Saturday, 1 October 2011

A Material Theory of Induction

In this paper, Norton offers his solution to the problem of induction. He does this by rejecting the notion that we need a universal schema for inductions. In the classic thinking on induction, we would take some finite number of observations and generalise to an indefinite number of cases according to the schema "Some A's are B's, so all A's are B's". But, as Hume pointed out, when we try to justify applying this schema, we find ourselves using an inductive argument and so applying the schema itself - a vicious circle therefore emerges rapidly.

Norton claims that inductions need not depend on a general schema at are but are rather local and grounded in background facts. If, in a particular domain, we know the right background facts, then some kinds of inductions are made legitimate. Take his example of "All samples of bismuth melt at 92 degrees". This claim is arrived at inductively by looking at a finite number of samples of bismuth. The relevant background facts that allow this inductive generalisation include things like "bismuth is an element"; "All samples of the same element have the same melting point"*...

One way of thinking about this is to imagine playing a game of justification with the induction sceptic. You say "All samples of bismuth melt at 92 degrees". She asks you to justify that claim. "Well," you say, "bismuth is an element and all samples of the same element have the same melting point." And so the next question: "Why do you think that all samples of an element will have the same melting point?" And so you answer that the melting point of a substance is substantially determined by its electronic structure, and all atoms of a given element have the same atomic structure. And so the game continues. At each stage, instead of trying to justify a general statement by appealing to some particular instances, you instead appeal to some even more general statement.

From this thought experiment, it is apparent that there is still a kind of regress at the heart of Norton's theory of induction. He claims that this is a less dangerous regress than in the standard understanding of Hume's problem, as it avoids vicious circularity. This approach seems to fit with scientific practice of taking some facts for granted when working in a particular domain. However, the crucial issue is pointed out by Norton himself: "What remains an open question is exactly how the resulting chains (or, more likely, branching trees) will terminate and whether the terminations are troublesome." (p. 668) He claims that we simply do not know for sure, but that there is a "real possibility of benign termination". This is doubtful - presumably these chains of justification will in fact terminate in simple generalisations about basic sensory experience. But these are grist to the original Humean mill. Norton has not solved the problem of induction.

It seems that there is also a problem with time. I claim that all samples of Bismuth melt at 92 degrees and thus that the next sample of Bismuth I encounter will melt at that temperature. Now the induction sceptic asks how I know this. I respond with the above mentioned facts about elements and so on. She responds "How do you know that these things will continue to be true in the future?" What local facts do I appeal to to justify my expectation that the future will be like the past? Is this not exactly the same problem that afflicts the standard account of induction? If my response is to appeal to universal generalisations (which imply the relevant future directed claims) then I seem to be missing the point. The sceptic can, at every stage ask "yes, but how do you know that these things will continue to be true in the future?" Or she can ask "How do you know that these generalisations, made on the basis of past evidence, will hold in the future?" Likewise, appeal to more general generalisations won't help respond to the sceptics worry.

* Except sulphur. Elemental sulphur comes in different allotropes, or molecular arrangements, which means that different samples may have different melting points...


  1. Seamus, why do you include a footnote specifically about the allotropy of sulphur? Many elements have allotropes. A sample of pure carbon for instance has widely different physical properties (including different melting points) depending on whether the atoms are configurated as diamond, graphite, buckyballs, ...

  2. Sulphur is the example Norton himself mentions. I didn't know the phenomenon was more widespread. Thanks for correcting us!

    (In my defense, I think Dean added the footnote, and he used to be a chemist so he should know better!)