Presentism and Existence-Entailing Relations: An Aporetic Tetrad

It is plausibly maintained that all relations are existence-entailing. To illustrate from the dyadic case: if R relates a and b, then both a and b exist.   A relation cannot hold unless the things between which or among which it holds all exist.  A weaker, and hence even more plausible, claim is that all relations are existence-symmetric: if R relates a and b, then either both relata exist or both do not exist. Both the stronger and the weaker claims rule out the possibility of a relation that relates an existent and a nonexistent. (So if Cerberus is eating my cat, then Cerberus exists. And if I am thinking about Cerberus, then, given that Cerberus does not exist, my thinking does not relate me to Cerberus.  This implies that  intentionality is not a relation, though it is, as Brentano says, relation-like (ein Relativliches).)

But if presentism is true, and only temporally present items exist, then no relation connects a present with a nonpresent item. This seems hard to accept for the following reason.

I ate lunch  an hour ago. So the event of my eating (E) is earlier than the event of my typing (T). How can it be true that E bears the earlier than relation to T, and T bears the later than relation to E, unless both E and T exist? But E is nonpresent. If presentism is true, then E does not exist.  And if E does not exist, then E does not stand in the earlier than relation to T.  If, on the other hand, there are events that exist but are nonpresent, then presentism is false.

How will the presentist respond? Since E does not exist on his view, while T does, and E is earlier than T, he must either (A) deny that all relations are existence-symmetric, or deny (B) that earlier than is a relation. He must either allow the possibility of genuine relations that connect nonexistents and existents, or deny that T stands in a temporal relation to E.

To  fully savor the problem we  cast it in the mold of an aporetic tetrad:

1. All relations are either existence-entailing or existence-symmetric.

2. Earlier than is a relation.

3. Presentism: only temporally present items exist.

4. Some events are earlier than others.

Each limb of the tetrad is exceedingly plausible.  But they cannot all be true:  any three, taken together, entail the negation of the remaining limb.  For example, the first three entail the negation of the fourth.  To solve the problem, we must reject one of the limbs.  Now (4) cannot be rejected because it is a datum.

Will you deny (1) and say that there are relations that are neither existence-entailing nor existence-symmetric?  I find this hard to swallow because of the following argument.  (a) Nothing can have properties unless it exists.  Therefore (b) nothing can have relational properties unless it exists. (c) Every relation gives rise to relational properties:  if Rab, then a has the property of standing in R to b, and b has the property of standing in R to a.  Therefore, (d) if R relates a and b, then both a and b exist.

Will you deny (2) and say that earlier than is not a relation?  What else could it be?

Will you deny presentism and say that that both present and nonpresent items exist?  Since it is obvious that present and nonpresent items cannot exist in the present-tense sense of 'exists,'  the suggestion has to be that present and nonpresent (past or future) items exist in a tenseless sense of 'exist.'  But what exactly does this mean?

The problem is genuine, but there appears to be no good solution, no solution that does not involve its own difficulties.

Comments

[William]

A good tetrad. Testing it on 'Aristotle was born before Caesar'. I agree that

2. 'was born before' is a relation

3. Neither Aristotle nor Caesar exist any longer

4. The lifetime of Aristotle was before the lifetime of Caesar

This clearly entails that some relations are not existence entailing. Are they 'something' entailing? Probably yes. If Aristotle was born before Caesar, someone (Aristotle) was born before someone (Caesar).

[Bill Vallicella]

You solve the problem by denying (1). OK, but what justifies the rejection of (1) over the rejection of (3, or less plausibly, (2)? Furthermore, you didn't respond to the argument I gave in support of (1). Roughly, how can an item have properties or stand in relations without existing?

It may also be that you are contradicting views you maintained earlier about existence. If I understood you then, you were maintaining that there is no difference between 'Something is F' and 'Some existing thing is F.' Now you are maintaining that if dyadic R holds, then there is some pair between which it holds, while denying that if some dyadic R holds, then there exists a pair between which it holds.

[Steven]

Is denying presentism really so bad?

[bossmanham]

What if one were to say that past events at one time existed, but no longer do? Would this then not preserve the earlier than later than relation?

If something did exist, then that thing did have properties. That would mean that a relational property does exist, in that, while a past moment did exist before, now the present moment does exist. Something did exist prior to something else existing?

[Bill Vallicella]

No doubt, if something did exist, then it did have properties. But past items do not exist now, so they cannot stand in relations to items that do exist now.

[Jan]

I think there is a more basic problem here that does not presuppose presentism. Dr. Vallicella claims:

Shared existence or non-existence (SENE): If R relates a and b, then either both relata exist or both do not exist.

