1 D. Armstrong, What is a Law of Nature? (Cambridge: Cambridge University Press 1983) and A World of States of Affairs (Cambridge: Cambridge University Press 1997); F. Dretske, ‘Laws of Nature,’ Philosophy of Science 44 (1977) 248-68; M. Tooley, ‘The Nature of Laws,’ Canadian Journal of Philosophy 7 (1977) 667-98

2 In what follows Is halluse the terms regularity and uniformity to refer to general facts and the term generalization to refer to a statement or proposition asserting the existence of such facts. If a generalization is true, then there exists the corresponding regularity. Some (but not necessarily all) versions of semantic anti-realism that are consonant with the anti-realism and minimalism of this paper may wish to make this a biconditional.

3 P. Lipton, Review of Bird, Philosophy of Science, British Journal of the Philosophy of Science 50 (1999), 165

4 Here I am discussing only realism and anti-realism about semantics, not about science. There are connections, but none of them are in play in this discussion. The concept of a criterion originates with Wittgenstein, but I make no claim that the concept as I use it is exactly his. G.P. Baker discusses Wittgenstein's concept at length in ‘Criteria: A New Foundation for Semantics,’ Ratio 16 (1974) 156-89. I differ with Baker/Wittgenstein in that the latter take the fulfillment of a criterion to provide certainty (the absence of doubt). While criteria (as I understand them) can confer this, they do not have to — one might have a reasonable suspicion (but not knowledge) that defeating conditions are satisfied, in which case doubt might well be appropriate. Baker discusses an earlier incarnation of the criterion concept in Wittgenstein, which he calls the H-relation. The H-relation gives a priori probabilistic justification. This he rejects on the grounds that later Wittgenstein held that only a posteriori relations are probabilistic and that an H-relation will not provide certainty. Even if this is a correct understanding of Wittgenstein, that does not make the H-relation incoherent. My use of the criterion concept is perhaps closer to the H-relation than the C-relation (criterial relation) as Baker spells it out.

5 I take it without argument that is E is evidence for P then possessing E gives one some degree of warrant (other things being equal) for asserting P. E may not be enough to give one a full warrant for asserting P since the evidence may not be enough to allow one to know P. See T. Williamson, ‘Knowing and Asserting,’ Philosophical Review 105 (1996) 489-523. However, since possessing evidence for P brings one closer to knowing P, it therefore adds to one's justification for thinking P and being disposed to assert P.

6 C. Peacocke, A Study of Concepts (Cambridge, MA: The MIT Press 1992)

7 This stems from Peacocke's Principle of Dependence: ‘There can be nothing more to the nature of a concept than is determined by a correct account of the capacity of a thinker who has mastered the concept to have propositional attitudes to contents containing that concept’ (5). The P-characterization I give is modified in that I regard the conditions cited as giving necessary and sufficient conditions for concept possession. Without making the conditions sufficient, there is a danger that the characterization may not specify a unique concept.

8 T. Burge, ‘Content Preservation,’ Philosophical Review 102 (1993) 457-89. Burge's general description of the a priori does not tell us where a priori entitlement/warrant comes from. I contend that some comes from a grasp of the very concept being employed; but this need not exhaust the sources of a priori entitlement.

9 J. Pollock, ‘Nomic Probability,’ Midwest Studies in Philosophy 9 (1984) 177-204, at 180

10 We might ant to weaken clause (ii) to a non-absolute negative warrant to account for ceteris paribus laws.

11 P. Achinstein, The Nature of Explanation (Oxford: Oxford University Press 1983), 168

12 Clause (iii) need not reduce to zero the warrant provided by (i). Imagine that all observations of people under stress reveal that they have high blood pressure and that similarly all records show that people with salty diets have high blood pressure. Let Harry have high blood pressure, and be both stressed and have a salty diet. The fact that he fits into both regularities reduces the warrant he provides to each corresponding law. But he nonetheless provides some warrant for both laws. (My thanks to Hugh Mellor for pointing out the need for caution here.)

