Travels in Four Dimensions: Further Reading
LePoidevin (Robin)
Source: LePoidevin - Travels in Four Dimensions: The Enigmas of Space and Time, 2003
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Further Reading1 (Full Text)

  1. The Measure of All Things
    A gripping account of the pursuit of accuracy in timekeeping, centred on John Harrison's long wrestle, between 1727 and 1773, with the problem of devising a timepiece that would remain perfectly accurate at sea (thus allowing sailors to calculate their longitude) is Sobel (1996). 0. K. Bouwsma's story is reprinted in Westphal and Levenson (1993). A classic defence of conventionalism about metric is Reichenbach (1958). A very helpful introduction to the debate between conventionalism and objectivism, which dearly sets out the different responses to the threat of inaccessible facts and proposes a novel solution is Newton-Smith (1980, Ch. VII). The connection between the debate over metric and the laws of motion is discussed in Van Fraassen (1980, Ch. III.2).
  2. Change
    Aristotle's treatment of the relationship between time and change, and his definition of time, can be found in his Physics, Bk. IV: Hussey (1983). For a helpful discussion of Aristotle's account, see Lear (1982). For Leibniz's views on time, see his correspondence with Samuel Clarke: Alexander (1956), and his New Essays on Human Understanding: Remnant and Bennett (19812). A well-known and fascinating thought-experiment3 designed to show the limitations of verificationist attacks on the notion of temporal vacua is Shoemaker (19684). For a discussion and extension of this thought-experiment5, see Newton-Smith (1980, Ch. II). Another argument for the possibility of time without change is discussed in Lucas (1973). A detailed discussion of relationism about time is Hooker (19716). Butterfield (19847) is salutary and required reading for anyone who is tempted to analyse times in terms of possible events.
  3. A Box with No Sides?
    Descartes's letters to Princess Elizabeth and Henry More can be found in Cottingham, Stoothoff, Murdoch, and Kenny (19918). An excellent historical survey of theories of space is Jammer (1969); Ch. 2 explores the theological dimensions of the debate over absolute space. For Aristotle's arguments concerning the void see the Physics, Bk. III (Hussey 19839). For discussion of Aristotle's and other ancient views on the void, see Sorabji (1988). A collection of classic readings on space is Huggett (1999); see especially Ch. 4 for extracts from Aristotle and commentary, and Ch. 7 for extracts from Newton's Principia (including the famous bucket experiment) and commentary. For Leibniz's views on the relationship between space and the objects within it, see again his correspondence with Samuel Clark: Alexander (1956); extracts and commentary in Huggett (1999, Ch. 8). The relationist — absolutist debate, and its relationship to the debate over absolute motion, are discussed in van Fraassen (1980, Ch. IV.I), and in greater detail by Nerlich (1994a) and Dainton (2001). See also Hooker (1971). A very detailed, but difficult, examination of the debate is Earman (1989).
  4. Curves and Dimensions
    For an accessible introduction to non-Euclidean geometry, see Sawyer (1955, Ch. 6). For the history of geometry see Boyer (1968), especially Chs. VII and XXIV. See also van Fraassen (1985, Ch. IV.a). The significance of non-Euclidean geometry for the debate between the absolutists and relationists is very clearly articulated in Nerlich (1991) and Dainton (2001). Kant's argument concerning incongruent counterparts is presented in Kant (1768); an extract is reprinted in Huggett (1999, Ch. ii), which also provides commentary. See also Earman (1989, Ch. 7) and Walker (1978, Ch. IV), which provide useful exegeses of Kant's text, and Nerlich (1994a, Ch. 2), a particularly important discussion that reconstructs the argument in terms of chirality (he uses the term enantiomorphism), and on which my account is based. A very entertaining discussion of chirality and its philosophical and scientific interest is Gardner (1982).
  5. The Beginning and End of Time
    For a brief introduction to Big Bang cosmology, see Hawking (198610). Ancient arguments concerning creation and the beginning of time are discussed in Sorabji (1983, pt. III). Newton-Smith (1980) exploits number analogies in defining the beginning and end of time, discusses a number of arguments against a beginning, including ones put forward by Aristotle and Kant, and also considers the causal anomalies involved in a beginning and end of the universe. Kant's argument concerning infinity is explored in Moore (1990). Craig and Smith (1993) is an extended, and highly dialectical, exploration of the interaction between Big Bang cosmology, philosophy, and theology, including an assessment of Kant's arguments. For some background to Eliot's Four Quartets, see Tamplin (1988). Closed, or cyclic time is discussed at some length in Newton-Smith (1980, Ch. III). For historical sources for cyclic time and history, see Sorabji (1983, Ch. 12).
