Abstract
The notion that time is dynamic, that it flows or passes, is a common and ancient motif in the history of Western philosophy, at least as old as Heraclitus.1 The hymnist Isaac Watts poetically expressed this notion in the lines:
Time, like an ever rolling stream
Bears all its sons away;
They fly, forgotten, as a dream
Dies at the op’ning day.2
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References
For a brief survey, see Encyclopedia of Philosophy (1967), s.v. “Change,” by Milic Capek.
Isaac Watts, “O God, Our Help in Ages Past,” in The Hymnal (Waco, Tex.: Word Music, 1986), no. 52. The hymn is based on Psalm 90, but Watts’s hypostatization of time as a rolling stream derives from extra-biblical tradition.
John McTaggart Ellis McTaggart, The Nature of Existence, 2 vols., ed. C. D. Broad (Cambridge: Cambridge University Press, 1927; rep. ed.: 1968), 2: 10.
Ibid., 2: 11.
C. D. Broad, Examination of McTaggart’s Philosophy, 2 vols. (Cambridge: Cambridge University Press, 1938; rep. ed.: New York: Octagon Books, 1976), 2: 277–280.
Donald C. Williams, “The Myth of Passage,” Journal of Philosophy 48 (1951): 471.
George Santayana, The Realms of Being (New York: Charles Scribners Sons, 1942), p. 491. Cf. the oft-cited mischaracterization of the B-Theory by Hermann Weyl: “The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling upward along the life line of my body, does a section of this world come to life as a fleeting image in space which continuously changes in time” (Hermann Weyl, Philosophy of Mathematics and Natural Science, trans. Olaf Helmer, rev. ed. [Princeton: Princeton University Press, 1949], p. 116). Grünbaum bends over backwards in an attempt to place an acceptable interpretation on Weyl’s words (Adolf Grünbaum, Philosophical Problems of Space and Time, 2d ed., Boston Studies in the Philosophy of Science [Dordrecht: D. Reidel, 1973], pp. 328–329), for which he is chided by Smart as being “too kind” to Weyl, whose metaphor is “highly misleading” (J. J. C. Smart, “Introduction,” in Problems of Space and Time, ed. J. J. C. Smart, Problems of Philosophy [New York: Macmillan Co., 1964], p. 18). Such misleading characterizations of temporal becoming are all too frequent.
Williams, “Myth of Passage,” p. 461, says that on an A-Theory of time we speak as if “the perceiving mind were stationary while time flows by like a river, with the flotsam of events upon it.” Cf. his claim that it is the myth of passage which inclines one to the idea of time travel (Ibid., pp. 462–463). On the contrary, it is the B-theoretical ontology that so inclines one, for past events actually exist “back there” and future events “up ahead,” on the analogy of spatial locations to which one may travel. Wells himself, like Williams, presented a confused conflation of the A- and B-Theories (H. G. Wells, The Time Machine [New York: Berkeley Publishing, 1957], pp. 5–18). Contemporary proponents of time travel are inevitably B-theorists; for discussion see my Divine Foreknowledge and Human Freedom: The Coherence of Theism: Omniscience, Brill’s Studies in Intellectual History 19 ( Leiden: E. J. Brill, 1991 ), pp. 150–153.
Williams, “Myth of Passage,” p. 471.
See J. J. C. Smart, “The Temporal Asymmetry of the World,” Analysis 14 (1953–54): 79–83; idem, Philosophy and Scientific Realism, Intemational Library of Philosophy and Scientific Method (London: Routledge, Kegan & Paul, 1963), pp. 134–148; idem, “Introduction,” pp. 17–22, in which Williams’s article is anthologized; Encyclopedia of Philosophy (1967), s.v. “Time,” by idem, where “The Myth of Passage” serves as a heading for major sections of the article and bibliography and in which Smart refers to Williams’s article as a “brilliant criticism”; idem, “Time and Becoming,” in Time and Cause, ed. Peter Van Inwagen, Philosophical Studies Series in Philosophy ( Dordrecht: D. Reidel, 1980 ), pp. 3–4.
J. J. C. Smart, “The River of Time,” Mind 58 (1949): 483–494.
Ibid., p. 485.
Ibid., p. 483.
Ibid., p. 494.
