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McTaggart’s Paradox

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Part of the Synthese Library book series (SYLI,volume 293)

Abstract

Undoubtedly the most celebrated argument against an A-Theory of time is the attempt by the British idealist J. M. E. McTaggart to demonstrate that an Aseries of events is self-contradictory or leads to a vicious infinite regress of A-theoretic determinations.1 Indeed, Richard Gale has remarked that “If one looks carefully enough into the multitudinous writings on time by analysts, one can detect a common underlying problem, that being that almost all of them were attempting to answer McTaggart’s paradox.”2 Although McTaggart himself regarded his demonstration as a proof that time does not exist, certain contemporary B-theorists employ versions of his argument to prove the unreality of tense and temporal becoming, which, they claim, are not essential to time. Let us begin with McTaggart’s own statement of the argument.

Keywords

  • Actual World
  • Tensed Fact
  • Infinite Regress
  • Existential Quantifier
  • Ontological Argument

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References

  1. Published first as J. Ellis McTaggart, “The Unreality of Time,” Mind 17 (1908): 457–474, the argument appears in chapter 33 of McTaggart’s most important work, The Nature of Existence (1927), in which McTaggart responds to objections from Bertrand Russell and C. D. Broad, a B-theorist and an A-theorist respectively. For a good review of the literature see David J. Farmer, Being in Time: The Nature of Time in Light of McTaggart’s Paradox (Lanham, Md.: University Press of America, 1990).

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  2. Richard M. Gale, The Language of Time, International Library of Philosophy and Scientific Method (London: Routledge, Kegan & Paul, 1968), p. 6.

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  3. John McTaggart Ellis McTaggart, The Nature of Existence, 2 vols., ed. C. D. Broad (Cambridge: Cambridge University Press, 1927; rep. ed.: 1968), 2: 9.

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  4. McTaggart, Nature of Existence, 2: 12.

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  5. In secs. 327–328 McTaggart has a curious excursus on A-determinations as relations, his preferred view. He maintains that if anything is, for example, present, then it must be present in relation to something else outside the time series. For A-determinations change, but relations between members of the time series do not change. Hence, there must be some entity X outside the time series in relation to which one term of the A-series is uniquely present, the rest being past or future. McTaggart cannot imagine what X might be, and yet its existence, he insists, is foundational to the A-series.

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  6. So if A-determinations are relational, they must be relations to other terms in the time series. Buller and Foster point out that A-determinations could be construed as relations to items in either the A-series or the B-series (David J. Buller and Thomas R. Foster, “The New Paradox of Temporal Transience,” Philosophical Quarterly 42 [19921: 358–359). With respect to the A-series, an event E is future relative to some moment ten years ago. With respect to the B-series, E is past relative to 1 October 1994. McTaggart here addresses only the second option, which effectively reduces A-determinations to B-determinations. On the first option, A-determinations are changing relations, for the moment picked out by the A-position ten years ago changes every year, so that E is not changelessly future relative to a moment ten years ago. The difficulty with this option is that it iterates tenses relative to the present, which must then be present relative to the present relative to the present, and so on, which seems, as McTaggart complains, to be either a vicious circle or infinite regress. Perhaps for these reasons, with the possible exception of Schlesinger, no A-theorist has followed McTaggart in construing A-determinations as relations; most take them to be intrinsic properties.

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  7. McTaggart, Nature of Existence, 2: 21.

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  8. McTaggart, “Unreality of Time,” pp. 468–469.

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  9. Ibid., p. 469. The fact that he speaks of time’s being in time shows that he is contemplating an infinite regress of time dimensions, not an infinite regress of increasingly complex tenses.

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  10. David H. Sanford, “McTaggart on Time,” Philosophy 43 (1968): 373.

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  11. McTaggart, “Unreality of Time,” p. 469.

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  12. McTaggart, Nature of Existence, 2: 21–22.

