BIBLIOGRAPHY

The following abbreviations are used: A for Analysis; JP for journal of Philosophy; M for Mind; P for Philosophy; PAS for Proceedings of the Aristotelian Society; PQ for Philosophical Quarterly; PR for Philosophical Review; and PT for The Problem of Time, University of California Pub­lications in Philosophy, 18 ( 1935).

SECTION I. "WnAT, THEN, Is TIME?"

Critical surveys of traditional theories of time are in: J. A. Gunn, The Problem of Time, George Allen & Unwin, Lon­don, 1929; and M. F. Cleugh, Time, and Its Importance in Modern Thought, Methuen & Co., London, 1937. L. Wittgen­stein's diagnosis of Augustine's perplexities about time, which is developed by F. Waismann in the selection in this sec­tion, is to be fcund in Wittgenstein's books: The Blue and Brown Books, Basil Blackwell, Oxford, 1958, pp. 6, 26 ff., and Philosophical Investigations, tr. by G. E. M. Anscombe, Basil Blackwell, Oxford, 1953, pp. 42 ff. Articles in which the Wittgensteinian approach to Augustine is pursued are: 0. K. Bouwsma, "The Mystery of Time (Or, The Man Who Did Not Know What Time Is)," ]P, 51 (1954), re­printed in Bouwsma's Philosophical Essays, University of Nebraska Press, Lincoln, 1965; F. Waismann, "How I See Philosophy," in Contemporary British Philosophy, third series, H. D. Lewis, ed., George Allen & Unwin, London, 1956, especially pp. 45o-53; Ronald Suter, "Augustine on Time with Some Criticisms from Wittgenstein," Revue interna­tionale de philosophie, 16 ( 1962); and Richard M. Gale, "Some Metaphysical Statements about Time," ]P, 6o (1963).

BIBLIOGRAPHY 503

SECTION II. THE STATIC VERSUS THE DYNAMIC TEMPORAL

McTaggart's argument first appeared as "The Unreality of Time," M, 17 ( 1908), reprinted in his Philosophical Studies, Edward Arnold, London, 1934· Attempts to refute his argu­ment through the use of the B-Theory of Time are, in addi­tion to the D. Williams article in this section: C. D. Broad, "Time," in Encyclopaedia of Religion and Ethics, Charles Scribner's Sons, New York, 1922. Broad was under the in­fluence of Russell when he wrote this article, and completely reversed his position in his subsequent writings. For a de­tailed account of Broad's shifting views on time see C. W. K. Mundie, "Broad's Views about Time," in The Philosophy of C. D. Broad, P. A. Schilpp, ed., Open Court, La Salle, Ill., 1959; R. B. Braithwaite, "Time and Change," PAS, Supp. Vol. 8 (1928); and D. W. Gotshalk, "McTaggart on Time," M, 39 (1930). Bertrand Russell developed the B-Theory of Time in his: The Principles of Mathematics, Cambridge University Press, Cambridge, 1903, especially pp. 458-76; Introduction to Mathematical Philosophy, George Allen & Unwin, London, 1919, p. ;1.64; "The Philosophy of Logical Atomism," Monist, 28-29 (1918-1919) (see Lecture IV, where Russell discusses the philosophical importance of "emphatic particulars," which are later termed "egocentric particulars" in his An Inquiry into Meaning & Truth, W. W. Norton, New York, 1940, ch. vii). Russell's views about the reducibility of A-determinations to B-relations are developed and defended in: G. P. Adams, "Temporal Form and Ex­istence," in PT; N. Goodman, The Structure of Appearance, Harvard University Press, Cambridge, Mass., 1951; W. V. Quine, "Mr. Strawson on Logical Theory," M, 6z (1953); A. J. Ayer, "Statements about the Past," in his Philosophical Essays, Macmillan, London, 1954; Ayer, The Problem of Knowledge, Macmillan, London, 1956, particularly pp. 57-58 and 179-80; and J. J. C. Smart, Philosophy and Scientific Realism, Routledge & Kegan Paul, London, 1963, ch. vii. Attempts to show that space and time are analogous because of the complementarity between things and events appear in: R. Taylor, "Spatial and Temporal Analogies and the

