Slogans

The A-theory The B-theory

The A-theory, the B- 1. A-theory/B-theory: two questions The present time is All times are “on a par”.

theory, and Temporal 2. Propositional eternalism and temporalism

metaphysically special.
There are facts about which There are no such further facts.

Counterpart Theory 3. Temporal elitism and egalitarianism

4. The primordial objection to the B-theory
times are past, present and
future, over and above the facts
Pastness, presentness and
futurity “reduce” to be-
Cian Dorr about which times are before foreness and afterness.
St Andrews, 15/2/2012
5. The argument from spacetime which.
6. Temporal counterpart theory Time genuinely “flows” and We live in a “block universe”.
“passes”. There is “objective
7. A new kind of A-theory becoming”.
The facts themselves change. Change is just a certain kind of
pattern in the facts.

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My questions Modal analogues of these questions A further question about ‘flow’?

Fine: ‘Even if presentness is allowed to shed its light upon the
world, there is nothing in [A-theoretic] metaphysics to prevent
T1: Are there temporarily true propositions? that light being ‘frozen’ on a particular moment of time.’
• Yes: ‘Propositional temporalism’ M1: Are there contingently true propositions?
• No: ‘Propositional eternalism’ • Yes: ‘Propositional contingentism’
T2: Is the unit class of the present instant much more • No: ‘Propositional necessitism’ 1. For each instant t: at t, t is the only present instant.
M2: Is the unit class of the actual world much more 2. Some instant t is after the present instant.
natural than those of most instants?
3. If there is an instant t after the present such that at t, ϕ, then
• Yes: ‘Temporal elitism’ natural than those of most worlds?
it will be the case that ϕ.
• No: ‘Temporal egalitarianism’ • Yes: ‘Modal elitism’ 4. So for some instant t that is not present, it will be the case
• No: ‘Modal egalitarianism’ that t is the only present instant.
—Why put T2 this way?
5. So presentness is not “frozen”.

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A further question about “primitiveness”?

The A-theoretic outlook is consistent with regarding

‘At some instant t that is after the present, ϕ’ as a 1. A-theory/B-theory: two questions 1. A-theory/B-theory: two questions
reductive definition of ‘It will be the case that ϕ’. 2. Propositional eternalism and temporalism 2. Propositional eternalism and temporalism
• So, A-theorists need not regard tense operators as 3. Temporal elitism and egalitarianism 3. Temporal elitism and egalitarianism
‘primitive’ or ‘fundamental’.
4. The primordial objection to the B-theory 4. The primordial objection to the B-theory
• If you are determined to construe A-theory as a thesis 5. The argument from spacetime 5. The argument from spacetime
about fundamentality, it should be the thesis that the
fundamental facts undergo change, not the thesis that 6. Temporal counterpart theory 6. Temporal counterpart theory
“change” or any other particular bit of time-related
7. A new kind of A-theory 7. A new kind of A-theory
vocabulary is fundamental.
• But this thesis is not an optional extra for my A-theorists,
(assuming they go in for talk about fundamentality).

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 Instants: the basic role Elitists should be temporalists Temporalists should be elitists
t is accurate := every proposition that is true
(At-F) It will be that φ iff at some (At-∧) At t,(φ and ψ) iff at t,φ and simpliciter is true at t
future instant, φ at t,ψ
(At-P) It has been that φ iff at some (At-∨) At t,(φ or ψ) iff at t,φ or at
Claim 1: There is an accurate instant
past instant, φ t,ψ Suppose you think that the proposition, concerning • Argument: Every instant is accurate at itself. So it is
(At-¬) At t, not-φ iff not: at t, φ the present instant, that its unit class is more natural always the case that there is at least one accurate instant).
than those of most other times is true. So whenever anyone says that there are no accurate
(F-<) At t, it will be that φ iff at (Permanence) instants, they are wrong.
some t’ after t, φ If at t, φ, then always: at t, φ You would have to be mad to think that this
Claim 2: If temporalism is true, no non-present
(P-<) At t, it has been that φ iff at proposition is eternally true!
instant is accurate
some t’ before t, φ
• Argument: Every instant is present at itself. So when t is
non-present, the proposition that t is non-present is true
but not true at t.

