Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

The Univocity of ‘Exist(s)’: Obsessing Further

The general existential, 'Philosophers exist,' is reasonably construed as an instantiation claim:

G. The concept philosopher has one or more instances.

But a parallel construal seems to fail in the case of the singular existential, 'Socrates exists.'  For both of the following are objectionable:

S1.  The concept Socrates has one or more instances.

S2.  The concept Socrateity has one of more instances.

(S1) is objectionable because Socrates is not a concept (Begriff), but an object (Gegenstand), while (S2) is objectionable because there is no haecceity concept Socrateity (identity-with-Socrates), as I have already argued ad nauseam. (But see below for another go-round.)

On the other hand, 'exist(s)' across general and singular existentials would seem to be univocal in sense inasmuch as arguments like the following appear valid:

Philosophers exist
Socrates is a philosopher
————
Socrates exists.

Whatever the exact logical form of this argument, there does not seem to be an equivocation on 'exist(s)' or at least not one that would induce a quaternio terminorum.  (A valid syllogism must have exactly three terms; if there is an equivocation on one of them, then we have the quaternio terminorum, or four-term fallacy.)

Here then is the problem.  Is it possible to uphold a broadly Fregean understanding of 'exist(s)' while also maintaining the univocity of 'exist(s)' across general and singular existentials?  A broadly Fregean understanding is one that links existence with number.  The locus classicus is Frege, Foundations of Arithmetic, 65: 

In this respect existence is analogous to [hat Aehnlichkeit mit] number. Affirmation of existence is in fact nothing but denial of the number nought.  Because existence is a property of concepts the ontological argument for the existence of God breaks down.

To affirm the existence of philosophers, then, is to affirm that the number of philosophers is one or more, and to deny the existence of philosophers is to affirm that the number of philosophers is zero.  But then what are we saying of Socrates when we say that he exists?  That the number of Socrateses is one or more?  That can't be right:  'Socrates' is a proper name (Eigenname) not a concept-word (Begriffswort) like 'philosopher.'  It makes no sense to say that the number of Socrateses is one or more.  And when I say, with truth, that Socrates might never have existed, I am surely not saying that the number of Socrateses might always have been zero. 

London Ed doesn't see much of a problem here.  From his latest entry:

But why, from the fact that ‘Socrates’ is not a concept word, does it follow that there is no corresponding concept? [. . .] Why can’t ‘Socrates’ be semantically compound? So that it embeds a concept like person identical with Socrates, which with the definite article appended gives us ‘Socrates’?

From my point of view, Ed does not see the problem.  The problem is that if 'Socrates' expresses a concept, that concept can only be an haecceity concept, and there aren't any. It doesn't matter whether we call this concept 'Socrateity,' or 'person identical with Socrates.'

Ask yourself: Is the haecceity H of Socrates contingent or necessary?  Socrates is contingent.  And so one might naturally think that his haecceity must also be contingent.  For it is the ontological factor that makes him be this very individual and no other.  Haecceitas = thisness.  No Socrates, no haecceity of Socrates.  But then you can't say that the existence of Socrates is the being-instantiated of his haecceity, and the non-existence of Socrates is the non-instantiation of his haecceity.  For that presupposes that his haecceity exists whether or not he exists.  Which is absurd.

So haecceities must be necessary beings.  But now we have jumped from the frying pan into the fire.  Socrateity involves Socrates himself, that very individual, warts and all, mit Haut und Haar.  It is not a conjunction of multiply instantiable properties.  This is why identity — absolute numerical identity –is brought into the definition of H as, for example, 'person identical with Socrates.'  Hence an haecceity of a contingent being cannot be a necessary being.

The absurdity here is the attempt to make a necessarily existent abstract property out of a contingent concrete individual.  This is why I say that haecceity concepts/properties are metaphysical monstrosities.

It should also be pointed out that on a Fregean scheme, no concept is an object and no name is a predicate.  You cannot turn a name such as 'Socrates' into a predicate, which is what Ed is trying to do.

So the problem remains unsolved.  On the one hand, 'exist(s)' appears univocal across general and singular existentials.  And yet how can we make sense of this if we are not allowed to bring in haecceity properties?

