1 Tense and Ontology
In order to understand two approaches to the metaphysics of time, we must come to terms with an argument for the unreality of time due to John McTaggart in (McTaggart 1908). He made a distinction between two descriptions of a series of moments or events.
This is a dynamic series in which moments of time move from one determination to another. Moments or events are future, then present, and then past.
\[ \begin{array}{ccccccc} \cdots & m & & m' & & m'' & \dots\\ \cdots & present & & \textbf{future} & & future & \cdots \\ \end{array} \]
\[ \begin{array}{ccccccc} \cdots & m & & m' & & m'' & \dots\\ \cdots & past & & \textbf{present} & & future & \cdots \\ \end{array} \]
\[ \begin{array}{ccccccc} \cdots & m & & m' & & m'' & \dots\\ \cdots & past & & \textbf{past} & & present & \cdots \\ \end{array} \]
This is a static series in which moments of time or events stand in permanent relations to one another. Moments or events are earlier than or later than one another.
\[ \begin{array}{lllll} \cdots & m & m' & m'' & \dots\\ \end{array} \]
\(m\) is earlier than \(m'\)
\(m\) is earlier than \(m''\)
\(m'\) is earlier than \(m''\)
\(m'\) is later than \(m\)
\(m''\) is later than \(m'\)
\(m''\) is later than \(m\)
Unlike the A-series, there is no change involved in the B-series, since there is no change in what B-theoretic relations one moment bears to another.
1.1 Is Time Real?
John McTaggart made use of the distinction between an A-series and a B-series in order to argue for the unreality of time in (McTaggart 1908).1 His master argument proceeds from two main premises:
M1. If time is real, then there is an A-series.
M2. There is no A-series.
C. Therefore, time is not real.
1.1.1 No Time without Change
In support of M1, McTaggart offered an argument:
- If time is real, then there is change.
- If there is change, then there is an A-series.
- Therefore, if time is real, then there is an A-series.
Bertrand Russell found the second premise doubtful:
If my poker, for example, is hot on a particular Monday, and never before or since, the event of the poker being hot does not change. But the poker changes, because there is a time when this event is happening to it, and a time when it is not happening to it.
McTaggart simply denies that the mere fact that the poker is hot on a Monday but not hot on a different day is sufficient for change. Real change, for McTaggart, requires a moment in time to move from future to present to past.
1.1.2 No Change
In support of M2, McTaggart reasoned:
- If there is an A-series, then moments or events are future, present, and past.
- No moment or event is future, present, and past.
- Therefore, there is no A-series.
In support of the first premise, McTaggart argues that for a moment or event M to change from future to present to past, it must exemplify all three qualities: future, present, and past:
If M is past, it has been present and future. If it is future, it will be present and past. If it is future, then it has been future and it will be past. Thus all three characteristics belong to each event.
1.2 The A-Theory and the B-Theory of Time
McTaggart’s argument is valid, which means that we must either reject at least one premise or else embrace the unreality of time. Two approaches to the metaphysics of time arise in line with the rejection of each premise of the argument. A-theorists tend to reject M2, whereas B-theorists reject M1.
1.2.1 The A-Theory of Time
The A-theoretic picture of time maintains that there is an A-series of moments of time, which are subject to change from future to present to past. That means that they reject M2. To that purpose, they must respond to the argument McTaggart offers in support of that premise.
McTaggart is aware that the premise that moments are future, present, and past may seem doubtful when we switch to a tensed formulation of the relevant predications:
| m | is future | has been future |
| m | is present | is now present |
| m | is past | will be past |
McTaggart replies that this is a distinction without a difference, since there is a simple paraphrase for each tensed predication.
| m | has been future | is future at some past moment |
| m | is now present | is present at some present moment |
| m | will be past | is past at some future moment |
The issue now is that to the extent to which the relevant moments of time are part of an A-series, they each are future present and past, which is, for McTaggart, incoherent.
1.2.1.1 An Infinite Regress?
We may insist that talk of a past moment is talk of a moment that has been present, talk of a present moment is talk of a moment that is now present, and talk of a future moment is talk of a moment that will be present.
| m | is future at some past moment | is future at some moment that has been present |
| m | is present at some present moment | is present at some moment that is now present |
| m | is past at some future moment | is past at some moment that will be present |
McTaggart’s response is to insist that talk of a moment that has been present is talk of a moment that is present at some past time in which case we have just posponed the problem. In fact, we could iterate the process ad infinitum, which, for McTaggart, is by itself a reason to reject the existence of an A-series in the first place.
