Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

On an Argument for the Univocity of ‘Exist(s)’

Here is an argument adapted from Peter van Inwagen for the univocity of 'exist(s)' across general and singular existentials. 

a. Number-words are univocal.

b. 'Exist(s)' is a number-word.

Therefore

c. 'Exist(s)' is univocal.

(a) is plainly true.  The words 'six' and 'forty-nine' have the same sense regardless of what we are counting.  As van Inwagen puts it, "If you have written thirteen epics and I own thirteen cats, the number of your epics is the number of my cats." 

(b) captures the Fregean claim that ". . . existence is analogous to number.  Affirmation of existence is in fact nothing but denial of the number nought." (Foundations of Arithmetic, p. 65)

How so?  Well, to say that unicorns do not exist is equivalent to saying that the number of unicorns is zero, and to say that horses exist is equivalent to saying that the number of horses is one or more.  Surely that is true for both affirmative and negative general existentials.  Whether it is true for singular existentials is a further question.

Van Inwagen maintains "The univocacy [univocity] of number and the the intimate connection between number and existence should convince us that existence is univocal." 

I am not convinced.

Consider my cat Max Black.  I exclaim, 'Max exists!'  My exclamation expresses a truth.  Contrast the singular 'Max exists' with the general  'Cats exist.'   I agree with van Inwagen that the general  'Cats exist' is equivalent to 'The number of cats is one or more.'  But it is perfectly plain that the singular  'Max exists' is not equivalent to  'The number of Max is one or more.'  For the right-hand-side of the equivalence is nonsense, hence necessarily neither true nor false.

This question makes sense: 'How many cats are there in BV's house?'  But this question makes no sense: 'How many Max are there in BV's house?'  Why not?  Well, 'Max' is a proper name (Eigenname in Frege's terminology) not a concept-word (Begriffswort in Frege's terminology).  Of course, I could sensibly ask how many Maxes there are hereabouts, but then 'Max' is not being used as a proper name, but as a stand-in for 'person/cat named "Max" .'  The latter phrase is obviously not a proper name.

And so I deny the univocity of 'exist(s)' across general and singular existentials.

Andrew Bailey lodges the following objection to what I maintain:

You note that "‘Max exists’ is not equivalent to ‘The number of Max is one or more’", and that seems right.

But why think "The number of Max is one or more" is the way to say of Max that he exists using number-words? Why not, instead, "At least one thing is Max"? My suggestion, note, would align closely with the way one would ordinarily translate "Max exists" into the predicate logic: — 'Ex(x=Max)' — a statement of logic one might render in English as "there is at least one thing that is identical to Max".

Dr. Bailey is of course right that 'Max exists' can be translated into standard first-order predicate logic in the way he indicates and that this is equivalent in 'canonical English' to 'There is at least one thing that is identical to Max.'  Bailey's rebuttal seems to be the following:  Just as we can express 'Cats exist' as 'At least one thing is a cat,' we can express 'Max exists' as 'At least one thing is Max.'

But this response is unavailing.  Note that the 'is' in 'is a cat' is not the 'is' of identity, but the 'is' of predication, while the 'is' in 'is Max' is the 'is of identity.  So if Bailey tries to secure the univocity of 'exist(s)' in this way, he does so by exploiting an equivocation on 'is.'

Another possible rebuttal would be by invoking haecceities.  One might argue that there is no equivocation on 'is' because both of the following feature the 'is' of predication:

At least one thing is a cat

At least one thing is Max-identical.

On the second approach one secures the univocity of  'exist(s)' but at the expense of those metaphysical monstrosities known as haecceity properties.  The haecceity H of x is a property x cannot fail to instantiate, alone instantiates in the actual world, and that nothing distinct from x instantiates in any possible world.  If Max has such such a property — call it Maxity — then this property captures Max's haecceitas or thisness, where 'thisness' is to be understood as irreducible and nonqualitative.  If there is such a property, then it is the property of identity-with-Max or Max-identity. 

So if you want to maintain the univocity of 'exist(s)' across general and singular existentials, you must either conflate the 'is' of identity' with the 'is' of predication, or embrace haecceity properties.

Gentlemen, pick your poison!