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  13. Farmer, Being in Time, p. 87; so also Paul Marhenke, “McTaggart’s Analysis of Time,” in The Problem of Time, University of California Publications in Philosophy 18 (Berkeley: University of California Press, 1935), p. 151.

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  14. McTaggart, Nature of Existence, 2: 23.

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  15. McTaggart, “Unreality of Time,” p. 469.

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  16. McTaggart, Nature of Existence, 2: 22.

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  17. C. D. Broad, An Examination of McTaggart’s Philosophy, 2 vols. (Cambridge: Cambridge University Press, 1938; rep. ed.: New York: Octagon Books, 1976), 2: 317.

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  18. Ibid., 2: 227. Broad urged that both the policeman’s bull’s eye metaphor and the growing past metaphor of temporal becoming err in presupposing that phases of the world which have not yet supervened or have been already superseded in some sense co-exist with each other and the present. Smart’s retort, “If `coexist’ means `coexist now’ then we can reply that past and present stages do not coexist now but they coexist (using this verb tenselessly) and of course they coexist at different times” (J. J. C. Smart, “Time and Becoming,” in Time and Cause, ed. Peter Van Inwagen, Philosophical Studies Series in Philosophy [Dordrecht: D. Reidel, 1980], p. 9), is unworthy of Broad, who as a former B-theorist most certainly was aware of and did not confuse these two senses (Hastings’ Encyclopaedia of Religion and Ethics, s.v. “Time,” by C. D. Broad). His point is that by asserting the tenseless coexistence of all things/events (i.e., presupposing a B-theoretic ontology), one tums temporal becoming into a kind of qualitative change, which it is not, thereby landing one in McTaggart’s Paradox. For a contemporary analogue of the policeman’s bull’s-eye, see Errol E. Harris, The Reality of Time, SUNY Series in Philosophy (Albany, N. Y.: State University of New York Press, 1988), pp. 24, 31, who lands himself squarely in McTaggart’s Paradox by construing temporal becoming like a film (the B-series) passing over the lens of a projector (the present moment).

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  19. We may reserve discussion of these difficulties for chap. 7 on the myth of passage.

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  20. Broad, Examination,2: 308. By “presentedness,” Broad has reference to the specious present.

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  21. See Alvin Plantinga, The Nature of Necessity, Clarendon Library of Logic and Philosophy (Oxford: Clarendon Press, 1974), pp. 209–210. Broad himself said that Anselm’s argument presupposes that there “is sense in talking of a comparison between a non-existent term and an existent one; and it produces the impression that this is like comparing two existing terms, e.g., a corpse and a living organism, one of which lacks life and the other of which has it” (C. D. Broad, Religion, Philosophy and Psychical Research [London: Routledge, Kegan & Paul, 1953], p. 182).

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  22. For a good statement of this point, see Gale, Language of Time, pp. 30–31, 240. See also the very interesting piece by Franklin C. Mason, “The Presence of Experience and Two Theories About Time,” Southern Journal of Philosophy 35 (1997): 75–89, who argues from the presentness of experience to presentism. If all times are equally real and at two different times I make the judgement “The experiences I have now occur at present,” then one judgement must be false; but each is self-evidently true. So all times cannot be equally real; if there are A-facts, presentism is true.

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  23. Broad wrote, “Nothing has happened to the present by becoming past except that fresh slices of existence have been added to the total history of the world. The past is thus as real as the present. On the other hand, the essence of a present event is, not that it precedes future events, but that there is quite literally nothing to which it has the relation of precedence. The sum total of existence is always increasing and it is this which gives the time series a sense as well as an order” (C. D. Broad, Scientific Thought,pp. 66–67).

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  24. For a contemporary defense of this theory, see Michael Tooley, Time, Tense, and Causation (Oxford: Clarendon Press, 1997).

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  25. McTaggart, Nature of Existence, 2: 26. 41 Ibid., 2: 27.

