Four-dimensionalism: An Ontology of Persistence and Time
Sider (Ted)
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Amazon Customer Review 1

  1. Hud Hudson, in a review of Ted Sider's book, says, "This is simply a superb book in metaphysics - handsomely written, cleverly argued, and exceedingly clear." Of course, Hudson happens to agree with almost every thesis Sider defends in the book. But I don't. In fact, I happen to disagree with almost every position defended in Sider's book. So what do I think of the book? I think it is simply a superb book in metaphysics - handsomely written, cleverly argued, and exceedingly clear. And I think it is notable that both friends and foes of the views defended in the book will find it to be extremely valuable. That is a real mark of distinction in philosophy, and my hat is off to Sider for producing such an outstanding work.
  2. What is the book about? Mainly the question of whether physical objects have temporal parts. A temporal part of x is, roughly, an object that exists for a shorter time than x but that exactly overlaps x throughout its existence. Sider believes, for example, that you have a temporal part that exists (only) from noon to 1pm today, and that perfectly overlaps you throughout that time. His view allows him to give neat and clean solutions to all manner of metaphysical problems (including the problem of how a time traveler1 who meets his former self could be both sitting and standing at the same time), and to do various other wonderful things.
  3. Although this is primarily a work for academic philosophers, it is clear enough that non-philosophers will be able to follow it, and to benefit from a careful reading of it. I highly recommend Four-Dimensionalism to professional philosophers, philosophy students (both graduate and undergraduate), and anyone else who is interested in questions about time and space.

Amazon Customer Review 2
  1. 'Four-Dimensionalism' is a great book. Sider defends Four-Dimensionalism with great clarity and force. Four-Dimensionalism holds (roughly) that, just as you have spatial parts – e.g. hands, cells, simples, etc. – you have "temporal" parts. A temporal part is a part of you that exists at a certain time in your existence. A consequence of this view is that, at a particular moment, you don't "wholly" exist, because your existence is spread out in time2. (Four-Dimensionalism contrasts with Three-Dimensionalism, which holds that you "wholly exist" at every moment you exist.) What's nice about this book is that it takes a difficult, possibly obscure, view and makes it a joy to read about.
  2. The book begins with an "Introduction." Unlike most Introductions, Sider's is important to read because it begins by setting forth the philosophical method and picture Sider is utilizing. (In fact, at several points in the book, Sider falls back on the points he makes in the Introduction.) The book is divided into six chapters. The first presents the "Four-Dimensionalism" picture, and motivates it by showing its ability to handle certain conceptual problems. The second could stand alone, and is a defense of the "B-theory" of time, which Sider assumes for the remainder of the book. The third attempts to state exactly what the Three/Four-Dimensionalism fuss is about. The final three chapters, which take up the bulk of the book, constitute a defense of Four-Dimensionalism – the first two provide arguments for the view, the last defends it against objections. (The book also contains a sizable list of references.)
  3. Sider's writing is clear and easy to follow. At points, things get difficult, and some knowledge of physics is helpful for several sections; but on a whole, a limited amount of specialized knowledge is sufficient to appreciate this book. One thing I liked about it was Sider's approach. He argues that – when all the votes are in – Four-Dimensionalism is the best view, which allows him to be frank about the various strengths of arguments for and against his view. Many of his arguments are persuasive, and he's fairly systematic, considering many different objections. In the end, I learned much from it and would recommend it to anyone interested in metaphysics, ontology, or philosophy of time.

In-Page Footnotes ("Sider (Ted) - Four-dimensionalism: An Ontology of Persistence and Time")

Footnote 2: As Sider is a “stage theorist”, I doubt he agrees with this: it’s a perdurantist view rather than exdurantist.


Clarendon Press, Oxford, 2003. Badly adulterated by my annotations up to p. 25

"Parsons (Josh) - Review of Theodore Sider's 'Four-Dimensionalism'"

Source: Philosophical Quarterly, 2004, Vol. 54

Author’s Introduction
  1. "The truth," Quine says, "is that you can bathe in the same river twice, but not in the same river stage. You can bathe in two river stages which are stages of the same river, and this is what constitutes bathing in the same river twice. A river is a process through time, and the river stages are its momentary parts."
  2. Quine's view is four-dimensionalism, and that is what Theodore Sider's book is about. In Sider's usage, four-dimensionalism is the view that, necessarily, anything in space and time has a distinct temporal part, or stage, corresponding to each time at which it exists (p. 59). ...

COMMENT: Review of "Sider (Ted) - Four-dimensionalism: An Ontology of Persistence and Time".