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Non-factualism and relativism

Claim 3: Accuracy is the kind of property that makes Non-factualism about non-eternal propositions:
for naturalness in the class of its instances. • Propositions change their truth values, but 1. A-theory/B-theory: two questions
• It is quite easy to refer to PROPOSITIONS do not
2. Propositional eternalism and temporalism
• If you doubt this, take some other changeable natural • Some propositions are sometimes true and sometimes
3. Temporal elitism and egalitarianism
property, like being spherical. false, but no proposition is sometimes FACTUALLY true
• The class of things that are spherical (simpliciter) is and sometimes FACTUALLY false. 4. The primordial objection to the B-theory
natural—more natural than the class of things that will • The facts change, but the F*A*C*T*S don’t change. 5. The argument from spacetime
be spherical 1.46 years from now. 6. Temporal counterpart theory
• Say that t is accurate with regard to sphericity iff the If you can make sense of this ideology, you can use it
7. A new kind of A-theory
things that are spherical at t are exactly the spherical to resist the argument from temporalism to elitism:
things. This is a pretty natural property. only properties whose instantiation is a factual matter
make for naturalness.

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The horror of the modal B-theory Is the temporal B-theory horrible too? Is this ‘the problem of temporary intrinsics?’
No.
• The “primordial objection” is an objection to anyone
who denies (e.g.) that I am standing simpliciter (as
opposed to standing at this or that t), or that the Earth is
warming simpliciter.
• It makes no difference if we posit some other entities—
<shout, pound table, gnash teeth> our instantaneous temporal parts—and claim that they
are standing simpliciter.
• Also, the problem has nothing to do with intrinsicness. It
applies to obviously extrinsic properties like being
surrounded by bees. It applies to properties which
instantaneous temporal parts do not instantiate according
to Lewis, like being a child and being a kind person.

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 The manifold hypothesis From the manifold hypothesis to the B-theory
Every true proposition is entailed by Key Premise: If the manifold hypothesis is true,
1. A-theory/B-theory: two questions
• Truths about which spacetime points and regions there instants of time are hyperplanes.
are.
2. Propositional eternalism and temporalism • Truths which characterise the (4d) topological and 1.If the manifold hypothesis is true, no hyperplane
3. Temporal elitism and egalitarianism differential structure of spacetime. has a very natural unit class.
4. The primordial objection to the B-theory • Truths which characterise the distribution of certain 2.So, if the manifold hypothesis is true, no instant of
physical fields over spacetime. time has a very natural unit class.
5. The argument from spacetime
6. Temporal counterpart theory
• An appropriate “that’s all” claim. 3.So, if the manifold hypothesis is true, temporal
AND: the spacetime manifold is homogeneous. egalitarianism is true.
7. A new kind of A-theory
• There is no especially natural way to single out a 3d • Officially, temporal elitism only requires the unit class of
region. the present instant to be more natural than those of other
• Thus, nothing like the ‘glow of presentness’, e.g. no instants. But there is no plausible way out here.
natural ‘degree of futurity’ field. • I’m interested in the strategy of denying the Key Premise.
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Counterpart theorists escape the primordial Basic temporal counterpart theory

objection
1. A-theory/B-theory: two questions Lewis escapes the primordial objection to the modal BTCT
2. Propositional eternalism and temporalism B-theory. FΦ(a) := ∃x(CFxa ∧ Φ(x))
3. Temporal elitism and egalitarianism • For him, there is a perfectly good question whether PΦ(a) := ∃x(CPxa ∧ Φ(x))
Hubert Humphrey is ever president (absolutely,
4. The primordial objection to the B-theory
simpliciter), which is quite different from all the questions • ‘C xa’ means ‘x is a future-counterpart of a’;
F

5. The argument from spacetime about whether he is ever president “at w”. ‘CPxa’ means ‘x is a past-counterpart of a’.
6. Temporal counterpart theory Likewise, temporal counterpart theorists escape the • These are placeholders which different proponents of
BTCT can fill in in different ways.
7. A new kind of A-theory primordial objection to the temporal B-theory.
• There is a perfectly good question whether Herman is • Φ must be qualitative except for one or more occurrences
of the singular term a.
sitting (absolutely, simpliciter), which is quite different
from all the questions about whether he is sitting “at t”.

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What about purely qualitative claims? What about multiply de re claims?

