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The minimal A-theory


Timothy Williamson thinks that every object is a necessary, eternal existent. In defense of his view, Williamson appeals primarily to considerations from modal and tense logic. While I am uncertain about his modal claims, I think there are good metaphysical reasons to believe permanentism: the principle that everything always exists. B-theorists of time and change have long denied that objects change with respect to unqualified existence. But aside from Williamson, nearly all A-theorists defend temporaryism: the principle that there are temporary existents. I think A-theorists are better off without this added commitment, but I will not argue for that in any great detail here. Instead, I will contend that a very tempting argument for temporaryism is unsound. In the first half of the paper, I will develop the Moorean “common sense” argument for temporaryism and dispute its central premise, namely that temporaryism is the best generalization from our ordinary beliefs about creation, destruction, coming to be, and passing away. I will argue that given the pervasive vagueness in our ordinary beliefs and the background commitments of all A-theories, temporaryists cannot claim to have the common sense view because no party can accommodate most of our common sense beliefs. In the second half of the paper, I will propose a permanentist A-theory that explains all change over time as a species of property change. I call it the minimal A-theory, since it dispenses with the change in existence assumption. As we’ll see, the permanentist alternative performs well enough in explaining our ordinary beliefs, and it has better prospects for answering three objections commonly levied against A-theories.

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  1. 1.

    Hirsch (2009) and Hofweber (2009b).

  2. 2.

    Quine exegesis is no easy matter, but van Inwagen (1998) does an able job linking this methodological principle back to Quinean doctrines. Sider (2009) gives updated arguments for the principle. In the change debate, we see it explicitly assumed by A-theorists—Zimmerman (1998, p. 210) and Crisp (2004, pp. 16–17)—as well as B-theorists—Sider (2001, p. 17).

  3. 3.

    Examples of A-theories can be found in Prior (1998), Zimmerman (1998), Crisp (2003), Markosian (2004), Merricks (2007), Broad (1923), Adams (1989), Forrest (2006), and Williamson (2002).

  4. 4.

    In Chapt. 4 of Sullivan ((2011), I develop an A-theory that dispenses with tense operators in favor of tensed predicates. But the operator-free A-theory is irrelevant to the arguments of this paper since it presupposes permanentism.

  5. 5.

    We find versions of the temporal parts theory in Russell (1915), Quine (1950), Smart (1963), Lewis (1986), Price (1996), and Sider (2001). The view is sometimes called “four-dimensionalism.”

  6. 6.

    Thomson (1983), van Inwagen (1990), and Gibson and Pooley (2006). Gibson and Pooley give a relativistic gloss on what it is for an object to have a time-relational property. The views are sometimes called “endurantist B-theories.”

  7. 7.

    Williamson coins the terms “temporaryism” and “permanentism” in forthcoming work. I learned them at his 2010 Mesthene Lecture at Rutgers, “Actualism Versus Possibilism, Contingentism Versus Necessitism.” We can imagine an (albeit strange) A-theorist who thinks that temporarily there are only permanent existents. He might prefer temporary existence to be expressed as \(\neg\square\forall x\square\exists y(x=y). \) With minor amendments, all of the arguments to come should work equally well against this weaker form of the principle, and for ease of exposition, I will use the form above.

  8. 8.

    Frege and Russell seem to be the founders of this camp, because they argue that the content of a “tensed” sentence or thought must refer to a proposition with an explicit time reference. See Frege (1997, pp. 331–333) and Russell (1978, p. 32).

  9. 9.

    For example: Williamson (1998, 2000b, 2002, 2010).

  10. 10.

    Zimmerman (2008, p. 211).

  11. 11.

    Markosian (2004, p. 48).

  12. 12.

    At least neo-Quinean formulations of presentism entail the temporary existence principle.

  13. 13.

    For example, Broad (1923), Adams (1989), Tooley (1997) and Forrest (2006).

  14. 14.

    Lycan calls arguments of roughly this form plausibility comparison arguments and argues that they are the most charitable interpretation of the original Moore. See Lycan (2001). Like Lycan, I take “common sense” to mean (roughly) highly plausible for many people.

  15. 15.

    If you think “no brain in vat knows she has hands” is not commonsensical enough, we can break down the assumptions even further, perhaps: “Brains in vats don’t have hands” and “If Sullivan knows she has hands, then Sullivan has hands.”