Smart, “Temporal Asymmetry,” p. 81.
I6. Smart, Scientific Realism, p. 135.
Smart, “Introduction,” p. 22.
Arthur N. Prior, “Changes in Events and Changes in Things,” in Papers on Time and Tense (Oxford: Clarendon Press, 1968), p. 1. The chief exception to this rule has been George Schlesinger, who has repeatedly (and, I think, vainly) tried to defend the literal movement of what he calls the NOW along the B-series. See George Schlesinger, Aspects of Time (Indianapolis: Hackett, 1980); idem, “How Time Flies,” Mind 91 (1982): 501–523; idem, “How to Navigate the River of Time,” Philosophical Quarterly 35 (1985): 91–92; idem, “E Pur Si Muove,” Philosophical Quarterly 41 (1991): 427–441; idem, “A Short Defense of Transience,” Philosophical Quarterly 43 (1993): 359–361. Cf. Ned Markosian, “How Fast Does Time Pass?” Philosophy and Phenomenological Research 53 (1993): 829–844. For effective critiques of Schlesinger’s proposals, see L. Nathan Oaklander, Temporal Relations and Temporal Becoming (Lanham, Md.: University Press of America, 1984), pp. 74–75; idem, “McTaggart, Schlesinger, and the Two-Dimensional Time Hypothesis,” Philosophical Quarterly 33 (1985): 391–397; idem, “A Reply to Schlesinger,” Philosophical Quarterly 35 (1985): 93–94; Keith Seddon, Time: a Philosophical Treatment (London: Croon Helm, 1987), p. 19; David J. Buller and Thomas R. Foster, “The New Paradox of Temporal Transience,” Philosophical Quarterly 42 (1992): 357–366.
A. N. Prior, “Time after Time,” Mind 67 (1958): 244.
Prior, “Changes,” pp. 11–12.
Ferrel Christensen, “The Source of the River of Time,” Ratio 18 (1976): 140.
Smart, “Time and Becoming,” p. 4.
Ibid., p. 5. The argument makes little advance over Smart, “Introduction,” p. 21.
Now this use of `become’ is no more applicable to events than is the ordinary transitive use. Events do not come into existence; they occur or happen“ (Smart, ”River of Time,“ p. 486); talk of events’ coming into existence is ”a breach of logical grammar“ (idem, ”Temporal Asymmetry,“ p. 81); things come into existence, change, or stay the same, but to say that an event came into existence or changed would be ”absurd“ (idem, Scientific Realism, p. 135); ”...we can talk of continuants as coming into existence or ceasing to exist, but we cannot similarly talk of a `coming-into-existence’ itself as coming into existence or ceasing to exist“ (Encyclopedia of Philosophy, s.v. ”Time“).
Time and Becoming,“ p. 5.
P. J. Zwart, “The Flow of Time,” Synthèse 24 (1972): 135–141.
I am assuming that the universe is spatially finite. If Zwart’s characterization of the rate of flow of events bars this assumption, then it is inadequate, for there are many cosmological models which posit the spatial finitude of the universe. If he means that in a spatially finite universe, an infinite number of events occurs during a finite temporal interval, then this characterization only reinforces the necessity of focusing on the events of a single periodic process in order to obtain a rate of events’ flow.
Grünbaum, Philosophical Problems of Space and Time, p. 329.
Ibid., p. 325.
Smart, “Introduction,” p. 17.
Ibid., p. 18.
See analogous reasoning with regard to a nocturnal doubling of the universe in size in George Schlesinger, “What Does the Denial of Absolute Space Mean?” Australasian Journal of Philosophy 45 (1967): 46. The objection to the meaningfulness of the universe’s doubling in size or the flow of events’ doubling in rate is just one more example of the defunct positivism which has so influenced philosophy of space and time during the twentieth century. For obviously, that these doublings should take place and be accompanied by radical and sweeping changes in physical laws that serve to conceal what has happened is meaningful (and, if God exists, possible), whether anyone can verify it or not!
For discussion see my God, Time, and Eternity (Dordrecht: Kluwer Academic Publishers, forthcoming), chap. 5.
Encyclopedia of Philosophy, s.v. “Time.”