THE PHILOSOPHY OF TIME

Concept of Identity," ]P, 52 ( 1955), reprinted in Problems of Space and Time, J. J. C. Smart, ed., Macmillan, New York, 1964, which views are further elaborated on in his "Moving about in Time," PQ, 9 (1959); and B. Mayo, "Ob­jects, Events, and Complementarity," PR, 70 ( 1961). Tay­lor's position is criticized by: N. L. Wilson, "Space, Time, and Individuals," ]P, 52 ( 1955); W. J. Huggett, "Losing One's Way in Time," PQ, 10 ( 1960); J. Jarvis Thomson, "Time, Space, and Objects," M, 74 ( 1965); and J. W. Meil­and, "Temporal Parts and Spatio-Temporal Analogies," American Philosophical Quarterly, 3 ( 1966). The Mayo arti­cle is criticized by F. Dretske, "Moving Backward in Time," PR, 71 ( 1962). Other writings defending the B-Theory of Time are listed under Sections III and IV of this bibliography.

Answers to McTaggart's argument employing the A-Theory of Time are: C. D. Broad, Scientific Thought, Kegan Paul, Trench, Trubner, London, 1923; Broad, "Reply to My Critics," in The Philosophy of C. D. Broad, cited earlier in full; John Wisdom, "Time, Fact and Substance," PAS, 29 ( 1928-1929); E. W. Hall, "Time and Causality," PR, 43 (1934); P. Marhenke, "McTaggart's Analysis of Time," in PT; L. S. Stebbing, "Some Ambiguities in Discussions Con­cerning Time," in Philosophy and History, R. Klibansky and H. J. Paton, eds., Clarendon Press, Oxford, 1936; E. R. Bevan, Symbolism and Belief, Beacon Press, Boston, 1957, ch. iv; D. Pears, "Time, Truth, and Inference," in Essays in Conceptual Analysis, A. G. N. Flew, ed., Macmillan, Lon­don, 1956; M. Dummett, "A Defense of McTaggart's Proof of the Unreality of Time," PR, 69 ( 1960); Richard M. Gale, "Is It Now Now?" M, 73 ( 1964). Works defending tenets of the A-Theory of Time are: R. Collingwood, "Some Perplexities about Time with an Attempted Solution," PAS, 26 (1925-1926); W. R. Dennes, "Time as Datum and as Construction," in PT; D. S. Mackay, "Succession and Duration," in PT; E. W. Strong, "Time in Operational Analysis," in PT; J. N. Findlay, "Review of Ehrenfel's Cosmogony," P, 25 ( 1961); Findlay, "An Examination of Tenses," in Contemporary British Philosophy, third series,

BIDLIOGRAPHY 505 cited earlier in full; P. F. Strawson, Introduction to Logical Theory, Methuen & Co., London, 1952, especially pp. 15o-51; D. Y. Deshpande, "Professor Ayer on the Past," M, 65 (1956); W. S. Sellars, "Time and the World Order," in Min­nesota Studies in the Philosophy of Science, III, H. Feigl, G. Maxwell, and M. Scriven, eds., University of Minnesota Press, Minneapolis, 1962, reprinted in Science, Perception & Reality, Humanities Press, New York, 1963; K. W. Rankin, "Order and Disorder in Time," M, 66 (1957); A. N. Prior, "Time After Time," M, 67 ( 1958); Prior, "Thank Goodness That's Over," P, 34 ( 1959); Prior, "Changes in Events and Changes in Things," the Lindley Lecture, University of Kan­sas, 1962; Stuart Hampshire, Thought and Action, Viking Press, New York, 1g6o, ch. i; M. Black, "The 'Direction' of Time," A, 19 ( 1959); Black, "Review of G. J. Whitrow's The Natural Philosophy of Time" in Scientific American, zo6 ( 1962); L. E. Palmieri, "Empiricism and a Time-Line," PQ, 10 ( 1g6o); R. Taylor, "Pure Becoming," Australasian Journal of Philosophy, 38 ( 1g6o); David Shwayder, "The Temporal Order," PQ, 10 ( 1g6o); Richard M. Gale, "Dewey and the Problem of the Alleged Futurity of Yesterday," Philosophy and Phenomenological Research, 21 ( 1961); Gale, "Tensed Statements," PQ, 12 ( 1962), which article is criticized by J. J. C. Smart, '"Tensed Statements': A Com­ment," PQ, 12 ( 1962) ; by B. Mayo, "Infinitive Verbs and Tensed Statements"; and by I. Thalberg, "Tenses and 'Now'," both in PQ, 13 (1963), along with Gale's answer "A Reply to Smart, Mayo, and Thalberg on 'Tensed State­ments'," in the same issue. A further criticism of the original Gale paper is J. Rosenberg, "Tensed Discourse and the Eliminability pf Tenses," PQ, 16 ( 1966). Other articles by Gale are: "Existence, Tense and Presupposition," Monist, :)o ( 1966), and "McTaggart's Analysis of Time," American Phil­osophical Quarterly, 3 ( 1966). Other articles defending tEe A-Theory are listed under Sections III and IV. The prob­lem of detensing language is discussed in the articles by A. Duncan-Jones, P. N. Smith, B. Mayo, and L. J. Cohen inch. vii of Philosophy and Analysis, M. Macdonald, ed., Phil­osophical Library, New York, 1955·