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Bill Vallicella

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42 responses to “On an Argument for the Univocity of ‘Exist(s)’”

  1. London Ed Avatar
    London Ed

    >>Dr. Bailey is of course right that ‘Max exists’ can be translated into standard first-order predicate logic in the way he indicates
    << I corresponded with Dr Bailey about this and he now concedes that perhaps 'Max exists' can't be translated in this way. For suppose Max is vaporised and ceases to exist. Then 'Max does not exist' is true in English, but its translation into predicate logic ('~Ex x = Max') is false. Since he agrees that translation must preserve truth value, it follows that it cannot be a translation. Or at least I think he agreed that, perhaps he would like to comment.

    Reply
  2. Bill Vallicella Avatar
    Bill Vallicella

    >>Then ‘Max does not exist’ is true in English, but its translation into predicate logic (‘~Ex x = Max’) is false.<< Why? Because 'Max' has meaning only if Max exists? There is also this modal argument that I have given before, I think: Max is a contingent being. So it is possible that he not exist. If to exist = to be identical to something, then possibly not to exist is possibly to be diverse from everything. But then the possible nonexistence of Max = Max's possible self-diversity -- which is absurd. Note that possible diversity from everything entails possible diversity from Max. I seem to recall Bailey had some clever response to this.

    Reply
  3. Bill Vallicella Avatar
    Bill Vallicella

    But back to the main point, Ed. Have a convinced you that univocity fails?

    Reply
  4. Andrew Avatar
    Andrew

    London Ed,
    For what it’s worth, I don’t think that statements within a formal language like that of PL are true or false at all. They are, instead, uninterpreted syntactic items, and so they need not and may not ever express propositions at all (the primary bearers of truth and falsity). Notice that statements of English obey the usual disquotation rules, but statements in the language of PL do not. ‘Max Black is a cat’, for example, expresses the proposition that Max Black is a cat; but ‘ExFx’ does not expresses the proposition that ExFx, perhaps because there is no such proposition.
    The closest thing to alethic status that statements in the language of PL enjoy is truth-on-a-model. But truth-on-a-model is not truth, and truth-on-no-models is not falsity. So I do not infer from ‘S is true on no models’ that S is false or that S expresses a falsehood. Accordingly: where ‘a’ is a proper name, ‘~Ex(x=a)’ is true on no models of PL, but it doesn’t follow that ‘~Ex(x=a)’ is false or that it expresses a falsehood. Similarly, that ‘~Ex(x=Max)’ is true on no models of PL, but this does not imply that ‘~Ex(x=a)’ is false or that it expresses a falsehood.
    The following is a mouthful, but here goes. That one cannot say of Frodo, using ‘Frodo’ as a proper name, that he does not exist, in the language of PL, in a way that expresses something that could be true on a model of PL, is no reason to think that Frodo does, after all, exist, or that the canonical translation of ‘Frodo does not exist’ into ‘~Ex(x = Frodo)’ is somehow an inadequate translation or not a translation after all. It is reason, instead, to think that the resources of PL are of limited use when doing this sort of metaphysics. Perhaps a free logic (where constants need not be mapped to items in a domain) is required for *that* task.
    Or perhaps an inappropriate attraction to formalism has betrayed us, and we should make do with a natural language. English seems to work just fine.

    Reply
  5. Ed from London Avatar
    Ed from London

    >>Why? Because ‘Max’ has meaning only if Max exists?
    As I understand, because there is no model in which ‘~Ex x = Max’ is true.
    >> But back to the main point, Ed. Have [I] convinced you that univocity fails?
    No. We agree on the fundamentals of your argument above, and we agree (against the current orthodoxy) that univocity entails haecceity. We also agree that haecceity is absurd if it implies some really existing attribute, given your argument that I summarise here.

    haecceities are necessary beings, and so exist at all possible times in all possible worlds. But how, before Socrates came into existence, could there have been any such property as the property of being identical to him. There would have been simply nothing to give content to the proposition that it is Socrates.

    I.e. haecceity as ens reale is absurd. But we haven’t fully addressed the question of haecceity as ens rationis, a ‘merely’ Cambridge property.

