To: Chris M.
From: Geoffrey Klempner
Subject: Laws of nature vs. accidental generalizations
Date: 9th February 2010 13:54

Dear Christian,

Thank you for your email of 31 January, with your essay for the University of London BA Logic module, in response to the question, 'What is the difference between an accidentally true generalization and a law of nature?'

This is a good answer to the question, which would score in the mid- to high-60s. You have canvassed various positions that can be taken on the question of the status of scientific law as as opposed to accidental generalizations, and found both Humean and necessitarian accounts to be inadequate. Your own suggestion is that we 'bite the bullet' and give up the idea that scientific laws are exceptionless. 'Why not assume that no two electrons have exactly the same charge e and over time -- very long time frames -- the charge of a given electron will change (slowly, but somehow randomly).'

This conclusion seems to be based on what you perceive to be a fatal weakness in Hume's account, 'There cannot be anything additional to the mosaic of discreta out of which world history is composed.' If the history of the world is just a regular mosaic, why not allow that here and there the pattern changes randomly, as in a mosaic floor made by slightly drunk builders? What difference would it make?

I heard Nancy Cartwright give a paper at a conference (I can't remember where) where she gave the example of a tumbling leaf and the classic view that the movements of the leaf have a precise explanation in terms of the forces acting on it, even though it would be impossible to determine this in reality because of necessary limits on our powers of observation. Cartwright wanted to deny the classical view. There is no precise cause for the movements of the leaf. I thought she was stark raving mad. Surely, we don't know exactly why the leaf moves as it does, but the reason had better be that the laws of nature are what they are, and the leaf and its surrounding environment are what they are.

However, now I come to think of it, I can see that *if* one is prepared to allow, in a Humean spirit, that laws of nature are not required to be exceptionless, then Cartwright's view of the leaf follows. Whoa!

Hume is a bit difficult because he doesn't really emphasize the consequences of his own view. There are restricted generalizations, such as, 'All the coins in my pocket are silver' and unrestricted generalizations such as, 'All ravens are black' or 'All electrons have charge e' (your examples). What do we mean by an unrestricted generalization? We mean a generalization which applies to ALL places and ALL times, now and forever -- to infinity.

Hume's interest in these generalizations concerns our grounds for making them, our 'rational warrant' for believing them. And here he finds a foundational, and ultimately insoluble problem, to do with the justification for induction. However, apart from the question of what we can know, or what we are justified in believing, there is the question of what it is that we believe. The content of our belief is a proposition. A proposition has a truth value, true or false. To say, or to suppose that there are 'truths' of this kind, true unrestricted generalizations is a huge claim in itself. Forget about the fact that we have already given up on knowing their truth. The sheer possibility that they are true is something to wonder at, and surely would be the final word on the difference between accidental and genuine generalizations.

When we intend a generalization as a genuine generalization, we are aiming, in effect, at a target which is situated infinitely far away. An objection to this comes from the 'anti-realist' about truth and meaning. If you took two communities of investigators, one of which 'aimed' their generalizations at an infinitely far away target, and the other which merely claimed that we will never discover an exception, even though exceptions might still exist, there would be no difference in their scientific practice. The mental picture of an infinitely far away target is just that, a picture, or in Wittgenstein's words, 'a knob which turns, even though nothing turns with it.'

In practice, as Lewis says (he wasn't the first to say it), genuine generalizations have a place in the axiomatization of science. We treat them differently when we make investigations, test theories etc. In other words, the difference is structural, to do with our practice and the nature of science, rather than a difference 'in reality'. There really isn't much to say about 'how things are in reality', where this goes beyond accounting for what we actually do in carrying out our investigations.

All the best,

Geoffrey