  6. The Edge of Space
    Archytas' argument, and related arguments, against the edge of space are presented and discussed in Sorabji (1988i, Ch. 8). He also discusses arguments concerning extracosmic space. The difficulties the notion of an edge pose for our understanding of motion are pointed out in Nerlich (1994b). For discussion of Kant's First Antimony, see Broad (1978, Ch. 5) and Bennett (1974, Ch. 7). For readings on Aristotle's distinction between the actual/potential infinite distinction, see references under Chapter 7 below. An attempt to make sense of Kant's obscure argument from incongruent counterparts to the ideality of space is made in Broad (1978, Ch. 2) and van Cleve (1999). Poincare's thought experiment11 is presented in his (195212); extracts and discussion in Huggett (1999, Ch. 13). For a discussion of closed space see Sorabji (1988, Ch. 10).
  7. Infinity and Paradox
    The sources of Zeno's arguments can be found in Kirk, Raven, and Schofield (198313), Barnes (197814) and Huggett (1999). For discussion, see Huggett (1999), Owen (1957-815), Salmon (1970), Sorabji (1983), and Sainsbury (198816). For Aristotle's actual — potential infinite distinction, and its application to Zeno's paradoxes, see Lear (198817). The source of Thomson's Lamp is Thomson (195418). For discussion, see Sainsbury (1988). See also Clark and Read (198419), which argues against the possibility of completing uncountably many tasks in a finite time. Moore (1990) is a particularly helpful and wide-ranging discussion, covering all the above. It also presents an historical overview on theories of infinity and defends a version of finitism. The transition paradox is discussed at length in Sorabji (1983). Part V of Sorabji also discusses Ancient atomism, on which see also Barnes (1978) and Kirk, Raven, and Schofield (1983), for sources and commentary. Lloyd (1982, Ch. 4) shows how ancient atomism developed as a response to the problem of change (the problem being that change appears to involve something coming into being from nothing).
  8. Does Time Pass?
    Broad's views on time underwent an interesting development. Compare his (1923) discussion, from which the passage quoted is taken, with his encyclopaedia article (1921) and his exhaustive discussion (193820) of McTaggart's proof. McTaggart's21 proof originally appeared in his (190822), but see also the revised presentation in his (192723). For discussion and partial defence of the proof see Dummett (196024). A more critical discussion, which focuses on the legitimacy, or otherwise, of expressions such as ‘is present in the past', is Lowe (198725). A reconstruction in terms of token-reflexives is presented in Mellor26 (198127) and (199828). An unusual solution to the paradox, in terms of possible worlds, is presented in Bigelow (199129), and criticized in Oaklander (199430). Early statements of presentism are Lukasiewicz (1967) and Prior (197031). Versions of presentism are defended in Bigelow (199632) and Zimmerman (199833). The doctrine, in its various forms, is examined in Dainton (2001, Ch. 6). The B-theory is defended in Smart (1980), Mellor (1981, 1998), and Oaklander (1984). The most extensive critiques of the B-theory to date are Smith (1993) and Craig (2000). See also Teichmann (1995). For an important collection of papers on McTaggart's argument, the B-theory, and related issues, see Oaklander and Smith (1994). One issue not discussed here is the extent to which the A-theory, and the associated view of the future is unreal, is compatible with the Special Theory of Relativity. For arguments in favour of the view that they are incompatible, see Putnam (196734), Mellor (197435), and Nerlich (1998). For attempts at reconciliation, see Smith (1993, 199836), Dorato (1995), and Craig (2001). See also Dainton (2001, Chs. 16 and 17) for an introduction to Special Relativity and its philosophical consequences.
  9. Change again: Zeno's Arrow
    For sources and commentary on the Arrow, see Lee (1936), Barnes (1982), Kirk, Raven, and Schofield (1983), and Huggett (1999). For discussion, see Ross (1936), Owen (1957-8), Vlastos (196637), Grunbaum (1967), Salmon (1970), and Sorabji (1983). The suggestion that the Arrow is best understood in terms of motion in the present was made by Jonathan Lear, and his discussion is particularly helpful: see Lear (198138, 1988). The second reconstruction presented here is based (with a few details altered) on his account. For discussions of presentism, see the references under Chapter 8 above.