Related articles
A Question About God and Existence
Is God Beyond All Being?
God and Socrates: Two Different Ways of Existing?
Arguing with Kripke over Existence
Language and Reality
Direct and Indirect Reference

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27 responses to “The Univocity of ‘Exist(s)’: Obsessing Further”

  1. Josh Avatar
    Josh

    Isn’t the argument valid only if we say “All philosophers exist”?

    Reply
  2. Ed from London Avatar
    Ed from London

    >>It should also be pointed out that on a Fregean scheme, no concept is an object and no name is a predicate.
    Correct.
    >>You cannot turn a name such as ‘Socrates’ into a predicate,
    Correct.
    >>which is what Ed is trying to do.
    Where did I claim this?

    Reply
  3. Ed from London Avatar
    Ed from London

    >>For that presupposes that his haecceity exists whether or not he exists. Which is absurd.
    I agree.

    Reply
  4. Bill Vallicella Avatar
    Bill Vallicella

    Ed in his main entry says: >>the following three concepts all have a number
    C1: {any man at all}
    C2: {any man besides Socrates}
    C3: {satisfies C1 but not C2}
    If the number corresponding to C1 is n, then the number of C2 is n-1. And the number of C3 is of course 1, and if C3 is satisfied, then Socrates exists. Simple.<< C3 is the concept *man identical to Socrates.* What you want to say is that, just as *philosopher* has one or more instances, so too does *man identical to Socrates.* In this way you think to secure univocity. What you are not understanding is that there is no concept C3. It is an haecceity and I have already argued that there aren't any.

    Reply
  5. Ed from London Avatar
    Ed from London

    >>What you are not understanding is that there is no concept C3. It is an haecceity and I have already argued that there aren’t any.<< And I have already agreed that there aren't any! There is no such thing as an haecceity. But there is such a thing as the concept C3. Could you also specify exactly where I have tried to turn a name such as 'Socrates' into a predicate?

    Reply
  6. Bill Vallicella Avatar
    Bill Vallicella

    Ed,
    Do you agree that C3 is the concept *man identical to Socrates*?
    If so, do you agree that Socrates himself is a constituent of this concept?

    Reply
  7. London Ed Avatar
    London Ed

    >>Do you agree that C3 is the concept *man identical to Socrates*?
    Yes.
    >>If so, do you agree that Socrates himself is a constituent of this concept?
    No.

    Reply
  8. Bill Vallicella Avatar
    Bill Vallicella

    OK. If Socrates himself is not a constituent of C3, then what subconcept represents him there? *wisest Greek phlosopher* perhaps?

    Reply
  9. John Bavinck Avatar
    John Bavinck

    >>Ask yourself: Is the haecceity H of Socrates contingent or necessary? Socrates is contingent. And so one might naturally think that his haecceity must also be contingent.
    This line of reasoning misses a crucial distinction. The thing that *is in fact* the haecceity of Socrates –namely, Socrateity, is itself a *necessary* being, but *being-the-haecceity-of-Socrates* is a *contingent*, rather than essential, property of Socrateity.
    >>For it is the ontological factor that makes him be this very individual and no other. Haecceitas = thisness. No Socrates, no haecceity of Socrates.
    This is correct, but it doesn’t entail that its possible that Socrateity doesn’t exist. What it entails is that Socrateity will lack the property of *being-the-haecceity-of-Socrates* in any world where Socrates doesn’t exist. Socrateity *itself* will exist in such worlds of course (as all properties do), it just won’t be a thisness of anything in any such world.
    Instead, it will be just an uninstantiated property; distinguishable from other uninstantiated properties by virtue of its own peculiar individuating modal properties; ie *possibly-being-the-thisness-of-Socrates* etc…

