A Brief History of the A-Theory/B-Theory Debate about Time

by Cheryl E. Fitzgerald

The dispute between the B-theory (tenseless theory) and the A-theory (tensed theory) concerns, respectively, whether time consists entirely of the serial relations of simultaneous with, earlier than, and later than, or that the notions of past, present, and future are necessary metaphysical features of time in addition to or in place of the serial relations. The serial relations are referred to as B-relations. The notions of past, present, and future are not consistently fleshed out by various A-theorists; some argue that they are properties of events and objects, and are so called A-properties, while others argue that they represent sentential tense operators based on A. N. Prior’s tense logic, or variations of it. ). “Tense” and “tenseless” are used as technical terms in the A-theory/B-theory debate, which is paradigmatically exemplified in the title of Mellor’s 1987 paper in his discussion with G. Priest, “Tense, Tense and TENSE” [1987]. The word “tense” is rarely use in its normal grammatical sense in the philosophy of time. Philosophers talk of tensed or tenseless facts, tensed or tenseless propositions, tensed or tenseless beliefs, tensed or tenseless truth conditions, and the like. This is the point Mellor emphasizes about the technical use of “tense” in his article.

The B-Theories, The Detensers

The general thesis of the B-theory is that the nature of time and all temporal facts can be described without the use of tensed language, such as tensed verbs, temporal indexicals or pronouns, such as “now,” “yesterday,” etc., and predicates such as “past,” “present,” and “future,” etc. The B-theory argues that time is static: despite appearances, time has no “flow” or “passage,” but rather is more like what we would understand as a timeline, such that objects and events are located at times. Events exist equally or ontologically on par regardless of whether they are earlier than 2007, simultaneous with 2007, or later than 2007. This notion of time is referred to as the B-series, so named by McTaggart. An object’s or event’s temporal location never changes, and thus, the fact that it is located at a particular time is true at any and all times. Such a fact, it is argued, is therefore tenseless.

One of the logical problems that contributed to the prevalence of the B-theory in the early 20^th century concerned some of Frege’s work in the late 19^th century. Frege was deeply troubled by sentences whose truth-values were indeterminate because they varied over time. One intuition was that truth is objective and unalterable; true sentences, or specifically, what they express, never become false, and vice versa. Another intuition was that what sentences express is complete enough to be true or false. Frege referred to the complete sense express by a sentence-token as a “thought;” but now philosophers talk of “propositions” instead of thoughts. Frege argued that in order for a proposition about an object or event whose existence is temporally limited to possess an unchanging truth-value, it must include in its content the relevant time, or date, of the utterance of the sentence expressing that proposition. The sentence or utterance itself “does not suffice for the expression of the thought…If a time-indication is conveyed by the present tense one must know when the sentence was uttered in order to grasp the thought correctly. Therefore, the time of utterance is part of the expression of the thought” [Frege, “Thoughts,” Logical Investigations, p. 10]. The important element is that the thought (proposition) must be complete enough to capture all of the relevant information about a state of affairs in order to be able to pick out that state of affairs alone. This has been referred to as the “cognitive significance” [Kaplan, 1989], “cognitive content” [Salmon, 2003, p. 119] or “information value” [Craig, 2000a, p. 29] of a sentence. While we need not be Fregeans about propositions, we can agree to what Frege what at least trying to accomplish. It is necessary that such an analysis treats only of sentence tokens, and not sentence types.

With Frege began the tenseless date-reference theory, which argued that a tensed sentence refers to the date of its tokening, and the tense itself expresses a determined, tenseless temporal B-relation between the date and the event to which it refers.[1] Some notable date-reference B-theorists are Frege, Russell, Quine, Nelson Goodman, Paul Fitzgerald, Clifford Williams, and William Lycan. The purpose of this analysis by early B-theorists was to replace tensed sentences by translating them into tenseless ones that preserve the meaning of the original tensed sentences, and would, therefore, express explicitly the metaphysical reality that true tensed sentences implicitly express. The preservation of meaning requires that both of the sentences, tensed and tenseless, possess identical propositional content. However, this project was argued to be impossible by demonstrating that a competent language-user cannot infer from a tenseless date-sentence whether the event it is about is past, present, or future. Further, it was argued that from a tensed sentence alone, one cannot infer the relevant date that is part of the tenseless proposition; even a present tensed sentence requires the additional information of what date is present.