Alan Padgett, God, Eternity, and the Nature of Time, Library of Philosophy and Religion ( New York: St. Martin’s, 1992 ), pp. 125–130.
Prior, “Time after Time,” p. 244; cf. idem, “Changes in Event and Changes in Things,” p. 2.
Smart, “Time and Becoming,” p. 4.
The insignificance for the reality of temporal process of failing to be representable on a Minkowski diagram is underlined by N. Lawrence, “Temporal Passage and Spatial Metaphor,” in The Study of Time Il, ed. J. T. Fraser and N. Lawrence ( Berlin: Springer Verlag, 1975 ), pp. 196–205.
Encyclopedia of Philosophy, s.v. “Time.”
Similarly, Christensen’s objection to Prior’s characterization of the rate of time’s flow fails, since Prior did not conceive of it as a literal motion (Christensen, “Source of the River of Time,” p. 132).
Padgett, God, Eternity, and the Nature of Time, p. 111.
Paul Fitzgerald, “Is the Future Partly Unreal?” Review of Metaphysics 21 (1967–68): 421–423; cf. idem, “The Truth about Tomorrow’s Sea Fight,” Journal of Philosophy 66 (1969): 308.
Paul Fitzgerald, “Nowness and the Understanding of Time,” in PSA 1972, Boston Studies in the Philosophy of Science 20, ed. Kenneth F. Schaffner and Robert S. Cohen ( Dordrecht: D. Reidel, 1974 ), p. 260.
Fitzgerald, “Future Partly Unreal,” p. 422, 427; idem, “Tomorrow’s Sea Fight,” p. 309.
Contra see Craig, Divine Foreknowledge and Human Freedom, pp. 43–63.
For a similar conflation of ontology and semantics on the part of an A-theorist, see Genevieve Lloyd, “Time and Existence,” Philosophy 53 (1978): 215–228. She wants to deny bivalence for future-tense propositions on the basis of the unreality of future things, but she cannot bring herself to endorse Prior’s view that by parallel reasoning there are no past-tense facts either. Thus, she is forced to hold that something’s being past does not “take it beyond reality” or “remove it altogether from the order of things.” She seems to be approximating the model of time in Broad’s Scientific Thought, which we saw to be incoherent.
These considerations also serve to answer the objections of Melvin M. Schuster, “On the Denial of Past and Future Existence,” Review of Metaphysics 21 (1967–68): 447–467, who claims that the presentist’s view that some event E existed at t, but no longer exists at t2 is contradictory because at t2 he wants to deny E’s existence at all times, yet he must admit it exists at t,. In saying things have ceased to exist, Schuster asserts, the presentist must admit that they existed at prior times. But when he claims that nothing outside the present exists, he must deny their existence. Schuster is obviously confused. He thinks that “E existed in the past” means “E has (present tense) existence at that past time.” But the former statement is not to be understood as the latter admittedly incoherent statement but as “It was the case that E exists.” The reality of the past and future consists in the present truth or falsity of past-and present-tense statements. At t2 the presentist does not wish to deny that “E existed at t,” is true; nor is this inconsistent with his believing truly at t2 “E does not exist.”
Fitzgerald, “Future Partly Unreal,” p. 428.
Fitzgerald, “Tomorrow’s Sea Fight,” p. 307.
See discussion in my The Tenseless Theory of Time: a Critical Examination, Synthèse Library (Dordrecht: Kluwer Academic Publishers, forthcoming), Pt. I, sec. 1.
Williams, “Myth of Passage,” p. 459.
Aristotle Physics 4.10.217b33–218a9. For an excellent discussion of the early history of this conundrum, see Richard Sorabji, Time, Creation and the Continuum (Ithaca, N. Y.: Cornell University Press, 1983 ), pp. 7–63. Augustine in particular agonized eloquently over this problem ( Augustine, Confessions 9. 15–28 ).
Bertrand Russell, Human Knowledge ( New York: Simon and Schuster, 1948 ), p. 181.
C. D. Broad, “A Reply to My Critics,” in The Philosophy of C. D. Broad, ed. Paul Arthur Schilpp, Library of Living Philosophers (New York: Tudor, 1959), pp. 769–772, in response to Robert Leet Patterson, “A Critical Account of Broad’s Estimate of McTaggart,” in Philosophy of C. D. Broad, p. 155, who had demanded what the notion of an event-particle is: “That nothing is real except the event particle which is present? But this will leave us with a reality which has no duration at all.”