go6 THE PHILOSOPHY OF TIME

The Either-Way-Will-Work Theory of Time is put forth in J. ]. C. Smart, '"The River of Time;" in Essays in Con­ceptual Analysis, cited earlier in full, as well as in the Findlay and Smart .articles included in this volume. The only phi­losopher who has defended the view that neither the A- nor the B-Series alone is sufficient to account for our concept of time is L. 0. Mink, "Time, McTaggart and Pickwickian Language," PQ, 10 ( 1960).

SECTION III. THE OPEN FUTURE Aristotle's discussion of future contingents, which is articu­

lated and criticized in the Rescher and Bradley articles in this volume, has inspired a fantastic number of commentaries, criticisms, and defenses. Among these are: Cicero, De Fato; Ammonius, Commentarius in Aristotelis De Interpretatione, Adolf Busse, ed., in the Berlin Academy edition of the Com­mentaria in Aristotelem Graeca, Berlin, 1897; Boethius, Minora Commentaria in Librum Aristotelis de Interpreta­tione, and Ma;ora Commentaria ... , in Patrologiae Cursus Completus, J. P. Migne, ed., Latin series, Vol. 64, Paris, 1891. Also, Commentarii in Librum Aristotelis "Peri Her­meneias," C. Meiser, ed., Leipzig, 1877, 188o; Abii Na~r al­Fiiriibi, Alfarabi's Commentary on Aristotle's De Interpreta­tione, W. Kutsch and S. Marrow, eds., Beyrouth, 1960; St. Anselm, Tractatus de concordia praesentiae, et praedestina­tionis, et gratiae dei cum Iibera arbitrio, Migne, ed., Patro­logia, Latin series, Vols. 158-59; Abelard, Dialectia, L. M. de Rijk, ed., Assen, 1956, and "Editio super Aristotelem de Inter­pretatione" in Pietro Abelardo: Scritti Filosofici, M. dal Pra, ed., Milano, 1954; Averroes, Commentarium Medium in Aris­totelis "De Interpretatione," Juntine edition of Aristotelis omnia quae extant Opera cum Averrois Cordubensis com­mentarii, Venice, 1562; Albertus Magnus, In libros II Perihermeneias (in Opera omnia), A. Borgnet, ed., VoL I, Paris, 1890, pp. 373-757; St. Thomas Aquinas, In Libros "Perihermeneias" Exposition, tr. by J. T. Oesterle, Marquette University Press, Milwaukee, 1962, see Lecturae 13-15; William of Ockham, "Analysis of Ockham's Tractatus de Praedestinatione et de Praescientia Dei et de Futuris Con-