    Reply
  6. Alex Leibowitz Avatar
    Alex Leibowitz

    Isn’t there another option, to say that the statement, “Max exists,” is simply not logically well-formed? I’ve met many philosophers, for instance, with the intuition that it is not gramatically correct to say things such as, “There is Max”, whereas the statement about cats easily translates (“Cats exist” = “There are cats.”)

    Reply
  7. Ed from London Avatar
    Ed from London

    >>Isn’t there another option, to say that the statement, “Max exists,” is simply not logically well-formed?
    What about here:

    The Christ myth theory (also known as the Jesus myth theory, Jesus mythicism or simply mythicism) is the hypothesis that Jesus of Nazareth never existed

    Emphasis mine.

    Reply
  8. Bill Vallicella Avatar
    Bill Vallicella

    >>I.e. haecceity as ens reale is absurd. But we haven’t fully addressed the question of haecceity as ens rationis, a ‘merely’ Cambridge property.<< But 'surely' this is even more absurd than the haecceity properties that PvI embraces. What on earth could you mean by saying that the haecceity of Socrates is a merely Cambridge property of him? Being thought to be a liar is a merely Cambridge property of Hillary. How could any property like that be bound up with Hillary's identity and numerical distinctness from everything else?

    Reply
  9. Bill Vallicella Avatar
    Bill Vallicella

    Alex,
    The question you raise is really off-topic since we are assuming that both ‘Cats exist’ and ‘Max exists’ are well-formed, the only question being whether ‘exist(s)’ is being used in the very same sense in both. PvI says yes, I say no.
    In any case, isn’t it just a datum, a given, that the following sentences are well-formed, meaningful, and possessed of a truth-value:
    Jesus exists/Jesus does not exist/ Jesus never existed/That Jesus ever existed is denied by some.

    Reply
  10. Ed from London Avatar
    Ed from London

    That article is a useful compendium of the different ways of denying existence. See below for some examples. The majority involve the simple negative existential, i.e. ‘Jesus did not exist’. Some of them have Meinongian flavour, denying that a historical Jesus existed, but perhaps leaving it open that a mythical Jesus did exist? See also ‘Jesus was not a historical figure’, as though there could be other kinds of figure. And what about ‘Jesus’ historicity’? So ‘historicity’ is something a figure could possess? See also ‘Jesus was a totally mythical character’. So perhaps historicity and mythicity are not mutually exclusive? Can there be a figure who is not totally mythical, but not totally historical either?
    This all suggests a confusion about how to express the assumption underlying the Christ Myth theory, and perhaps there is something in the claim that ‘Jesus never existed’ is not well-formed. But clearly the theory must claim something, regardless of how well or badly the claim is expressed?

    ‘The beginnings of the formal denial of the existence of Jesus can be traced to late 18th-century France’
    ‘Jesus was a totally mythical character’
    ‘Bauer initially left open the question of whether an historical Jesus existed at all.’
    ‘Abraham Dirk Loman … doubted that Jesus was a historical figure’
    ‘several writers published arguments against Jesus’ historicity’

    Reply
  11. Ed from London Avatar
    Ed from London

    >> But ‘surely’ this is even more absurd than the haecceity properties that PvI embraces. What on earth could you mean by saying that the haecceity of Socrates is a merely Cambridge property of him?<< More later, as I said.

    Reply
  12. Bill Vallicella Avatar
    Bill Vallicella

    Ed,
    Interesting, but you are drifting away from the topic. Tell me how haecceities could be entia rationis.
    Andrew,
    You didn’t tell me whether you accept my refutation of your refutation.

    Reply
  13. Ed from London Avatar
    Ed from London

    >> Tell me how haecceities could be entia rationis.
    On which I said ‘more later’. Some of us are entrusted with saving the world, Bill.
    But to start with, can we explore the connection of haecceity and back-reference? Consider

    Frodo journeyed in Gondor and journeyed in Mordor

    Here we understand that the (linguistic) predicate ‘journeyed in Gondor’ and the (linguistic) predicate ‘journeyed in Mordor’ attach to the same linguistic subject, namely the proper name ‘Frodo’. I say this is ‘signified’, i.e. anyone who understands how the signs are used, understands that the second predicate is affirmed of the same subject as the first is affirmed of. Thus anyone who understands what is thus signified understands that if the statement is true, a single individual (Frodo) is said to satisfy the two separate predicates.
    Now consider