The tenseless token-reflexive theory made a slight alteration to the date-reference theory: instead of arguing that a tensed sentence refers to the date, it rather expresses a B-relation to the utterance itself. Some notable token-reflexive B-theorists are Reichenbach, J. J. C. Smart (in his earlier work), Michael Dummett, D. C. Williams, and Adolf Grünbaum. Token-reflexivity was expressed with phrases such as, “earlier than this utterance,” “simultaneous with this utterance,” and “later than this utterance.” Early token-reflexive B-theorists claimed the same goal of eliminating tensed language by translating it into tenseless language. However, it was argued that tensed sentences and their supposed tenseless token-reflexive translations also could not have identical semantic content. If the token-reflexive sentence is to translate the meaning of the tensed sentence, then the token to which the tenseless translation refers must be the tensed sentence, since it is argued that the tensed sentence possesses this token-reflexivity implicitly. But since the tenseless translation was meant to replace the tensed sentence, then presumably, there would never have been a tensed sentence in the first place for the “this” in the token-reflexive translation to refer to. It follows that it either refers to an utterance that does not exist, or it refers to itself. Since it cannot be the former, it must be the latter. However, if it refers to itself, then it cannot be a translation of a tensed sentence at all.

It was generally accepted that the original goal of translating and eliminating tensed sentences from the language is impossible.[2] The significance of the ineliminability of tense from language is argued to be that, so long as there are some true tensed sentences, they must be true in virtue of something about the world itself, which cannot be captured by tenseless language. But with the publication of Real Time in 1981, D. H. Mellor began a new movement with a new goal for the B-theory: to demonstrate that the truth conditions of all tensed sentences require only tenseless facts, making tensed facts superfluous; if tensed facts are superfluous, then they ought to be to eliminated from our ontology. Instead of arguing that the tenseless date-sentences and/or tenseless token-reflexive sentences express the meaning of tensed sentences, they argued that the tenseless sentences give all of the facts needed to account for the truth of the tensed sentences. Both the date-reference theory and the token-reflexive were transformed according to the new goals. Some New B-theorists are Smart (in his later work), Murray MacBeath, Richard Gale (in his later work), L. Nathan Oaklander, Robin Le Poidevin, Heather Dyke, and Theodore Sider.

A common objection is that the B-theory does not account for our experience [Oaklander, 2004] that time “flows” and “passes,” nor does it account for the cognitive significance of tense. That tense is cognitively significant was demonstrated by most of the arguments against the old B-theories. For example, knowing that, “The house is (tenseless) on fire later than this utterance,” will not provide one with the needed information for knowing when to act appropriately. The insight gained from the philosophical work in indexicals provided B-theorists with material to respond to these objections. They treated tense in the way that we treat spatial indexicals, expressions of “here,” “there,” etc. The analogy of space and time is still part of the B-theory today, especially for those theorists who incorporate physical theories, such as special and/or general relativity and Minkowski spacetime into their theories. The analysis and treatment of indexicals still plays an important role in many current B-theories by harnessing the analogy of time with space.

The A-Theories, The Tensers

The general thesis of the A-theory is that there exists a metaphysically privileged time, referred to by “the present,” and it is dynamic, that time “flows” or “passes.” The general thesis has been fleshed out in a variety of ways depending on what one believes the general thesis actually means and the consequences drawn from that meaning. The consequences are not always subtle, and some A-theories provide radically different ontologies, explications of the “flow” of time, and how the theory fits in with our currently most accepted physical scientific theories. Some notable A-theorists are Richard Gale (in his earlier work), Richard Taylor, C. D. Broad, A. N. Prior, William Lane Craig, Michael Tooley, Quentin Smith, George Schlesinger, Dean Zimmerman, and Thomas Crisp.

