¹ Augustine, , Confessions, Chadwick, H. (trans.) (Oxford: OUP, 1998)Google Scholar, 11.14.17.

² It may be that the truth-conditions of tensed statements can be given without any commitment to the so-called ‘tensed facts’ which the A-theorist accepts and the B-theorist denies. The use just noted of the English present tense to express neutrality about whether the event described is past, present or future can be harnessed by the B-theorist to describe his tenseless facts, so the difficulty in stating the point at issue between the presentist, the gradualist and the eternalist does not apply to the debate between the A-theorist and the B-theorist.

³ Baldwin gives a clear statement of the relational truth-conditions of tensed judgements and shows why the semantics of tense does not alone resolve the debate about the A-series (Baldwin, T., ‘Back to the Present’, Philosophy 74, No. 288 (April 1999), 177–97)CrossRefGoogle Scholar. Baldwin's (R2) (op. cit, 185) makes clear that we can get the phenomenon of token-reflexivity without assuming that the judgement makes self-reference. Baldwin does assume that there are tenseless descriptions, but these are never explained or distinguished from tense-inspecific descriptions.

⁴ Zimmerman, D., ‘Temporary Intrinsics and Presentism’, Metaphysics: The Big Questions, van Inwagen, P. and Zimmerman, D. (eds) (Malden, Mass.: Blackwell, 1998), 206–219Google Scholar.

⁵ Mott, P., ‘Dates, Tenseless Verbs and Token-Reflexivity’, Mind 82, No. 325 (January 1973), 73–85CrossRefGoogle Scholar.

⁶ Fine, K., ‘Necessity and Non-Existence’, Modality and Tense: Philosophical Papers (New York: OUP, 2005), 322CrossRefGoogle Scholar; though note that Fine takes ‘exists’ to be a tensed predicate.

⁷ The objections discussed in this paragraph and footnote 9 were raised by Barry Lee.

⁸ Note that while ‘√2 is irrational, though he did not know it’ is also acceptable in the context, ‘√2 will be irrational, though he will not know it’ said of a future Pythagoras rediscovering the famous theorem after a mathematical dark age is also acceptable if a little unusual.

⁹ But what of worlds without times? Since the proposition expressed by ‘3 is prime’ is necessary, it must be true of those worlds, even if the sentence expressing it does not exist. Some care is needed here when we address the question of which proposition is expressed by an elliptical use of the present tense, for ‘a is, was and will be F’ is not equivalent to ‘a is always F’. The former is the conjunction of three statements, each of which is false of a world without time, because the truth-conditions of each require a relation between the time of utterance and the time at which the object instantiates the property. But, if the logical form of the latter is ‘For all t, a is F at t’, then, on the standard understanding of the universal quantifier, it is trivially true in a world without times. But then ‘3 is even’ would also be true at the timeless world, so we cannot take its apparent tenselessness to consist in its equivalence to ‘3 is always prime’ on pain of denying the necessity of number theory and much else besides. Of course, the timeless world is only a problem if it is coherent, and we might doubt that genuine timelessness rather than time without change is really coherent. Certainly, no principle of recombination could ever get us to this conclusion (see Efird, D. and Stoneham, T., ‘What is the Principle of Recombination?’, dialectica 62, No. 4 (December 2008), 483–94)CrossRefGoogle Scholar.

¹⁰ Szabó, Z., ‘Counting across Times’, Philosophical Perspectives 20, No. 1 (November 2006)CrossRefGoogle Scholar, fn. 4.

¹¹ Jucas, J., The Future (Oxford: OUP, 1989), 16–7Google Scholar.

¹² This move can be found in Bryan Frances' unpublished 2004 paper ‘Existence, Quantification and Time’, http://www.personal.leeds.ac.uk/~phljwm/CMM%20site/Online_papers/ExistenceTime.pdf (accessed 28/11/2008). He has since refined the move considerably in ‘The Relation of Existence to Time’, http://www.fordham.edu/philosophy/frances/presentism.doc (accessed 28/11/2008), so that the disagreement is not over the extension of the fundamental ontological concept, but over which ontological concept is the fundamental one. This gets around worry (2) below.

¹³ The point that the semantics of quantification does no ontological work until one has independently specified a domain is made against T. Sider's four dimensionalism by McCall, S. and Lowe, E. J.: ‘As an ontologist, Sider is free to stipulate that his domain is restricted to temporal parts and mereological fusions thereof, but his choice is not dictated by quantification theory or its semantics’ (‘The 3D/4D Controversy: A Storm in a Teacup’, Nous 40, No. 3 (October 2006), 572)Google Scholar.

¹⁴ Of course, if the falsity of <p> has the same presupposition, it is not false either, so this presentist thesis would entail a failure of bivalence.

¹⁵ As formulated, (TM₁) only speaks about what is true now, and that is sufficient to generate a disagreement between the presentist and the eternalist. But the presentist also owes us an account of what was true and what will be true, for if it is true now that there was a British Empire, then surely it was once true that there is a British Empire. Intuitively we might think that it is now true that there was a British Empire because it was once true that there is a British Empire, a truth which was made true then by the existence of the British Empire. But the presentist (unlike the gradualist) cannot accept this without qualification, for it seems to imply that the present truth of <There was an Empire> is in virtue of a truthmaker which did exist but does no longer. Typically presentists will say that the ‘because’ in the last sentence but one misreads the truthvalue link: <a was F> is true iff <a is F> was true. The intuitive view takes the righthand side to explain the lefthand side, but the presentist thinks that is not possible (given (TM₁)), so claims that the truthmaker for the lefthand side can be a truthmaker for the righthand side. This means that they need to find present truthmakers for past tense claims, or deny that they are either true or false, which is exactly what we should expect, since a presentist is an anti-realist about the past (see Dummett, M., ‘The Reality of the Past’, reprinted in Truth and other Enigmas (London: Duckworth, 1978)Google Scholar).

¹⁶ Armstrong, D., Truth and Truthmakers (Cambridge: CUP, 2004), 11CrossRefGoogle Scholar.

¹⁷ In fact, there needs to be another assumption here to get the claim that the possible future which will happen at W is not the same as the one which will happen at W', namely that there cannot be possible worlds which are indiscriminable at all times. But no such metaphysical assumptions are needed for the necessary truth of <only one of the possible futures will happen>.

¹⁸ Since propositions with proper truthmakers may also have improper ones, this definition needs to be used with care.

¹⁹ Strictly, the Open Future entails the disjunction Presentism or Gradualism.

²⁰ An ancestor of this paper was read at a workshop on Temporal Externalism in Toronto in 2006, sponsored by the British Academy, and a parent at the Mathematical Physics Research Group in York in 2007. I am grateful to Barry Lee and David Efird for generous and helpful comments.