    Frodo journeyed in Gondor and Frodo journeyed in Mordor

    I claim that this says the same thing. (Or to satisfy nitpickers who dislike the agentless ‘says’, anyone who utters that utterance, on the understanding it is an ordinary utterance in English, will say that …). If so, and given that ‘Frodo’ cannot refer in extralinguistic reality, it follows that the significance of the second ‘Frodo’ is simply to attach the two predicates together, just as in the first formulation. It has no meaning other than that, since it does not occur in the first formulation, and since nothing additional is stated of Frodo in the second formulation. No property or relation or anything like that is asserted. Thus ‘Frodo’ is simply a ‘meaningless mark’ in Mill’s sense, i.e. it does have meaning or significance, but does not signify anything true of external reality, beyond what the first formulation asserts. Thus (to put it awkwardly) Frodo-ness is a being of reason.
    Finally:

    Frodo journeyed in Gondor and another person journeyed in Mordor

    Here the same ‘property’ of Frodo-ness is invoked, because ‘another’ means in this context ‘different in number from Frodo’. Or rather, anyone who understands the third statement understands that two individuals are said to satisfy the predicates ‘journeyed in Gondor’ and ‘journeyed in Mordor’ respectively. So what do we mean by ‘only one individual satisfies ‘Frodo’ in the same sense’. We mean that when a proper name like ‘Frodo’ is used in the same sense in many different sentences, the predicates of those sentences are all signified (or denoted) to be satisfied by a single individual, i.e. just one individual. But our formulation is awkward. It’s not the the proper name is satisfied, for there is no corresponding property in reality that guarantees satisfaction. Rather, it’s the predicates which are satisfied, and the proper name signifies that the same individual satisfies them.
    In that respect ‘haecceity’, i.e. Frodo-ness, is a being of reason.

    Reply
  14. Andrew Avatar
    Andrew

    Bill,
    I didn’t reply to your reply because I’m not sure what to make of it. But here’s an initial thought:
    I don’t find it particularly surprising that a rendition of ‘Max exists’ using number-words uses ‘is’ differently than does a rendition of ‘cats exist’ using number-words. Nor do I yet see why it is a problem. You call this an ‘equivocation’. Is it a bad equivocation, though? Equivocations are bad when terms change meaning across premises in an argument; has that happened here? Or has another (bad) kind of equivocation shown its face?
    Here’s one reason to think that the equivocation is not naughty in any deep way: every predication is equivalent to an identity. We can move freely between both uses of ‘is’ and preserve truth. ‘Bill is a philosopher’, for example, is equivalent to ‘There is some philosopher to which Bill is identical’. The one statement is true if and only if the other is true. This equivalence holds in PL, too. Proofs in both directions (don’t worry; they’re short!):
    Fa –> Ex(Fx and x = a)
    1. Fa (assume)
    2. a = a (=-introduction)
    3. Fa and a = a (1 & 2, &-introduction)
    4. Ex(Fx and x = a) (3, existential-introduction)
    Ex(Fx and x = a) –> Fa
    1. Ex(Fx and x = a) (assume)
    2. Fa (1, existential elimination)
    So, for every predicative use of ‘is’, there’s an equivalent statement that deploys the ‘is’ of identity. With such an equivalence result in mind, its hard to find the equivocation you identity objectionable. I may be missing something here, though.
    What do you think?

    Reply
  15. Andrew Avatar
    Andrew

    Quick correction: should you suspect that the ‘is’ in ‘There is some philosopher to which Bill is identical’, above, is not the ‘is’ of identity, try this instead: ‘There is some philosopher that Bill is’.
    Or: ‘There is some philosopher — so-and-so, let us say — such that Bill is so-and-so’.
    Or (if I’m allowed to department from pure English): ‘There is some philosopher x such that Bill is x’

    Reply
  16. Ed from London Avatar
    Ed from London

    Andrew – I expect Bill will refer you to the syllogism right at the beginning of the OP. Note the assumption of ‘univocal’.