  16. 16.

    There is, of course, an equally good way of expressing “No mere brain in vat knows Sullivan has hands” as \(\neg\exists x(B(x)\wedge K(x,\alpha)).\)

  17. 17.

    “Frosty will be destroyed.” and “The Sun came to be.” employ more fine-grained tense operators than □ but entail sentences that obey the more general schema.

  18. 18.

    For example, see Sider (2001, pp. 212–215).

  19. 19.

    For versions of the logic objections, see Williamson (1998) and Sider (2001, pp. 76–78). For an overview of options for handling the objection, see Sullivan (2012).

  20. 20.

    Williamson gives this argument in Williamson (1998, p. 265), though the point has been in the literature since Prior. For replies to the problem of past singular terms, see Prior (2003, pp. 16–17) and Markosian (2004). Prior thinks names for merely past or future objects are tacit descriptions. Markosian treats them as Fregean senses. Another approach treats them as names for uninstantiated essences. Inspiration for versions of the essence semantics can be found in Plantinga (1974) and Adams (1989, pp. 29–31).

  21. 21.

    Sider gives a nice presentation of this problem in Sider (2001, pp. 25–35). For an extended discussion of presentist answers to the motion problem, see Zimmerman (Forthcoming).

  22. 22.

    The argument of this section roughly follows a style of argument Sider uses on behalf of the temporal parts theory of change in Sider (2001, pp. 120–139).

  23. 23.

    Lewis and Fine are leading proponents of supervaluationism. See Fine (1975) and Lewis (1993). Most supervaluationists concede that “candidate” is also vague, and so they adopt higher order supervaluations as well. There are multiple precisifications for “candidate denotation” in a given context.

  24. 24.

    See Williamson (1994).

  25. 25.

    See also Evans (2002).

  26. 26.

    See Barnes (2010) and Baker (2007, pp. 121–141).

  27. 27.

    It isn’t even clear we should quantify over quantum “objects.” We’ve yet to settle the category for waves and fields.

  28. 28.

    Compare to the paraphrases that would seem appropriate for “All stars gradually redden” and “One snowman will gradually yellow.” We’d regiment these as:

    $$ D_{L}\left\{\begin{array}{l}\forall x(Star(x)\rightarrow\neg\square\triangle(Rx\vee\neg Rx)).\\ \exists x(Snowman(x)\wedge\neg\square\triangle(Yx\vee\neg Yx)). \end{array}\right. $$
  29. 29.

    Some physicalists go even further, assuming unconditionally that everything is essentially spatiotemporally located.

  30. 30.

    An objection in this spirit (directed at B-theorists) can be found in Yourgrau (1987).

  31. 31.

    Zimmerman (1998, p. 212).

  32. 32.

    Prior (1998, p. 80).

  33. 33.

    Russell (1978, p. 29).

  34. 34.

    For example Dorr argues for a “no brute necessities” principle—metaphysical theories should try to reduce or eliminate primitive necessity claims. Many essentialist claims are brute necessities. See Dorr (2004, 2008).

  35. 35.

    For details on this proposal, see Sullivan (2011).

  36. 36.

    I am grateful to Dean Zimmerman for suggesting the limited essentialist view and still uncertain as to whether he could become a poached egg.

  37. 37.

    Quine (1953, p. 4).

  38. 38.

    Schaffer (2009, p. 362). Emphasis is mine.

  39. 39.

    Fine (2009) and Hofweber (2009a).

  40. 40.

    The account is developed most fully in a trilogy of papers: Williamson (1998, 2000a, 2002).

  41. 41.

    For example, Lowe and Merricks think that objects come into and out of existence, but it is a primitive matter when they begin and when they end. See Merricks (1998) and Lowe (1996, pp. 41–43).


  1. Adams, R. M. (1989). Time and thisness. In H. Wettstein, J. Almog, & J. Perry (Eds.), Themes from Kaplan (pp. 23–42). Oxford: Oxford University Press.

    Google Scholar 

  2. Baker, L. R. (2007). The metaphysics of everyday life: An essay in practical realism. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  3. Barnes, E. (2010). Ontic vagueness: A guide for the perplexed. Nous, 44, 601–627.