"Sider (Ted) - Precis of Four-Dimensionalism"

Source: Philosophy and Phenomenological Research LXVII, No. 3, May 2004, pp. 642-647

Philosophers Index Abstract
    I defend the spatio-temporal ontology of Russell, Smart, Quine, and Lewis, including four-dimensionalism (the doctrine of temporal parts, on my usage) and eternalism (realism about past and future objects). Presentism (the main rival to eternalism) is mistaken because it is difficult to reconcile with special relativity, because it requires reality to have noncategorical fundamental features, and because the presentist's tensed language cannot express the fundamental facts of space-time structure. Three-dimensionalism (the rejection of temporal parts) is mistaken because it precludes the possibility of time travel1, is difficult to combine with space-time relationalism, leads to the incoherent position that existence is vague, and forces a suboptimal resolution of the paradoxes of material coincidence. Objections to four-dimensionalism (e.g., the problem of motion in homogenous entities) can be answered. I also defend a robust realism about ontology.


"Sider (Ted) - Four-Dimensionalism: Introduction"

Source: Sider - Four-dimensionalism, Introduction

  • According to 'four-dimensionalism', temporally extended things are composed of temporal parts. Most four-dimensionalists identify ordinary continuants — the persisting objects ordinary language quantifies over and names — with aggregates of temporal parts ('space-time worms'), but an attractive alternate version of four-dimensionalism identifies ordinary continuants with instantaneous temporal slices and accounts for temporal predication using temporal counterpart theory.
  • Arguments for four-dimensionalism include the following:
    1. Either substantivalism or relationalism about space-time is true, but given substantivalism one might as well identify continuants with regions of space-time, which have temporal parts, or with instantaneous slices of space-time, whereas relationalism about space-time cannot be made to work without temporal parts.
    2. It can never be vague how many objects exist; if temporal parts do not exist, then a restrictive account of which filled regions of space-time contain objects must be given, but no such account can be given that is plausible and non-vague.
    3. Four-dimensionalism — especially the alternate, counterpart-theoretic version — provides the most satisfying overall account of the 'paradoxes of material constitution', in which numerically distinct material objects (e.g. statues1 and lumps of clay) apparently share exactly the same parts.
  • Objections to four-dimensionalism (involving, e.g., motion in homogeneous substances and de re modal2 properties) may be answered.
  • While logically independent of the question of four-dimensionalism, the book also defends related theses, including
    1. A robust meta-ontology according to which unrestricted existence-statements are non-vague, non-analytic, and uninfected by human convention;
    2. The B-theory of time (the opposite of presentism);
    3. Unrestricted composition; and
    4. Counterpart theory (both modal3 and temporal).

"Sider (Ted) - The Four-Dimensional Picture"

Source: Sider - Four-dimensionalism, Chapter 1

Author’s Abstract
  • Four-dimensionalism may be made vivid by pictures: an object with temporal parts persisting through time is like a road with spatial parts extending across space.
  • The attraction of this picture emerges informally from consideration of change1, statues, and lumps of clay2, and the Ship of Theseus3.

"Sider (Ted) - Against Presentism"

Source: Sider - Four-dimensionalism, Chapter 2

Author’s Abstract
  • The 'B-theory' of time says that all temporal facts 'reduce' to tenseless facts about a manifold of equally real past, present, and future objects; the 'A-theory' denies this reduction. Presentism is a version of the A-theory that denies the existence of part of the B-theorist's manifold: the part containing merely past and future objects.
  • Some say that the B-theory cannot account for the irreducibly temporal nature of our psychological attitudes, but this is incorrect. B-theorists can defend temporal versions of well-known theories of 'indexical', or 'de se', attitudes.
  • Presentism, on the other hand, is vulnerable to powerful objections:
    1. The irreducible tense-operators to which presentists must appeal are objectionably ungrounded in reality.
    2. Presentists cannot account for the fundamental 'cross-time spatial relations' that ground the structure of space-time, and thus cannot account for spatiotemporal continuity, acceleration, and other states of motion.
    3. Presentism conflicts with the special theory of relativity.

  1. Two issues in the philosophy of time: ontology and tense – 11
  2. Cross-time spatial relations – 25
  3. The truth-maker objection – 35
  4. Presentism and special relativity – 42

"Sider (Ted) - Three- and Four-Dimensionalism Stated"

Source: Sider - Four-dimensionalism, Chapter 3

Author’s Abstract
  • Four-dimensionalism may be given a rigorous and canonical formulation acceptable to both its supporters and opponents; meaningful debate as to the truth of this thesis may then proceed.
  • This is more difficult for three-dimensionalism, since its defining slogan 'objects are wholly present' seems either trivial ('at any time at which an object exists, anything that is then part of it exists') or too strong ('at any time at which an object exists, anything that is ever part of it exists').
  • Nevertheless, several theses in the neighbourhood of three-dimensionalism may be stated, even if none is a canonical formulation.
  • Finally, the three-dimensionalism/four-dimensionalism debate is orthogonal to the debate over presentism: both presentists and non-presentists can articulate versions of three- and four-dimensionalism whose truth may then be debated.