    Reply
  17. Bill Vallicella Avatar
    Bill Vallicella

    Ed,
    I want to talk about the real world with its cats and such, but you always what to talk about purely fictional items such as Frodo. What I was expecting to hear from you was a story about how an existing thing such as Max the cat could have an haecceity that is a mere ens rationis.
    Pure ficta have no place in this discussion since we are talking about existence, and pure ficta do not exist. Yes, I know PvI thinks that pure ficta do exist as abstract objects, but we both reject that view.

    Reply
  18. Andrew Avatar
    Andrew

    I wondered about that, Ed; but the argument under consideration in the opening paragraph doesn’t claim that ‘is’ is univocal; only that number-words and ‘exists’ are. Or maybe I don’t get your point.

    Reply
  19. Bill Vallicella Avatar
    Bill Vallicella

    Andrew,
    The issue is whether ‘exist(s)’ is univocal across general and singular existentials. In other words, does it have exactly the same sense across the two types of existential? Do you agree that this is the question on the table?
    I don’t deny that ‘Bill is a philosopher’, for example, is equivalent to ‘There is some philosopher to which Bill is identical’.
    It seems obvious to me that in ‘Cats exist’ and ‘Max exists’ ‘exist(s)’ is not being used in the same sense. In the first it means that the concept CAT has one or more instances, while in the second it does NOT mean that the concept Max has one or more instances — for the simple reason that Max is not a concept.
    To preserve univocity you have to bring in an haecceity concept — Maxity, identity-with-Max — if you don’t you are stuck with an equivocation of ‘exist(s).’

    Reply
  20. Bill Vallicella Avatar
    Bill Vallicella

    Cats exist iff something is feline. And Max exists iff something is Max. In ‘Something is feline’ and ‘Something is Max’ is ‘is’ being used in the same sense? Obviously not. Ergo, etc.

    Reply
  21. Ed from London Avatar
    Ed from London

    >>I want to talk about the real world with its cats and such, but you always want to talk about purely fictional items such as Frodo.<< The reason is to demonstrate that (a) the semantics of fictional sentences are the same as the semantics of sentences ‘about’ the real world but (b) the semantics of the fictional sentence cannot have an ontological counterpart, because there is absolutely nothing in reality corresponding. How else would you show this? >> What I was expecting to hear from you was a story about how an existing thing such as Max the cat could have an haecceity that is a mere ens rationis.
    If Max ‘has’ it, then it cannot be a real being. ‘Being of reason’ typically means something appropriate to our way of thinking or talking or mode of expression, which has no counterpart in reality. The best way of showing this is to use fictional discourse, as above.
    What I hoped I had compellingly demonstrated was that there is something corresponding to haecceity predication in fictional discourse, thereby proving that nothing real could correspond to it. Clearly not.

    Reply
  22. Ed from London Avatar
    Ed from London

    >> In ‘Something is feline’ and ‘Something is Max’ is ‘is’ being used in the same sense? Obviously not. Ergo, etc.<< Is it obvious, once we adjust for the different grammatical categories ('feline' is adjective, 'Max' is proper name)? If we can say there are such things as cats, can’t we say there is such a thing as Max? Apart from the singular and plural form, isn’t the word is/are being used in precisely the same sense?

    Reply
  23. Bill Vallicella Avatar
    Bill Vallicella

    I want you to focus on the difference between ‘For some x, Fx’ and ‘For some x, x = a.’
    >>If Max ‘has’ it, then it cannot be a real being.<< That is just false. If Max is sleepy, you cannot infer that sleepiness is a relational property of Max.

    Reply
  24. David Brightly Avatar
    David Brightly

    Is this a sound argument?

    1. Max exists
    2. Max is a cat
    —————–
    3. Some cat exists
    4. Cats exist

    If it is, how do we prise ‘exists’ in (1) away from ‘exist’ in (4)?

    Reply
  25. Bill Vallicella Avatar
    Bill Vallicella

    Hi David,
    Yes, your argument is sound, and yes it presents a challenge I need to address. This may be a crisper and clearer way to put the challenge:
    1. Island volcanos exist.
    2. Stromboli is an island volcano.
    —————
    3. Stromboli exists.
    Puzzle: the argument is plainly valid and sound and yet how could it be if there is an equivocation on ‘exist(s)’?
    Solution: The argument is an enthymeme the suppressed premise of which is
    0. Necessarily, if Fs exist, and x is an F, then x exists.
    The point is that the equivocation is systematic as opposed to accidental like the equivocation on ‘bank’ as among ‘blood bank’ ‘money bank’ and ‘river bank.’
    The general and singular senses of ‘exist(s)’ are distinct but necessarily and systematically connected.