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  26. Levison concurs: “…if we do not assume that there is (tenselessly) any event which successively occupies past, present, and future temporal positions, then McTaggart’s incompatibility argument cannot get off the ground” (Arnold B. Levison, “Events and Time’s Flow,” Mind 96 [1987]: 350).

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  27. Storrs McCall, “Objective Time Flow,” Philosophy of Science 43 (1976): 337–362; cf. idem, A Model of the Universe, Clarendon Library of Logic and Philosophy (Oxford: Clarendon Press, 1994).

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  28. McCall, “Objective Time Flow,” p. 337.

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  29. Smart, “Time and Becoming,” p. 7.

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  30. McCall, “Objective Time Flow,” p. 348.

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  31. McCall writes, “If it be objected that the universe-tree which we have spoken of as constituting `the universe’ is a different universe-tree from one instant to the next, so that the extensions of `past event,’ `present event,’ and `possible future event’ change with time, then it can only be replied that this is correct, and reflects the dynamic character of theory D” (McCall, “Objective Time Flow,” p. 347). The different instants at which the whole tree is different are the hyper-instants, since on a single tree the universe is different from one co-ordinate time to another and yet this does not yield a dynamic theory. To get dynamism, the extensions of past, present, and possible future must change with hyper-time, not just on a single tree.

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  32. McCall, Model of the Universe, pp. 30–31.

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  33. Andros Loizou explains, “…no event or state of affairs is ever present simpliciter—it is present by implicit or explicit reference to a kind of events or states of affairs, as when we speak of the present eclipse, or by reference to a time scale, as when we speak of the present hour or day, and so on” (Andros Loizou, The Reality of Time [Brookfield, Ver.: Gower, 1986], p. 156; see also D. H. Mellor, Real Time [Cambridge: Cambridge University Press, 1981], pp. 17–18; Alan Padgett, God, Eternity, and the Nature of Time [New York: St. Martin’s Press, 1992], p. 115). Broad never discerned this solution and so was forced into adopting the Augustinian view that the present is a durationless instant or “event particle” and finally into espousing—ironically—the existence of a second time dimension in which the present event particle endures (C. W. K. Mundle, “Broad’s Views about Time,” in The Philosophy of C. D. Broad, ed. Paul Arthur Schilpp, Library of Living Philosophers [New York: Tudor, 1959], p. 367; C. D. Broad, “A Reply to My Critics,” in Philosophy of C. D. Broad, pp. 767–772)!

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  34. Mellor, Real Time, pp. 89–90.

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  35. Ibid., p. 24. Cf. L. Nathan Oaklander, “Zeilicovici on Temporal Becoming,” Philosophia 21 (1991): 329: “On the traditional tensed, or A-theory of time, the NOW is a particular or a property that moves along an ordered, but as yet non-temporal, C-series. The terms of the C-series exist (tenselessly) in unchanging relations to each other, and these unchanging relations become temporal relations as the NOW moves across them, so that one term, e is NOW when another term, e’ is future and then, when the NOW `hits’ e’, that is, when e’ is present, e is past.”

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  36. Broad, “Reply to My Critics,” p. 766.

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  37. Robin Le Poidevin, Change,Cause, and Contradiction: A Defense of the Tenseless Theory of Time (London: Macmillan, 1991), p. 30.

