1. Lecture 9 Time: the A-theory and the B-theory
Dr. Donnchadh O’Conaill
21/2/2017
Metaphysics University of Helsinki

2. 1. Introduction: two responses to McTaggart
P1: If there is no change, then time is not real
P2: change requires that events form an A-series
P3: the A-series entails contradictions
P4: therefore the A-series is impossible
C: therefore time cannot be real
Two popular responses:
(i) accept P1, deny P2 – i.e., time is possible without appealing to the A-series
(ii) accept P1 and P2, deny P3 – i.e., time requires the A- series, and the A-series does not lead to contradictions

3. The A-theory and the B-theory
These responses give rise to the B-theory and the A- theory of time, respectively
B-theory: all temporal facts are captured by the B-series - no (irreducible) A-series facts
i.e., no irreducible fact of the matter about what time it is now or at present – this is a matter of our temporal perspective or way of talking
A-theory: irreducible A-series or tensed facts – the difference between past, present and future is built into the nature of time itself

4. B-theory: two main claims
(1) Tense not an objective feature of reality: “the concepts of past, present, and future have significance relative only to human thought and utterance and do not apply to the universe as such” (Smart 1963, 132)
The passing of time is not an objective feature of reality
(2) Four-dimensionalism / eternalism: time is a dimension in which things are spread out, like spatial dimensions
Location in this temporal dimension makes no ontological difference - entities in the past and future are just as real as those which exist now

5. 2. Criticisms of the B-theory: tensed truths
If there are no tensed facts, how can tensed statements (e.g., ‘The lecture is taking place now’) be true?
B-theorist: distinguish tensed from tenseless verbs:
‘John is tall’ – tensed, truth of this sentence depends on when it was written or uttered
‘Brasilia is the capital of Brazil in 2014’ – tenseless, truth- value does not depend on when it is uttered
Truth of tensed statements can be accounted for by (i) tenseless statements (ii) B-theoretic relations, e.g., earlier than, later than

6. 3. The Old B-theory
Tenseless translations of tensed sentences, i.e., sentences with the same meaning or semantic content
Two versions of the old B-theory:
(1) token-reflexive analysis
A sentence is token-reflexive if each utterance / token of the sentence refers to the token itself: e.g.,
‘This sentence is spoken by Donnchadh’
Each token of a tensed sentence refers to the time at which it is uttered, and this can be expressed by a tenseless sentence:

7. “‘He runs’ means ‘He runs (tenseless) simultaneous with this utterance’ and ‘He ran’ means ‘He runs (tenseless) earlier than this utterance” (Smart 1963, 134)
(2) Date analysis: translation into tenseless sentences stating the date or time at which an event occurs
S: ‘It is raining now’
If uttered at 4pm on February 21st 2017, S means the same as T: ‘It rains at 4pm on February 21st 2017’
Here ‘rains’ is tenseless, as is T

8. Counterexamples to the Old B-theory
‘Thank goodness that’s over!’
“not only is this, when said, quite clear without any date appended, but it says something which it is impossible that any use of a tenseless copula with a date should convey. It certainly doesn’t mean the same as, e.g., ‘Thank goodness the date of the conclusion of that thing is Friday, June 15th 1954’, even if it be said then. Nor, for that matter, does it mean ‘Thank goodness the conclusion of that thing is contemporaneous with this utterance’. Why should anyone thank goodness for that?” (Prior 1959, 17) (more examples: Dainton 2010, 32)

9. 4. The New B-theory
Accepts that tenseless translations of tensed sentences cannot be provided
Aim instead to provide tenseless statements of the truth-conditions of tensed statements
Truth-conditions: necessary and sufficient conditions for an utterance’s being true
‘John is an only child’ is true if and only if John has no siblings
If we can give tenseless truth conditions for tensed sentences, no need to posit tensed facts to explain the truth of tensed sentences

10. Two versions of the New B-theory
(3) Token-reflexive version
Consider an utterance of S: ‘It is raining now’
An utterance of S is true if and only if an event of raining is simultaneous with this utterance
(4) Date version
S, if uttered at 4pm on February 21st 2017, is true if and only if it rains at 4pm on February 21st 2017
Neither version seeks to provide a translation of S – the sentences stating the truth conditions do not have the same meaning as the tensed sentences

11. 5. Three versions of the A-theory
All versions of A-theory agree that tense is real - disagree on which objects and events exist
First version: Moving Spotlight – eternalism plus real tense
“We are naturally tempted to regard the history of the world as existing eternally in a certain order of events. Along this, and in a fixed direction, we imagine the characteristic of presentness as moving, somewhat like the spot of light from a policeman's bull's-eye traversing the fronts of the houses in a street. What is illuminated is the present, what has been illuminated is the past, and what has not yet been illuminated is the future” (Broad 1923, 59)

12. In the Moving Spotlight view, change in tense is not a change in whether or not some entity exists, but in what tensed property an entity has
Second version: Growing Block – tense is real, and change in tense is existential change
i.e., for x to be present is for it to begin to exist
The past exists, and the future does not: “The sum total of existence is always increasing, and it is this which gives the time-series a sense”, i.e., direction (Broad 1923, 66-67)

13. Presentism
Third version: presentism – the only things which exist are those which are present
For an entity to become present is for it to begin to exist; for it to become past is for it to cease to exist
Unlike other forms of the A-theory, threatens four- dimensional view of time

14. Why presentism?
Common-sense view? We can’t doubt the existence of the present, and we can experience it changing
Can we perceive things which are not present? E.g., light from stars which are now dead?
Yes, but our experiences themselves must be present
What is past has ceased to exist: this a way in which location in time seems fundamentally different to laction in space
The future is not fixed, and so future entities do not (yet) exist

15. 6. Presentism and truths about the past
Singular proposition: denotes objects using a name or demonstrative, not a description:
‘Socrates is human’, ‘That is a table’
Vs ‘The teacher of Alexander is human’
Singular propositions often held to depend for their existence or truth on the objects which they are about: these objects are constituents of the propositions
Can the presentist explain singular propositions about non-present objects: ‘Socrates was a philosopher’

16. One possible response: backward-looking properties
E.g., I am (now) such that I was once an infant
Can a proposition have a backward-looking property, the property of having been true?
Or the world has a backward-looking property, the property of being such that Socrates was a philosopher
Second response: unexemplified haecceties, i.e., a haecceity which continues to exist after its bearer has ceased to be?
‘Socrates was a philosopher’ is a singular proposition which directly refers to Socrates in virtue of having his haecceity as a constituent

17. Works cited C. D. Broad (1923) Scientific Thought. London: Kegan Paul.
A. N. Prior (1959) ‘Thank Goodness that’s Over’ Philosophy 34 (128): 12-17
J. J. C. Smart (1963) ‘The Space-Time World’ in Philosophy and Scientific Realism. London: Routledge