B-theory of time

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The B-theory of time is the name given to one of two positions regarding philosophy of time. B-theorists argue that the flow of time is an illusion, that the past, present and future are equally real, and that time is tenseless. This would mean that temporal becoming is not an objective feature of reality.

B-theory is often drawn upon in theoretical physics,[1] and in theories such as eternalism.


J.M.E. McTaggart, who coined the term "B-theory of time".

The labels, A-theory and B-theory, are derived from the analysis of time and change developed by Cambridge philosopher J. M. E. McTaggart in "The Unreality of Time" (1908), in which events are ordered via a tensed A-series or a tenseless B-series. It is popularly assumed that the A theory represents time like an A-series, while the B theory represents time like a B-series.[2] The terms A and B theory are sometimes used as synonyms to the terms presentism and eternalism, but arguably presentism does not represent time being like an A-series since it denies that there is a future and past in which events can be located.

Events (or "times"), McTaggart observed, may be characterized in two distinct, but related, ways. On the one hand they can be characterized as past, present or future, normally indicated in natural languages such as English by the verbal inflection of tenses or auxiliary adverbial modifiers. Alternatively events may be described as earlier than, simultaneous with, or later than others. Philosophers are divided as to whether the tensed or tenseless mode of expressing temporal fact is fundamental.[2] Some philosophers have criticised hybrid theories, where one holds a tenseless view of time, but asserts that the present has special properties, as falling foul of McTaggart's paradox.[3]

The debate between A-theorists and B-theorists is a continuation of a metaphysical dispute reaching back to the ancient Greek philosophers Heraclitus and Parmenides.[4][5] Parmenides thought that reality is timeless and unchanging.[6] Heraclitus, in contrast, believed that the world is a process of ceaseless change, flux and decay[clarification needed].[7] Reality for Heraclitus is dynamic and ephemeral. Indeed, the world is so fleeting, according to Heraclitus, that it is impossible to step twice into the same river.[8] The metaphysical issues that continue to divide A-theorists and B-theorists concern the reality of the past, the reality of the future, and the ontological status of the present.

B-theory in metaphysics

The difference between A-theorists and B-theorists is often described as a dispute about temporal passage or 'becoming' and 'progressing'. B-theorists argue that this notion is purely psychological.[9] Many A-theorists argue that in rejecting temporal 'becoming', B-theorists reject time's most vital and distinctive characteristic.[10] It is common (though not universal) to identify A-theorists' views with belief in temporal passage.[2]

B-theorists such as D.H. Mellor[11] and J.J.C. Smart[12] wish to eliminate all talk of past, present and future in favour of a tenseless ordering of events, believing the past, present, and future to be equally real, opposing the idea that they are irreducible foundations of temporality. B-theorists also argue that the past, present, and future feature very differently in deliberation and reflection. For example, we remember the past and anticipate the future, but not vice versa. B-theorists maintain that the fact that we know much less about the future simply reflects an epistemological difference between the future and the past: the future is no less real than the past; we just know less about it.[13]

B-theory in theoretical physics

The B-theory of time has received support from the physics community.[14][15] This is likely due to its compatibility with physics and the fact that many theories such as special relativity, the ADD model, and brane cosmology, point to a theory of time similar to B-theory.[16]

In special relativity, the relativity of simultaneity shows that there's no unique present, and that each point in the universe can have a different set of events that are in its present moment.

Many of special relativity's now-proven counter-intuitive predictions, such as length contraction and time dilation, are a result of this. Relativity of simultaneity implies eternalism (and hence a B-theory of time), where the present for different observers is a time slice of the four dimensional universe. This is demonstrated in the Rietdijk–Putnam argument and additionally in an advanced form of this argument called the Andromeda paradox, created by mathematical physicist Roger Penrose.[17]

It is therefore common (though not universal), for B-theorists to be four-dimensionalists, that is, to believe that objects are extended in time as well as in space and therefore have temporal as well as spatial parts. This is sometimes called a time-slice ontology.[18]


In 'Presentism and the Space-Time Manifold', Dean Zimmerman notes that A-theory is 'almost certainly a minority view among philosophers', while B-theory has 'achieved broad acceptance'; despite this there are still a number of philosophers who maintain opposition for B-theory.

Irreducibility of tense

Earlier B-theorists argued that one could paraphrase tensed sentences (such as "the sun is now shining") into tenseless sentences (such as "on September 28, the sun shines") without loss of meaning.[19][20] Later B-theorists argued that tenseless sentences could give the truth conditions of tensed sentences or their tokens.[21][22] Quentin Smith states that "now" cannot be reduced to descriptions of dates and times, because all date and time descriptions, and therefore truth conditionals, are relative to certain events. Tensed sentences, on the other hand, do not have such truth conditionals.[23] The B-theorist could argue that "now" is reducible to a token-reflexive phrase such as "simultaneous with this utterance," yet Smith states that even such an argument fails to eliminate tense. One can think the statement "I am not uttering anything now," and such a statement would be true. The statement "I am not uttering anything simultaneous with this utterance" is self-contradictory, and cannot be true even when one thinks the statement.[24] Finally, while tensed statements can express token-independent truth values, no token-reflexive statement can do so (by definition of the term "token-reflexive").[25] Quentin Smith claims that current proponents of the B-theory argue that the inability to translate tensed sentences into tenseless sentences does not prove the A-theory of time.[26]