BffiLIOGRAPHY

tingentibus," in Philosophical Writings, sel. and ed. by Philotheus Boehner, Thomas Nelson & Sons, New York, 1957, pp. 42o-41. The text of this tract was edited by Boehner in the Franciscan Institute Publications, Philosophy Series, no. 2, St. Bonaventure, 1945; L. Baudry, La Querelle des Futurs Contingents, Louvain, 1465-1475; Textes Inedits, Paris, 1950; Thomas Hobbes, De Corpore,· ch. x, "Of Power and Act" in The Metaphysical System of Hobbes, M. W. Calkins, ed., Open Court, Chicago, 1905, pp. 76-8o; C. S. Peirce, Collected Papers, C. Hartshorne and P. Weiss, eds., Harvard University Press, Cambridge, Mass., 1931-1958, see pas­sim in Vols. III, V, VI; 0. Hamelin, Le Systeme d'Aristote, Paris, 1920, 2d ed. 1931; Jan Lukasiewicz, "Three-Valued Logic" (in Polish), Ruch Filozoficzny, Vol. 5 (1920), pp. 169-71; Lukasiewicz, "Philosophische Bemerkungen zu mehr­wertigen Systemen des Aussagenkalktils," Comptes Rendus des Seances de la Societe des Sciences et des Lettres de Varsovie, Classe III, Vol. 23 (1930), pp. 51-77; Lukasie­wicz and A. Tarski, "Untersuchungen· tiber den Aussagen­kalktil," Comptes Rendus des Seances de la Societe des Sci­ences et des Lettres de Varsovie, Classe III, Vol. 23 (1930), pp. 1-21; M. Wajsberg, "Aksjomatyzacia trojwarosciowego rachunku zdan," Comptes Rendus des Seances de la Societe des Sciences et des Lettres de Varsovie, Classe III, Vol. 24 ( 1931), pp. 126-48; C. A. Baylis, "Are Some Propositions Neither True nor False?" Philosophy of Science, 3 ( 1936); A. Becker, Die Aristotelische Theorie der Moglichkeit­schlilsse, Berlin, 1933; Becker, "Bestreitet Aristotles die Gtil­tigkeit des Tertium non datur ftir Zukunftsaussagen?" Actes du Congres International de Philosophie Scientifique, VI, Paris, 1936, pp. 69--74; J. Maritain, Introduction to Logic, tr. by I. Choquette, Sheed & Ward, New York, 1937, pp. 97, 135-36; C. J. Ducasse, "Truth, Verifiability, and Propositions abo~t the Future," Philosophy of Science, 8 ( 1941); D. Amand, Fatalisme et liberte dans l'Antiquite grecque, Louvain, 1945; J. Isaac, Le Peri Hermeneias en Occident de Boece a Saint Thomas, Paris, 1949; Pears, "Time, Truth, and Inference," cited earlier in full; D. Williams, "The Sea Fight Tomorrow," in Structure, Method, and Meaning, Paul Henle

so8 THE PHILOSOPHY OF TIME

et al., eds., Liberal Arts Press, New York, 1951. See also L. Linsky, "Professor Donald Williams on Aristotle," PR, 63 ( 1954), and Williams' reply, "Professor Linsky on Aris­totle," in the same issue; B. Mates, Stoic Logic, University of California Publications in Philosophy, 26 ( 1953), 28-29; A. N. Prior, "In What Sense Is Modal Logic Many-Valued?" A, ( 1953); Prior, "Three-valued Logic and Future Con­tingents," PQ, 3 ( 1953) (see also the review by T. Sugihara in The journal of Symbolic Logic, 19 (1954), 294). W. V. Quine, "On a So-called Paradox," M, 62 ( 1953); G. Ryle, "It Was to Be," in Dilemmas, Cambridge University Press, Cambridge, 1954; R. J. Butler, "Aristotle's Sea Fight and Three-valued Logic," PR, 64 (1955); A. N. Prior, Formal Logic, Oxford University Press, Oxford, 1955, pp. 24o-5o; F. Waismann, "How I See Philosophy," in Contemporary British Philosophy, third series, cited earlier in full; G. E. M. Anscombe, "Aristotle and the Sea Battle," M, 65 ( 1956). See the review by E. J. Lemmon in The journal of Symbolic Logic, 21 (1956), 388-89; C. K. Grant, "Certainty, Neces­sity, and Aristotle's Sea-Battle," M, 64 ( 1957); R. Taylor, "The Problem of Future Contingents," PR, 66 ( 1957), which is criticized by R. Albritton, "Present Truth and Fu­ture Contingency" in the same issue; A. N. Prior, Time and Modality, Clarendon Press, Oxford, 1957; H. Putnam, "Three­valued Logic," Philosophical Studies, 8 ( 1957); Jan Lukas­iewicz, Aristotle's SyUogistic from the Standpoint of Modern Formal Logic, 2d ed. enl., Oxford University Press, Oxford, 1957, pp. 155-56; J. T. Saunders, "A. Sea-Fight Tomorrow?" PR, 67 ( 1958); J. King-Farlow, "Sea-Fights Without Tears," A, 19 ( 1959); J. Hintikka, "Necessity, Universality, and Time in Aristotle," Ajatus, 20 ( 1959) ; Hintikka, "The Once and Future Sea Fight," PR, 73 ( 1964); R. J. Butler, a re­view of Saunders (1958), Bradley (reprinted in this book), and Wolff (1960) in The Journal of Symbolic Logic, 25 (1960), 343-45; R. Montague, "Mr. Bradley on the Future," M, 59 ( 1960); C. Strang, "Aristotle and the Sea Battle," M, 69 ( 1960); P. Wolff, "Truth, Futurity and Contin­gency," M, 69 ( 1960); R. M. Gale, "Endorsing Predic­tions," PR, 70 ( 1961); Gale, "Can a Prediction 'Become