  1. Why fuss over formulation? – 53
  2. Four-dimensionalism stated – 55
  3. What is three-dimensionalism? – 63
  4. Perdurance1, endurance, presentism, and eternalism – 68

"Sider (Ted) - In Favour of Four-Dimensionalism, Part 1"

Source: Sider - Four-dimensionalism, Chapter 4

Author’s Abstract
  • Some traditional arguments for four-dimensionalism are weak: denying four-dimensionalism
    → Does not prohibit the application of modern logic to natural language,
    → Does not imply the A-theory of time, and
    → Is consistent with special relativity.
  • Others have some force but are inconclusive:
    → The argument from analogies between time and space, and
    → Lewis's argument from temporary intrinsics1.
  • Some new arguments fare better.
    1. Only four-dimensionalists can admit certain (admittedly exotic) possibilities involving timeless objects and time travel2 into one's own past.
    2. Either substantivalism or relationalism about space-time is true. Given substantivalism (and a sensible, flexible theory of de re modal3 predication), one might as well identify continuants with regions of space-time, which have temporal parts. Alternatively, one could identify continuants with instantaneous slices of space-time and employ temporal counterpart theory; either way, we have a four-dimensionalist metaphysics of continuants. On the other hand, relationalism about space-time cannot be made to work without temporal parts. So either way, we have an argument for four-dimensionalism.
    3. It can never be vague how many objects exist; if temporal parts do not exist then a restrictive account of which filled regions of space-time contain objects must be given; but no such account can be given that is plausible and non-vague.

  1. Russell's argument from parsimony – 75
  2. The argument from logic – 76
  3. The A-theory of time is incoherent – 78
  4. Four-dimensionalism and special relativity – 79
  5. Space and time are analogous – 87
  6. The problem of temporary intrinsics4 – 92
  7. Arguments from exotica – 98
  8. The argument from spacetime – 110
  9. The argument from vagueness – 120

"Sider (Ted) - In Favour of Four-Dimensionalism, Part 2: The Best Unified Theory of the Paradoxes of Coincidence"

Source: Sider - Four-dimensionalism, Chapter 5

Author’s Abstract
  • We need a general solution to a cluster of related paradoxes in which numerically distinct material objects appear to share exactly the same parts. Those paradoxes include the statue1 and the lump of clay, undetached parts, fission, fusion and longevity, vague identity, and conventional identity.
  • A good solution is given by the 'worm theory', according to which continuants are aggregates of temporal parts; a better solution is given by the 'stage theory2', according to which continuants are instantaneous temporal parts, whose temporal properties are understood via temporal counterpart theory.
  • There are other solutions that do not appeal to temporal parts: Wiggins's constitution theory, Burke's dominance view, Gallois's temporary identity3 theory, eliminativism, and mereological essentialism. But these are arguably inferior: some are insufficiently general, others are subject to powerful criticisms.

  1. The threat of coincidence – 141
  2. The worm theory and coincidence – 152
  3. Coinciding three-dimensional objects – 154
  4. Burke's dominance account – 161
  5. Temporary identity4 – 165
  6. Eliminativism – 176
  7. Mereological essentialism – 180
  8. The stage view5 – 188

"Sider (Ted) - Arguments against Four-Dimensionalism"

Source: Sider - Four-dimensionalism, Chapter 6

Author’s Abstract
  • If four-dimensionalism is an ontological, rather than conceptual or ordinary-language, thesis, some traditional objections are misguided. It then does not require any particular semantics for tensed claims, does not imply any conceptual or epistemic priority of stage-talk, and does not preclude a distinction in ordinary thought between processes and things.
  • A more metaphysical traditional objection is that four-dimensionalism precludes genuine change, but there is no good reason to regard the four-dimensionalist's conception of change as non-genuine.
  • A better objection: four-dimensionalism assigns the wrong modal1 properties to continuants. Reply: everyone, not just a four-dimensionalist, should accept a 'flexible' account of de re modal2 predication. Counterpart theory is one such account, but not the only one.
  • Best objection: four-dimensionalism precludes motion in homogeneous substances. Reply: it is only four-dimensionalism plus Humean supervenience3 that has the consequence, and even then, motion in homogenous substances may be allowed in many cases, assuming a holistic account of genidentity.

  1. Linguistic and epistemic objections – 209
  2. The no-change objection – 212
  3. A crazy metaphysic – 216
  4. The modal4 argument – 218
  5. Motion in homogeneous substances – 224

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