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  38. Contra the presupposition of Eddy M. Zemach, “Time and Self,” Analysis 39 (1979): 143–147; David Zeilicovici, “A (Dis)solution of McTaggart’s Paradox,” Ratio 28 (1986): 187. This sort of hybrid A-B-Theory, such as is defended by Smith (Quentin Smith, “The Infinite Regress of Temporal Attributions,” Southern Journal of Philosophy 24 [19861: 383–396; idem, “The Logical Structure of the Debate about McTaggart’s Paradox,” Philosophy Research Archives 14 [1988–891: 371–379, the latter being a reply to L. Nathan Oaklander, “McTaggart’s Paradox and the Infinite Regress of Temporal Attributions: a Reply to Smith,” Southern Journal of Philosophy 25 [1987]: 425–431) has been aptly characterized by Fitzgerald as a “property acquisition model” of temporal becoming (Paul Fitzgerald, “Nowness and the Understanding of Time,” in PSA 1972, BSPS 20, ed. Kenneth F. Schaffner and Robert S. Cohen [Dordrecht: D. Reidel, 1974], p. 261). But while we can perhaps make sense of, say, “The presidency of Bill Clinton presently has presentness,” it does not seem intelligible to assert, “The Battle of Waterloo presently has pastness,” since the Battle of Waterloo does not exist or occur at the present time. Yet Smith’s view that the pastness or futurity of an event presently inheres in that event seems to imply such a conclusion. So long as event e is present, we can make sense of Smith’s contention that the futurity of e’s pastness presently inheres in e and likewise that the pastness of e’s futurity presently inheres in e. But if e is a past or future event, it seems unintelligible to claim that presentness inheres in the inherence of pastness/futurity in e, since e does not presently exist so as to sustain the inherence of any properties in it. Perhaps Smith would prefer to say of a past event that pastness presently inheres in the inherence of presentness in e. But then events never lose or acquire their property of presentness; what changes is the tense of presentness’s inherence in e. But that interpretation seems as unintelligible as the first interpretation; for how can pastness presently inhere in e’s presentness, if e is a past event, since e’s presentness does not exist at the present time?

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  39. See E. J. Lowe, “The Indexical Fallacy in McTaggart’s Proof of the Unreality of Time,” Mind 96 (1987): 64–66, who seems, however, unduly diffident about tensed ascriptions of presentness to events, e.g., “E will be present,” which is unobjectionable so long as “present” is not an indexical synonymous with “now,” as Lowe mistakenly believes. Cf. E. J. Lowe, “Comment on Le Poidevin,” Mind 102 (1993): 171–173, where he objects to embedding one temporal indexical in the scope of another. But as the phenomenon of double indexing attests, such embedding is common and unproblematic, so long as we use the proper indexical, e.g., “Yesterday he promised to call today.” Lowe’s objection is really directed at failures to change the indexical words appropriately. But in ascriptions of presentness to an event, e.g., “Ninety years ago WWI was present,” Lowe fails to see that “present” is not an indexical word. In general the point of such paraphrases as offered in the text is to make it perspicuous that the original locutions do not in fact involve the ontological commitments some might take them to have (cf. William P. Alston, “Ontological Commitments,” Philosophical Studies 9 [1958]: 8–17).

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  40. John Wisdom, “Time, Fact and Substance,” Proceedings of the Aristotelian Society 29 (1928–29): 83. Following Wisdom are L. Susan Stebbing, “Some Ambiguities in Discussions concerning Time,” in Philosophy and History, ed. Raymond Klibansky and H. J. Paton (New York: Harper & Row; Harper Torchbooks, 1963), pp. 114–116; Richard Swinburne, “Tensed Facts,” American Philosophical Quarterly 27 (1990): 118. Mink indicts the Wisdom-Stebbing response because, while it does not make sense to ask “When is x present?”, it does make sense to ask “When was x present?” The statement “x is past” must mean, not merely entail, “x is past at a moment of time which is present” because it is equivalent to “x was present at a moment of time which was past” (Louis O. Mink, “Time, McTaggart and Pickwickian Language,” Philosophical Quarterly 10 [19601: 257). I must confess that the force of this argument escapes me. Mink seems to take “x was present at a moment of time which was past” to be the answer to “When was x present?” But if this is the answer, then it is absurd to ask “When was x present?” for the answer is the tautologous “in the past!” A proper answer would be to give a date, and a similar answer could be given to the query, “When is x present?”

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  41. It is not clear whether Smith, “Infinite Regress,” pp. 383–396 and Smith, “Logical Structure,” pp. 371–379 means to assert a regress of meanings or entailments, for he speaks both of providing an analysis of “E is present” and of drawing a series of entailments from it. If he really means to provide an analysis of the meaning of “E is present,” then his regress is not benign.