C. S. Peirce, “On Continuous Series and the Infinitesimal,” in The New Elements of Mathematics, 5 vols., ed. Carolyn Eisele, vol. III/1: Mathematical Miscellanea (The Hague: Mouton, 1976), pp. 125–127. See also A. W. Moore, The Infinite (London: Routledge, 1990), pp. 104, 122, 156–158.
Frank J. Tipler, “Achieved Spacetime Infinity,” Nature 325 (15 January 1987), p. 20. When one reads Penrose, on the other hand, it seems pretty clear that he takes singular points and the c-boundary on which they lie as idealizations only (Roger Penrose, “Singularities of Spacetime,” in Theoretical Principles in Astrophysics and Relativity, ed. Norman R. Lebovitz, William H. Reid, and Peter O. Vandervoort [Chicago: University of Chicago Press, 1978], pp. 217–243). See also note 89 below.
Sorabji, Time, Creation and the Continuum, pp. 12–13.
For a brief statement of this point, see Encyclopedia of Philosophy, s.v. “Time.” See also the interesting proposal of Hugh R. King, “Aristotle and the Paradoxes of Zeno,” Journal of Philosophy 46 (1949): 657–670, who seeks to elude the problem by maintaining that there is no advance of the present through time; rather the present is stationary, so to speak, and the past issues out of it. On this model, the future is unreal, the past is real, and the present is the boundary of the past. “The act of becoming lies, so to speak, outside the extensive continuum of space and time” (Ibid., p. 69); it is the bound of physical time. But it is not clear that such a model would not involve a sort of mirror-image of Zeno’s Paradoxes, e.g., how can an event-particle recede one instant into the past, since the present instant has no immediate predecessor? Or how could the past grow instant by instant?
William James, Some Problems of Philosophy (1911; rep. ed.: New York: Longmans, Green and Co., 1931 ), pp. 181–183.
Alfred North Whitehead, Process and Reality, corr. ed., ed. David Ray Griffin and Donald W. Sherburne ( New York: Free Press, 1978 ), p. 68.
Alfred North Whitehead, Science and the Modern World ( New York: Macmillan Co., 1925 ), p. 127.
Whitehead, Process and Reality, p. 68.
Ibid.
Ibid., p. 69.
Ibid., p. 35.
He explains,“A duration...is an epoch, i.e., an arrest.... Time is sheer succession of epochal durations.... Thus the divisibility and extensiveness is within the given duration. The epochal duration is not realised via its successive divisible parts, but is given with its parts....
Adolf Grünbaum, “Relativity and the Atomicity of Becoming,” Review of Metaphysics 4 (1950–51): 143–186. A revised version of this piece later appeared in idem, Modern Science and Zeno’s Paradoxes (London: Allen & Unwin, 1968 ).
Grünbaum, “Atomicity of Becoming,” p. 143.
Ibid., p. 154.
Grünbaum, “Atomicity of Becoming,” p. 172.
Ibid., pp. 168–169.
Ibid., p. 165.
See, for example, Grünbaum, Modern Science and Zeno’s Paradoxes. For a discussion of the “modern Eleatics” and their infinity machines, see the appendix “The Kalam Cosmological Argument and Zeno’s Paradoxes,” in Wm. L. Craig, The Kalam Cosmological Argument, Library of Philosophy and Religion (London: Macmillan, 1979), pp. 175–188. See in this connection the Auseinandersetzung between J. Q. Adams, “Grünbaum’s Solution to Zeno’s Paradoxes,” Philosophia 3 (1973): 43–50, and Adolf Grünbaum, “Reply to J. Q. Adams’ `Grünbaum’s Solution to Zeno’s Paradoxes’,” Philosophia 3 (1973): 51–57. Adams gives an illustration involving a relay race in which runners traverse progressively shorter distances and, observing that there is no last runner to carry the baton to the end of the course, demands how anybody could be there at the finish, holding the baton. Griinbaum’s response is to assimilate the A-theoretical temporal race to a tenselessly existing continuum, as is evident in his remark, “If [Adams] has not succumbed to the temptations of the threshold-fallacy in drawing this inference, why does he regard his question `how does the baton get there?’ as more legitimate than the following hypothetical silly question, which he would presumably dismiss as mathematically untutored: `How can a sequence of order type w+l have a last element while being devoid of a next-to-the-last element, so that the last element is preceded by an infinite progression of order type w?”’ (Ibid., p. 55). Adams’s question is legitimate because it concerns a causal, temporal order, not a logical, tenseless order.