He gives an excellent argument for this claim. If a does not exist, a has no properties. But if aRb, then a has the property 'being in relation with b'. Therefore, aRb implies a and b exist. However, there seems to be a strong counterexample to SENE:

(*) Cerberus has more heads than Vallicella's cat.

This proposition seems to me both meaningful, true and positing a relation. How can SENE and (*) be both true? The most natural way is to claim that Cerberus enjoys some sort of existence. I propose two alternative solutions

P1: If a exists in a possible world W, then a exists as an immaterial essence or idea in the actual world AW.
P2: If a exists in a possible world W and is comprehended by a mind in the actual world AW, then a exists as an immaterial essence or idea in AW.

Of course neither ideas nor essences possess heads. Therefore, (*) is to be understood as an abbreviation of

(**) Were the essence of Cerberus instantiated, the instantiation would have more heads than Vallicella's cat.

Now, P1 implies P2. Is P1 true? Let's consider

(***) Ceterus has more heads than The Cat.

Ceterus is a quadruple-headed cat inhabiting a world W' that I have just comprehended. (***) is the same type of proposition as (*), and thus meaningful, true and positing a relation. Was (***) true before I comprehended Ceterus? I am inclined to say 'yes', but I am not sure. Therefore, I am inclined to accept P1 over P2. On the other hand, P1 considerably inflates our ontology.

The solutions allows us to make sense of propositions similar to 'Superman is faster than Usain Bolt'. Returning to the problem of the existence of the past, let's consider

UBvsJO: Usain Bolt is faster than Jesse Owens.

Can we make sense of this proposition under presentism? I think we can. The world of the past is a possible world and is inhabited by Owens. Thus, UBvsJO can be understood under presentism in the same way (*) can, that is

UBvsJO': Were the essence of Jesse Owens instantiated, the instantiation would be slower than Usain Bolt.

However, under presentism I still cannot make sense of Vallicella's

(2) An event e of the past is earlier than an event e' of the present.

My solution proposes to treat the past as a possible world, thus loosing its temporal relation to the present. Presentism has been assumed arguendo, I do not commit myself to it.

[William]

[Bill]>>>You solve the problem by denying (1). OK, but what justifies the rejection of (1) over the rejection of (3, or less plausibly, (2)? Furthermore, you didn't respond to the argument I gave in support of (1). Roughly, how can an item have properties or stand in relations without existing?
It may also be that you are contradicting views you maintained earlier about existence. If I understood you then, you were maintaining that there is no difference between 'Something is F' and 'Some existing thing is F.' Now you are maintaining that if dyadic R holds, then there is some pair between which it holds, while denying that if some dyadic R holds, then there exists a pair between which it holds.

Guilty on all charges. I see no easy way of resolving this. I have no good reply to the argument you made in defence of (1). On the other hand, the truth of 2-4 clearly entail the falsity of (1). "Roughly, how can an item have properties or stand in relations without existing?" - well, that is a statement (or rather a rhetorical question). Perhaps an item can have properties or stand in relations without existing? On the apparent (in fact real) contradiction between what I have said here and things I made have said elsewhere, I think it is quite bad form in discussions like these to hold a speaker to anything they may have said in earlier discussions. The important thing in philosophy is not to take sides. We are interested in the quality of arguments, which we savour like a good wine (or reject, like a bad one).

On the relation thing, isn't

-- is dead and -- is alive

logically a relation? For example, it truly relates 'Caesar' in the first position, and 'Obama' in the second. And falsely relates 'Caesar' and 'Mark Antony', also 'Dave Cameron' and 'Obama'. Just a thought, for this reduces your problem to how any statement about a no-longer existing object can be true. We could solve this by postulating that '-- no longer exists' is not a real predicate, or rather does not express a real property. Then perhaps 'X is before Y' does not express a real relation.

But then (as I observed in the other post) there is the problem of causation. Surely *something* must exist at some moment immediately prior to the present in order to bring the present into existence?

[Bill Vallicella]

William,

Yes, the truth of (2)-(4) entails the falsity of (1). But note that any three limbs, taken together, entails the negation of the remaining one. So the inconsistent tetrad gives rise to four valid arguments each of which issues in the negation of one of the limbs.

The problem is that we have no good reason to prefer one of these arguments over the others. My hunch is that the central propblems of philosophy are absolutely insoluble. Of course, one can plump for a 'solution' but only by being arbitrary and dogmatic. But as I say, this is a hunch I am exploring.

I like the British phrase 'bad form,' but whereas an ad hominem in the form of a personal attack would be very bad form indeed, an ad hominem which points out an inconsistency in the interlocutor's views doesn't seem that bad. I do admit, though, that it distracts attention from the issue at hand.