BIDLIOGRAPHY 509 True'?" Philosophical Studies, 13 ( 1962); W. and M. Kneale, The Development of Logic, Oxford University Press, Oxford, 1962; A. J. Ayer, "Fatalism," The Concept of a Person and Other Essays, Macmillan, London, 1963; Z. Jordan, "Logical Determinism," Notre Dame Journal of Formal Logic, 4 ( 1963); N. Rescher, "An Interpretation of Aristotle's Doc­trine of Future Contingency and Excluded Middle," in Studies in the History of Arabic Logic, University of Pitts­burgh Press, Pittsburgh, 1963; Rescher, "Aristotle's Theory of Modal Syllogisms and Its Interpretation" in The Critical Approach to Science and Philosophy, M. Bunge, ed., Free Press, London, 1964; and N. Pike, "Divine Omniscience and Voluntary Action," PR, 74 ( 1965). The above articles by Lukasiewicz, Pears, Ryle, Prior, Butler, Taylor, Gale, Jordan, and Rescher defend Aristotle's doctrine of future contingents by employing certain tenets of the A-Theory of Time; while the articles by Ducasse, Williams, and Quine criticize Aris­totle from the standpoint of the B-Theory of Time.

The Master Argument of Diodorus, which is taken up in tl1e Rescher article in this book, is commented on by: E. Zeller, "Ueber den Kyrieuon des Megarikers Diodorus," Sitzungsberichte der Koniglichen Akademie der Wissenschaf­ten zu·Berlin, Berlin, 1882; N. Hartmann, "Der Megarische und der Aristotelische Moglichkeitsbegriff," Sitzungsberichte der Preussischen Akademie der Wissenschaften, philo­sophisch-historische Klasse, Jahrgang, 1937; V. Goldschmidt, Le system stoicien et ridee de temps, Paris, 1953; B. Mates, Stoic Logic, cited earlier in full; S. Sambursky, "On the Pos­sible and the Probable in Ancient Greece," Osiris, 1.2 ( 1956); Prior, "Diodorus and Modal Logic," PQ, 8 ( 1958); S. Sambursky, Physics of the Stoics, Macmillan, New York, . 1959; 0. Becker, "Zur Rekonstruction des Kyrieuon Logos des Diodorus Kronos," Erkenntnis und Verantwortung: Festschrift fur Theodor Litt, J. Derbolav and F. Nicolin, eds., Dusseldorf, 1960; Pierre-Maxime Schuh!, Le Domina.. teur et les possibles, Paris, 1960; W. and M. Kneale, The Development of Logic, cited earlier in full; Hintikka, "Aris­totle and the 'Master Argument' of Diodorus," American Philosophical Quarterly, 1 ( 1964); and N. Rescher, Tem-

510 THE PHILOSOPHY OF TIME

poral Modalities in Arabic Logic, Supp. Series of Founda­tions of Language, Dordrecht, 1967.