The natural extension of BCTC to purely qualitative First bad idea:

Second bad idea:
ϕ: WILL ϕ(a,b) := ∃x∃y(CFxa ∧ CFyb ∧ ϕ(x,y))
WILL ϕ(a,b) := ∃x∃y(CFxa ∧ CFyb ∧ Hxy ∧ ϕ(x,y))
WILL ϕ := ϕ WAS ϕ(a,b) := ∃x∃y(CPxa ∧ CPyb ∧ ϕ(x,y))
WAS ϕ(a,b) := ∃x∃y(CPxa ∧ CPyb ∧ Hxy ∧ ϕ(x,y))
WAS ϕ := ϕ • Singleton-Herman will fail to have Herman as a member.
• Argument: let a be something that has a future- • WAS (Herman is asleep and Prop is false), where Prop is • H might be something like ‘belongs to the same
the proposition that Herman is asleep. hyperplane’.
counterpart, and let F be a qualitative predicate.
• Then WILL ϕ • There are infinitely many people who have been mothers • This does not resolve the Prince Charles problem.
WILL (ϕ ∧ (Fa∨¬Fa)) [by tense logic] of Prince Charles. • Any two things, even if they are not H-related, will always
be H-related, and will always have been H-related.
∃x(CFxa ∧ Φ ∧ (Fx∨¬Fx)) [by BCTC] • There are infinitely many people who have been
Φ identical to Prince Charles.
• There are infinitely many people who have lived in
All change is de re change North America.

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Better idea:
WILL ϕ(a,b) := ∃x∃y∃R(FC(R) ∧ Rxa ∧ Ryb ∧ ϕ(x,y))
WAS ϕ(a,b) := ∃x∃y∃R(PC(R) ∧ Rxa ∧ Ryb ∧ ϕ(x,y)) The picture: 1. A-theory/B-theory: two questions
• ‘FC(R)’ means ‘R is a future-counterpairing’. The qualitative facts do not change. The haecceitistic 2. Propositional eternalism and temporalism
• If we have the notion of an ‘n-second counterpart’ (for facts do change. 3. Temporal elitism and egalitarianism
real n), and think that each thing has at most one n-
second counterpart, we could understand FC(R) to • ‘Each man in his time plays many parts’. 4. The primordial objection to the B-theory
mean ∃n>0∀x∀y(Rxy Cnxy). • There is some good sense in which it makes sense to think 5. The argument from spacetime
of ordinary objects as having “spacetime locations” which
• Suppose Herm1 is Herman’s +60-second counterpart, and are medium-sized 3d regions. Each ordinary object is 6. Temporal counterpart theory
Herm2 is Herm’s +60-second counterpart. Let H1 and H2 constantly “moving up the manifold”. 7. A new kind of A-theory
be Herm1’s and Herm2’s qualitative profiles. When
Herman has H1, Herm1 will have H2.
• Herman will never be identical to anyone else.

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Counterparts and propositional temporalism Counterparts and temporal elitism Not hyperplanes!
What plays the instant role?

We must respect the temporal T-schema: (At-F) It will be that φ iff at some (At-∧) At t,(φ and ψ) iff at t,φ and What could ‘at h’ mean when h is a hyperplane?
future instant, φ at t,ψ
The proposition that ϕ(a) is such that ALWAYS, it is (At-P) It has been that φ iff at some (At-∨) At t,(φ or ψ) iff at t,φ or at • Suggestion: ‘at h, Φ(a)’ means ‘∃x(x is a temporal
true iff ϕ(a). past instant, φ t,ψ counterpart of a ∧ x is “located” in h ∧ Φ(x)’.
• This is easy. Just say that for any qualitative ϕ, (At-¬) At t, not-φ iff not: at t, φ • But this will give us the view on which infinitely many
counterpairing R, objects x and y, and propositions p, q, people have been mothers of Prince Charles, etc. This is
if Rxy and Rpq, and p = the proposition that ϕ(x), then q (F-<) At t, it will be that φ iff at (Permanence) not the case on our version of temporal counterpart
some t’ after t, φ If at t, φ, then always: at t, φ theory!
= the proposition that ϕ(y).
(P-<) At t, it has been that φ iff at
some t’ before t, φ

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A better answer: counterpairings What about Permanence?

x is a future instant := x is a future-counterpairing If we accept plausible essentialist claims about

x is a past instant := x is a past-counterpairing mathematical entities, then counterpairings
x is a present instant := x is the identity relation (construed as mathematical functions) do not obey
• Provided that we require that ∀x∃yRyx and Permanence.
∀x∀y∀z((Ryx ∧ Rzx)→y=z), this will give us all the role • If we want an ontology of instants, we need to posit them
barring Permanence. as something new: each instant “corresponds to” a
• And clearly, the unit class of the identity relation is much counterpairing, but not always the same one.
more natural than the unit classes of most • The present instant is the one that corresponds to the
counterpairings. So temporal elitism is vindicated. identity counterpairing. This looks like a natural feature!

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