Grünbaum, Philosophical Problems of Space and Time, pp. 633, 636, 850.
Adolf Grünbaum, “Modem Science and the Refutation of the Paradoxes of Zeno,” in Zeno’s Paradoxes, ed. Wesley C. Salmon ( Indianapolis: Bobbs-Merrill, 1970 ), p. 173.
G. J. Whitrow, The Natural Philosophy of Time, 2d ed. ( Oxford: Clarendon Press, 1980 ), p. 200.
As supposed by R. M. Blake, “The Paradox of Temporal Process,” Journal of Philosophy 23 (1926): 650–653. It is interesting that in response to Whitehead’s challenge, “How does the succeeding interval get started?” Blake has to appeal to non-zero intervals of time as the units of becoming: “by the occurrence of a part of it which is earliest of some set of fractional parts, but which itself contains various sets of fractional parts within each of which sets some members of the set are earlier than others” (Ibid., p. 654). Except for the language of temporal parts, this solution comes very close to that which I defend below and is inconsistent with an instantaneous present, since what becomes present is never an instant, but a (conceptually divisible) finite temporal interval.
James, Some Problems of Philosophy, pp. 185–186.
Adolf Grunbaum, “A Consistent Conception of the Extended Linear Continuum as an Aggregate of Unextended Elements,” Philosophy of Science 19 (1952): 288–306. This early piece, also excerpted from Grunbaum’s doctoral dissertation, was subsequently revised and corrected in the first edition of Philosophical Problems of Space and Time, pp. 158–176, and again in Modern Science and Zeno’s Paradoxes, pp. 114–140. His final remarks and corrections are to be found in Appendix 10 to the second edition of Philosophical Problems of Space and Time, pp. 808–820.
Grünbaum, Philosophical Problems of Space and Time, p. 164.
Ibid., p. 809.
Ibid., p. 171.
Gerald Massey, “Toward a Clarification of Grünbaum’s Concept of Intrinsic Metric,” Philosophy of Science 36 (1969): 337.
Grünbaum, Philosophical Problems of Space and Time, pp. 811–812.
Ibid., p. 477.
Ibid., pp. 815–819.
Broad himself was disquieted by another difficulty in the notion of the instantaneous present which again goes all the way back to Aristotle: the problem of the ceasing instant (Broad, “Reply to My Critics,” p. 768. See also Aristotle Physics 4.10.218a9–11, 16–21. For a historical survey, see Sorabji, Time, Creation and the Continuum, pp. 7–63). Broad noticed that if we say that each present temporal phase is literally instantaneous, then we must say that at one and the same instant a temporal phase supervenes and is superseded, which sounds palpably absurd. In other words, the present and/or its contents come to be and cease to be simultaneously, which is self-contradictory. This difficulty, which closely resembles the ancient sorites paradoxes concerning starting and stopping, does not, however, seem to present any new, insuperable problem for Broad’s view. Sorabji explains, “...we must distinguish between the present and the perfect tense: we can never say, using the present tense, that the present instant is ceasing to exist. But we can say of what we once called the present instant that it has ceased to exist. When? The...answer would be: at any subsequent instant you like, however close—a millionth of a second later, or a two millionth. There will be no first subsequent instant” (Sorabji, Time, Creation and the Continuum, p. 10). In contemporary cosmology, the relation of the initial cosmological singularity to moments of time is conceived along these lines; the singularity is not a moment of time, but bounds time, and there is no first instant of time and, hence, no instant at which the singularity ceases to exist. No matter how close one approaches it in the open interval (0, 1], it will at every instant have ceased to exist. This example serves to bring out the fact that the problem of the ceasing instant is not endemical to the A-Theory; even B-theories of tenselessly existing instants face the question of when an event which exists at some instant ceases to exist, and the answer will be the same. If there is a problem for Broad’s view arising from the ceasing instant, it will be the same difficulty as raised above concerning the impossibility of instantaneous becoming, namely, that on his view instants must have immediate precursors and successors, which is impossible. Unless the difficulties appertaining to the becoming of a durationless interval can be resolved, the A-theorist ought, therefore, to reject the underlying equation between the present and the present instant.
