¹ van Inwagen, Peter, ‘Why is there anything at all?’, in his Ontology, Identity, and Modality. Essays in Metaphysics (Cambridge: Cambridge University Press, 2001), 61Google Scholar.

² van Inwagen, ‘Why is there anything at all?’, 61, fn. 6, says that the essence of his argument was anticipated by Nozick, Robert, Philosophical Explanations (Cambridge, Massachusetts: Harvard University Press, 1981), 127–28Google Scholar. True, but it is also important to note that Nozick's is a sketch of an argument rather than a full argument, and there also seem to be some differences between what Nozick and van Inwagen say, for instance in Nozick the infinity of possible worlds (it is not even clear that they are possible worlds in Nozick's argument) seems to play no role.

³ van Inwagen, ‘Why is there anything at all?’, 57.

⁴ Heil, John, ‘Contingency’, in Goldschmidt, T. (ed.), The Puzzle of Existence: Why is there Something rather than Nothing? (New York and London: Routledge, 2013), 174Google Scholar; E. J. Lowe, ‘Metaphysical Nihilism Revisited’, in T. Goldschmidt (ed.), The Puzzle of Existence, 187.

⁵ van Inwagen, ‘Why is there anything at all?’, 62 (italics in the original).

⁶ Gillies, Donald, Philosophical Theories of Probability (London and New York: Routledge, 2000), 67Google Scholar.

⁷ van Inwagen, ‘Why is there anything at all?’, 62.

⁸ Mawson, Tim, ‘Why is there anything at all?’, in Nagasawa, Y. and Wielenberg, E. (eds), New Waves in Philosophy of Religion (Basingstoke: Palgrave Macmillan, 2009), 43Google Scholar; cf. Matthew Kotzen, ‘The Probabilistic Explanation of Why there is Something rather than Nothing’, in T. Goldschmidt (ed.), The Puzzle of Existence, 218–219, fn. 6.

⁹ Mawson, ‘Why is there anything at all?’, 44, 53.

¹⁰ I am indebted to David Efird for pressing the issue of the universality of the accessibility relation in connection with the topic of this paper.

¹¹ That is, it is a very safe assumption assuming that there is a proposition – as opposed to a sentence – that says of itself that it is true. But I have defended this assumption. See Rodriguez-Pereyra, Gonzalo, ‘Grounding is not a strict order’, Journal of the American Philosophical Association 1 (2015), 527CrossRefGoogle Scholar.

¹² What makes it true in those worlds where it is true? The fact that it is true. That is, the truthmaker of the truth-teller is the fact that it is true. See Rodriguez-Pereyra, ‘Grounding is not a strict order’, 520, 525, where I argue that the fact that the truth-teller is true is the alethic-fact ground of the fact that the truth-teller is true; but the alethic-fact grounding relation is a relation linking the truthmaker of a proposition and the fact that it is true; so it follows that the truthmaker of the truth-teller is the fact that it is true.

¹³ van Inwagen, ‘Reflections on the Chapters by Draper, Russell, and Gale’, in Howard-Snyder, D. (ed.), The Evidential Argument from Evil (Bloomington and Indianapolis: Indiana University Press, 1996), 239Google Scholar.

¹⁴ The loops example that is to follow was suggested to me by Øystein Linnebo who, nevertheless, is skeptical about the truth-teller and the loops of propositions each one of which says that the next one is true.

¹⁵ I have wondered whether the example could be made to work with finite lists of propositions each one of which says that the next one is true and the last one says of itself that it is true (and where the 1-list is the truth-teller itself). The members of such lists can consistently be all true or all false. Here is an argument that the example does not work with such lists. It is plausible that there is only one proposition that says of itself that it is true, and so it is plausible that there is only one proposition that says of the truth-teller that it is true, and only one proposition that says of the latter proposition that it is true, and so on. So, if in a world the members of the n-list are all true (false), the members of the n+1-list must all be true (false). This means that there are at most two empty worlds varying according to the truth-value of the members of the lists: one in which all the members of all lists are true and one in which all the members of all lists are false.

¹⁶ Efird, David and Stoneham, Tom, ‘The Subtraction Argument for Metaphysical Nihilism’, The Journal of Philosophy 102 (2005), 311–312CrossRefGoogle Scholar.

¹⁷ van Inwagen, ‘Why is there anything at all?’, 58.

¹⁸ Ibid., 57.

¹⁹ Such empty worlds differing with respect to the geometry of space will also differ with respect to the counterfactuals holding in them, since the different geometry of space in different worlds would ground different counterfactuals.

²⁰ E. J. Lowe claimed that van Inwagen's argument presupposes that all abstract objects are necessary (Lowe, ‘Why is there anything at all?’, Proceedings of the Aristotelian Society, Supplementary Volume LXX (1996), 115). But, in fact, as I have already pointed out, what it presupposes is that abstract objects that do not depend on concrete ones are necessary and that none of their intrinsic properties are contingent.