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  42. Mink charges that the refusal to analyze A- characteristics in terms of B-characteristics has serious negative consequences, e.g., complex tenses cannot be analyzed as complications of simple ones without the same explanation’s applying to simple tenses as well, such as analyzing the past tense as past with respect to the present (Mink, “Time,” p. 258). But the A-theorist could maintain that requirements of real tense necessitate a minimum of three determinations and no more.

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  43. Mellor, Real Time, pp. 3–4. Failing to assimilate this point is Ferrel Christensen, “McTaggart’s Paradox and the Nature of Time” Philosophical Quarterly 24 (1974): 289–299. He insists that tenses are adverbial operators, not predicates, because the latter generates an infinite regress. But the regress in question is, as Wisdom saw, entirely benign. For this reason one cannot agree with Shorter that “If we read the sentences `E is future’ and `E is past’… as containing a purely predicative copula, they are entirely compatible” (Shorter, “Reality of Time,” p. 325). For these sentences mean the same thing as “E will be” and “E has been” respectively, which are incompatible.

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  44. A. N. Prior, “Precursors of Tense Logic,” in Past, Present and Future (Oxford: Clarendon Press, 1967), p. 18.

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  45. Christensen, “McTaggart’s Paradox,” p. 297.

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  46. Quentin Smith, Language and Time (New York: Oxford University Press, 1994), p. 166.

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  47. A. N. Prior, “The Notion of the Present,” Studium Generale 23 (1970): 245. Similarly, Christensen has recently asserted, “To be present is simply to be, to exist, and to be present at a given time is just to exist at that time—no less and no more” (F. M. Christensen, Space-like Time [Toronto: University of Toronto Press, 1993], p. 168; cf. p. 226).

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  48. Prior, “Notion of the Present,” pp. 246–247.

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  49. See the incisive critique by Alvin Plantinga, “On Existentialism,” Philosophical Studies 44 (1983): 1–20.

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  50. For helpful anthologies and bibliographies, see Alvin Plantinga, ed., The Ontological Argument, with an Introduction by Richard Taylor (Garden City, N. Y.: Doubleday, 1965), and John H. Hick and Arthur C. McGill, eds., The Many-faced Argument (New York: Macmillan Co., 1967).

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  51. Immanuel Kant, Immanuel Kant’s “Critique of Pure Reason, trans. Norman Kemp Smith (London: Macmillan, 1929), pp. 504–505 (A598/B626–A599/B627); cf. p. 502 (A595/B623).

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  52. Alvin Plantinga, God and Other Minds (Ithaca, N. Y.: Cornell University Press, 1967), pp. 29–38.

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  53. Ibid., p. 35. Plantinga adds a further qualification which I omit for simplicity’s sake.

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  54. Alvin Plantinga, The Nature of Necessity, Clarendon Library of Logic and Philosophy (Oxford: Clarendon Press, 1974), p. 61.

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  55. Ibid., p. 137. Here Plantinga declines to take the easy way out of the classical argument for merely possible objects by denying that existence and non-existence are properties. So he says most of the arguments against their being properties are inconclusive and at best show existence, if a property, to be atypical. He does not repudiate his analysis in God and Other Minds and himself comes to the conclusion that non-existence is, at least, not a property.

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  56. Plantinga, God and Other Minds, p. 36.

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  57. C. D. Broad, “Arguments for the Existence of God,” [1925], in Religion, Philosophy and Psychical Research, International Library of Psychology, Philosophy, and Scientific Method (New York: Humanities Press, 1969), pp. 182–183.

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  58. Plantinga objects to Broad’s characterization of “There are cats and none of them fails to exist” as a platitude, since this sentence entails that cats do exist and so is not a mere tautology (Plantinga, God and Other Minds, p. 41). But perhaps we need not construe “mere platitudes” as tautologies; we could take Broad to be saying that the complex sentences analyzing existential propositions become redundant (of course, if there are cats, they exist!), while the sentences analyzing genuinely characterizing propositions do not.