Taylor's piece on "Fatalism" has evoked the following literature: J. T. Saunders, "Professor Taylor on Fatalism," A, 23 ( 1962); B. Aune, "Fatalism and Professor Taylor," PH, 71 (1962); R. Taylor, "Fatalism and Ability," A, 23 (1962); P. Makepeace, "Fatalism and Ability, II," ibid.; Saunders, "Fatalism and Linguistic Reform," ibid.; R. Abelson, "Tay­lor's Fatal Fallacy," PR, 72 ( 1963); R. Sharvy, "A Logical Error in Taylor's 'Fatalism'," A, 23 ( 1962); Saunders, "Fatalism and the Logic of 'Ability'," A, 24 ( 1963); Tay­lor, "A Note on Fatalism," PR, 72 (1963); Sharvy, "Tautol­ogy and Fatalism," /P, 61 ( 1964); S. Cahn, "Fatalistic Ar­guments," ibid.; Taylor, "Comment," ibid.; Saunders, "Fatal­ism and Ordinary Language," /P, 62 ( 1965); and Diodorus Cronus (Richard Taylor), "Time, Truth and Ability," A, 25 ( 1965).

Discussions of Dummett's problem concerning whether a cause can be later than its effect are found in: M. Dummett and A. Flew, "Can an Effect Precede Its Cause?" ( sympo­sium), PAS, Supp. Vol. 28 (1954); M. Black, "Why Can­not an Effect Precede Its Cause?" A, 16 ( 1956); A. Flew, "Effects Before Their Causes? Addenda and Corrigenda," A, 16 ( 1956); M. Scriven, "Randomness and the Causal Order," A, 17 ( 1957); A. J. Ayer, The Problem of Knowledge, cited earlier in full; D. F. Pears, "The Priority of Causes,'" A, 17 (1957); Flew, "Causal Disorder Again," A, 17 (1957); R. M. Chisholm and R. Taylor, "Making Things to Have Happened," A, 20 ( 1960); S. Gorovitz, "Leaving the Past Alone" (a criticism of Dummett's "Bringing About the Past") PR, 73 ( 1964); and R. M. Gale, "Why a Cause Cannot Be Later Than Its Effect," Review of Metaphysics, 19 ( 1965). Also to be consulted on this topic are the articles by Flew and Ducasse in The Philosophy of C. D. Broad, cited earlier in full.

Mayo's thesis that future, unlike past, individuals cannot be identified is defended in some form by the following per­sons: C. S. Peirce, CoUected Papers, C. Hartshorne and P. Weiss, eds., Vol. IV (1933), #172, and also Vol. II

BmLIOGRAPIIY 511 (1932), ##146-48, and Vol. V (1934), #447; Broad, Scien­tific Thought, cited earlier in full, p. 77; G. Ryle, "It Was to Be," cited earlier in full; Prior, Time and Mod<Jlity, cited earlier in full; Prior, "Identifiable Individuals," Review of Metaphysics, 13 ( 1g6o); J. Margolis, "Statements about the Past and Future," PR, 72 ( 1963); and R. M. Gale and I. Thalberg, "The Generality of Predictions," JP, 62 ( 1965). The following pieces have been critical of the generality of predictions thesis: P. T. Geach, Reference and Generality, Cornell University Press, Ithaca, N.Y., 1962, p. 29; and A. J. Ayer, The Concept of a Person and Other Essays, cited earlier in full, pp. 249-50.

SECTION IV. HUMAN TIME

Works expounding or criticizing some version of the doc­trine of the "specious present" (which is taken up in the article by Mabbott in this volume) arc: W. James, The Prin­ciples of Psychology, Henry Holt, New York, 1890, Vol. I; W. P. Montague, "A Theory of Time Perception," in The Ways of Things, pp. 363-81; E. Husserl, The Phenomenology of Internal Time-Comcioumess, ed. by M. Heidegger and tr. by J. S. Churchill, Indiana University Press, Bloomington, Ind., 1964; Broad, Scientific Thought, cited earlier in full; L. E. Akeley, "The Problem of the Specious Present and Physical Time," ]P, 22 ( 1925); C. D. Broad, An Examina­tion of McTaggart's Philosophy, Cambridge University Press, Cambridge, 1938, Part II, vol. I, pp. 281 ff.; Mabbott, "The Specious Present," M, 64 ( 1955); P. Fraisse, The Psychology of Time, tr. by J. Leith, Eyre and Spottiswoode, 1964. '

