there cannot even be a plausible and precise assumption that justifies inductive inferences. Any precise assumption that justifies inferences must be too specific to be plausible. For example, in justifying predictions about the future, an assumption that does the job cannot help but privilege specific properties to "project" into the future. But the specificity of the properties undermines the assumption: why those properties rather than alternatives? My target in this thesis is the second of these problems. I am happy to concede that any justification of inductive inference requires assumptions, and in particular an assumption of the Uniformity of Nature. But I think it should be plausible and stated precisely, and we should prove that some reasonable inductive inferences follow from it.

In Part I of this thesis, I articulate a plausible candidate for the Uniformity of Nature and prove that it does the job. Roughly, it is that the universe is governed by chancy laws that are invariant under time-shifts. In Part II, I refine Goodman's New Riddle into a precise and formidable challenge to any plausible assumption that provides a foundation for inductive inference. I argue that substantive inductive inferences are in tension with a kind of Inductive Empiricism. In a foundational context, Inductive Empiricism is hard to deny. Furthermore, its tension with inductive inference is inescapable where basic evidence and hypotheses are standard propositions (sets of possibilities). However, having stated this problem precisely, I suggest a way of understanding the assumption from Part I that evades the problem in Part II. I articulate this in Part III. The key idea is that the basic empirical observations are modelled as "sensor readings", which can be the same or different at distinct times in a physically meaningful way, and thus contain slightly more information than standard propositions. Part IV examines a proposal to expand the scope of a theory of inductive inference, like the one offered in Part I. Lin (2022) argues for a way to extend inductive theories on a sequence of empirical observations to cases that will never be observed, without adding any further assumption. I show that Lin's argument fails because it faces a version of the New Riddle argument described in Part II.

If successful, my argument shows that there can be a foundational theory of inductive inference, not altogether different from the foundational theory of deductive inference. There is an important difference, however: theories of induction build upon themselves in a non-monotonic way. So, we should not expect there to be a foundational theory that also instructs you and me. Unlike the foundational theory of deduction, which still guides mathematicians' proofs, the foundational theory of induction does not guide you, me or scientists (like some sort of all-encompassing scientific method). Rather, through our evolutionary inheritance, which has processed millions of years of empirical data on our behalf, it quietly underpins the inductive methods we use today. Show more