[Bill Vallicella]

Are Caesar and Obama related in that Caesar is dead but Obama is not? This looks to be, if a relation at all, an internal relation, one that supervenes on monadic properties of the relata. But I should think that earlier than and indeed all temporal and spatial relations are external. This opens up a whole other can of worms.

[Bill Vallicella]

Jan,

Thanks for your excellent contribution. I am unclear about (P1) and (P2). First, 'immaterial essence or idea' is unclear. Is that the 'or' of identity or the 'or' of disjunction? Ideas exist only in minds; immaterial essences can exist outside minds.

I don't see how the actual past could be viewed as a merely possible world, if that is what you are suggesting. One has to be able to accommodate the distinction between, say, Kierkegaard's break-up with Regine Olsen (an actually past event) and K's marriage to O ( a merely possible past event).

[William]

Against those who have questioned presentism: we don't need anything as strong as presentism to get the problem that Bill mentions above. We only have to assume that some things cease to exist. Then the 'modified tetrad' below is equally problematic.

1. All relations are either existence-entailing or existence-symmetric.

2. Earlier than is a relation.

3. Partial-presentism: some events no longer exist

4. Some no-longer-existing events are earlier than others.

If we deny partial presentism, it follows that nothing whatsoever can cease to exist. How could we allow for the possibility of any kind of change if this were true? Yet it leads to the puzzle. If some events no longer exist, then (4) immediately follows - the events that no longer exist, must have existed before some event happening now. then (2) being earlier than is a relation. Which contradicts (1).

[Bill Vallicella]

William,

Your tetrad is consistent. The birth of Aristotle is earlier than the birth of Caesar. That fact makes (4) true. These two events no longer exist, and the one is earlier than the other. So (2) and (3) are true. Since neither event exists, (1) can also be true.

To get inconsistency, you must delete 'or existence-symmetric' from (1).

Am I right?

[David Brightly]

I've been puzzling over this for a week. My feeling is that we must retain (2) and (4) but that (1) is problematic regardless of the status of (3), as I think WW has shown. So how to address Bill's argument for (1)?

Let's distinguish between 'temporal' properties/relations, which explicitly involve time, and 'atemporal' properties/relations, which do not. I'll write Pxt for x has property P at time t.. Bill's argument for (1) is couched in the present tense, but if we are not to presuppose some form of presentism, we can render Bill's principle (a) (Nothing can have properties unless it exists) as

(a) ∀x ∀P ∀t Pxt --> Ext

where Ext abbreviates 'x exists at time t'. x ranges over a domain of objects/events past and present; P ranges over the temporal properties under consideration; t ranges over whatever times past and present we require. (a) generalises to relations---replace Pxt with Rzyxt, say and quantify over z and y as well. I want to say that Bill's argument works for temporal properties but not for atemporal properties. Are there any such things? Yes, because from any temporal property P we can derive an atemporal property P* by existentially quantifying over time:

(b) P*x <--> ∃t Pxt

So, for example, from CRxt, ie, x crosses the Rubicon at time t, we derive CR*x, ie, x once crossed the Rubicon, or x sometime crosses the Rubicon (the tense here is irrelevant).

Putting (a) and (b) together we can derive

(c) P*x --> ∃t Ext <--> E*x

where E* is the 'atemporalisation' of E. E*x says that x exists at some time. x and P are arbitrary in (c) so we get an atemporal analogue of (a)

(d) ∀x ∀P P*x --> E*x

Now, Earlier-than, though it may not be the atemporalisation of a temporal relation, is nevertheless atemporal. It makes no sense to say something like 'lunching was before typing at teatime'. So I claim that Bill's principle (a) fails to get started with Earlier-than.

[Bill Vallicella]

Thanks for that, David, although I find it puzzling. Aren't you in effect simply upholding (1) and (a) by construing 'exists' tenselessly?

>>Now, Earlier-than, though it may not be the atemporalisation of a temporal relation, is nevertheless atemporal. It makes no sense to say something like 'lunching was before typing at teatime'. So I claim that Bill's principle (a) fails to get started with Earlier-than.<<

I agree completely with the first two sentences. If e1 occurs earlier than e2, then that is the case at all times. (The same goes for later than, and simultaneous with.) Perhaps you could explain to me how your conclusion follows from these two sentences. 'Nothing can have properties unless it exists' strikes me as consistent with your two sentences.

[David Brightly]

Hello Bill,
Am I construing 'exists' tenselessly? Quite possibly. I'm trying to get clear what this might mean. Would you agree that 'exists tenselessly' is equivalent to my E* property?

My argument is that your principle (a) as reformulated in my own (a) does not apply to 'earlier-than' (ET) since my (a) quantifies over temporal properties/relations only and 'earlier-than' is atemporal. It would seem though that ETxy --> E*x & E*y.