1.2.1.2 How to Take Tense Seriously
In response to McTaggart, C. D. Broad draws a helpful distinction in (Broad 1934) between two styles of predication:
| Tenseless Predication | Tensed Predication |
|---|---|
| Two is even | Two is now my favorite number |
| Two has been my favorite number | |
| Two will be my favorite number | |
| The lecture is part of a colloquium | The lecture is now underway |
| The lecture has been underway | |
| The lecture will be underway |
One important difference between the two uses of the expression ‘is’ is that the statements in which it occurs as a tensed copula are often only temporarily true, whereas the statements in which it occurs as a tenseless predicate are sometimes permanently true. To disambiguate, we may use capital letters when we mean the predication to be tenseless.
Now, McTaggart’s infinite regress arises only when one insists on an analysis of tense in terms of tenseless predication. In McTaggart’s case the proposed analysis takes the form:
| Tensed Predication | Tenseless Predication |
|---|---|
| \(m\) has been \(F\) | \(m\) IS \(F\) at some moment \(m'\), which IS past. |
| \(m\) is now \(F\) | \(m\) IS \(F\) at some moment \(m'\), which IS present. |
| \(m\) will be \(F\) | \(m\) IS \(F\) at some moment \(m'\), which IS future. |
Broad agrees that given the proposed analysis, we are led into an infinite regress. But we should simply reject McTaggart’s invitation to paraphrase the tense in the way he suggests. The proper conclusion from McTaggart’s argument is that tensed predication is irreducible and cannot be analyzed in terms of tenseless predication.
\(A\)-theorists of time tend to take tense seriously much like C. D. Broad recommended in response to McTaggart. They take the B-series to leave something out, namely, which time is now, which times are past, and which times are future. As (Zimmerman 2005) puts the point in p. 431:
The essence of the A-theory is the objectivity of the distinction between past, present, and future. What is presently true is true, simpliciter, not merely true relative to a time or utterance or situation.
Of course B-theorists understand now differently. They take the word ‘now’ to act as an indexical for the moment of utterance. That is, the word ‘now’ picks out different times for different utterances of the sentence ‘I’m now in Peru’ at different times. But that is one reason why the A-theorist will reject the B-theorist attempt to translate ‘m is past’ in terms of ‘earlier than’ and ‘now’:
| m is past | m is earlier than now |
| m is earlier than the time of utterance |
1.2.2 The B-Theory of Time
The B-Theory of time makes do without the A-series or the distinction between past, present, and future. Here is J.J. C. Smart in (Smart 1963), p. 132:
One can easily get the idea that the notions of past, present, and future apply objectively to the universe. In contrast, I shall argue that the concepts of past, present, and future have significance only relative to human thought and utterance and do not apply to the universe as such. They contain a hidden anthropocentricity. So also do tenses. On the other hand, the concepts of ‘earlier’, ‘simultaneous’, and ‘later’ are impeccably non-anthropocentric. I shall argue for a view of the world as a four-dimensional continuum of space-time entities, such that out of relation to particular human beings or other language users there is no distinction of ‘past’, ‘present’, and ‘future’. Moreover, the notion of the flow of time is the result of similar confusions. Our notion of time as flowing, the transitory aspect of time…, is an illusion which precents us seeing the world as it really is.
The B-theorist pictures time as a fourth dimension perfectly akin to the usual three spatial dimensions: length, width, and height. For the sake of simplicity, we will draw spacetime diagrams that represent time as another dimension T alongside two spatial dimensions X and Y. The diagram below represents the spatiotemporal trace left by each a two-dimensional and a one-dimensional object:
1.3 Temporal Ontology
We should distinguish two questions:
Are past and future events and objects just as real as present events and objects are?
Presentists answer no
What is real is what is now the case. Past events and objects have been real and they have existed, but they no longer do. On the other hand, future events and objects are yet to be, which means that they do not yet exist.
Growing Block Theorists answer no but they qualify their answer.
What is real is both what has been the case and what is now the case. Once something comes into existence it remains in existence. Future events and objects, however, are yet to be, which means that they do not exist.
Eternalists reply yes
Temporal location makes no difference to existence. Both dinosaurs and Mars outposts exist, but they are located either in the remote past or in the future. The fact that they are removed from the time of utterance makes them no less real than present events and objects.
Is the totality of facts fixed and permanent or is it subject to change?
A-Theorists opt for change
What is the case now will not be the case in the future and may not have been the case in the past.
B-Theorists argue for permanence
The totality of facts is fixed and permanent, and change is to be understood in terms of different determinations at different times.
We will now settle on the B-theoretic eternalist model of time on which time is just one dimension of a four-dimentsional manifold, which hosts the totality of facts.
We will refer to excerpts reprinted in (Inwagen and Zimmerman 1991).↩︎