Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

Caesar Is No More: The Aporetics of Reference to the Past

Here is London Ed's most recent version of his argument in his own words except for one word I added in brackets:

1. There is no such thing as Caesar any more.

2. The predicate 'there is no such thing as — any more' is satisfied by
Caesar.

3. If a relation obtains [between] x and y, then there is such a thing as y.

4. (From 2) the relation 'is satisfied by' obtains between the predicate '–
is not a thing any more' and Caesar.

5. (3, 4) There is such a thing as Caesar.

6. (1, 5) contradiction.

Premiss (1) is Moorean. There is no longer any such thing or person as Caesar. (Or if you dispute that for reason of immortality of Caesar, choose some mortal or perishable object). (2) is a theoretical. (3) is a logical truth, and the rest is also logic. You must choose between (1) and (2), i.e. choose between
a Moorean truth, and a dubious theoretical assumption.

(1) is indeed 'Moorean,' i.e., beyond the reach of reasonable controversy.  (2) is indeed theoretical inasmuch as it involves an optional albeit plausible parsing in the Fregean manner of the Moorean sentence.

Ed tells us that (3) is a logical truth.  I deny that it is.  A logical truth is a proposition true in virtue of its logical form alone.  'Every cat is a cat' is an example of a logical truth as are 'No cat is a non-cat' and 'Either Max is a cat or Max is not a cat.'  One can test for logical truth by negating the proposition to be tested.  If the result is a logical contradiction, then the proposition is a logical truth.  For example, if we negate 'Every cat is a cat' we get 'Some cat is not a cat.' The latter sentence is a logical contradiction, so the former sentence is a logical truth. The latter is a logical contradiction because its logical form — Some F is not an F — has only false substitution-instances.

Negating (3) yields 'A relation obtains between x and y, but there is no such thing as y.'  But this is not a logical contradiction in the strict and narrow sense defined above.  Suppose I am thinking about the Boston Common which, unbeknownst to me, ceases to exist while I am thinking about it.  I stand in the 'thinking about' relation to the Common during the whole period of my thinking despite the fact that at the end of the period there is no such thing as the Boston Common.  There are philosophers who hold that the intentional relation is a genuine relation and not merely relation-like as Brentano thought, and that in some cases it relates an existing thinker to a nonexisting object. 

Now there are good reasons to reject this view as false, but surely it is not false as a matter of formal logic.  If it is false, it is false as a matter of metaphysics.  A philosopher such as Reinhardt Grossmann who holds that the intentional relation is a genuine relation that sometimes relates an existent thinker to a nonexistent object is not contradicting himself. 

Since (3) is not a logical truth, one way to solve Ed's problem is by rejecting (3) and holding that there are genuine relations that relate the existent to the nonexistent.  One could hold that the relation of satisfaction is such a genuine relation: it relates the existing predicate to the nonexistent emperor: Caesar satisfies the predicate despite his nonexistence.

Note that I am not advocating this solution to the puzzle; I am dismissing Ed's dismissal of this putative solution.  I am rejecting Ed's claim that one is forced to choose between (1) and (2).  One can avoid the contradiction by denying (3), and one is not barred from doing so by logic alone.

Ed claims that (1) and (5) are logical contradictories.  But they are not.  Just look carefully at both propositions and you will see.  Ed thinks they are contradictories because he assumes that 'There is no such thing as y any more' is logically equivalent to 'There is no such thing as y.'  But to make that assumption is to to assume the substantive metaphysical thesis known in the trade as

Presentism:  Necessarily, only temporally present concrete objects exist.

Given Presentism, (1) and (5) are indeed contradictory.  This is why I said earlier  that Ed's argument cannot get off the ground without Presentism.  For suppose we reject Presentism in favor of the plausible view that both past and present concreta exist, i.e., are within the range of our unrestricted quantifiers.  Then Ed's puzzle dissolves.  For then there is such a thing as Caesar, it is just that he is past.  The relation of satisfaction connects a present item with a past item both of which exist. Or, since Ed is allergic to 'exist': both of which are such that there such things as them.