Whitrow, Natural Philosophy of Time, p. 200.
Whitrow explains, “Acceptance of the ideas of spatial and temporal atomicity in physics does not, of course, preclude us from applying mathematical concepts of space and time involving numerical continuity in our calculations, but the infinite divisibility associated with these concepts will then be purely mathematical and will not correspond to anything physical” (Ibid., p. 201). Penrose analogously distinguishes between a physical interpretation and a mathematical treatment of entities involving lengths of 10–13 cm or less (Penrose, “Singularities,” pp. 217–218). He explains that as a singularity is approached, ordinary physical objects, even elementary particles, cannot exist due to the mounting gravitational tidal forces. Without particles to probe the geometry, he says, it is hard to see how the description of a continuous background space-time could then be meaningfully sustained. Although this breakdown occurs already at radii of space-time curvature of 104“ cm, most physicists continue to employ classical notions of space-time geometry all the way until the Planck length. At this scale a new physics is required to proceed further.ideal future endpoints to future-endless timelike (or null) curves,” which, interpreted realistically, is self-contradictory (Ibid., p. 221).
Milic Capek, The Philosophical Impact of Contemporary Physics (Princeton: D. Van Nostrand, 1961, p. 234; cf. idem, “The Fiction of Instants,” in The Study of Time, ed. J. T. Fraser, F. C. Haber, and G. H. Müller ( Berlin: Springer Verlag, 1972 ), pp. 332–344.
Capek, Philosophical Impact of Contemporary Physics, p. 231. Whitrow seems to miss the point of Capek’s objection when he rejoins that if in nature time is a succession of minimal processes, then these cannot have beginnings and ends (Whitrow, Natural Philosophy of Time, p. 204). For while it is correct that no processes can proceed from an initial to a final state during a chronon, still if the interval itself has a definite, positive length it would have beginning and end points.
Sorabji, Time, Creation and the Continuum, pp. 367, 382–383. Sorabji himself is arguing that one cannot infer atomicity of time from atomicity of space and uses the two clock illustration to show that space might be atomic without time’s being atomic.
Ibid., p. 383.
Grünbaum, Modern Science and Zeno ‘s Paradoxes, p. 246.
Blake fails to appreciate this fact when, in response to James and Whitehead’s atomic views of time, he complained that a whole, every part of which is simultaneous, cannot be properly characterized as a duration or involve a definite lapse of time (Blake, “Temporal Process,” p. 649). If we take “duration” and “lapse” purely extensively, however, then it is easy to see how a chronon which occurs as a whole can have a finite temporal extension. But if we take these terms transitively, then it is no part of the atomist’s doctrine that chronons themselves each endure through time; rather they are the units of duration, which is, on that account, discontinuous. The real problem for Whitehead, it seems to me, is that the temporal parts of a chronon must, as parts, be earlier/later than one another, which contradicts the idea that they all exist simultaneously when a chronon is present or actual. The temporal atomist should deny that chronons have parts, even if chronons are conceptually divisible. Everything that happens at a chronon happens simultaneously, which implies that change occurs in leaps.
Grünbaum, Modern Science and Zeno’s Paradoxes, pp. 247–249.
For a defense of such an interpretation see Simon J. Prokhovnik, Light in Einstein’s Universe (Dordrecht: D. Reidel, 1985); see further Tim Maudlin, Quantum Non-Locality and Relativity, Aristotelian Society Series 13 (Oxford: Blackwell, 1994), chaps. 7, 8.
As one commentator has recently remarked, “every known ontology that is compatible with the phenomena, as codified by quantum theory, is `grotesque’ in some way” (Henry P. Stapp, “Transcending Newton’s Legacy,” in Some Truer Method, ed. Frank Durham and Robert D. Parrington [New York: Columbia University Press, 1990 ), p. 233 ).
