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Tuesday, January 01, 2013

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Happy New Year!

You ask: whether presentism has the resources to express its own thesis? I'm not entirely sure I understand this, because to understand it properly we would have to understand what the thesis was, and therefore would have the resources to express it.

Perhaps the problem is that the presentist thesis requires a theory of truth for which modern predicate logic has no resources. The theory of truth in MPL starts with the relation of 'satisfaction' between a predicate and any object. A sentence combining the name of the object and the predicate is true when the predicate is satisfied by the object, otherwise it is false. For example the predicate "—is a Roman" is satisfied by any person who is of Roman origin. It is not satisfied by any English, American or French person. (Nor is it satisfied by rocks, particles, planets etc). But then we have to explain how '— was a Roman' can be satisfied, since 'Caesar was a Roman' is clearly true. The predicate '—was a Roman' seems to be satisfied by that man, but the verb phrase 'is satisfied' is in the present tense, and therefore (since the presentist allows that any subject of a present tense affirmative statement exists) Caesar exists in some sense. But that is 'weak' presentism, if I understand you right. Caesar exists in some qualified sense, but not simpliciter. Strong presentism cannot be expressed using the standard assumptions of modern predicate calculus.

Actually I see you have tried to express the presentist thesis: You say "The presentist, however, maintains that what did exist, but no longer exists, does not exist at all". Let's express that 'not ... at all' by saying that there is no domain containing what did exist, but no longer exists. So it is easily expressed. But we are now faced with the task of explaining what makes "Caesar existed, but no longer exists" true. It clearly is a Moorean truth. But if true, it follows that the predicate "—existed, but no longer exists" is satisfied, and therefore the object satisfying it is in some domain. But then strong presentism, as defined, is false.

Thanks for the comments, Ed.

1. 'Caesar existed but no longer exists' is a Moorean truth.

2. If a predicate is true of x, then x exists.

3. Wholly past individuals do not exist. (Impilication of presentism).

This is an inconsistent triad: the first two propositions entail the negation of the third. And yet each prop. is extremely plausible.

You solve the problem by rejecting (3). But why wouldn't it be equally reasonable to deny (2)? Palle Yourgrau once argued that past individuals are nonexistent objects.

Or we could put God to work.

We affirm (1) and (2) but substitute for (3)

3* Wholly past individuals exist as accusatives of the divine intellect.

(This may be Rhoda's sol'n. I'd have to reread his paper to be sure.)

>>You solve the problem by rejecting (3).

Actually I don't. What I reject (as always) is that there is any such relation as 'satisfying', between a predicate and some object. For if there is such a relation, it must relate existing things. The inconsistent triad is therefore

1. 'Caesar existed but no longer exists' (Moorean truth)
2. The truth of any affirmative subject-predicate sentence requires the existence of a 'satisfaction' relation between the predicate and some object.
3. Satisfaction is a relation between existing objects.

For (from 1,2) the satisfaction relation exists between '—existed but no longer exists' and some object (namely Caesar). From (3), it follows that this object (Caesar) exists. But that contradicts (1), that Caesar no longer exists. So one of the three above must be false.

Is (3) true? Well, satisfaction goes with the idea of a domain of objects, and surely if the domain exists, the objects exist? For we can say that some object was, but is no longer in the domain. And if an object is no longer in the domain, then surely that is what changes the truth value of a sentence like 'Caesar is a man'.

>>Palle Yourgrau once argued that past individuals are nonexistent objects.

I don't see the difference between this and 'weak' presentism. I.e. past individuals 'are' (present tense) objects in some sense, but not existing ones.

So you reject (2) of your triad. But it seems to that a subject-predicate sentence is true iff the predicate is true of the subject (or rather the referent of the subject). Do you deny the following equivalence: 'Tom is tall' is true iff 'tall' is true of Tom?

Is there any difference between the locutions:

'Tall' is true of Tom
and
Tom satisfies 'tall'?

Why is it more reasonable to abandon (2) rather than (3)?

>> Do you deny the following equivalence: 'Tom is tall' is true iff 'tall' is true of Tom?

No, because you have pulled the verb (and hence the tense) out of the predicate. For the same reason I accept that 'Tom was tall' is true iff 'tall' was true of Tom. But there are strong grounds for rejecting

'Tom was tall' is true iff 'was tall' is satisfied by Tom.

The difference is that the predicate 'was tall' now includes the verb 'was', meaning that we have to express the relation in terms of a present tense verb phrase 'is satisfied'.

Regarding (3), I think I can avoid any difficulty by replacing 'Caesar existed' by 'there was such a thing as Caesar'. And we can replace (3) by

(3a) If a relation has relata, then it has such things as those relata.

But then it is true that there was such a thing as Caesar, but that there is no longer such a thing. Hence, if there is a satisfaction relation, we must agree that "there was such a thing as – " is satisfied by Caesar, and so must agree that the relation 'is satisfied by' has two relata, namely Caesar and the predicate "there was such a thing as – ". But if it currently has such relata (as it must, to make the proposition currently true), then it has such things as those relata. Yet we agreed there was no such thing as one of them, for there is no such thing as Caesar.

Your only way of escape is to deny that there are such things as the things related, while conceding that it relates these things. But that seems heroic.

In summary, the inconsistent triad is now

1a. There was such a thing as Caesar but now there is no longer such a thing.
2. The truth of any affirmative subject-predicate sentence requires a 'satisfaction' relation between two relata: the predicate and some object.
3a. If a relation has relata, then it has such things as those relata.

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