13 Apart from my use of criteria, the two approaches differ in that I introduce the concept of law by the criteria that justify its use, while Pollock explains nomic probability in terms of the propositions that are justified by use of that concept. Maybe this is not a deep contrast, since the requirement of harmony between introduction and elimination rules extends to criteria. Note that Pollock's own example of the concept ‘red,’ which I mention above (516), follows my approach, in that the ‘red’ is explicated by the criterial conditions that license its use (rather than by the assertions licensed by its use).

14 P. Strawson, Introduction to Logical Theory (London: Methuen 1963), 256f.

15 D. Lewis, Counterfactuals (Oxford: Blackwell 1973), 73

16 Armstrong (The Nature of Explanation, 40) gives an argument of this kind: he says that the complex fact that all Fs are Gs cannot explain the fact that all observed Fs are Gs since the latter fact is part of the former one. All Fs are Gs = all observed Fs are Gs and all unobserved Fs are Gs. By the assumption stated the first conjunct does not explain why all observed Fs are Gs. Nor could the second conjunct. Therefore the conjunction does not. And so the fact that all Fs are Gs does not explain why all observed Fs are Gs. But we do want it to be possible that the law that Fs are Gs explains why all observed Fs are Gs. Hence the law cannot be identical with the regularity. Clearly the notion of observability is otiose to Armstrong's argument. On the one hand the fact that all Fs are Gs is itself something which may be explained by its being a law that Fs are Gs, and on the other hand, Armstrong's argument may be adapted, as I do, to show that a regularity cannot explain any single instance of it (whether observed or not).

17 In an atomistic metaphysics — which this paper does not endorse — we might identify the ontological content of a fact P with the facts corresponding to the propositions that are the conjuncts when P is expressed in conjunctive normal form

18 C.G. Hempel, Aspects of Scientific Explanation (New York: Free Press 1965)

19 Foster, for example, says that an extrapolative inference is an inference to the best explanation (to a law, where laws involve natural necessity) and then a deduction from the law that the observed regularity will continue to hold (‘Induction, Explanation and Natural Necessity,’ Proceedings of the Aristotelian Society 83 [1983], 90). Foster also remarks that the inference to the law may be justified in a way that a direct inference to the regularity is not precisely because of the greater content and explanatory power of the former (88-91).

20 N. Goodman, Fact, Fiction and Forecast (London: University of London 1954)

21 For instance, Goodman writes, ‘We may concentrate at present upon simple universal hypotheses in categorical or hypothetical form — that is, upon hypotheses ascribing a certain predicate to everything in the universe of discourse or to everything to which a certain other predicate applies’ (94).

22 Armstrong's and Tooley's positions are also subjected by John Carroll (Laws of Nature [Cambridge: Cambridge University Press 1994], 161-74) to criticisms that tend in the same direction as those presented here.

23 A.J. Bird, Philosophy of Science (Montreal: McGill-Queen's University Press 1998)

24 This debate turns, in part, on speculation about what people would say in the face of scientific discoveries of a certain sort. The current employment of a concept may not determine the outcome and other factors may influence future usage. For this reason, the distinction between criteria and symptoms may, as Wittgenstein realized, be somewhat fluid. Note that the rejection of scientific eliminativism for hunger is not to say that necessarily there is hunger. All hunger behavior could be faked. On the criterial view the defeaters for the existence of hunger must occur at the folk-psychological level, not at the physiological level.

25 Papineau, for example, is explicit about the need for terms such as ‘cause’ and ‘physically necessitates’ to appear in the explication of theoretical terms. See D. Papineau, ‘Theory-Dependent Terms,’ Philosophy of Science 63 (1996) 1-20. These cannot be eliminated (and so explicated) in a Ramsey/Lewis style definition of a theoretical term.