1 For example it is often supposed that time travel involves changing the past and is therefore logically impossible. But time travel does not involve changing the past. See Dwyer, L. “Time Travel and Changing the Past,“ Philosophical Studies (May 1975CrossRefGoogle Scholar).

2 See, e.g., Horwich, P. “On Some Alleged Paradoxes of Time Travel,“ Journal of Philosophy (August 1975CrossRefGoogle Scholar); Lewis, D. “The Paradoxes of Time Travel,” American Philosophical Quarterly 13 (April 1976Google Scholar). Harrison, J. “Dr. Who and The Philosophers Or Time Travel for Beginners,” Aristotelian Society Supplimentary Volume 14, 1971Google Scholar.

3 Gale, R. The Language of Time (London: Routledge & Kegan Paul Ltd., 1968Google Scholar). See part three, “logical Assymmetries Between the Past and the Future.”

4 Swinburne, R. Space and Time (Macmillan & Co., 1968CrossRefGoogle Scholar).

5 Black, M. “Why Cannot an Effect Precede Its Cause?” Analysis 16 (1956CrossRefGoogle Scholar).

6 Flew, A. “Can An Effect Precede Its Cause?” Aristotelian Society Supplement 28 (1954Google Scholar); see also “Effects Before Their Causes? Addenda and Corrigenda,” Analysis 16 (1956); “Causal Disorder Again,” Analysis 17 (1957); “Magicians, Alarm Clocks and Backward Causation: A Comment,“ Southern Journal of Philosophy (Winter 1973).

7 Dissenters from the popular view include Dummett and Scriven: see Dummett, M. “Can an Effect Precede Its Cause?” Aristotelian Society Supplement 28 (1954CrossRefGoogle Scholar); “Bringing About the Past,” Philosophical Review (1964). See also Scriven, M. “Randomness and the Causal Order,” Analysis 17 (1956CrossRefGoogle Scholar). Both writers try to construct plausible counter-examples to the popular view. Dummett constructs cases involving magicians, tribal dancing, alarm clocks, coin tossing, etc., while Scriven constructs a case involving precognition. Neither mentions time travel.

8 “All things no matter what their qualities are bits of spacetime,” Alexander, S. Space, Time and Diety (London, 1920), p. 223Google Scholar; “The scene of action of reality is … a four dimensional world in which space and time are linked together indissolubly,” H. Weyl, Space-Time-Matter, p. 217. “The universe consists without residue of the spread of events in space-time,” Williams, D. “The Myth of Passage,” Journal of Philosophy (1951), p.458Google Scholar. Earman, John has shown how neglect of spacetime has led philosophers to overlook important issues in the philosophy of space and time. See his “Space-Time or How to Solve Philosophical Problems and Dissolve Philosophical Muddles Without Really Trying,” Journal of Philosophy (May 1970CrossRefGoogle Scholar).

9 See for example Kronheimer, E.H. and Penrose, R. “On the Structure of Causal Spaces,” Proceedings of the Cambridge Philosophical Society (1967CrossRefGoogle Scholar); Carter, B. “Causal Structure in Space-Time,” General Relativity and Gravitation, 1 (1971CrossRefGoogle Scholar).

10 Capek, M. “Time in Relativity Theory: Arguments for a Philosophy of Becoming,” in Fraser, J. T. (ed), The Voices of Time (New York: G. Brasiller, 1966Google Scholar).

11 Gödel, K. “Example of a New Type of Cosmological Solutions to Einstein's Field Equations,” Review of Modern Physics 21 (1949CrossRefGoogle Scholar); “A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy,” in Schilpp, P.A. (ed.), Albert Einstein: Philosopher-Scientist (New York, Harper Row: 1949)Google Scholar. All page references to Gödel will be to this latter paper.