    Reply
  10. Bill Vallicella Avatar
    Bill Vallicella

    Very good comment, John.
    If there is the haecceity Socrateity, then it exists in every metaphysically possible world. But it is instantiated in only some such worlds. It follows that being-instantiated is an accidental, not an essential, property of Socrateity.
    We of course agree about this.
    We differ in that you assume that there are haecceity properties whereas I argue that there cannot be any. In effect, you beg the question against me.
    I grant that IF there are haecceities, and they are necessary beings, and Socrates is a contingent being, then there are worlds in which Socrateity is not the haecceity of Socrates, where ‘of’ is given a *de re* reading. But this requires that the content of Socrateity be specifiable without reference to the actual Socrates. It requires, in other words, that Socrates himself is not a constituent of Socrateity.
    This is what I deny. I deny that the content of Socrateity can be specified without bring in Socrates himself. Why? Because Socrateity is a nonqualitative thisness: it is not compounded of multiply instantiable properties. This is why ‘Socrateity’ is introudced using phrases like ‘identity-with-Socrates.’
    Identity here is absolute, numerical identity. Socrateity, then, is the supposed property of being Socrates himself. By my lights, this ‘property’ is a metaphysical monstrosity. One cannot somehow transform the very identity of a concrete contingent individual into an abstract necessary being that can exist whether or not the thing whose identity it is exists.
    So I say you beg the question against me. You assume what I have arged against. So, while your distinction makes sense relative you your assumption, it does nothing to show that there are haecceities.

    Reply
  11. Bill Vallicella Avatar
    Bill Vallicella

    A better model of Socrates’ haecceity is his singleton. Socrates is not the same as {Socrates}. The former is concrete, the latter is (arguably) abstract. A man is not a set. But they are both contingent as we should expect: no Socrates without Socrateity, and no Socrateity without Socrates.
    Now imagine someone who says that Socrates’ singleton exists in worlds in which Socrates does not exist. The objection would be: in those worlds there is nothing to give content to the singleton. In tose worlds it would be { }.
    A similar absurdity is perpetrated by those who accept haecceity properties. They are saying in effect: there is a property whose very content involves necessary reference to an individual, and this property can have the content it has even in worlds in which the individual does not exist.

    Reply
  12. Bill Vallicella Avatar
    Bill Vallicella

    Must London exist for my thought (thinking) of London to be of London?
    Depends on whether ‘of London’ is taken de re or de dicto.
    Must Socrates exist for Socrateity to be of Socrates?
    Depends on whether ‘of Socrates’ is read de re or de dicto.
    My answers: Obviously I can think of London whether or not it exists. If I am thinking of that great city over an interval of time during which it passes out of existence, does my intentional object change in any way?
    Socrateity cannot exist unless Socrates exists. For the whole content of the property is provided by the particular. The whole content of my thought about London is NOT provided by London itself.

    Reply
  13. Bill Vallicella Avatar
    Bill Vallicella

    Memo to Ed:
    Please carefully study Bavinck’s comment and my replies and then you will understand better what is at issue here.

    Reply
  14. Ed from London Avatar
    Ed from London

    >>Please carefully study Bavinck’s comment and my replies and then you will understand better what is at issue here.<< I read them, and I agree he is begging the question against you. It is impossible that if there is a thing as Socrateity, it could lack the property of *being-the-haecceity-of-Socrates* in any world where Socrates doesn't exist. Your objection is that it requires that the content of Socrateity be specifiable without reference to the actual Socrates. Have I understood the point at issue? But we are drifting a bit here. I have given a clear argument. Do you agree that *person living on BV’s street* is a concept, and that it can have a number? Do you agree that *person living on BV’s street apart from BV and his wife* is a concept, and has a number. If not, why not? Clearly it has a number, namely two less than the first concept. If you are the only people living on your street, then it has the number zero. So to say that no one apart from you and your wife live on the street, is to say that no other such people exist. So why isn’t the second concept also a concept? Are you just assuming it is not, or is the assumption about number a starting point, a premiss? If the latter, then it is a concept. And if both of these are concepts, it follows that any concept that is the union or disjunction of those concepts is also a concept. Or are you denying that?
    Note that this all began with the connection between number and existence, and univocity. You began with the assumption that wherever we can say ‘the number of Cs is n’, then ‘Cs exist’ is univocal, for it means that n > 0.
    Another thought. If you really are denying that *person living on BV’s street apart from BV and his wife* is a concept, then why don’t you deny *person living on BV’s street* is a concept, given that it embeds ‘BV’s street’ which is a singular concept. If you deny that, then practically any descriptive term whatever has to be ruled out, given there will be a singular element embedded somewhere. What about *person living on a street in Phoenix apart from BV’s street*. What about *person not living in Phoenix*? You will end up with ‘first dog born at sea’ or something like that. Or can we even allow that? Are we talking about seas on Earth, or on different planets? If the former, then we have an embedded singular term, which you want to rule out. Ha.
    >>OK. If Socrates himself is not a constituent of C3, then what subconcept represents him there? *wisest Greek philosopher* perhaps?<< No, the singular concept *person identical with Socrates*. >> Must London exist for my thought (thinking) of London to be of London?
    No. Neither did Moses have to exist in order for me to think of Moses. Likewise for Frodo Baggins.

