Demonstrative Induction and the Skeleton of Inference

Abstract

It has been common wisdom for centuries that scientific inference cannot be deductive; if it is inference at all, it must be a distinctive kind of inductive inference. According to demonstrative theories of induction, however, important scientific inferences are not inductive in the sense of requiring ampliative inference rules at all. Rather, they are deductive inferences with sufficiently strong premises. General considerations about inferences suffice to show that there is no difference in justification between an inference construed demonstratively or ampliatively. The inductive risk may be shouldered by premises or rules, but it cannot be shirked. Demonstrative theories of induction might, nevertheless, better describe scientific practice. And there may be good methodological reasons for constructing our inferences one way rather than the other. By exploring the limits of these possible advantages, I argue that scientific inference is neither of essence deductive nor of essence inductive.

Acknowledgements

An earlier version of this paper was presented to the Society for Exact Philosophy meeting in La Jolla, California and to the philosophy department at Southern Methodist University. I want to thank members of the audience there for helpful comments. Thanks also to John Norton (for commenting on a prior draft) and Bradley Armour‐Garb (who engaged induction as a lunchtime conversation topic on many occasions.)

Notes

[1] Of course, scientific inferences are not generally offered as deductive. Einstein did not present the derivation as a demonstrative induction (Dorling 1995, §2). This is no mark against demonstrative theories, as accounts of how scientific inference should be understood and not of how it was understood by scientists; ‘inductions are reconfigured as deductive inferences with suppressed premises’ (Norton 2003, 652, my emphasis). In the final section, I return to the issue of whether demonstrative theories are meant to be descriptive or normative.

[2] One might worry that the observation equivocates between two kinds of equivalence. Logical systems that share the same set of valid inferences are semantically equivalent. Proof systems that are intertranslatable are proof‐theoretically equivalent. For sound and complete proof systems, however, this distinction does not matter. Most examples of demonstrative inductions are not fully formalized, but there is no reason to think that they could not be formalized in a language with a sound and complete proof theory. As such, we can ignore this complication in what follows.

[3] Wittgenstein makes a similar point when he observes that there must be a way of following a rule that is not an explicit interpretation of the rule (1953, §201); the Tortoise’s trick is to insist that the rule must be interpreted explicitly for each instance before it can be followed. Stroud (1979, 195) also notes the affinity between Carroll and Wittgenstein.

[4] The distinction between high and low externality is similar to the distinction between observational and theoretical language. Although the latter might be more familiar to philosophers, it has the unfortunate effect of suggesting a binary distinction rather than a matter of degree. Even allowing that a report might be ‘more or less observational’, the distinction suggests a continuum with pure observation at one end and pure theory at the other and so creates unnecessary difficulties. For example, van Fraassen (1980) argues that the distinction between theoretical and observational language is a category mistake. No such charge can be leveled at the distinction between high‐ and low‐externality reports.

[5] The high‐externality claim might be derived from background theory; e.g., the constancy of the speed of light may be derived from Maxwell’s equations. But then the claim is a theoretical constraint rather than an observation report.

[6] Motivated by Quinean worries about meaning and translation, one might argue that there is no fact of the matter as to which of two equivalent proof systems an observed agent is using—and so that demonstrative theories of induction necessarily fail as description accounts. I have nothing helpful to say about the nature of translation here, but it suffices to note that such a Quinean argument would provide an independent route to the conclusion I argue for below. That line of argument would offer no help to champions of demonstrative induction.

[7] Of course, it is sometimes possible to fruitfully distinguish between theories and research programmes; e.g. Schell and Magnus (2007). For Worrall’s criterion to be general, however, it must always or almost always be possible.

[8] Bain (1999) provides an illustrative example by reconstructing an argument by Steven Weinberg. Briefly, the argument is that ‘local quantum field theory is the only way to reconcile the principles of quantum mechanics with special relativity and Cluster Decomposition’ (Bain 1999, 6). Bain thinks that this answers a specific kind of underdetermination worry by showing that there is no other theory that has all of these virtues (Bain 1999, 12). Yet underdetermination arguments typically turn on ‘empirical equivalence’, not equivalence with respect to strongly stated theoretical desiderata. An anti‐realist who does not believe the principles of quantum mechanics will not believe their deductive consequences either. Weinberg’s argument thus presumes a great deal of physical theory that could only be established by (partly) ampliative means. The ampliative support for some of the premises may be pushed back, but the contingency and inductive risk do not go away.

[9] A systematic discussion of what ampliative rules must assume about the world is given in Kelley (1996).

[10] The resolution of this issue will depend ultimately on what counts as evidence. It is no surprise that Bird (2006) begins his discussion by accepting a specific account of evidence.