To: Craig S.
From: Geoffrey Klempner
Subject: Distinction between laws and accidental generalizations
Date: 16th April 2009 10:43

Dear Craig,

Thank you for your email of 2 April, with your University of London Methodology essay on the topic, 'What distinguishes a law from an accidentally true generalization?'

This looks more like a set of notes than an essay. I understand that you want to cover all possible variations of the question of what distinguishes a law from an accidental generalization. However, if I were composing the question, I would restrict it to one of the 'demarcation criteria' which you list. Each of the sections deserves an essay in itself.

You seem to express a common misunderstanding of Hume, when you say, 'Hume famously could not see how the necessity of laws could be known.' There are in fact two separate issues here, depending on how we interpret the idea of 'knowing' the necessity.

The first concerns the putative 'necessary connection' between cause and effect. Hume's argument against the belief in a metaphysical 'necessary connection' is that all that is actually given to us in experience is the cause and the effect. Our conviction that there is something else, a 'link' between cause and effect is merely the product of the way our minds work, in calling up a 'lively idea' of an effect whenever we encounter a particular type of cause that we have encountered before. In other words, belief in the existence of a necessary connection is simply false, a philosophical error which his 'theory of human nature' exposes.

The second issue concerns our belief in induction. Hume's argument here is that there can be no proof of the uniformity of nature, nor any proof of an empirical generalization. Human beings, being finite, are incapable of inspecting indefinitely many instances. The uniformity of nature, like any law, is itself up for grabs. A law, on this view, is simply an unrestricted empirical generalization. What makes a law a law, is that the generalization is true (even though we can never know this with certainty).

Is this enough to distinguish a 'law' from an accidentally true generalization? Its main problem is that it puts a very heavy weight on the notion of truth -- possibly, a weight which that notion is unable to bear. What does its 'being' true consist in, given that there is no way, in principle, that it can be known to be true (or, given that only a being with infinite sensory powers could determine its truth by exhaustive observation)?

There are indeed two ways to interpret Hume's position here: as a traditional sceptic (which implies a 'truth' which cannot be known) or more radically as rejecting the idea of knowledge-transcendent truth.

The latter approach leads to one or other of the various forms of 'anti-realist' theory according to which the question to decide is not the truth conditions of a statement of the form, 'XYZ is a scientific law' but rather how in practice we demarcate laws from non-laws. All the things you mention are relevant here: for example, that laws support counterfactual conditionals, involve projectible predicates, belong to deductive systems. As you remark, there is always room to revise our judgement (as in the case of Bode's 'law').

What marks these overlapping criteria as 'anti-realist' is that one gives up any attempt to state, in non-circular terms, what 'makes it true' that a putative law a law. If you ask what makes it true that, 'all bodies attract one another with a force proportional to the inverse square of their distance', the only response is that, indeed, all bodies attract one another with a force proportional to the inverse square of their distance. A 'truth' like this, referring as it does to all places and all times, cannot be accidental. However, for the anti-realist, to assert this 'as true' is vacuous.

Philosophers of science who regard themselves as taking a broadly 'realist' approach with regard to the ontology of, say, physics would still be anti-realists about the truth of laws, on this view.

In response to your counterexamples: We don't know whether any Big Bang universe will initially expand, because we can't rule out an infinite number of Big Bangs. On the other hand, we do know that 'all centaurs drink beer' is false because 'centaur' is not a natural kind word. (Cf. Kripke and Putnam on natural kinds.) If it turns out that there are centaur-looking creatures somewhere in the universe, the fact that they all drank beer would not confirm the generalization nor would the fact that some did not drink beer disconfirm it. How closely has a creature to 'resemble' a centaur in order to be one? There is no answer to that question, and hence no way to determine, in principle, whether the generalization in question applies or not.

All the best,

Geoffrey