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; Padgett, God, Eternity, and the Nature of Time, p. 115 ).
F. M. Christensen, Space-like Time ( Toronto: University of Toronto Press, 1993 ), p. 123.
Henri Bergson, Duration and Simultaneity, trans. Leon Jacobsen, with an Introduction by Herbert Dingle, Library of Liberal Arts (Indianapolis: Bobbs-Merrill, 1965), p. 53. Bergson’s misguided attack upon relativity theory has led to an unfortunate neglect of his otherwise interesting thoughts on the nature of time. For a good discussion see Philip Turetzky, Time, Problems of Philosophy (London: Routledge, 1998), chap. 13.
A. N. Prior, “The Notion of the Present,” Studium Generale 23 (1970): 245. Cf. Christensen, Space-like Time, pp. 168; 226.
A. N. Prior, Papers on Time and Tense ( Oxford: Oxford University Press, 1968 ), p. 123.
A. N. Prior, unpublished manuscript, courtesy of Peter P hrstram and Per Hasle.
As Grünbaum points out, infinite divisibility does not by itself give rise to Zeno’s paradoxes, for these result only if we postulate an actual infinity of points ab initio. “...any attribution of (infinite) `divisibility’ to a Cantorian line must be based on the fact that ab initio that line and the intervals are already `divided’ into an actual dense infinity of point-elements of which the line (interval) is the aggregate. Accordingly, the Cantorian line can be said to be already actually infinitely divided” (Grünbaum, Philosophical Problems of Space and Time, p. 169). By contrast if we think of the line as a whole as logically prior to any points designated on it, then it is not an ordered aggregate of points nor actually infinitely divided. On the view I am suggesting, a line is not even an infinity of potential points, but the points designated on it are potentially infinite in number. Pari passu an interval of time as a whole duration is logically prior to the (potentially infinite) divisions we may make of it. Cf. Peirce’s proposal that we replace points by series. Then every part of a line is still a series and divisible into further series. “Let any mode of measure be carried to its limit of precision. Still each number will designate not an indivisible part; but a series of series, ad infinitum” (Peirce, “Continuous Series,” p. 126).
The non-instantaneous character of present intervals has led to some very interesting developments in durational logic, stemming from the work of the medieval thinker Jean Buridan. See Peter P hrstrem and Per F. V. Hasle, Temporal Logic, Studies in Linguistics and Philosophy 57 (Dordrecht: Kluwer Academic Publishers, 1995), pp. 43–51; C. L. Hamblin, “Instants and Intervals,” in The Study of Time, ed. J. T. Fraser, F. C. Haber, and G. H. Müller ( Berlin: Springer Verlag, 1972 ), pp. 324–331.
Augustine Confessions 11.15.19–20.
Andros Loizou, Reality of Time, pp. 44–45. Loizou’s view is that an interval may be present even though it is not wholly present (i.e., not all its parts are present). I prefer to say that an interval may be present simpliciter even though we can divide it into sub-intervals which are not every one present. Thus, the present minute is qua minute present simpliciter, but if we divide it into seconds, then only one second is qua second present simpliciter. If any sub-interval of an interval is present, then the whole interval is as such present.
Aristotelian space was not symmetrical, so that the symmetry of space is a contingent matter. But the A-theorist, especially if he distinguishes between metaphysical and physical time, will not be apt to admit that time could be symmetrical.
See Sarah Waterlow, “Backwards Causation and Continuing,” Mind 83 (1974): 372–387.
Grünbaum, Philosophical Problems of Space and Time, pp. 315–316.
Smart, “Temporal Asymmetry,” pp. 82–83
Steven Savitt, “The Direction of Time,” British Journal for the Philosophy of Science 47 (1996): 364 (first emphasis mine).
Isaac Newton, Sir Isaac Newton’s ‘Mathematical Principles of Natural Philosophy’ and his ’System of the World,’ trans. Andrew Motte, rev. with an Appendix by Florian Cajori, 2 vols. (Los Angeles: University of California Press, 1966 ), vol. 1, p. 6.
Ibid., p. 545.
Craig Callender, “What is `The Problem of the Direction of Time’?” Philosophy of Science 64 (1997): S 223–234.
