4 B-Theories
The B-Theory provides different answers to the questions on tense and ontology we isolated:
- Are there objective differences between past, present, and future?
- Are present events and objects more real than past and future events and objects?
The answer to the first question is negative. B-theorists compare the distinction between past, present, and future to the contrast between putative spatial determinations such as being local and being elsewhere. To be sure, a lecture at GFS108 may at a certain time strike us as a local event, whereas a session of Congress is elsewhere. What is less clear is that the distinction marks an objective difference between the two events, one, in particular, that is not just a matter of perspective. Whether a certain event or object counts as local or whether it lies elsewhere is just a matter of perspective and depends on your own location in space. For after all, what is local for some speakers may lie elsewhere for others and vice versa. Likewise, there is no objective distinction between past, present, and future. Instead, whether an event or object counts as past, present, and future for you depends on your own location in spacetime. What is present for some speakers may in fact be past for others and vice versa.
That suggests an egalitarian attitude towards all spatially located events and objects. It would be a mistake to claim that local events and objects are in fact more real than events and objects located elsewhere. Kangaroos are no less real for the mere fact that they are not local but rather are located elsewhere in Australia. The proponent of the B-Theory claims that time is no different from space in these respects.
But while these answers are programmatic, they question remains of how to implement the view.
4.1 The Reduction of Tense
Let us return to McTaggart’s distinction between A- and B-facts. Unlike A-facts, B-facts concern the relative location of events with respect to one another and are permanent. These facts, as McTaggart characterized them, concern the relations earlier than, simultaneous with and later than. In contrast to them, A-facts are subject to change: events and objects are future, then they become near future. After they become present, they begin to recede into the near past and farther into the past. These facts are temporary. What is now future, will become present and the will recede into the past.
One area of disagreement for A- and B-theorists is the question of whether A-facts are prior to (or ground) B-facts or whether instead B-facts are prior to (or ground) A-facts. The A-theory offers a reduction of B-facts to A-facts:
| B-facts | A-facts |
|---|---|
| \(m\) is earlier than \(m'\) | \(m\) is now past and \(m'\) is now present, or \(m\) is now present and \(m'\) is now future, or etc |
| \(m\) is later than \(m'\) | \(m\) is now present and \(m'\) is now past, or \(m\) is now future and \(m'\) is now present, or etc |
| \(m\) is simultaneous with \(m'\) | \(m\) and \(m'\) are now present, or \(m\) and \(m'\) are now future but it will be the case that they are both present, or \(m\) and \(m'\) are now past but it has been the case that they have both been present |
The B-Theory of time reverses the order of explanation. B-facts are prior to (and ground) A-facts, which depend on a given perspective.
| A-facts | B-facts |
|---|---|
| \(m\) is future | \(m\) is later than now |
| \(m\) is present | \(m\) is now |
| \(m\) is past | \(m\) is later than now |
In this respect, A-facts are not different from a family of perspectival facts expressed by utterances of covertly indexical sentences. Consider the distinction between:
Joshua Tree is to the East.
Santa Monica is to the West.
To claim that Joshua Tree is to the West is to claim that Joshua Tree bears a certain spatial relation to the spatial coordinates of the speaker at the time of utterance. The utterance is true if made in Los Angeles, but false when made in Tucson, AZ.
The B-Theorist may use the word now to single out the temporal coordinates of the speaker at the time of utterance of sentences that contain it. The sentence ‘m is later than now’ expresses different propositions in different contexts. A given context \(C\) includes the time of utterance of the sentence, and the utterance expresses the fact that m is later than that time. More generally
| sentence | utterance | proposition |
| \(m\) is later than now | … at a context \(C\) … at context \(D\) |
\(m\) is latter than the time of utterance |
| \(m\) is now | … at a context \(C\) … at context \(D\) |
\(m\) is simultaneous with the time of utterance |
| \(m\) is earlier than now | … at a context \(C\) … at context \(D\) |
\(m\) is earlier than the time of utterance |
4.2 ‘Now’ as an Indexical
The A-theorist understands the word differenty. For she takes the word ‘now’ to correspond to an objective, perspective-independent property of being present. This is an objective property an event briefly exemplifies before receding into the past.
There is an important parallel with the word ‘actually’. Compare:
It is actually the case that there human outposts in the Arctic.
It is merely possibly the case that there are human outposts in Mars.
Two treatments of the word come to mind. One could treat the relevant sentences as covertly indexical:
There are human outposts in the Arctic at the world at which the utterance is made.
There are human outposts in Mars at a world that is possible relative to the world at which the utterance is made.
Alternatively, we could take the word to stand for an absolute and perspective-independent property: being actual. That is a property human outposts in the Arctic exemplify but human outposts in Mars do not. The view that emerges, which we may call actualism, is parallel to the presentist variant of the A-theory.