    Reply
  26. Ed from London Avatar
    Ed from London

    >>>>If Max ‘has’ it, then it cannot be a real being.<< >>That is just false. If Max is sleepy, you cannot infer that sleepiness is a relational property of Max.
    Yes I meant to say ‘it cannot be a being of reason’.

    Reply
  27. Ed from London Avatar
    Ed from London

    David: >>Is this a sound argument?
    1. Max exists
    2. Max is a cat
    —————–
    3. Some cat exists
    4. Cats exist
    If it is, how do we prise ‘exists’ in (1) away from ‘exist’ in (4)?
    << If that is sound, then what about

    1. Frodo does not exist
    2. Frodo is a hobbit
    3. Some hobbit does not exist etc

    The prising apart has already been done, in supposing that the ‘is’ of the copula is separate from ‘exist’, and thus treating ‘exists’ is a predicate. If it is a predicate, then of course it is univocal. The Frege-Inwagen point, in relating ‘exist’ to number, is that it is a quantifier, not a predicate.
    The counter-argument is that ‘Max exists’ doesn’t have an adequate quantification. There is ‘Ex x = Max’, but that does not have the meaning, in predicate logic, that we want it to have.

    Reply
  28. Ed from London Avatar
    Ed from London

    >>I want you to focus on the difference between ‘For some x, Fx’ and ‘For some x, x = a.’
    The first means ‘there is such a thing as an F’
    The second means ‘there is such a thing as a’
    Both occurrences of the italicised ‘is’ mean the same, hence there is no equivocation.

    Reply
  29. Bill Vallicella Avatar
    Bill Vallicella

    Not so. The first means ‘Something is F,’ e.g., ‘Something is feline.’ The second means ‘Something is identical to a,’ e.g., ‘Something is identical to Max.’
    Are you confusing the ‘is’ of predication with the ‘is’ of identity? That would be quite a lapse for the proprietor of the Logic Museum.

    Reply
  30. London Ed Avatar
    London Ed

    >>Are you confusing the ‘is’ of predication with the ‘is’ of identity? That would be quite a lapse for the proprietor of the Logic Museum.<< No. I meant the first 'there is', as in 'there is such a thing as ...' This is actually quite a common form of dispute among philosophers when there are two different forms A and B. One philosopher claims that A is the paradigm form. The other claims that B is. How do we decide?

    Reply
  31. London Ed Avatar
    London Ed

    >>Are you confusing the ‘is’ of predication with the ‘is’ of identity? That would be quite a lapse for the proprietor of the Logic Museum.<< Humph: the Logic Museum is mostly about traditional and scholastic/Aristotelian logic, which does not really distinguish between the two forms of 'is', or at least not those two forms (secundum and tertium adiacens is a different distinction). Modern philosophical logic does. Why? Because modern logic dispenses with the copula. Instead of the identity ‘some man is some animal’, we have the so-called propositional functions animal(x) and man(x). Here of course you absolutely need the distinction between the ‘is’ of identity and of predication. You have a copy of Sommers? Right, see p.121

    Clearly, it is only after one has adopted the syntax [of predicate logic] that prohibits the predication of proper names that one is forced to read ‘a is b’ dyadically and to see in it a sign of identity.

    So poo to that.

    Reply
  32. Bill Vallicella Avatar
    Bill Vallicella

    But surely it is irrelevant to bring in pre-Fregean logic when the dispute is over van Inwagen’s univocity claim, a claim he makes in the context of Fregean logic.