Griinbaum's thesis that temporal becoming is psychological or mind-dependent is alsq espoused by: B. Russell, "On the Experience of Time," Mohist, 25 ( 1915); .R. M. Blake, "On Mr. Broad's Theory of Time," M, 34 ( 1925); Braithwaite, "Time and Change," cited earlier in full; A. S. Eddington, The Nature -of the Physical World, Macmillan, New York, 1928; Eddington, Space, Time, and Gravitation, Cambridge University Press, Cambridge, 1920; H. Weyl, Philosophy of Mathematics and Natural Science, based on a tr. by Olaf

512 THE PIDLOSOPHY OF TIME

Helmer, Princeton University Press, Princeton, N.J., 1949; H. Bergmann, Der Kampf um das Kausalgesetz in der fiingsten Physik, F. Vieweg and Son, Braunschweig, 1929; C. J. Ducasse, Nature, Mind, and Death, Open Court, La Salle, Ill., 1951; A. Griinbaum, Philosophical Problems of Space and Time, Alfred A. Knopf, New York,. 1963. Those who have argued that becoming is not Inind-dependent are: C. D. Broad, "Time and Change," PAS, Supp. Vol. 8 ( 1928); H. Reichenbach, "Die Kausalstruktur der Welt und der Unterschied von Vergangenheit und Zukunft," Berichte der Bayerischen Akademie Miinchen, Mathematisch-Natur­wissenschaftliche Abteilung (November 1925); P. Marhenke; "McTaggart's Analysis of Time," cited earlier in full; L. S. Stebbing,, "Some Ambiguities in Discussions Concerning Time," cited earlier in full; H. Reichenbach, The Direction of Time, University of California Press, Berkeley, 1956; M. Capek, The Philosophical Impact of Contemporary Physics, D. Van Nostrand, Princeton, N.J., 1961; and G. J. Whitrow, The Natural Philosophy of Time, Thomas Nelson & Sons, London and Edinburgh, 1961. Some philosophers, using H. Reichenbach's treatment of tensed verbs as token-reflexive words in his Elements of Symbolic Logic, Macmillan, New York, 1947, have argued that becoming is subjective because A-determinations involve a reference to the subject qua language-user: among the defenders of this view are Ayer, The Problem of Knowledge, and Smart, Philosophy and Scientific Realism., both cited earlier in full. Those who have argued that tensed verbs are not token-reflexive are: Wisdom, "Time, Fact, and Substance," cited earlier in full; Broad, An Examination of McTaggart's Philosophy, cited earlier in full; F. B. Ebersole, "Verb Tenses as Expressers and Indica­tors," A, 12 ( 1952); J. Jorgensen, "Some Reflections of Re­flexivity," M, 62 ( 1953); Findlay, "An Examination of Tenses," cited earlier in full; K. W. Rankin, "Referential Identifiers," American Philosophical Quarterly, 1 ( 1964); R. M. Gale, "The Egocentric Particular and Token-Reflex­ive Analyses of Tense," PR, 73 (1964); and Gale, "Pure and Impure Descriptions," Australasian Journal of Philosophy, 1966.

THE !BIDLIOGRAPHY' TIME

Some of the significant treatments of time by existentialists are: M. Heidegger, Kant and the Problem of Metaphysics, tr. by J. S. Churchill, Indiana ·University Press, Blooming­ton, Ind., 1962; Heidegger, Being and Time, tr. by J. Mac­quarrie and E. Robinson, Harper & Row, New York, 1962; Jean-Paul Sartre, Being and Nothingness, tr. by H. Barnes, Philosophical Library, New York, 1956; and M. Merleau­Ponty, Phenemenology of Perception, tr. by C; Smith, Rout­ledge & Kegan Paul, London, 1962.

For a detailed bibliography of B. L. Whorl's writings see Language, Thought, and Reality, J. B. Carroll, ed., Massa­chusetts Institute of Technology Press, Cambridge, Mass., 1956.