See Arthur Eddington, The Nature of the Physical World, introd. by Sir Edmund Whittaker, Everyman’s Library (London: J. M. Dent & Sons, 1928, rep. ed. 1964), pp. 75–110; Max Black, “The Direction of Time,” Analysis 19 (1958–59): 54–63; Bernard Mayo, “The Open Future,” Mind 71 (1962): 1–14; John Earman, “An Attempt to Add a Little Direction to `The Problem of the Direction of Time’,” Philosophy of Science 41(1974): 15–47; Lawrence Sklar, Space, Time, and Spacetime (Berkeley: University of California Press, 1976), pp. 352–411; Kenneth Denbigh, Three Concepts of Time (Berlin: Springer Verlag, 1981), pp. 15–47; Paul Horwich, Asymmetries in Time (Cambridge, Mass.: MIT Press, 1987), pp. 37–71; Steven Savitt, Time’s Arrow Today (Cambridge: Cambridge University Press, 1996 ); Huw Price, Time’s Arrow and Archimedes’ Point ( New York: Oxford University Press, 1997 ).
Sklar, Space, Time, and Spacetime, p. 399. Cf. idem, “Up and Down, Left and Right, Past and Future,” in The Philosophy of Time, ed. R. Le Poidevin and M. MacBeath, Oxford Readings in Philosophy ( Oxford: Oxford University Press, 1993 ), p. 101.
Black, “Direction of Time,” p. 62.
Ibid., p. 63.
Sklar, Space, Time, and Spacetime, p. 399. In his “Time in Experience and in Theoretical Description of the World,” in Time’s Arrow Today, p. 218, Sklar observes that basing the asymmetry of time on thermodynamics, though self-evident to many philosophers of science, seems “manifestly absurd” and “so ludicrous as to be dismissed without argument” by many perceptive philosophers.
Grünbaum, Philosophical Problems of Space and Time, p. 290.
Also relevant at this point are the anti-relationalist arguments of Sydney Shoemaker, “Time without Change,” Journal of Philosophy 66 (1969): 363–381; cf. W.-H. Newton-Smith, The Structure of Time, International Library of Philosophy (London: Routledge, Kegan & Paul, 1980), chaps. 4, 10.
Sklar, Space, Time, and Spacetime, p. 401.
Ibid., pp. 403–404.
See discussion in Earman, “Direction of Time,” pp. 29–45, who notes that nobody maintains that space is asymmetrical because of the de facto asymmetries between left-and right-handed objects. Why then is time supposed to be different from space in this respect? See also the somewhat confused discussion by Denbigh, Three Concepts, pp. 15–39; idem, An Inventive Universe (London: Hutchinson, 1975), pp. 40–52; also Mayo, “Open Future,” pp. 3–4.
As Denbigh says, “What natural processes actually display is a mutual consistency or parallelism (e.g., of entropy change, statistically if not absolutely) but they do not in themselves display the qualities of being earlier than or later than. These qualities have to be read into the physical situation by the observer” (K. G. Denbigh, “In Defense of the Direction of Time,” Studium Generale 23 119701: 238).
Sklar, Space, Time, and Spacetime, p. 399.
Ibid., p. 402.
Idem, “Up and Down,” p. 116. Cf. idem, Physics and Chance ( Cambridge: Cambridge University Press, 1993 ), p. 410.
Idem, Space, Time, and Spacetime, pp. 410–411.
Price, Time’s Arrow, pp. 34–36.
Ibid., p. 37; cf. Craig Callender, “The View from No-when,” British Journal for the Philosophy of Science 49 (1988): 135–159.
But see the excellent comments on “The Second Law and the Difference between Past and Future,” by Carl Friedrich von Weizsäcker, The Unity of Nature, trans. Francis J. Zucker (New York: Farrar, Strauss, & Giroux, 1980), esp. pp. 138, 141, 145.
McTaggart, Nature of Existence, 2: 30.
Ibid., 2: 271.
Mellor, Real Time, p. 140.
See my The Tenseless Theory of Time: a Critical Examination, Synthèse Library (Dordrecht: Kluwer Academic Publishers, forthcoming), chap. 7.
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Craig, W.L. (2000). The Myth of Temporal Passage. In: The Tensed Theory of Time. Synthese Library, vol 293. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9345-8_7
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