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  59. Plantinga, God and Other Minds, p. 40.

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  60. Plantinga, Nature of Necessity, p. 150. J0 Ibid., p. 163; cf. 158–160.

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  61. Plantinga, God and Other Minds, p. 41.

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  62. See Jerome Schaffer, “Existence, Predication, and the Ontological Argument,” in Many-faced Argument, p. 234. Schaffer’s difficulties with Kant’s argument that existence is not a property are implicitly met by Plantinga’s analysis exposited above.

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  63. G. E. Moore, “Is Existence a Predicate?” [1936], in Ontological Argument, pp. 73–80.

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  64. William P. Alston, “The Ontological Argument Revisited,” in Ontological Argument, p. 88.

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  65. Plantinga, Nature of Necessity, chaps. 7, 8.

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  66. Thomas Aquinas De ente et essentia 3; idem, Summa theologiae la. 3. 5. ad 2; idem Summa contra gentiles 1. 22. 7. In this Aquinas was anticipated by the Arabic philosopher ibn Sina, as pointed out by F. Rahman, “Essence and Existence in Avicenna,” Mediaeval and Renaissance Studies 4 (1958): 1–17. Of course, Thomas uses “essence” in the Aristotelian sense, not in the sense of an individual essence; but the salient point is that existence is an instantial act.

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  67. Russell’s very confused statement of this view may be found in Bertrand Russell, “The Philosophy of Logical Atomism,” [1918], in Logic and Knowledge, ed. Robert Charles Marsh (London: George Allen & Unwin, 1956), pp. 232–241. Russell says that if you take any propositional function like xis a man and assert that it is sometimes true, that gives you the fundamental meaning of “existence.” When one says, “Men exist,” what one means is that there is at least one value for x such that x is a man is true. So existence is a predicate or property of a propositional function. “It is of propositional functions that you can assert or deny existence” (Ibid., p. 232). On Russell’s view, then, individual objects do not exist. This seems crazy until we appreciate the fact that Russell has completely redefined “existence.” When he says that it is a property of propositional functions, he is not using the word in the sense expressed when we say that there are propositional functions. Rather he redefines the word to indicate the property being sometimes true. We might be inclined to say that he is at liberty to define words as he pleases, but insist that there is some correlative concept to existence that would apply to individual objects in the world. But, incredibly, Russell denies this: “It is a sheer mistake to say that there is anything analogous to existence that you can say about them” (Ibid., p. 241). Thus, Russell’s view really is crazy. In any case, Russell’s view is problematic because propositional functions are neither true nor false; propositions are. So existence must be the property being of the form x is a (where “ ” is filled by a common noun denoting a thing) and having a value for x such that the resulting proposition is sometimes true. Unfortunately, Russell identifies the notion of sometimes with the notion of the possible, so that even if the proposition is only possibly true, the sentence expressing it, e.g., “Unicorns exist” is true.

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  68. Smith, Language and Time, pp. 168–169. This is unfortunate, since Russell’s view is not representative of philosophers who hold that existence is not a property. See, e.g.,Moore’s rejection of Russell’s characterization of existence as a property of propositional functions (Moore, “Is Existence a Predicate?” p. 81).

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  69. For example, Smith takes it for granted that “There is an explosion” ascribes the property being exemplified to the property of exploding. But there is no reason to think that the act of exemplification is a property (not to mention that no reason has been given to think that exploding is ascribed by this sentence either). Smith also assumes that the state of affairs described by the proposition John is running has the concrete individual John as a constituent. But since states of affairs are typically construed as abstract entities existing necessarily, John, as a concrete contingent, cannot be part of one.

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  70. Smith, Language and Time, p. 172.

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  71. Ernest Sosa, “The Status of Becoming: What Is Happening Now?” Journal of Philosophy 76 (1979): 28.