Noted logician and philosopher Arthur Prior (originator of tense logic) has also drawn a distinction between what he calls A-facts and B-facts. The latter are facts about tenseless relations, such as the fact that the year 2025 is 25 years later than the year 2000. The former are tensed facts, such as the Jurassic age being in the past, or the end of the universe being in the future. Prior asks the reader to imagine having a headache, and after the headache subsides, saying "thank goodness that's over." Prior argues that the B-theory cannot make sense of this sentence. It seems bizarre to be thankful that a headache is earlier than one's utterance, anymore than being thankful that the headache is later than one's utterance. Indeed, most people who say "thank goodness that's over" are not even thinking of their own utterance. Therefore, when people say "thank goodness that's over," they are thankful for an A-fact, and not a B-fact. Yet, A-facts are only possible on the A-theory of time.[27]

Endurantism and perdurantism

Opponents also charge the B-theory with being unable to explain persistence of objects. The two leading explanations for this phenomenon are endurantism and perdurantism. The former states that an object is wholly present at every moment of its existence. The latter states that objects are extended in time and therefore have temporal parts.[28][29] Hales and Johnson explain endurantism as follows: "something is an enduring object only if it is wholly present at each time in which it exists. An object is wholly present at a time if all of its parts co-exist at that time."[30] Under endurantism, all objects must exist as wholes at each point in time. However, an object such as a rotting fruit will have the property of being not rotten one day and being rotten on another. On eternalism, and hence the B-theory, it seems that one is committed to two conflicting states for the same object.[28] The spacetime (Minkowskian) interpretation of relativity adds an additional problem for endurantism under the B-theory. On the spacetime interpretation, an object may appear as a whole at its rest frame. On an inertial frame, however, that same object will have proper parts at different positions, and therefore will have different parts at different times. Hence, it will not exist as a whole at any point in time, contradicting the thesis of endurantism.[31]

Opponents will then charge perdurantism with having numerous difficulties of its own. First, it is controversial whether perdurantism can be formulated coherently. An object is defined as a collection of spatio-temporal parts, which are defined as pieces of a perduring object. If objects have temporal parts, this leads to difficulties. For example, the rotating discs argument asks the reader to imagine a world containing nothing more than a homogeneous spinning disk. Under endurantism, the same disc endures despite that it is rotating. The perdurantist supposedly has a difficult time explaining what it means for such a disk to have a determinate state of rotation.[32] Temporal parts also seem to act unlike physical parts. A piece of chalk can be broken into two physical halves, but it seems nonsensical to talk about breaking it into two temporal halves.[33] Chisholm argued that someone who hears the bird call "Bob White" knows "that his experience of hearing 'Bob' and his experience of hearing 'White' were not also had by two other things, each distinct from himself and from each other. The endurantist can explain the experience as "There exists an x such that x hears 'Bob' and then x hears 'White'" but the perdurantist cannot give such an account.[34] Peter Van Inwagen asks the reader to consider Descartes as a four-dimensional object that extends from 1596-1650. If Descartes had lived a much shorter life, he would have had a radically different set of temporal parts. This diminished Descartes, he argues, could not have been the same person on perdurantism, since their temporal extents and parts are so different.[35]