SEcTION V. ZENo's PARADOXES OF MoTION For a discussion of the historical Zeno and the subsequent

treatments of his paradoxes see: F. Cajori, "The History of Zeno's Arguments on Motion," American Mathematical Monthly, 23 ( 1915); Cajori, "The Purpose of Zeno's Argu· ments on Motion," Isis, 3 ( 1920-1921); Zeno of Elea, text, with tr. and notes by H. D. P. Lee, Cambridge University Press, Cambridge, 1936; C. B. Boyer, The Concepts of the Calculus, Hafner, New York, 1949; G. Vlastos, "Zeno's Race Course," Journal of the History of Philosophy, 4 ( 1966); Vlastos, "Zeno," in The Encyclopedia of Philosophy, P. Ed­wards, ed., Collier, New York, 1967; and W. C. Salmon's Introduction to Zeno's Paradoxes, Salmon, ed., Bobbs-Merrill, New York, 1967.

What I have termed the "Metaphysical Replies" to Zeno are in: H. Bergson, Time and Free Will, tr. by R. L. Pogson, George Allen & Unwin, London, 1910; Bergson, An Intro­duction to Metaphysics, tr. by T. E. Hulme, G. P. Putnam's Sons, New York, 1912; W. James, Some Problems of Phi­losophy, Longmans, Green, London, 1911; A. N. Whitehead, Process and Reality, Macmillan, New York, 1929; A. Edel, "Aristotle's Theory of the Infinite," New York, 1934, not publ.; J. 0. Wisdom, "Why Achilles Does Not Fail to Catch the Tortoise," M, so (1941); A. P. Ushenko, "Zeno's Para­doxes," M, 55 ( 1946); H. R. King, "Aristotle and the

THE PHILOSOPHY OF TIME

Paradoxes of Zeno," ]P, 46 ( 1949). Criticisms of these vari­ous metaphysical replies are in: A. 0. Lovejoy, "The Prob­lem of Time in Modem French Philosophy," PR, 21 ( 1912); R. M. Blake, "The Paradoxes of Temporal Process," ]P, 23 ( 1926); G. Santayana, Winds of Doctrine, Charles Scribner's Sons, New York, 1926; B. Russell, A History of Western Philosophy, Simon & Schuster, New York, 1945, chapter on "Bergson"; A. Griinbaum, "Relativity and the Atomicity of Becoming," Review of Metaphysics, 4 ( 1950).

The problem of completing an infinite number of tasks, which is central to the Thomson article, is discussed by the following authors: Weyl, Philosophy of Mathematics and Natural Science, cited earlier in full; H. B. Smith, "Mr. Blake and the Paradox of Zeno," ]P, 34 ( 1923); Max Black, "Achilles and the Tortoise," A, 11 ( 1951), reprinted with new comments and other articles on Zeno in Problems of Analysis, Cornell University Press, Ithaca, N.Y., 1954; R. Tay­lor, "Mr. Black on Temporal Paradoxes," A, 12 ( 1951); J. 0. Wisdom, "Achilles on a Physical Race Course," A, 13 ( 1952); Taylor, "Mr. Wisdom on Temporal Paradoxes," A, 13 ( 1952); L. E. Thomas, "Achilles and the Tortoise," A, 13 ( 1952); A. Griinbaum, "Messrs. Black and Taylor on Temporal Paradoxes," A, 13 ( 1952); J. Watling, "The Sum of an Infinite Series," A, 13 ( 1952); J. M. Hinton and C. B. Martin, "Achilles and the Tortoise," A, 14 ( 1954); G. Ryle, "Achilles and the Tortoise," in Dilemmas, cited earlier in full; D. S. Shwayder, "Achilles Unbound," ]P, 52 ( 1955); G. E. L. Owen, "Zeno and the Mathematicians," PAS, 58 ( 1957-1958); Whitrow, The Natural Philosophy of Time, cited earlier in full; P. Benacerraf, "Tasks, Super-tasks, and the Modem Eleatics," ]P, 59 ( 1962); E. TeHennepe, "Lan­guage Reform and Philosophical Imperialism: Another Round with Zeno," A, 23 ( 1963); C. S. Chihara, "On the Possibility of Completing an Infinite Process," PR, 7 4 ( 1965); and Vlastos, "Zeno's Race Course," cited earlier in full.

For a discussion of the mathematical continuum and its relevance to Zeno's paradoxes see: B. Russell, The Principles of Mathematics, cited earlier in full; Russell, Our Knowledge of the External World, Open Court, Chicago, 1914.