David Hugh Mellor (1938 – 2020), emeritus professor of philosophy at the University of Cambridge, is known for his important contributions to metaphysics, philosophy of science, and philosophy of the mind, with studies, for example, on probability, time, causation, properties, and decision theory. His work stands in the Cambridge tradition of F. P. Ramsey and Richard Braithwaite, in whose honor he has edited anthologies and the works of Ramsey. Mellor’s philosophy of time profits from this broad field of interest and combines them systematically; he is one of the advocates of the “new tenseless theory of time.”
Two important theories of the early 20th century have influenced Mellor and, as he claims, the whole modern theory of time: McTaggart’s A- and B-series theory of time (1908) and Einstein’s special theory of relativity, published in 1905. Agreeing with McTaggart’s argument against the reality of the dynamic, tensed view of time, Mellor adopts a theory of time based on the B series, which acknowledges only the static scale of the B series as fundamental for any concept of time. In contrast to McTaggart, Mellor does not conclude that time is unreal. He shows that the concept of spacetime as it is presented in the special theory of relativity does not spatialize time. In fact time differs from space in this concept, and that becomes obvious in the formalization of the theory. Time is therefore a problem in its own right. Mellor’s position can be characterized as a B series of time that argues for the reality of time—more precisely: time as the causal dimension of spacetime.
A and B Series of Time Differentiated
The first step on the way to Mellor’s theory of time is the differentiation between the A and B series of time established by McTaggart. The A series orders facts in relation to the present moment as past, present, or future. Their relation to each other does not change, but their qualification as past, present, or future changes with the flow of time. The B series orders facts or events only with respect to their successive occurrence, no matter which of them is the present one. Therefore it does not need the concept of a flowing time. In everyday language, facts involving time are usually expressed in A sentences; that is, by using tensed verbs. Mellor argues that all tensed propositions or beliefs have B facts as their truth conditions. The crucial question is what makes tensed sentences, or A sentences like “Peter arrived yesterday,” true.
Mellor’s answer to this question in general is the following: A sentences have B facts as their truth condition. That means they depend, first, on facts like the time when the sentence is uttered and, second, on whether the event that is mentioned really occurred at the time that the sentence says it did. Both conditions can be expressed in B terms as follows: (1) The sentence was uttered on March 2nd, and Peter arrived on March 1st; (2) Peter really arrived on March 1st. If both conditions obtain, the A sentence is true. If the truthmakers were A facts, they would cause contradictions, because the fact that Peter arrived yesterday would have to obtain in order to make the statement true if uttered on March 2nd and not obtain to make it false when uttered on March 3rd. The central thought in Mellor’s B theory is that A sentences need B truthmakers in order not to fall prey to contradictions. He does not want to do away with the way of expressing subjective perspectives of time in A sentences. On the contrary, he recognizes the necessity of A sentences and A beliefs within a concept of agency.
As agents, Mellor explains, we depend on our A beliefs existentially. A true A belief at the right time is needed for an action to succeed. But, first, A beliefs are necessary to cause an agent to act. I need the belief that my train arrives at 2 o’clock, for instance, to cause me to leave the house by 1:30. For the success of this action, my catching the 2 o’clock train, the belief that the train arrives at 2 o’clock must be true. Again, the condition for this truth is not the A fact of it now being 2 o’clock, but the B fact that the train arrives at 2 o’clock. The function of A beliefs is to cause agents to act. Therefore A beliefs are indispensable. Beliefs about what is happening now are needed for any action.
Mellor states that the conviction that what is perceived is also present is not grounded in facts but in pragmatic beliefs. The presence of a perception is usually confused with the alleged presence of the object. This plays no role in everyday life, because the time light needs to travel from most objects to the eye and the time needed to process the information is negligible; in the case of cosmo- logic events, however, the events we perceive now may have happened millions of years ago. On the one hand, the fact remains that there is no presence in the strict physical sense of the word; on the other hand, as species we would never have survived if we had not taken the prey just seen or perceived the predators following us as present. So it is pragmatic and existentially necessary to have A beliefs.