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  72. Cf. Reinhardt Grossmann, The Existence of the World, The Problems of Philosophy: Their Past and Present (London: Routledge, 1992), p. 20; cf. p. 102.

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  73. Quentin Smith, The Felt Meanings of the World (West Lafayette, Ind.: Purdue University Press, 1986), pp. 161–162.

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  74. Since Smith goes on to deny that being is a “real predicate” (Ibid., p. 173), it follows that neither is presentness.

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  75. Interestingly, Christensen interprets Prior’s view as holding that the notions of having occurred, occurring presently, and being going to occur are “modes of being, not relations (or properties)” and endorses this view himself (Christensen, Space-like Time, p. 122; cf. pp. 61, 123, 174). This interpretation is not quite right, however, since Prior held the past and the future to be unreal, so that these tense determinations cannot, like presentness, be construed as modes of being. Notice, too, that if we take necessity and contingency to be also modes of existence (Ibid., p. 61), then things have complex, or mixed, modes of being: a thing may exist (i) atemporally and necessarily, (ii) atemporally and contingently, (iii) temporally and necessarily, or (iv) temporally and contingently. Whether all these mixed modes are broadly logically possible is a matter of debate (see my God, Time, and Eternity [Dordrecht: Kluwer Academic Publishers, forthcoming]).

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  76. William Godfrey-Smith, critical notice of Real Time, by D. H. Mellor, Australasian Journal of Philosophy 61 (1983): 110. Godfrey-Smith’s criticism is correct as far as it goes, but Mellor insists that his argument succeeds whether `P’ and `F’ are construed as predicates or operators, and so one cannot cut off debate here.

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  77. Cf. Robin Le Poidevin and D. H. Mellor, “Time, Change, and the `Indexical Fallacy’,” Mind 96 (1987): 536, who point out that eliminating complex tenses by stating when a proposition is true merely results in the incompatible properties being truth values rather than tenses. Mellor insists, “The plain fact is that nothing can have mutually incompatible properties, whether they be tenses or truth values: neither events, things, facts, propositions, sentences, nor anything else” (Mellor, Real Time, p. 96). The fact that the predicates `P’, `F’, etc., can be construed as tense logical operators undercuts the analysis of David H. Sanford, “Infinite Regress Arguments,” in Principles of Philosophical Reasoning, ed. James H. Fetzer, APQ Library of Philosophy (Totowa, N. J.: Rowman & Allanheld, 1984), pp. 98–101, who charges that any expression containing both F and P is a vacuous tense expression, since such a determination can neither be gained nor lost. Thus, he says, in (3) two of the conjuncts are vacuous, and all that is being asserted is Ne. But the fact that expressions containing both F and P are not vacuous becomes evident when we, in Prioresque fashion, insert units of time into the formulae, e.g., PmF(m+n)e (A. N. Prior, “The Formalities of Omniscience,” in Papers on Time and Tense [Oxford: Clarendon, 1968], pp. 29–32). And Sanford’s analysis fails to address the alleged contradiction that if Ne is true, then Pe and Fe cannot also be true, thus precluding a complete description of reality. Le Poidevin and Mellor are absolutely correct that the contradiction involved in a complete description of reality is eliminable only by giving tenseless B-series truth conditions of A-tensed sentences—but one thereby loses real tense.

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  78. So D. W. Gottschalk, “McTaggart on Time,” Mind 39 (1930): 38; see also Smith, “Logical Structure,” pp. 372–373.

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  89. These are all theses defended by A. N. Prior. Cf. the similar exposition of the views of Prior in contrast to those of Quine by Jeremy Butterfield, “Prior’s Conception of Time,” Proceedings of the Aristotelian Society 84 (1983–84): 193–209.