  10. Interfering with History
    A very readable history of the calendar, with an account of the shift from the Julian to the Gregorian calendar, the problems that it was intended to solve, and the consequences, is Duncan (1998). For an introduction to the issues involving the reality/unreality of the future, and its bearing on our status as free agents, see Smith and Oaklander (1995). Discussion of these issues as they arose in ancient times is provided by Hintikka (1973), Sorabji (1980), and Lucas (198939). The last of these defends a version of the ‘open future' account. On the reality of the past, see Dummett (196940), who defends an 'anti-realist' account. For a discussion of the philosophical dimensions of the passage from Orwell's Nineteen Eighty-Four quoted here, see Wright (1986). On time travel, see Harrison (197141), Lewis (197842) (introduces the external — personal time distinction, and argues that the time-traveller is a free agent in the sense that anyone is a free agent), MacBeath (198243) (explores the causal anomalies of time travel), and Ray (1991, Ch. 8) (puts time travel in the context of spacetime physics). For a defence of the coherence of backwards causation, see Dummett (196444), and arguments for its incoherence, see Mellor (1981, 1998). Mellor's argument in his (1981) is criticized in Riggs (199145) and Weir (198846) (who puts the issue in the context of closed, or cyclic, time).
  11. Other Times and Spaces
    An excellent and very readable discussion of the multiverse hypothesis, its theistic rival, and the probabilistic reasoning used to motivate them, is Leslie (198947). Leslie also briefly discusses the two-slit experiment. The branching spaces interpretation of the experiment is closely related to what is often called the ‘many worlds' interpretation of quantum mechanics (although there is considerable dispute over the correct interpretation of the interpretation). For a philosophical introduction to quantum mechanics, see Lockwood (1989). The many worlds, or ‘many minds', interpretation was the subject of a symposium, the (highly technical) papers being published in the June 1996 issue48 of the British Journal for the Philosophy of Science. Disunified space is the subject of a classic paper by Quinton (196249). In that paper Quinton puts forward a fantasy designed to show that, under certain conditions, we might regard our experience as providing evidence for disunified space. He rejects the temporal parallel, however, as does Swinburne (1981, Ch. 10), which nevertheless considers it in sympathetic detail (see also Ch. 2 on disunified space). The temporal parallel is given support in Newton-Smith's (1980) discussion of Quinton's thought experiment50. See also Hollis (196751).
  12. The Arrows of Time
    An important recent discussion of the arrow(s) of time, which clearly presents the view that the classic way of articulating the problem of the direction of time is ill-posed, and which defends a novel treatment of causation, is Price (1996). The issue of what kind of reduction is appropriate in reductionist theories of direction is taken up by Sklar (198152), who argues in favour of a theoretical reduction rather than one in terms of meaning. For a discussion of the psychological arrow, see Newton-Smith (1980). The thermodynamic and causal arrows are discussed in Dainton (2001), which also tackles the tricky issue of how the asymmetry of causation is to be explained. The causal analysis of time is subject to lengthy and detailed criticism in Sklar (197453). Tooley (1997) is an intriguing attempt to explain temporal and causal asymmetry in terms of the unreality of the future, but appealing only to B-series facts. The importance of causation in explaining our experience of time, and in particular its direction, is well articulated in Mellor (1981, 1998). On the issue of dimensionality: a two-dimensional model for time's passage is presented in Schlesinger (198254) and criticized by MacBeath (1986). For an ingenious discussion of what might count as evidence for two-dimensional time, see MacBeath (199355).
  13. Concluding Thoughts
    The human significance of time, as revealed by the history of Western and Eastern thought about time, is discussed in Fraser (1968, pt. I). On the significance of the A-theory / B-theory debate for our views on death, see Le Poidevin (199656). The reconciliation of human freedom with the B-theory is the subject of Oaklander (1998). The ethical dimension of the debate is explored in Cockburn (1997, 1998). The issue of whether the B-theory requires a revision in our ordinary views of persistence through time has been the subject of much debate. For arguments that it does, see Lowe (1998a, 1998b); that it does not, Mellor (1981, 1998).