    Article  Google Scholar 

  4. Broad, C. D. (1923). Scientific thought. London: Routledge and Keegan Paul, Ltd.

    Google Scholar 

  5. Crisp, T. (2003). Presentism. In M. J. Loux & D. W. Zimmerman (Eds.), The Oxford handbook of metaphysics (pp. 211–246). Oxford: Oxford University Press.

    Google Scholar 

  6. Crisp, T. (2004). On presentism and triviality. Oxford Studies in Metaphysics, 1, 15–20.

    Google Scholar 

  7. Dorr, C. (2004). Non-symmetric relations. Oxford Studies in Metaphysics, 1, 155–194.

    Google Scholar 

  8. Dorr, C. (2008). There are no abstract objects. In J. Hawthorne, T. Sider, & D. W. Zimmerman (Eds.), Contemporary debates in metaphysics (pp. 11–31). Oxford: Blackwell.

    Google Scholar 

  9. Evans, G. (2002). Can there be vague objects? In Collected papers (pp. 176–177). Oxford: Clarendon Press.

  10. Fine, K. (1975). Vagueness, truth and logic. Synthese, 30, 265–300.

    Article  Google Scholar 

  11. Fine, K. (2009). The question of ontology. In D. J. Chalmers, D. Manley, & R. Wasserman (Eds.), Metametaphysics: New essays on the foundations of ontology (pp. 157–177). Oxford: Oxford University Press.

    Google Scholar 

  12. Forrest, P. (2006). General facts, physical necessity, and the metaphysics of time. Oxford Studies in Metaphysics, 2, 137–154.

    Google Scholar 

  13. Frege, G. (1997). Thought. In M. Beaney (Ed.), The Frege reader (pp. 325–345). Oxford: Blackwell.

    Google Scholar 

  14. Gibson, I & Pooley, O. (2006). Relativistic persistence. Philosophical Perspectives, 20, 157–198.

    Article  Google Scholar 

  15. Hirsch, E. (2009). Ontology and alternative languages. In D. J. Chalmers, D. Manley, & R. Wasserman (Eds.), Metametaphysics: New essays on the foundations of ontology (pp. 231–259). Oxford: Oxford University Press.

    Google Scholar 

  16. Hofweber, T. (2009a). Ambitious, yet modest, metaphysics. In D. J. Chalmers, D. Manley, & R. Wasserman (Eds.), Metametaphysics: New essays on the foundations of ontology (pp. 260–289). Oxford: Oxford University Press.

    Google Scholar 

  17. Hofweber, T. (2009b). The meta-problem of change. Nous, 2, 286–314.

    Article  Google Scholar 

  18. Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell.

    Google Scholar 

  19. Lewis, D. (1993). Many, but almost one. In Papers in metaphysics and epistemology (pp. 164–182). Cambridge: Cambridge University Press.

  20. Lowe, E. J. (1996). Subjects of experience. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  21. Lycan, W. (2001). Moore against the new skeptics. Philosophical Studies, 103, 35–53.

    Article  Google Scholar 

  22. Markosian, N. (2004). A defense of presentism. Oxford Studies in Metaphysics, 1, 83–106.

    Google Scholar 

  23. Merricks, T. (1998). There are no criteria of identity over time. Nous, 32, 106–124.

    Article  Google Scholar 

  24. Merricks, T. (2007). Truth and ontology. Oxford: Oxford University Press.

    Book  Google Scholar 

  25. Plantinga, A. (1974). Naming and necessity. Oxford: Clarendon Press.

    Google Scholar 

  26. Price, H. (1996). Time’s arrow and Archimedes’ point: New directions for the physics of time. Oxford: Oxford University Press.

    Google Scholar 

  27. Prior, A. N. (1998). The notion of the present. In P. van Inwagen & D. W. Zimmerman (Eds.), Metaphysics: The big questions (pp. 80–82). Oxford: Blackwell.

    Google Scholar 

  28. Prior, A. N. (2003). Changes in events and changes in things. In P. Hasle, P. Ohrstrom, T. Brauner, and J. Copeland (Eds.), Papers on time and tense (pp. 7–20). Oxford: Oxford University Press.