    Reply
  15. Ed from London Avatar
    Ed from London

    I agree with this:

    IF there are haecceities, and they are necessary beings, and Socrates is a contingent being, then there are worlds in which Socrateity is not the haecceity of Socrates, where ‘of’ is given a *de re* reading. But this requires that the content of Socrateity be specifiable without reference to the actual Socrates. It requires, in other words, that Socrates himself is not a constituent of Socrateity.

    And with this:

    I deny that the content of Socrateity can be specified without bring in Socrates himself. Why? Because Socrateity is a nonqualitative thisness: it is not compounded of multiply instantiable properties.

    Doesn’t it make you pause that I am agreeing with almost everything you are saying?
    I will say it again: for the reasons you suggest, there are no such things as haecceities.

    Reply
  16. Bill Vallicella Avatar
    Bill Vallicella

    Ed,
    It is not enough that there be a concept involving Socrates, that concept has to be capable of existing whether or not he exists.
    Let me try to explain the problem as directly as I can.
    Assume that for cats to exist is for the property *cat* to be instantiated. My question is simply this: can we extend this analysis to singulars such as Max the cat? I say No. I say this because there is no property P whose instantiation is the existence of Max.
    The two main requirements on P are as follows: P exists necessarily; P if instantiated is instantiated by Max, by Max alone, and not possibly by anything distinct from Max.
    No property satisfies these two requirements.
    Now the univocity question is this: Is ‘exist(s)’ univocal in ‘Cats exist’ and ‘Max exists’? It would be iff the first is replaceable by ‘*Cat* is instantiated’ and the second by ‘*___*’ is instantiated where the gap is filled by the name of an haecceity. But there are no haecceities. So the gap can’t be filled. So univocity fails.
    Alles klar?

    Reply
  17. David Brightly Avatar
    David Brightly

    I think we are focusing too narrowly on ‘exists’. Something very similar arises for general predicates:

    something runs ↔ *runs* is instantiated,
    Max runs → *runs* is instantiated.

    But

    *runs* is instantiated ⇸ Max runs

    and I think you would say a fortiori that there is no (necessary?) property P such that

    P is instantiated → Max runs

    But from this we would not conclude that ‘runs’ is not univocal. Rather we would put this asymmetry down to the singular/general distinction.

    Reply
  18. Bill Vallicella Avatar
    Bill Vallicella

    David,
    Are you saying that just as there is univocity across ‘Cats run’ and ‘Max runs,’ there is likewise univocity across ‘Cats exist’ and ‘Max exists’?
    Well, there is univocity in the running case.
    Cats run: For any x, if x is a cat, then x runs.
    Applying Universal Instantiation: If Max is a cat, then Max runs.
    ‘x runs’ is a univocal first-level predicate in both the general and the singular sentences. No problem at all.
    But existence is very different from running!

    Reply
  19. David Brightly Avatar
    David Brightly

    >> Are you saying that just as there is univocity across ‘Cats run’ and ‘Max runs,’ there is likewise univocity across ‘Cats exist’ and ‘Max exists’?
    No. I’m saying that the general existential ‘something runs’ (↔ there is something that runs) is equivalent to ‘the property *runs* is instantiated’, but that the singular existential ‘Max runs’, though sufficient for ‘the property *runs* is instantiated’, is not necessary.

    Reply
  20. Ed from London Avatar
    Ed from London

    >>Alles klar?<< Slightly. Your shift from ‘concept’ to ‘property’ is confusing, but I think this is explained by your last sentence where you say ‘the gap is filled by the name of an haecceity’. I think your argument is that if ‘*C*’ is the name of a concept (e.g. ‘*man*’, ‘*person who resides outside Arizona*’), then ‘C’ names a property. Thus ‘man’ names a property (the property of being a man), and it names that property even in a world where no men exist.
    But ‘person who resides outside Arizona’ cannot be the name of a property, because in a world where Arizona does not exist, the property of residing outside Arizona is not specifiable without reference to the actual Arizona.
    Have I understood the argument right?