The origin of the A-theory is largely reactionary against the translation project of the old B-theory. A-theorists’ arguments centered on demonstrating the shortcomings of the tenseless translations, especially that they are not meaning preserving, and that any competent language user who knows only the tenseless sentences about some particular event would never be able to infer whether the event is past, present, or future. It was concluded that the meaning of tense expresses something that cannot be captured by tenseless language. A-theorists share the feeling that, “language furnishes us, as it were, a sort of window on the world whereby we may apprehend the factual objectivity of tense. [A-theorists] argue that the ineliminability or irreducibility of tense in language and its indispensability for human life and action make it plausible that tense is a feature of reality as well as of language” [Craig, 2000a, p. 19]. The philosophical work on indexicals was attractive to A-theorists because they argued it proved that indexical language cannot be replaced by non-indexical language, which seems to suggest something metaphysically special about indexicality. There are two common camps into which A-theorists fall, presentists and A-property theorists.

Presentism is the purest and most radical A-theory, for it argues that the present is the only time that exists. The entire presentist ontology is exhausted by what is contained in the present; to exist is equivalent to being present. Some presentists have founded their syntactics on A. N. Prior’s tense logic, so that all tensed sentences are analyzed into sentences in the scope of some temporal operator(s), namely, “It was the case that,” “It is the case that,” and “It will be the case that.” But those who reject a Quinean treatment of sentential and existential operators argue that tense operators and the sentences within their scope are unable to provide a metaphysics of time. Instead, they restrict their theory to analyses of natural language tensed sentences.

If the presentist accepts there are true sentences about what is past, then he must likely adopt a NeoFregean or Plantingian theory of propositions, whose content does not contain the objects themselves, but contains essences, or concepts, or senses. The presentist should reject Kaplanesque propositions, whose content does contain the objects themselves, since the object of a past tensed sentence doesn’t exist in the presentist ontology. And surely such sentences as, “Hegel used to be alive,” are true for the presentist. The analysis of such sentences and the NeoFregean/Plantingian propositions they express would, arguably, reveal the metaphysical nature of the world they are about.

The radical thesis of presentism is rejected by the A-property theorist, who instead claims that the tenses refer to or express A-properties, pastness, presentness, and futurity. In other words, the semantic content of tense is a property, and thus, is part of the corresponding state of affairs. Objects and events exemplify these properties at different times, but in succession according to the directional “flow” of time. These A-properties, arguably, endow objects and events with a temporal nature, without which they cannot be part of the world. However, A-property theorists do not all agree on the metaphysical status of the future. A-property theorists who do accept the existence of the future are not forced into choosing NeoFregean or Plantingian propositions, but may adopt Kaplanesque propositions, unless there are other reasons to reject them.

One distinctive objection to the A-property theory lies in the enforcement of McTaggart’s Paradox. Briefly, the objection is that pastness, presentness, and futurity are inconsistent properties, for, when an object possesses one, then by definition alone, it cannot possess the other two. It is necessary for the A-property theorist’s explanation of the dynamic nature of time that all objects and events do possess all of these properties. But the objector argues that this cannot be explained without contradiction and/or begging the question. It is not the consensus that McTaggart’s Paradox is valid, but this has not stopped it from being a lively point of debate today.

Resources

Craig, William Lane (2000a), The Tensed Theory of Time, Dordrecht; Boston: Kluwer.

Kaplan, David (1989), “Demonstratives: An Essay on the Semantics, Logic, Metaphysics, and Epistemology of Demonstratives and Other Indexicals,” in Joseph Almog, John Perry, and Howard Wettstein, eds., Oxford: Oxford University Press, p. 481-563.

Oaklander, L. N. (2004), The Ontology of Time, Buffalo, NY: Prometheus Books.

Priest, G. (1987), “Tense, Tense, and TENSE,” Analysis 46: 184187.

Salmon, Nathan (2003), “Tense and Intension,” in Aleksandear Jokic and Quentin Smith, eds., Time, Tense, and Reference, Cambridge, MA: MIT Press.

---

[1] I leave this admittedly vague for the sake of only introducing the general thesis of the theory. But there are distinctions to be made between direct and indirect reference to the date, as well as between the substantival and reductionist theories of time. A substantival theory of time claims that time is metaphysically independent of the events in time, and that time contains those events. A reductionist theory claims that time is not independent of the events in time, but rather that a time is just a set of simultaneous events. A time would not contain those events, but is defined as that set of events.

[2] I do not wish to imply that no one today believes that it is possible.