So a second way to solves Ed's puzzle is by rejecting the Presentism that he presupposes.

So I count at least three ways of solving Ed's puzzle: reject (2), reject (3), reject the tacit assumption of Presentism which is needed for (1) and (5) to be contradictory.

My inclination is to say that the puzzle is genuine, but insoluble. And this because the putative solutions sire puzzles as bad as the one we started with.  Of course, I haven't proven this.  But this is what my metaphilosophy tells me must be the case.

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Bill Vallicella

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20 responses to “Caesar Is No More: The Aporetics of Reference to the Past”

  1. Peter Lupu Avatar
    Peter Lupu

    Bill,
    A wonderful and well thought out outline of the issues raised by Ed’s example.
    One comment on your concluding sentence: “…the putative solutions sire puzzles as bad as the one we started with.”
    I do not think one can take you to mean this literally. After all, according to your display of the puzzle, it leads to a logical contradiction (i.e., 6). But you do not mean to claim that each of the three solutions you outline are “as bad” in the sense that they also lead to a strict logical contradiction. Perhaps each of them features certain weaknesses; but whatever these weaknesses may be, as long as they do not lead to a formal contradiction or something equivalent, they cannot be “as bad” as the puzzle itself.

    Reply
  2. Bill Vallicella Avatar
    Bill Vallicella

    That’s a good criticism, Peter. The original puzzle is as bad as it gets, leading as it does to a formal contradiction. Unless I can show that each proposed solution also leads to a contradiction, then those solutions cannot be as bad as the original puzzle. And that might be hard to show.
    Point taken!

    Reply
  3. edward Avatar
    edward

    1. Just to note I did not say that ‘There is no such thing as y any more’ is logically equivalent to ‘There is no such thing as y.’ Rather, it implies it. The ‘any more’ part tells us that there was once such a thing as y. (And distinguishes this from the case where something never existed, such as a chimera). Therefore ‘There is no such thing as y any more’ is equivalent to ‘there is no such thing as y and there was such a thing as y’. This (logically) implies ‘there is no such thing as y’.
    Since this is merely a quarrel about definitions, let’s change (1) to
    (1A) There is no such thing as y and there was such a thing as y.
    (2A) The predicate ‘there is no such thing as – and there was such a thing as –‘ is satisfied by Caesar.
    (3A) If a relation obtains [between] x and y, then there is such a thing as y.
    (4A) (From 2A) the relation ‘is satisfied by’ obtains between the predicate ‘there is no such thing as – and there was such a thing as –‘ and Caesar.
    (5A) (3A, 4A) There is such a thing as Caesar.
    (6A) (1A, 5A) Contradiction.
    2. You deny that 3 (or 3A) is a logical truth. Therefore you deny that “R(a,b) therefore Ex R(a,x)” is a truth of logic? You are saying that “There is no such person such that John loves that person” is consistent with “John loves Mary”??
    >>’Some cat is not a cat’ … a logical contradiction because its logical form — Some F is not an F — has only false substitution-instances.
    And I say “There is no such F such that John loves that F and John loves some F” has only false substitution-instances.
    >>Suppose I am thinking about the Boston Common which, unbeknownst to me, ceases to exist while I am thinking about it. I stand in the ‘thinking about’ relation to the Common during the whole period of my thinking despite the fact that at the end of the period there is no such thing as the Boston Common. There are philosophers who hold that the intentional relation is a genuine relation and not merely relation-like as Brentano thought, and that in some cases it relates an existing thinker to a nonexisting object.
    << In that case, 'Predicate P is satisfied by N' would have to be an intentional relation. Is that where the argument is going? (Might be an interesting direction too).

    Reply
  4. Richard E. Hennessey Avatar
    Richard E. Hennessey

    Might it not be that “There is no such thing as Caesar any more” would be better regarded as a manner of speaking, one asserting something like “The noun “Caesar” no longer has a reference”?