    Reply
  21. Bill Vallicella Avatar
    Bill Vallicella

    >>Your shift from ‘concept’ to ‘property’ is confusing,<< Why should it be confusing? We are on Fregean ground. Begriff = concept = objective concept. Here in the Anglosphere we generally prefer 'property' since 'concept' has a subjective ring to it. Same with der Gedanke, literally, 'thought.' 'Proposition' is the preferred translation in the Anglosphere. Here is my argument in clearer form: Now the univocity question is this: Is 'exist(s)' univocal in 'Cats exist' and 'Max exists'? It would be iff the first is replaceable by '*Cat* is instantiated' and the second by '*Maxity* is instantiated' where *Maxity* is the haecceity property, identity-with-Max. But there are no haecceities. So the second replacement cannot be made, and univocity fails. It is SO obvious. If 'exist(s)' is a 2nd level pred in both sentences, as univocity requires, then you need haecceities, but you agree that there ain't any.

    Reply
  22. Ed from London Avatar
    Ed from London

    >>We are on Fregean ground.
    Ah I didn’t realise you meant that. Yes, Frege holds that an expression like ‘cat’ is a proper name for an objective Platonic Concept that exists in every possible world, if it exists at all. Isn’t that assumption (namely that a concept expression is the proper name of something) fundamental to your argument? Why should it be true?
    And you still haven’t answered my killer question, whether e.g. *person who resides in the Phoenix Metropolitan Area* is a concept or not. I can see why you are reluctant to answer it. It clearly has a number (4,192,887 according to Wikipedia), as does *person who resides in the city of Phoenix* (1,445,632), and of course we can combine these concepts *person who resides in the Phoenix Metropolitan Area but outside the city of Phoenix* (4,192,887 minus 1,445,632). But ‘Phoenix’ is a proper name, and according to your argument any concept-expression that includes a proper name cannot signify a concept. For if Phoenix does not exist, the property of residing in Phoenix is not specifiable without reference to the actual Phoenix.

    Reply
  23. Bill Vallicella Avatar
    Bill Vallicella

    Ed,
    I can grant you that those are all concepts and that numbers are assignable to them.
    My point is not that “any concept-expression that includes a proper name [of a contingent being] cannot signify a concept” but that such an expression cannot signify a concept that can be a necessary being.
    Socrateity needs to exist in every possible world if we are to be able to say that Socrates’ existence/nonexistence/possible nonexistence = Socrateity’s being insantiated/being noninstantiatied/being instantiated in the actual world but not in every world.
    Ist es jetzt nicht sonnenklar?

    Reply
  24. Ed from London Avatar
    Ed from London

    >>My point is not that “any concept-expression that includes a proper name [of a contingent being] cannot signify a concept” but that such an expression cannot signify a concept that can be a necessary being.<< So *person who resides in the Phoenix Metropolitan Area* is a concept, but is not a necessary being? Hence the following two are concepts: C1: *man* C2: *man who is not Socrates* And on the principle that we can combine any two concepts to create a third, it follows that this is a concept:
    C3: *person satisfying C1 but not C2*
    >> Ist es jetzt nicht sonnenklar?
    I don’t know the German for ‘clear as mud’.

    Reply
  25. Ed from London Avatar
    Ed from London

    ‘klar wie Schlamm’?

    Reply
  26. Bill Vallicella Avatar
    Bill Vallicella

    What we have here is a failure to communicate.
    Have you studied plural predication? That is relevant to this topic as well.

    Reply
  27. London Ed Avatar
    London Ed

    >>What we have here is a failure to communicate.
    OK. What I failing to understand is this:
    >>My point is not that “any concept-expression that includes a proper name [of a contingent being] cannot signify a concept” but that such an expression cannot signify a concept that can be a necessary being.<< I understand your first point. You are not claiming that "any concept-expression that includes a proper name [of a contingent being] cannot signify a concept". This suggests (though doesn't imply) that you agree that some concept-expressions (just some, or all?) that include a proper name do or can signify concepts. But then you add "such an expression cannot signify a concept that can be a necessary being". Do you mean that there are some concepts that are not necessary beings? This confuses me because I thought your whole argument depended on all concepts being necessary beings. We are in a strange morass. I don't think plural predication has anything to do with this.

    Reply

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