To: Scott B.
From: Geoffrey Klempner
Subject: What is a law of nature?
Date: 11th April 13:30

Dear Scott,

Thank you for your email of 1 April, with your essay for the University of London BA Methodology module, in response to the question, 'What is a law of nature?'

You've covered the essential points, although I was a bit confused by your introduction where seemed to be talking about the concept of causality rather than the concept of a law of nature. Hume talks about causality and also about the uniformity of nature, but his argument against the accepted view of causation is not the same as his sceptical argument to the effect that induction cannot be justified: these are two different, although connected, lines of thought.

Hume's argument against causation is, as you state, along the lines of asking what 'impressions' our putative 'idea' of causation is derived from. When we see one billiard ball 'cause' another billiard ball to move, all we actually see is one billiard ball move, followed by another billiard ball moving. What Hume offers, instead, is an 'error theory', which seeks to account for our forming the mistaken belief that causes are real, while at the same time offering an alternative analysis of causation in terms of the truth of universal generalizations.

Hume's argument regarding induction is merely that inductive inference cannot be justified, either inductively or deductively. It's simply something we do. It is true that Hume has an explanation of why we reason inductively -- which interestingly involves both causation and induction (in terms of the natural operations of the human mind). It is a question which sometimes turns up in the Modern Philosophy paper, why Hume is not guilty of inconsistency here.

To see why the nature of causation and laws of nature are distinct questions, consider the theory according to which there is no such thing as 'causal influence' but there do exist objective laws of nature, obtaining by natural necessity. It is this natural necessity which distinguishes your example of 'metal expands when heated' and 'all Manchester United managers are non-French'. Conversely, it is also possible to hold the view that causation a real relation between objects, but that there are no laws of nature as such. Elizabeth Anscombe in her article on Causation argues against the Humean view that a causal statement entails a universal generalization.

However, it remains the case that one possible view of the difference between laws of nature and merely accidental generalization is that laws of nature involve causation whereas accidental generalizations do not. However, it is not open to someone to hold this view if they also want to argue (as, e.g. Hempel) that causation can be analysed by the deductive-nomological model, i.e. that talk of causation reduces to deductions of instances from scientific laws, e.g., 'The heat caused the metal to expand' is true because it follows from 'All metal expands when heated' and 'This metal was heated'.

The latter part of your essay is concerned with contrasting the Ramsey-Lewis (Humean) view of laws of nature with the Armstrong-Dretske-Tooley view, according to which laws of nature 'state necessitating relationships between the properties involved'. This sounds very grand, but I'm not convinced that is is so very different from the alternative, deflationary view.

What is a 'necessitating relationship' and how does one recognize such a relationship when it obtains? Consider the standard way we explain regularities on a macroscopic scale in terms of microstructural properties of the physical materials involved. For example, 'Water expands when frozen.' When a sample of water is cooled, its volume contracts until it reaches 4 degrees Centigrade, then it begins to expand. The explanation is in terms of the property of the 'hydrogen bond' in the H20 molecule. I recall this from my physics/ chemistry A-level days. You can explain the process on a blackboard. What do the A-level students 'see' when the see and understand this explanation? They see the (hypothesized) physical mechanism.

But this is no different in principle from 'seeing' that the white billiard ball moved because it was hit by the black billiard ball. In other words, right at bottom we are talking once more about things that always happen, regularities. If you keep pressing the question of the nature of the 'necessitating relationship', you find yourself back once more with regularities. Whenever we *can't* find the mechanism, we still assume that one can, in principle, be found. So I am sceptical about whether the two views that you contrast ultimately are so different from one another.

All the best,

Geoffrey