12 For General Relativity, unlike Newtonian physics and Special Relativity, the topology of the underlying space-time depends on the given physical situation. Some solutions to the Einstein-Maxwell field equations, e.g., the Gödel universe, Taub-NUT space, de Sitter and anti de Sitter spacetime, and the Kerr solution admit closed time-like curves. Regarding the Kerr family of gravitational fields, although they contain closed timelike lines which are not removable by taking a covering space, they are the only solutions of Einstein's equations known at present which could represent the exterior field of a rotating body in asymptotically flat space. One of the most important problems in General Relativity today is that concerning the singularities and other pathological features arising in gravitational collapse. The final fate of massive stars is to collapse behind an event horizon to form a ‘black hole.’ The Kerr solutions, including the unavoidable breakdown of the causality postulate, appear to be the only possible exterior solutions for black holes. For a discussion of the above mentioned cosmological models and spacetime singularities see Penrose, R. “Structure of Spacetime,” in Wheeler, J.A. and Witt, C. De Battelle Rencontres (New York, W.A. Benjamin, 1968Google Scholar). See also Hawking, S.W. and Ellis, G. The LargeScale Structure of Space-Time (Cambridge University Press, 1973CrossRefGoogle Scholar); and Misner, C. Wheeler, J.A. and Thorne, K. Gravitation (San Francisco: W.H. Freeman & Co., 1972), part VIIGoogle Scholar.

13 Demonstrated by Geroch, R. “Topology in General Relativity,” Journal of Mathematical Physics 8 (1967CrossRefGoogle Scholar).

14 Feynman, R. The Theory of Fundamental Processes (New York: W.A. Benjamin, 1961), esp. chap. 5Google Scholar.

15 Proper time is the time interval between x and y in figure 2 as measured by an (idealized) clock whose world line is the given curve. I mention this lest it be thought that on his journey the time traveller ages (roll over Methuselah!) almost 5000 years.

16 Op. cit. When quoting Gale I shall substitute the letters x, y for Gale's L,E, respectively.

17 In one science fiction story, a man fascinated by tales of Christ's crucifixion goes back in time to witness the event for himself only to find that he and his twelve followers cause such a stir that he is crucified.

18 I have elsewhere (see note 1) criticised Gorovitz for invoking such forces; Gorovitz, S. “Leaving the Past Alone,” Philosophical Review (1964CrossRefGoogle Scholar). Lewis, D. op. cit., p. 149Google Scholar, makes a similar point.

19 J. Mackie, “The Direction of Causation,” Philosophical Review (1966), p. 455.

20 Flew makes this response to Brier who wants to use the distinction between changing and affecting the past. See Brier, R. “Magicians, Alarm Clocks and Backward Causation,” Southern Journal of Philosophy (Winter 1973CrossRefGoogle Scholar). My arguments here against Flew thus constitute a defence of Brier's position. See also Dwyer, L. “How to Affect, But Not Change, The Past,” Southern Journal of Philosophy (1977CrossRefGoogle Scholar).

21 Lehrer, K. “Decisions and Causes,” Philosophical Review (1963CrossRefGoogle Scholar).

22 Goldman, A. “Actions, Predictions and Books of Life,” American Philosophical Quarterly (1968Google Scholar).

23 (See footnote 12). Also consider what Hawking has to say about the empirical evidence: “The view has been expressed that singularities are so objectionable that if the Einstein equations were to predict their occurrence this would be a compulsive reason for modifying them. However the real test of a physical theory is not whether its predicted results are aesthetically attractive but whether they agree with observation. So far there are no observations which would show that singularities do not occur” (as quoted in Misner, Wheeler and Thorne, op. cit., p.939). For a discussion of the empirical possibility of Gödel's model as well as some observations concerning the ramifications of those models for our understanding of the nature of Time see Stein, H. “On The Paradoxical Time Structures of Gödel”, Philosophy of Science 37 (1970CrossRefGoogle Scholar).

24 For two nice summaries of the sorts of arguments which have been put forward both in support and denial of these claims as well as references to the individual philosophers who have taken positions in the debate see “The Philosophy of Time,” ed. R. Gale., Introduction to section iii, see also Fitzgerald, P. “The Truth About Tomorrow's Sea Fight,” journal of Philosophy (June 5, 1969CrossRefGoogle Scholar).