2. ‘We can agree with Frank Jackson, David Chalmers, Saul Kripke, David Lewis [and many others] … that metaphysical necessity is necessity in the widest sense’; Stalmaker, RobertWays a World Might Be (Oxford: Clarendon Press, 2003), 203CrossRefGoogle Scholar.

3. ‘The truths of logic and mathematics are analytic propositions or tautologies’, and ‘a proposition is analytic when its validity depends solely on the definitions of the symbols it contains’; A. J. Ayer Language, Truth, and Logic, 2nd edn (London: Victor Gollancz, 1946), 77, 78. By ‘validity’ he surely means in more precise terminology ‘truth-value’.

4. Brian Leftow, private correspondence, where he adds that he is ‘broadly functionalist on [the divine events involved]’. Leftow's view of what makes necessary sentences true is developed at length in his forthcoming book on necessity.

5. For my account of a posteriori metaphysical necessity see section 1 of my ‘From mental/physical identity to substance dualism’, in P. van Inwagen & D. Zimmerman (eds) Persons, Human and Divine (Oxford: Clarendon Press, 2007). I give there a more precise definition of what I have called here a ‘canonical description’ and call there an ‘informative designator’.

6. In their Introduction to their collection Conceivability and Possibility (Oxford: Oxford University Press, 2002), 4, T. Gendler & J. Hawthorne write that ‘the notion of metaphysical possibility is standardly taken to be primitive’, adding in a footnote ‘in contemporary discussions at any rate’. They explain (5) that ‘metaphysical possibility is more expansive than nomological possibility, less expansive than narrow logical possibility’. But we need more clarification than that in order to have a useful notion with which to operate.

7. Leftow identifies his distinction between broad and narrow logical modality with distinctions made by both Plantinga and Kripke; (141), n. 2 (160) and n. 42 (162). But for Plantinga, narrow logical necessity includes only ‘truths of propositional logic and first-order quantification theory’. See Alvin Plantinga The Nature of Necessity (Oxford: Clarendon Press, 1974), 1–2. Broad logical necessity seems, however, for Plantinga, as for Leftow, to include all metaphysical necessity (in my sense), other than narrow logical necessity. Kripke does not, as far as I know, use the terms ‘narrowly’ and ‘broadly’ ‘logically necessary’, but distinguishes between a priori and a posteriori necessity and (what I think amounts to the same distinction) between de dicto and de re necessity. See Kripke, SaulNaming and Necessity (Oxford: Blackwell Publishing, 1982Google Scholar), passim.

8. Leftow's (150) account of ‘absolute necessity’ as necessity ‘given the truth of … a null set of sentences’ seems to me to apply only to logical necessity. I suggest that metaphysical non-logical (that is, a posteriori ) necessity is best understood as differing from this in being relative to the existence of certain objects, e.g. ‘Hesperus is Phosphorus’ is necessary given that Hesperus exists.

9. Leftow cites (155) an unfortunate sentence of mine in private correspondence wrongly suggesting that it is against the rules to let a contradictory sentence count as true only ‘when doing logic’. I certainly hold that no contradictory sentence can ever be true. But my point is that some sentences which have the form ‘p and not-p’ do not express contradictions. For example, ‘it is and it isn't raining’ may be used to describe the situation where there are just a few spots of rain falling.

10. Hume (if we read his ‘imagine’ as ‘conceive’) states a weaker relation between these concepts: ‘'tis an established maxim in metaphysics, that whatever the mind clearly conceives includes the idea of possible existence, or in other words, nothing we imagine is absolutely impossible’; Treatise of Human Nature 1.2.2.

11. This understanding of necessity which he sometimes calls ‘metaphysical necessity’ is that of Leibniz. Thus he writes of ‘a necessity which takes place because the opposite implies a contradiction (which necessity is called logical, metaphysical, or mathematical)’; H. G. Alexander (ed.) The Leibniz–Clarke Correspondence (Manchester: Manchester University Press, 1956), Leibniz's fifth paper, §4. Leibniz thinks however (see n. 17 below) that this necessity arises ultimately from God necessarily thinking the thoughts which have this character.

12. See, for example, Swinburne The Christian God, 112.

13. See Robert Adams's article ‘Divine necessity’, republished in his The Virtue of Faith (Oxford: Oxford University Press, 1987), 213–214.

14. My reason for suggesting that this is what lies behind Leftow's view that there can be logically necessary truths, the negations of which do not entail contradictions, is that in discussing (151) my attempt to prove the necessity of ‘Nothing can be red and green all over’, he asserts that I cannot ‘simply insist’ ‘that something entailed by being the one colour contradicts something entailed by being the other’, I ‘must show’ it. And showing it, he claims, involves the argument having a certain form. But, I am suggesting that there is no way of proving an unrecognized entailment except by appealing to recognized entailments (although, I grant, the form of an argument may help us to recognize an entailment). I was trying to appeal to an entailment which almost everyone would recognize. But if I have an opponent who doesn't recognize it, that doesn't mean that I haven't proved the contradiction; it only means that my opponent can't recognize that I've proved the contradiction. Some of the disagreement about this example may arise from a misunderstanding about what ‘Nothing can be red and green all over’ is supposed to mean. I am understanding ‘red’ as ‘pure red’ and ‘green’ as ‘pure green’. So I am not claiming that it is a ‘narrow logical’ necessity that there cannot be reddish-green surfaces. It does however seem to be a feature of our colour-detecting mechanisms that surfaces do not normally look reddish-green; and since the colour of things is the way they normally look, surfaces are not normally reddish-green. Leftow's reference to C. L. Hardin Color for Philosophers (Indianapolis IN: Hackett, 1988), 124–126 suggests that he may have understood the disputed sentence in a different way from myself.

15. See Alston, WilliamBeyond ‘Justification’ (Ithaca NY: Cornell University Press, 2005), 26Google Scholar: ‘The parties to at least the most radical of the disputes about epistemic justification are using “justified” to pick out different properties of beliefs. They differ more strongly than disagreeing about a common object; they are talking about different things under the label “justified”.’

16. If (as Leftow (145) claims) ‘there are widespread intuitions that entailment is not a vague concept’, these must be philosophers' intuitions about propositions. It seems totally implausible to suppose that the entailments of sentences of ordinary language are never vague, as my discussion of ‘epistemically justified’ illustrates. Leftow must be claiming that vagueness about whether one sentence entails another consists in indeterminacy about which proposition (with totally determinate entailments) is expressed by the former sentence.

17. ‘The understanding of God is the region of eternal truths and of the ideas on which they depend, and … without Him there would be nothing real in the possibilities – not only nothing existent, but also nothing possible … . Necessary truths depend solely on [God's] understanding of which they are the internal object’; G. W. Leibniz Monadology, Mary Morris (tr.) Leibniz's Philosophical Writings (London: J. M. Dent & Sons, 1934), sections 43 and 46. For a modern statement of this view see Morris, T. V. & Menzel, C. ‘Absolute creation’, American Philosophical Quarterly, 23 (1986), 353–362Google Scholar.

18. E. J. Lemmon ‘Sentences, statements, and propositions’, in B. Williams & A. Montefiore (eds) British Analytical Philosophy (London: Routledge and Kegan Paul, 1966).

19. I am citing private correspondence with Leftow – see n. 4 above.

20. Plantinga, AlvinGod, Freedom, and Evil (London: George Allen & Unwin, 1974), 111Google Scholar, 108.