²¹ van Inwagen, ‘Why is there anything at all?’, 67.

²² Ibid., 65.

²³ Ibid., 65.

²⁴ Ibid., 66.

²⁵ van Inwagen, ‘Why is there anything at all?’, 66.

²⁶ Ibid., 70.

²⁷ For van Inwagen there are no non-existent entities: see van Inwagen, ‘Meta-ontology’, Erkenntnis 48 (1998), 235Google Scholar.

²⁸ This is a simplification in two ways. First, each one of those four states is not maximal since they do not include anything about the rest of the world. Second, each one of those four states is not maximal since they do not fully specify the way in which the coin fails to land, or lands heads, or lands tails, or lands on its edge.

²⁹ van Inwagen, ‘Reflections on the Chapters by Draper, Russell, and Gale’, 223–25, and ‘Why is there anything at all?’, 63.

³⁰ van Inwagen, ‘Reflections on the Chapters by Draper, Russell, and Gale’, 239.

³¹ Erik Carlson and Erik Olsson consider worlds (‘universes’ in their terminology, but their universes correspond to van Inwagen's worlds: Carlson and Olsson, ‘The Presumption of Nothingness’, Ratio 14 (2001), 208, fn. 22Google Scholar) containing only a fair coin and a coin-tossing mechanism that repeatedly tosses the coin until tails comes up and then it never tosses the coin again. They think it is clear that worlds where tails comes up on the first toss are more probable than worlds where there is a sequence of heads before the first tails comes up (‘The Presumption of Nothingness’, 209–11). I am not convinced. While I agree that, within each world, before the coin lands for the first time, the sequence T (0.5 chance) is more probable than the sequences HT (0.25 chance), HHT (0.125 chance), and so on, it does not follow from this that a world where tails comes up on the first toss is more probable (i.e. has a greater probability of being the actual world) than worlds where tails comes up on the second toss, or the third toss, and so on. For nothing in the way they present their example entails that Reality is ‘loaded’ in any way and, in particular, nothing in their example entails that Reality is ‘loaded’ towards worlds where tails comes up on the first toss.

³² van Inwagen, ‘Why is there anything at all?’, 60, and Metaphysics (Boulder, Colorado: Westview Press. 2002), 122.

³³ van Inwagen, ‘Why is there anything at all?’, 60.

³⁴ van Inwagen, ‘Why is there anything at all?’, 60.

³⁵ As I understand it, Earl Conee makes this sort of criticism to what he calls the statistical explanation of why there is something rather than nothing, although he does not refer to van Inwagen's argument (Conee, E. and Sider, T., Riddles of Existence. A Guided Tour of Metaphysics (Oxford: Oxford University Press, 2014), 122Google Scholar.

³⁶ van Inwagen, ‘Why is there anything at all?’, 61, fn. 5.

³⁷ Benjamin Schnieder, ‘On the relevance of grounds’ (forthcoming), argues that in no case does the fact that something is necessary grounds its obtaining. Even if Schnieder is right, that does not affect my central point, which is that having a high probability, even probability 1, does not explain the obtaining or occurring of anything.

³⁸ Thus I disagree with Hempel, according to whom showing that a certain event was to be expected is what enables one to understand why it happened. See Hempel, Carl G., ‘Aspects of Scientific Explanation’, in his Aspects of Scientific Explanation and Other Essays in the Philosophy of Science (New York: The Free Press, 1965), 337Google Scholar.

³⁹ That if a claim does not answer the question of why something happened, then it does not explain why it happened, is obviously the case if explanations are answers to why-questions. See van Fraassen, Bas, The Scientific Image (Oxford: Clarendon Press, 1980), 134CrossRefGoogle Scholar. But the point I am making does not commit me to this theory of explanation. For, whatever the right theory of explanation, it is independently plausible that what does not answer a question ‘Why p?’ is not an explanation of why p.

⁴⁰ I thank Paul Audi, Eduardo Barrio, Earl Conee, Eleonora Cresto, Eileen Daly-Boas, Richard Dees, David Efird, James Grant, Anil Gomes, John Heil, Alison Hills, Peter van Inwagen, Nick Jones, Kolja Keller, John Komdat, Jonathan Kvanvig, Brian Leftow, Øystein Linnebo, Kris MacDaniel, Tim Mawson, Hugh Mellor, Deborah Modrak, Alex Paseau, Martin Pickup, Lucas Rosenblatt, Benjamin Schnieder, Jannai Shields, Tom Sinclair, Damian Szmuc, Tuomas Tahko, Edward Wierenga, Alastair Wilson, Tim Williamson, and Ezequiel Zerbudis for discussion on the content of previous versions of this paper.