Mellor explains this necessity in terms of evolution: It was necessary for the survival of humanity and even animals to have such A beliefs. Furthermore he thinks that having an A belief is more basic than having a language. It is not necessary to be able to express an A belief or to have a concept of the self or the present for acting on such a belief. The range of A beliefs is not limited to sentences about time. All subjective perspectives, all beliefs about time, place, and the subjective situation belong to its range. A beliefs are subject-relative, which means they belong to the subject that has them in order to cause it to act: “I” have to believe something at the present moment “now” in order to act. No one would act on someone else’s belief or on the belief in true B sentences alone.
Besides granting A beliefs a pragmatic necessity, Mellor also says that A sentences have different meanings from their B analogues and therefore cannot be replaced by B sentences. Although A sentences and their B analogues have the same content according to Mellor, they have a different character, because their relation to their truth conditions differs. While a B sentence, for example, “It is raining at t (let t be the exact time)” is always true (if and only if it rained at t); the A sentence “It is raining now” will only be true if said at the time t; if said before or after t, it may be false. This is the reason why Mellor says that A sentences “mean the functions from any B-time to their B-truth-conditions at t.” In other words: The truth of an A sentence depends on the position of its token on the B scale of time (when it is uttered) in relation to the B-scale position of its content, the event or fact expressed in the A sentence.
The fact that A sentences constantly change their truth values is crucial for Mellor’s version of a B theory of time. Their constant change is caused by the constant change of our A beliefs, which determine our perception or understanding of time. A beliefs about what is now change nearly every moment, and their spatial analogues about what is here change similarly. Through the constant change of A beliefs, Mellor explains how the impression of flowing time arises. Despite the fact that the flow of time does not exist as a property of time itself, it is a psychological truth. The phenomenon of flowing time is a mere construction of our minds, which are constantly concerned with changing A beliefs. It is important to stress the point that the psychological and dynamic character of A beliefs does not invalidate them in their function. According to Mellor, these subjective beliefs, or at least some of them, are also fundamental to a concept of the self, even though they do not deserve such a concept to function as a cause of agency. The concept of the self is a second-order belief. A beliefs belong to the first-order beliefs that make us eat if we perceive food; no concept of self is needed for this belief to cause an action, according to Mellor.
Mellor’s tenseless theory of time explains how subjective sentences involving time can be made true by nonsubjective truthmakers. It becomes obvious that he acknowledges the tensed view of time as essential only for time-consciousness and in a pragmatic perspective, but from that he does not infer an ontological relevance of the A series. Only the static B series is of ontological relevance. In order to strengthen the ontological argument, Mellor raises the question of what time is. This question entails, among others, the problems of the difference between time and space and of time as the dimension of change, as well as the question of causation.
Time and Space Contrasted
In fact, if time should be a subject of ontology, then it must not be reducible to something else. In special relativity it could seem as if time had been identified with space. Mellor attempts to show that this is not the case. Even though time resembles space in more than one way, it is not the same thing. The four dimensions of spacetime seem to be treated quite equally, because both space and time are systems of order, and time can be represented as a dimension just like space—the three dimensions of space are combined with the one dimension of time. Nevertheless they are not equal. Mellor explains that a difference between spacelike and timelike separations of events or entities is made in special relativity. The three dimensions of space represent an array of possible ways by which things can be in contact, interact, or fail to do so. The dimension of time has basically the same function, but, in contrast to space, things in time can fail to be in contact although they are in the same place, because they are there at different times, or in different words, it is possible for two things or events to occupy exactly the same place, because they can do it at different times. These kinds of separations are called timelike separations. They are treated differently from spacelike ones. This can be shown in the mathematical formalization of distances in spacetime: The spacetime separation has a positive sign if it represents a spacelike separation and a negative one if it represents a timelike one. Therefore time differs from space in special relativity.
In the next step, time is described as the dimension of change, which leads to the definition of time as the causal dimension of spacetime. Time defined this way is marked off from space not only in terms of formalization but also by nature. McTaggart characterizes time as the dimension of change. Mellor seeks to defend this view without sharing McTaggart’s opinion that the A series, which had just been shown as containing contradictions, is fundamental. Taking the A series as fundamental for change would lead to contradiction in the concept of change.