    Reply
  5. Bill Vallicella Avatar
    Bill Vallicella

    Richard,
    Thanks for your comment. Your suggestion amounts to rejecting (2). (2) is a parsing of (1) in which the predicate is first-level. Your metalinguistic parsing involves a second-level predicate ‘____ no longer has reference.’
    On your approach, Caesar’s no longer existing is his name’s no longer referring. But then it seems you must say that Obama’s still existing is his name’s still referring. But surely the metaphysical ground of Obam’s exisitng cannot be his name’s referring.
    London Ed won’t understand what I just said, but I expect him to raise a different objection: (1) is about Caesar, a nonlinguistic thing, it is not about a name.
    Right, Ed?

    Reply
  6. David Brightly Avatar
    David Brightly

    Ed,
    You are missing what I took to be your own point made in the Scollay Square thread, and on which we seemed in agreement:
    >> 2. You deny that 3 (or 3A) is a logical truth. Therefore you deny that “R(a,b) therefore Ex R(a,x)” is a truth of logic? You are saying that “There is no such person such that John loves that person” is consistent with “John loves Mary”??
    Suppose R denotes ‘_held hands with_’. John held hands with Mary does not imply that there is someone John held hands with. Mary may have died. It does imply that for someone, John held hands with that someone.
    It’s a subtle difference in interpretation of ‘∃’, which also explains the presentism/anti-presentism controversy.

    Reply
  7. Peter Lupu Avatar
    Peter Lupu

    If I had to choose between the alternatives Bill outlined, Presentism is the one that must go for a variety of reasons, some of which were discussed in several posts in the past. My reason is simple: while Presentism has cogent alternatives, the same cannot be said about (2) and (3); at least I do not see viable alternatives for them. However, I do not know whether Bill wants to embark on a discussion about the relative merit of alternatives to each of his candidates for rejection.

    Reply
  8. Jan Avatar
    Jan

    “There is no such thing as Caesar any more” is not equivalent to “The noun “Caesar” no longer has a reference” because the latter is false; there are multiple dogs called Caesar and a restaurant near me to boot. Noun having no referent is a fact about language. It can change as the language evolves — from referring, to not referring, to referring again. A thing cannot however have two beginnings of existence which it would were existence just reference.

    Reply
  9. Bill Vallicella Avatar
    Bill Vallicella

    Jan,
    You are missing the point that in discussions like this proper names such as ‘Caesar’ are being used with the usual assumptions supplied by context. Thus we are talking about Julius Caesar the Roman emperor who was stabbed by Brutus, etc. ‘Max Black’ in my house refers to one of my cats; at a philosophy conference it refers to a philosopher of note.

    Reply
  10. Bill Vallicella Avatar
    Bill Vallicella

    Ed writes,
    >>Therefore ‘There is no such thing as y any more’ is equivalent to ‘there is no such thing as y and there was such a thing as y’. This (logically) implies ‘there is no such thing as y’.<< This is right, but only if each occurrence of 'is' is read as present-tensed. But it is a non sequitur if the last occurrence of 'is' is untensed. Example. 'There is no such philosopher as Quine any more' is logically equivalent to 'There was such a philosopher as Quine & there is now no such philosopher as Quine. But it does not follow that Quine does not exist, i.e., that there is (untensed) no such philosopher as Quine. That would follow only if Presentism is true and only temporally present concreta exist.

    Reply
  11. Bill Vallicella Avatar
    Bill Vallicella

    Ed sez: >>You deny that 3 (or 3A) is a logical truth. Therefore you deny that “R(a,b) therefore Ex R(a,x)” is a truth of logic? You are saying that “There is no such person such that John loves that person” is consistent with “John loves Mary”??<< We can agree that the following is a logical truth: If a stands in R to b, then something is such that a stands in R to it. If the Father begets the Son, then something is such that the Father begets it. If Pegasus captures Bellerophon, then something is such that Pegasus captures it. The last two sentences are substitution-instances of the logical formula. But you won't say that Bellerophon exists, and Peter Lupu won't say that the Son exists. My point is that it is not a logical truth that if a stands in R to b, then b exists. Why can't past objects be nonexistent objects?