4.3 No Irreducible Tensed Facts
The B-theory rejects the existence of irreducibly tensed facts, which the A-theorist sometimes takes to explain some aspects of our experience of time. Consider the puzzle:
You wake up in a hospital ward after an episode of amnesia. You are reliably informed that you are either a patient who underwent a very painful operation just yesterday or one who will tomorrow experience an operation, which may cause some pain and discomfort. Which one would you prefer to be?
If we simply measure the pain associated to each operation, you may have reason to prefer to be the patient who will experience some pain and discomfort tomorrow. On the other hand, most would seem to prefer to be the patient who already underwent a very painful operation just yesterday.
The presentist has an answer:
- You prefer to be the first patient because the very painful operation is no more part of reality. A much less painful experience will come into existence, but you would rather anticipate some discomfort than a very painful experience.
The spotlight theorist provides a different answer:
- You prefer to be the first patient because the very painful operation has ceased to be present. A much less painful experience lies in the future and will be present, but they would rather anticipate some discomfort than a very painful experience.
The presentist is not impressed by that answer. If the very painful operation is just as real as present events and objects, then it is just as painful as we described it and it is not clear how receding into the past is supposed to help explain our preferences.
The B-theorist has fewer resources to explain the preference:
- You prefer to be the first patient because the very painful operation took place earlier. A much less painful experience comes later, but you would rather anticipate some discomfort and a very painful experience.
The presentist is even less impressed. If the very painful operation is just as real as the future less painful one, should you not prefer to be the patient with the less painful experience?
How should the B-theorist respond? (Sider 2003) draws an analogy with the question of whether there are irreducibly indexical or personal facts? Consider John Perry’s case:
Rudolf Lingens is an amnesiac lost into the Stanford Library when he stumbles into a book entitled ‘Rudolf Lingens: A Complete Biography’. He reads the book with special interest, and comes to have access to a great variety of facts to do with Lingens:
Lingens has three siblings.
Lingens began his career as an engineer, etc.
It seems like there are important facts beyond his ken:
I have three siblings
I began my career as an engineer,
I am Rudolf Lingens.
There are two potential morals:
- There are irreducibly indexical or personal facts beyond the facts that describable in an impersonal language without indexicals.
- Some attitudes and relations to impersonal propositions are irreducibly perspectival. The attitudes expressed by sentences that involve indexicals require a certain vantage point, one to which the amnesiac Rudolf Lingens has no access.
(Sider 2003) outlines a parallel response to the challenge above:
- There are no irreducibly tensed facts.
- Some attitudes and relations to facts and events is irreducibly perspectival.
Episodes of relief that a given operation is over require the subject to be located after the relevant operation. Episodes of anxiety that a new operation is imminent, on the other hand, require the subject to be located prior the relevant event. Relief, in other words, is only appropriate for past events, whereas anxiety is appropriate for future events.
Attitudes like relief and anticipation are not merely two-place relations between a subject and a proposition, but rather a three-place relation between a subject, a time, and a proposition, and the time has to be appropriately related to the proposition in question.
4.4 Against Temporal Passage
The B-theory of Time accepts the existence of a four-dimensional manifold, whose regions are occupied by equally real events and objects. The fact that some events and objects, e.g., dinosaurs, are found in spatiotemporal regions that precede now by millions of years does not make them less real than objects now.
Reality is static and change is just variation in what features something exemplifies at different spacetime regions. The global pattern of exemplification, however, is permanent and not subject to further change. The B-theory makes no room for the view that time passes.
(Smart 1949) characterizes passage as a metaphor:
we think of ourselves as stationary, watching time go by, just as we may stand on a bridge and watch leaves and sticks float down the stream underneath us. Events, we sometimes think, are like such leaves and sticks; they approach from the future, are momentarily in the present, and then recede further and further into the past. Thus instead of speaking of our advance through time we often speak of the flow of time.
But there is, for him, nothing over and above a metaphor:
we cannot talk about time as a river, about the flow of time, of our advance through time, or of the irreversibility of time without being in great danger of falling into absurdity.
There are several routes towards absurdity for Smart, but we will just focus on one.
- If time passes, then there is a fact of the matter as to the rate at which it passes
- There is no fact of the matter as to the rate at which time passes.
- Time does not pass.
When we discuss the rate at which a car moves through space, we measure how long it takes for the car to cover a certain distance in space, e.g., 40 miles per hour. To measure the rate at which the present moves through time, we would seem to look at how long it takes for the present to move from one time to another. There are, on the face of it, two options:
Measure how long it takes for the present to move from time to another relative to another time dimension.
Endorse the utterly uninformative answer that the present moves at a rate of one second per second.
The first option seems a departure from the A-theory, since nothing in the dynamic view of time requires the existence of another time dimension. And even if one accepted the existence of such a dimension, further questions would immediately arise as to whether time passes through that dimension as well.
The second option may seem to involve a perfectly coherent answer to the question of the rate of passage, but some object it is not particularly illuminating and that there is something to be learned from the impossibility of such an answer.