Mellor wants to give an account of change from the B theory’s point of view and in respect to special theory of relativity. The first question that arises here is, What is change? The answer Mellor gives is the following: A thing has undergone a change when it possesses incompatible properties at different times; change is a variation over time in the properties of a thing or an entity. This definition excludes various events that might in general be called changes but that do not meet the conditions of the definition: Mellor claims that spatial variation cannot be called change, because the properties that are subject to change have to be intrinsic, not relational. Changes in relational properties are not changes in the thing; they are a variation in its relation to some other thing. Neither spatial variation nor variation in temporal parts or in relational properties can be defined as change, because there is no change in intrinsic properties of the thing. Mellor also states a difference between things and events: Both terms denote particulars, but events, because they are stretched over a certain period of time, consist of temporal parts, while things do not have temporal parts, they are wholly present at more than one time. This is why only things can undergo change in the strict sense of the word, meaning they can possess incompatible intrinsic properties at different times.
McTaggart’s restriction of change to the A series was due to the fact that B facts never change; being true at one time means that a B fact is always true. The sentence “It is raining at t” will always be true if it really rained at t. Facts that change are A facts: that it is raining now might obtain at the present moment and be false a few minutes later because it has stopped raining in the meantime. McTaggart’s reason for change relying on the A series is the possibility of continuity. The continuous change of the A series (of the present state to a past one and so on) constitutes the flow of time, and therefore time can be the dimension of change only if the A series exists. Since the A series contains a contradiction, time as the dimension of change does not exist. Mellor does not share McTaggart’s conclusion. Although the B series account of change is being criticized for not being able to explain the continuity of change, Mellor attempts to show that indeed it can. If change is described as the possession of incompatible properties at different B times, which entails that every single B fact at its B time does not change, that does not mean that the succession of different B facts cannot be a continuous change. The facts in themselves need not change for change to occur: they only have to follow each other along a causal chain.
For Mellor, causality is the basic concept that grants time reality. Time differs from space in spacetime, because only in the temporal order are causes and effects necessarily separated. In space, cause and effect can occupy the same place, but they do not occur at the same time. According to Mellor it is not time that fixes the causal order (that would mean accepting the A series), it is causation that gives time its direction: Time order is synonymous with the causal order. Mellor gives several reasons for adopting a causal theory of time order (see Mellor, 2005). In short, his basic assumptions are that (1) causation links only events separated in time, not in space, because causation is never unmediated, and (2) causes always precede their effects. On the basis of these assumptions, a causal theory can explain the differences between past and future as well as the continuity of change. The causal concept of time explains why, according to Mellor, “We can perceive but not affect the past, and affect but not perceive the future” without the necessity to state moDalí or ontological differences between past, present, and future.
A profound survey of Mellor’s approach to the philosophy of time can be found in Real Time II; for a concise and informative entry into his thinking, his article “Time” in the Oxford Handbook of Contemporary Philosophy is recommended. A deeper understanding concerning the theoretical fundamentals of the definition of time as the causal dimension of spacetime is given by The Facts of Causation.
See also Causality; Determinism; McTaggart, John M. E.; Metaphysics; Ontology; Time, Relativity of; Space and Time; Spacetime Continuum; Relativity; Special Theory of; Time, Real; Time Travel
Lillehammer, H., & Rodriguez-Pereyra, G. (Eds.). (2003). Real metaphysics. Essays in honour of D. H. Mellor. London: Routledge.
Mellor, D. H. (1981). Real time. New York: Cambridge University Press.
Mellor, D. H. (1991). Matters of metaphysics. New York: Cambridge University Press.
Mellor, D. H. (1993). The unreality of tense. In R. Le Poidevin & M. MacBeath (Eds.), The philosophy of time (pp. 47-59). New York: Oxford University Press.
Mellor, D. H. (1995). The facts of causation. London: Routledge.
Mellor, D. H. (1998). Real time II. London: Routledge.
Mellor, D. H. (2001). The time of our lives. In Anthony
O’Hear (Ed.), Philosophy at the new millennium
(pp. 45-59). New York: Cambridge University Press.
Mellor, D. H. (2005). Time. In F. Jackson & M. Smith (Eds.), The Oxford handbook of contemporary philosophy (pp. 615-635). New York: Oxford University Press.
Oaklander, N., & Smith, Q. (Eds.). (1994). The new theory of time. New Haven, CT: Yale University Press.