In-Page Footnotes

Footnote 1: This requires reference to the Le Poidevin’s Bibliography. Where I have the book / paper, I’ve provided links to my database (on the first occasion). Where I don’t, and don’t care, you’ll have to refer to the book to find the full reference.

Footnote 2: See "Leibniz (Gottfried), Remnant (Peter), Bennett (Jonathan) - New Essays on Human Understanding".

Footnote 4: See "Shoemaker (Sydney) - Time Without Change".

Footnote 6: See "Hooker (Clifford A.) - The Relational Doctrines of Space and Time".

Footnote 7: See "Butterfield (Jeremy) - Relationism and Possible Worlds".

Footnote 8: See "Descartes (Rene), Cottingham (John), Stoothoff (Robert), Murdoch (Dugald), Kenny (Anthony) - The Philosophical Writings of Descartes Vol III - The Correspondence".

Footnote 9: See "Aristotle, Waterfield (Robin) & Bostock (David) - Physics", as an alternative.

Footnote 10: See "Hawking (Stephen) - A Brief History of Time - From the Big Bang to Black Holes".

Footnote 12: See "Poincare (Henri) - Science and Hypothesis".

Footnote 13: See "Kirk (G.S.), Raven (J.E.) & Schofield (M.) - The Presocratic Philosophers".

Footnote 14: See "Barnes (Jonathan) - The Presocratic Philosophers".

Footnote 15: See "Owen (G.E.L.) - Zeno and the Mathematicians".

Footnote 16: See "Sainsbury (Mark) - Paradoxes".

Footnote 17: See "Lear (Jonathan) - Aristotle - The Desire to Understand".

Footnote 18: See "Thomson (James F.) - Tasks and Super-Tasks".

Footnote 19: See "Clark (Peter) & Read (Stephen) - Hypertasks".

Footnote 20: I only seem to have "Broad (C.D.) - McTaggart's Arguments Against the Reality of Time" by Broad on this topic. This is an extract from An Examination of McTaggart's Philosophy.

Footnote 21: Some unmentioned items on McTaggart are:-
"Oaklander (L. Nathan) - McTaggart's Paradox and Smith's Tensed Theory of Time",
"Corish (Denis) - McTaggart's Argument", and
"Currie (Gregory) - McTaggart at the Movies".

Footnote 22: See "McTaggart (J. McT. E.) - The Unreality of Time".

Footnote 23: See
"McTaggart (J. McT. E.) - Time (The Unreality of Time)", and
"McTaggart (J. McT. E.) - Time".
The latter is a cut-down version of the former; it has the original page-numbers, but otherwise no advantages.

Footnote 24: See "Dummett (Michael) - A Defense of McTaggart's Proof of the Unreality of Time".

Footnote 25: See "Lowe (E.J.) - The Indexical Fallacy in McTaggart's Proof of the Unreality of Time".

Footnote 26: Why not "Mellor (D.H.) - McTaggart's Proof".

Footnote 27: See "Mellor (D.H.) - Real Time".

Footnote 28: See "Mellor (D.H.) - Real Time II".

Footnote 29: See "Bigelow (John) - Worlds Enough For Time".

Footnote 30: See "Oaklander (L. Nathan) - Bigelow, Possible Worlds and the Passage of Time".

Footnote 31: See "Prior (Arthur N.) - The Notion of the Present".

Footnote 32: See "Bigelow (John) - Presentism and Properties".

Footnote 33: See "Zimmerman (Dean) - Temporary Intrinsics and Presentism".

Footnote 34: See "Putnam (Hilary) - Time and Physical Geometry".

Footnote 35: See +P 17186P+.

Footnote 36: See "Smith (Quentin) - Absolute Simultaneity and the Infinity of Time".

Footnote 37: See "Vlastos (Gregory) - A Note on Zeno's Arrow".

Footnote 38: See "Lear (Jonathan) - A Note on Zeno's Arrow".

Footnote 39: See "Lucas (J.R.) - The Future - An Essay on God, Temporality and Truth".

Footnote 40: See "Dummett (Michael) - The Reality of the Past".

Footnote 41: See "Harrison (Jonathan) - Dr. Who and the Philosophers or Time-Travel For Beginners".

Footnote 42: See "Lewis (David) - The Paradoxes of Time Travel".

Footnote 43: See "MacBeath (Murray) - Who Was Dr Who's Father?".

Footnote 44: See "Dummett (Michael) - Bringing About the Past".

Footnote 45: See "Riggs (Peter J.) - A Critique of Mellor's Argument against 'Backwards' Causation".

Footnote 46: See "Weir (Susan) - Closed Time and Causal Loops: A Defence against Mellor".

Footnote 47: See "Leslie (John) - Universes".

Footnote 48: See:-
"Lockwood (Michael) - 'Many Minds' Interpretations of Quantum Mechanics", and the replies …
"Brown (Harvey) - Mindful of Quantum Possibilities",
"Butterfield (Jeremy) - Whither the Minds?",
"Deutsch (David) - Comment on Lockwood",
"Loewer (Barry) - Comment on Lockwood",
"Papineau (David) - Many Minds Are No Worse than One", and
"Saunders (Simon) - Comment on Lockwood".

Footnote 49: See "Quinton (Anthony) - Spaces and Times".

Footnote 51: See "Hollis (Martin) - Times and Spaces".

Footnote 52: See "Sklar (Lawrence) - Up and Down, Left and Right, Past and Future".

Footnote 53: See "Sklar (Lawrence) - Space, Time and Spacetime".

Footnote 54: See "Schlesinger (George N.) - How Time Flies".

Footnote 55: See "MacBeath (Murray) - Time's Square".

Footnote 56: See "LePoidevin (Robin) - Arguing for Atheism: An Introduction to the Philosophy of Religion".

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