    Reply
  12. edward ockham Avatar
    edward ockham

    (David) >>It’s a subtle difference in interpretation of ‘E’, which also explains the presentism/anti-presentism controversy.
    Yes, but can we return to that interesting point later? It is Bill’s position I am trying to understand.
    (Bill) >>We can agree that the following is a logical truth: If a stands in R to b, then something is such that a stands in R to it.
    By something, you mean something that is not necessarily b itself? But then why would that be a logical truth? Could you clarify that one?
    >>My point is that it is not a logical truth that if a stands in R to b, then b exists.
    Sure, but I wasn’t claiming that, since it would involve the (different) question of what ‘exists’ means.

    Reply
  13. edward ockham Avatar
    edward ockham

    >>Example. ‘There is no such philosopher as Quine any more’ is logically equivalent to ‘There was such a philosopher as Quine & there is now no such philosopher as Quine. But it does not follow that Quine does not exist, i.e., that there is (untensed) no such philosopher as Quine. That would follow only if Presentism is true and only temporally present concreta exist.
    << I always assumed the tensed reading for 'is no such thing as ...'. And, as above, I have no view on the meaning of 'exists', nor on the meaning of 'presentism'.

    Reply
  14. David Brightly Avatar
    David Brightly

    Bill,
    If I have you right you are saying (comment at 04:34pm) that the following can all be true (and presumably are all true):

    1. there is now no such philosopher as Quine.
    2. there is (untensed) such a philosopher as Quine.
    3. Quine exists (untensed).

    I would like to know a bit more about the notion of untensed verbs. One question I have is Does the notion of untensedness apply to ‘ordinary’ verbs? For example, can the following be true together

    1. Tom no longer smiles.
    2. Tom does not smile now.
    3. Tom smiles (untensed).

    I have an inkling of what you might mean by ‘Quine exists (untensed)’ but not of what ‘Tom smiles (untensed)’ might mean.

    Reply
  15. Bill Vallicella Avatar
    Bill Vallicella

    Good questions, David.
    Just to rag on my friend Peter, I’ll change the example to ‘Peter smokes.’
    That does not mean that he smokes at every time, nor does it mean that he is smoking now. It means that he has the smoking habit and that there are times at which he smokes. But isn’t the ‘there are’ in ‘There are times at which he smokes’ untensed? Given that Peter is not smoking now, those time are not present but exist nonetheless.
    2 + 2 is 4. The ‘is’ in this sentence is not present-tensed. It is untensed or tenseless. Same with ‘Whales are mammals.’
    Your trio is consistent if ‘Tom smiles (untensed)’ is analyzed as ‘There are times in the actual world at which Tom smiles.’ That will be true if he smiled in the past. It is consistent with the first two propositions.

    Reply
  16. David Brightly Avatar
    David Brightly

    Bill,
    ‘2 + 2 is 4’ and ‘Whales are mammals’ express unchanging relationships so I’m happy to say these are untensed.
    But let me go back to the more vivid smoking example (apologies, Peter). We Brits are supposedly known for our irony. For us, to say

    1. Peter has given up the weed (ie, he no longer smokes)
    2. There are times when Peter smokes,

    is a way of saying that Peter hasn’t really given up smoking. The irony depends on (1) and (2) being in contradiction. In contrast,

    2*. There were times when Peter smoked

    is utterly bland, as (1) implies (2*). On the other hand (2*) does not preclude Peter’s smoking now. So to convey that Peter has smoked in the past we can use (2*) and hence we aren’t reliant on the untensed (2) to talk about the past. In which case we can eliminate potential confusion by agreeing not to use (2) to talk about a particular’s past.
    Or can you find an example where we must use an untensed verb?

    Reply
  17. Bill Vallicella Avatar
    Bill Vallicella

    David,
    I am not using the untensed (2) to talk about the past, but to state that, among the times of the actual world, some of them are times at which Peter smokes. Now if there is a time at which Peter smokes, but he has given up smolking, then that times must be in the past.
    It seems to me that I have shown that your trio of propositions is consistent.
    The issue is not whether we must use untensed verbs to speak of concreta.