  1. ^ "Brian Greene on the B-theory of time" https://www.youtube.com/watch?v=H1WfFkp4puw
  2. ^ a b c Markosian, Ned. "Time". Stanford Encyclopedia of Philosophy. Retrieved 28 December 2014. 
  3. ^ Callender, Craig (September 1, 2000). "Shedding Light on Time". Philosophy of Science. 67: S587. doi:10.1086/392848. 
  4. ^ Craig, William Lane (2011). The tenseless theory of time : a critical examination. Dordrecht: Springer. p. 22. ISBN 904815586X. 
  5. ^ Smart, J.J.C. (2010). Time and Cause Essays Presented to Richard Taylor. Springer Verlag. p. 7. ISBN 9048183588. 
  6. ^ Palmer, John. "Parmenides". Stanford Encyclopedia of Philosophy. Retrieved 29 December 2014. 
  7. ^ Graham, Daniel W. "Heraclitus". Stanford Encyclopedia of Philosophy. Retrieved 29 December 2014. 
  8. ^ This sentence has been translated by Seneca in Epistulae, VI, 58, 23.
  9. ^ Harrington, James. "What "Becomes" in Temporal Becoming?". American Philosophical Quarterly. 46 (3): 249. 
  10. ^ McTaggart, J. Ellis (1908). "The Unreality of Time". Mind (68): 458. 
  11. ^ "Philosophy Cambridge Mellor Time Tense". People.pwf.cam.ac.uk. Retrieved 2014-03-03. 
  12. ^ "Google Drive Viewer" (PDF). Docs.google.com. Retrieved 2014-03-03. 
  13. ^ Mellor, D. H. (1998). Real time II ([Online-Ausg.]. ed.). London: Routledge. p. 21. ISBN 0415097819. 
  14. ^ "Brian Green on B-theory of time" https://www.youtube.com/watch?v=H1WfFkp4puw
  15. ^ "Prof. Brian Greene: Past, present and future exist now" https://www.youtube.com/watch?v=f9AiPuIsqck/
  16. ^ https://www.youtube.com/watch?v=R1cexcjdyIE
  17. ^ Penrose, R. (1989). The Emperor's New Mind: "Concerning Computers, Minds, and Laws of Physics". New York and Oxford: Oxford University Press.
  18. ^ Clark, Michael (May 1978). "Time-slices of particular continuants as basic individuals: An impossible ontology". Philosophical Studies. 33 (4): 403–408. doi:10.1007/bf00354208. 
  19. ^ Williams, Clifford. "'Now', Extensional Interchangeability, and the Passage of Time". Philosophical Forum. 5: 405. 
  20. ^ Fisk, Milton. "A Pragmatic Account of Tenses". American Philosophical Quarterly. 8. 
  21. ^ Smart, J.J.C. (2010). Time and Cause Essays Presented to Richard Taylor. Springer Verlag. p. 11. ISBN 9048183588. 
  22. ^ Beer, Michelle. "Temporal Indexicals and the Passage of Time". Philosophical Quarterly. 38: 158. doi:10.2307/2219921. 
  23. ^ Smith, Quentin (1993). Language and time ([1. paperback issue] ed.). Oxford: Oxford University Press. p. 35. ISBN 0195082273. 
  24. ^ Smith, Quentin (1993). Language and time ([1. paperback issue] ed.). Oxford: Oxford University Press. p. 79. ISBN 0195082273. 
  25. ^ Smith, Quentin (1993). Language and time ([1. paperback issue] ed.). Oxford: Oxford University Press. p. 83. ISBN 0195082273. 
  26. ^ Smith, Quentin (1993). Language and time ([1. paperback issue] ed.). Oxford: Oxford University Press. p. 3. ISBN 0195082273. 
  27. ^ Markosian, John W. Carroll, Ned (2010). An introduction to metaphysics (1. publ., repr. ed.). New York: Cambridge University Press. pp. 169–170. ISBN 0521533686. 
  28. ^ a b Hawley, Katherine. "Temporal Parts". Stanford Encyclopedia of Philosophy. 
  29. ^ Lewis, David (2001). On the plurality of worlds ([Reprint.] ed.). Malden, Mass. [u.a.]: Blackwell Publishers. p. 202. ISBN 0631224262. 
  30. ^ Hales, Steven D.; Johnson, Timothy A. "Endurantism, Perdurantism, and Special Relativity". The Philosophical Quarterly. 53 (213): 532. 
  31. ^ Hales, Steven D.; Johnson, Timothy A. "Endurantism, Perdurantism, and Special Relativity". The Philosophical Quarterly. 53 (213): 535. 
  32. ^ Teller, Paul (2002). "The Rotating Disc Argument and Humean Supervenience". Analysis. 62 (3): 206–207. doi:10.1093/analys/62.3.205. 
  33. ^ Thomson, Judith Jarvis. "Parthood and Identity Across Time". Journal of Philosophy: 80. 
  34. ^ Muniz, Milton K. (ed.). Identity and Individuation. New York University Press. p. 15. ISBN 0814753752. 
  35. ^ Van Inwagen, Peter (1990). "Four-Dimensional Objects". Nous: 252–254. 


  • Clark, M (1978). "'Time-slices of particular continuants as basic individuals: An impossible ontology'". Philosophical Studies. 33: 403–408. doi:10.1007/bf00354208. 
  • Craig, W.L. (2001) The Tensed Theory of Time: A Critical Examination. Synthese Library.
  • Craig, W.L. (2000) The Tenseless Theory of Time: A Critical Examination. Synthese Library.
  • Davies, Paul (1980) Other Worlds. Harmondsworth: Penguin.
  • McTaggart, J.M.E. (1908). "'The Unreality of Time'". Mind. 17: 457–73. doi:10.1093/mind/xvii.4.457. 
  • McTaggart, J.M.E. (1927) The Nature of Existence, Vol II. Cambridge: Cambridge University Press.
  • Mellor, D.H. (1998) Real Time II. London: Routledge.
  • Prior, A.N. (2003) Papers on Time and Tense. New Edition by Per Hasle, Peter Øhrstrøm, Torben Braüner & Jack Copeland. Oxford: Clarendon.
  • Putnam, H. (2005). "A Philosopher Looks at Quantum Mechanics Again". British Journal for the Philosophy of Science. 56: 615–634. doi:10.1093/bjps/axi135. 
  • Quine, W. V. O. (1960) Word and Object, Cambridge, MA: M.I.T. Press.

External links

  • Markosian, Ned, 2002, "Time", Stanford Encyclopedia of Philosophy
  • Arthur Prior, Stanford Encyclopedia of Philosophy
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