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  101. This seems to me to solve the difficulty seen by James Cargile, “Tense and Existence,” in Cause, Mind, and Reality, ed. John Heil, Philosophical Studies Series 47 (Dordrecht: Kluwer Academic Publishers, 1989), p. 166, whose question, “If I refer to x, does not x have the property of being referred to?” reveals the tacit assumption that the properties referring to x and being referred to by y must be possessed by x and y at the same time, which begs the question. No reason has been given why these properties cannot be possessed by x and y respectively in succession. Wolterstorff, “Ontology without Events,” pp. 190–192 denies that past- (and future-) tense propositions have individuals as constituents. They are made up wholly of properties, which, being sempiternal, can be referred to at any time. Thus, being able to refer to past and future individuals, though impossible, is not necessary for stating the truth conditions of sentences about them. Contrast Adams, “Time and Thisness,” pp. 319–320. On the other hand, Roderick Chisholm, The First Person (Minneapolis: University of Minnesota Press, 1981), pp. 125126; idem, “Referring to Things that No Longer Exist,” in Action Theory and Philosophy of Mind ed. James Tomberlin, Philosophical Perspectives 4 (Atascadero, Calif: Ridgeway Publishing Co., 1990), p. 554, proposes to solve the problem by positing some sempiternal entity contemporaneous with both referent and referee which did have (or will have) the property of being such that there exists an x such that x is F. For the A-theorist God will nicely fill the role of the sempiternal entity. Cf. the eternalist solution proposed by Jonathan L. Kvanvig, “Adams on Actualism and Presentism,” Philosophy and Phenomenological Research 5 (1989): 297.

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  102. See, for example, Smith, Language and Time pp. 166–169.

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  103. Cf. the remarks of Peter Van Inwagen, “Indexicality and Actuality,” Philosophical Review 89 (1980): 406.

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  105. As noted by Van Inwagen, “Indexicality and Actuality,” p. 404; cf. Quentin Smith, “The New Theory of Reference Entails Absolute Time and Space,” Philosophy of Science 58 (1991): 411–416.

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  106. See Freddoso, “Accidental Necessity and Logical Determinism,” p. 264. He writes

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  107. I take the claim that the pure present is metaphysically primary to be tantamount to the assertion that for any moment t and any logically possible world w there is a set k of purely present-tense propositions such that (a) each member of k is true at t in w, and (b) k determines what is true at t in w in a temporally independent way, i.e., in a way which does not temporally depend on what has been or will be true at moments of w other than t“ (Ibid., p. 266).

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  108. That this implies a sort of power over the past (as well as the future) is explained by idem, “Accidental Necessity and Power over the Past,” Pacific Philosophical Quarterly 63 (1982): 54–68. For a discussion see my Divine Foreknowledge and Human Freedom pp. 83–90, 179–190. If one does not accept that propositions are tensed, then one could reformulate the metaphysical primacy of the pure present in terms of non-propositional, present-tensed features of reality (e.g. God’s de se knowledge of what He is creating).

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  109. See M. J. Cresswell, “Modality and Mellor’s McTaggart,” Studia Logica 49 (1990): 163–170.

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  111. See note 66. Tooley is a hybrid A-B-theorist in that he holds to the reality of the past and present, but not the future; he would avert McTaggart’s Paradox by denying that there are intrinsic properties of tense (Michael Tooley, Time, Tense, and Causation [Oxford: Clarendon Press, 1997], pp. 226–229). But I have already charged that Tooley’s “reality accretion” model must involve tensed facts; moreover, events seem to change on his view even in their relational tensed properties, since, e.g. a past event acquires the relational property past with respect to some event only once the latter becomes present (p. 323). Such change is all one needs to generate a McTaggart’s Paradox.

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  112. Smith, “Infinite Regress of Temporal Attributions,” p. 386.

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  113. Ibid. See also Smith, “Logical Structure,” pp. 373–374.

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  114. See David Lewis, On the Plurality of Worlds (Oxford: Basil Blackwell, 1986), pp. 93, 98, 137. For a critique see Van Inwagen, “Indexicality and Actuality,” pp. 415–417.

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Craig, W.L. (2000). McTaggart’s Paradox. In: The Tensed Theory of Time. Synthese Library, vol 293. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9345-8_6

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