    Google Scholar 

  29. Quine, W. V. (1950). Identity, ostension, and hypostasis. The Journal of Philosophy, 47, 621–633.

    Article  Google Scholar 

  30. Quine, W. V. (1953). On what there is. In From a logical point of view (pp. 1–19). New York: Harper and Ross.

  31. Russell, B. (1915). On the experience of time. The Monist, 25, 212–233.

    Google Scholar 

  32. Russell, B. (1978). Meinong’s theory of complexes and assumptions. In D. Lackey (Ed.), Essays in analysis (pp. 21–76). New York: George Braziller, Inc.

    Google Scholar 

  33. Schaffer, J. (2009). On what grounds what. In D. J. Chalmers, D. Manley, & R. Wasserman (Eds.), Metametaphysics: New essays on the foundations of ontology (pp. 347–383). Oxford: Oxford University Press.

    Google Scholar 

  34. Sider, T. (2001). Four-dimensionalism. Oxford: Oxford University Press.

    Book  Google Scholar 

  35. Sider, T. (2009). Ontological realism. In D. J. Chalmers, D. Manley, & R. Wasserman (Eds.), Metametaphysics: New essays on the foundations of ontology (pp. 384–423). Oxford: Oxford University Press.

    Google Scholar 

  36. Smart, J. J. C. (1963). Philosophy and scientific realism. New York: The Humanities Press.

    Google Scholar 

  37. Sullivan, M. (2011). The A-theory: A theory. Ph.D. thesis, Rutgers University.

  38. Sullivan, M. (2012). Problems for temporary existence in tense logic. Philosophy Compass, 7, 43–57.

    Article  Google Scholar 

  39. Thomson, J. J. (1983). Parthood and identity across time. The Journal of Philosophy, 80, 201–220.

    Article  Google Scholar 

  40. Tooley, M. (1997). Time, tense and causation. Oxford: Clarendon Press.

    Google Scholar 

  41. van Inwagen, P. (1990). Four-dimensional objects. Nous, 24, 245–255.

    Article  Google Scholar 

  42. van Inwagen, P. (1998). Meta-ontology. Erkenntnis, 48, 233–250.

    Article  Google Scholar 

  43. Williamson, T. (1994). Vagueness. London: Routledge.

    Google Scholar 

  44. Williamson, T. (1998). Bare possibilia. Erkenntnis, 48, 257–273.

    Article  Google Scholar 

  45. Williamson, T. (2000a). Existence and contingency. Proceedings of the Aristotelian Society, 100, 117–139.

    Article  Google Scholar 

  46. Williamson, T. (2000b). The necessary framework of objects. Topoi, 19, 201–208.

    Article  Google Scholar 

  47. Williamson, T. (2002). Necessary existents. In A. O’Hear (Ed.), Logic, thought, and language (pp. 233–251). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  48. Williamson, T. (2010) Necessitism, contingentism, and plural quantification. Mind, 119, 657–748.

    Article  Google Scholar 

  49. Yourgrau, P. (1987). The dead. Journal of Philosophy, 84, 84–101.

    Article  Google Scholar 

  50. Zimmerman, D. W. (1998). Temporary intrinsics and presentism. In P. van Inwagen & D. W. Zimmerman (Eds.), Metaphysics: The big questions (pp. 206–218). Oxford: Blackwell.

    Google Scholar 

  51. Zimmerman, D. W. (2008). The privileged present: Defending an A-theory of time. In D. W. Zimmerman, T. Sider, J. Hawthorne (Ed.), Contemporary debates in metaphysics (pp. 211–225). Oxford: Blackwell.

    Google Scholar 

  52. Zimmerman, D. W. (Forthcoming). Presentism and the space-time manifold. In The Oxford handbook of time. Oxford: Oxford University Press.

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I am grateful to Tom Donaldson, Andy Egan, Ben Levinstein, Ned Markosian, Ted Sider, Brad Skow, Jason Turner, Jenn Wang,and Dean Zimmerman for advice on drafts of this paper. I have also benefited extensively from feedback from audiences at Rutgers, Notre Dame, the 2011 Bellingham Summer Philosophy Conference, and a reading group at the University of Virginia.

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Correspondence to Meghan Sullivan.

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Sullivan, M. The minimal A-theory. Philos Stud 158, 149–174 (2012).

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  • A-theory of time
  • Time
  • Existence
  • Property change vague change
  • Essentialism