    Reply
  18. Peter Lupu Avatar
    Peter Lupu

    Bill,
    Thanks for advertising my weaknesses.
    Could someone present a crisp statement of the disagreement between Bill and Ed. I simply do not see what they seem to be disagreeing about, or what are they primarily disagreeing about. I think Bill presented a puzzle with clear premises and also three clear alternatives to resolve the puzzle. Now, Ed seems to object to some specific formulation of one of the premises (premise 1 I think), but I simply do not see that there is any fundamental issue that depends on the difference in formulation.
    As for premise (3), I think that perhaps we should be clearer about the term ‘relation’ in premise 3. Is the relation between concrete things, abstract necessary things, or for instance would a Cambridge Property such as ‘thinking about’ count? I think that ‘any more’ in premise (1) seems to suggest that the term ‘relation’ is intended by Bill to apply to contingent objects (since they may no longer exist). But I am not sure.

    Reply
  19. edward Avatar
    edward

    Peter: >>I simply do not see that there is any fundamental issue that depends on the difference in formulation.
    << My formulation deliberately avoids the word 'exist'. My reason is to preempt any appeal to some distinction between a wide and narrow sense of existence, the wide or Quinean or quantifier sense being given by the word 'something' or the existential quantifier, the narrow sense being (typically) given by the verb 'exist'. 'Thin' theories of existence of course deny any such distinction, and they collapse the 'existential' use into the quantifier one. I am not questioning the distinction here, simply trying to avoid any appeal to it.
    The distinction could be used to deny (3), namely the premiss that a relation must relate existing things. It could be argued that a relation could relate two things, with one or both of them being non-existing things. That is the strategy Bill seems inclinded to.
    My strategy is not to question the distinction, but rather to frame the problem in a way that it is existence in the wide, quantifier sense that is denied. Thus I say ‘There is no longer such a thing as X’ rather than ‘X no longer exists’. The latter formulation tempts us to think that there is still such a thing as X (i.e. it exists in the wide, quantifier sense) but that it has ceased to exist in the narrow sense. But if a thing no longer exists in the wide sense, i.e. there is no longer such a thing as ‘it’, then I claim that nothing can now be related to it. For a relation Rab must related two things, even if we accept the possibility of a non-existing thing. But if there are not even the two things any more (perhaps only one, perhaps none), how can the relation exist? If there is only one thing in the whole universe, how can there be a relation involving more than one thing? There can’t, and that is a logical truth.
    As to the deeper argument, it is premiss (2) that I am attacking, as undermining any support for a non-redundancy theory of truth. There are certain truths that we cannot explain by means of a ‘satisfaction’ relation between predicates and extra-mental objects.
    I hope that clears up any misunderstanding. In summary, my reason for my formulation is to avoid any appeal to a distinction between wide and narrow senses of existence. And the nature of the disagreement is about whether (2) is the weak premiss or not.

    Reply
  20. Alan Rhoda Avatar
    Alan Rhoda

    To add a little to what’s already been said, I’ll note that (4) doesn’t follow from (2) alone, but only from (2) and the additional premise:
    (7) Predicate satisfaction is a relation.
    (7) seems plausible, but is it true for *all* predicates, even ones like “lacks existence”? Consider
    (8) “There is no such thing as the largest prime number.”
    (8) is demonstrably true, but a parallel argument could be run replacing Caesar with the definite description “the largest prime”. The fundamental problem raised by Ed’s argument therefore has nothing to do with presentism or past reference per se, but with how to affirm a thing’s non-existence without thereby presupposing it’s existence.
    I suspect the flaw in the argument is either (7) or (2). Kant famously denied that existence is a real predicate. Whether that’s true or not, it seems even more plausible to deny that non-existence is a real predicate. “Caesar doesn’t exist” doesn’t assert “There exists an individual, Caesar, who stands in the satisfaction relation to the predicate ‘lacks existence’”, but simply “It is not the case that the individual, Caesar, exists.”

    Reply

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