    Reply
  33. Ed from London Avatar
    Ed from London

    >>But surely it is irrelevant to bring in pre-Fregean logic when the dispute is over van Inwagen’s univocity claim, a claim he makes in the context of Fregean logic.<< What exactly is VI’s univocity claim? Your OP says the argument ‘is adapted’. The only quote is ‘The univocacy [univocity] of number and the the intimate connection between number and existence should convince us that existence is univocal.’ But then you worry about an equivocation on ‘is’, and I am confused. I am particularly confused because the word ‘is’ really appears twice in questions like ‘Is there any cat apart from Max?’. The expression ‘apart from Max’ unpacks into ‘who is not identical with Max’. So which is the equivocated ‘is’? And it seems perfectly clear to me that ‘cat apart from Max’ is a noun phrase representing a concept which can be satisfied by any number of cats, indeed any cat whatsoever apart from him. So if I ask whether there are such cats, why am I equivocating? And can’t I ask about the number of cats you own, apart from Max? Is it one, two, etc, or just zero?
    Moreover we commonly distinguish expressions like ‘cats apart from Max’, and ‘cats including Max’. How many cats do you have apart from him? And how many, including him? I bet the second number is exactly 1 more than the first.
    Thus the copula ‘is’ plus a common noun (‘cat apart from Max’) is always univocal, in my book. I agree the ‘is’ in ‘is black’ is different from in ‘is [identical with] Max’, but that’s not the one I am interested in.

    Reply
  34. Bill Vallicella Avatar
    Bill Vallicella

    It seems obvious to me that in ‘Cats exist’ and ‘Max exists’ ‘exist(s)’ is not being used in the same sense. In the first it means that the concept CAT has one or more instances, while in the second it does NOT mean that the concept Max has one or more instances — for the simple reason that Max is not a concept.
    If ‘exist(s)’ is a 2nd-level predicate as per Frege, then either ‘Max exists’ is meaningless or ‘exist(s)’ does not have the sense of a 2nd-level predicate.

    Reply
  35. Ed from London Avatar
    Ed from London

    Doesn’t address my argument. Let C1 and C2 be the following concepts:
    C1: {any man at all}
    C2: {any man besides Socrates}
    We agree that both determine a number of men. And we agree that if the number corresponding to C1 is n, then the number corresponding to C2 is n-1.
    What about concept {satisfies C1 but not C2}? Surely the number corresponding to that is 1. And not only that, but it will always be Socrates, and none other. QED.

    Reply
  36. David Brightly Avatar
    David Brightly

    Bill, Ed,
    All three of the arguments that we have just put forward are ‘conversationally inept’. They all use a proper name without first introducing it via an existential claim. To make sense of an initial ‘Max is a cat’ we have to supply the existential: ‘There is a cat named ‘Max”. We could call this the ‘mention before use’ rule for proper names. Thereafter ‘Max exists’ is true but uninformative, and ‘Cats exist’ follows by existential generalisation. Likewise an initial ‘Frodo is a hobbit’ has to be understood as making the existential claim ‘There is a hobbit called ‘Frodo”. A subsequent ‘Frodo does not exist’ simply denies this existential claim. It’s another way of saying ‘There are no such things as hobbits’. So ‘Frodo does not exist’ and ‘Frodo is a hobbit’ are in contradiction, and absurdities follow. Similarly, the initial ‘Stromboli is an island volcano’ is enthymematic for ‘There is an island volcano called ‘Stromboli”, from which we infer the uninformative ‘Stromboli exists’.
    What I am doing here is extending into natural language the rules observed by mathematicians in their proofs. A new name may be introduced only on the back of a general existential claim: ∃x.P(x) ⊢ P(a), where ‘a’ is a new logical constant. This is the rule somewhat confusingly called ‘existential elimination’. Singular existential denials occur as the conclusions of reductio ad absurdum arguments. ‘a does not exist’ is colloquial for ~∃x.P(x) where ∃x.P(x) is the existential hypothesis under which the name ‘a’ was introduced.
    It’s my contention that if we follow the mathematicians in these simple rules of logical hygiene some of the puzzles in this area evaporate. As far as I can see the rules are consistent with Ed’s ‘story-relative’ theory of reference.

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  37. Bill Vallicella Avatar
    Bill Vallicella

    >>Likewise an initial ‘Frodo is a hobbit’ has to be understood as making the existential claim ‘There is a hobbit called ‘Frodo”. A subsequent ‘Frodo does not exist’ simply denies this existential claim. It’s another way of saying ‘There are no such things as hobbits’. So ‘Frodo does not exist’ and ‘Frodo is a hobbit’ are in contradiction, and absurdities follow.<< You seem to be denying the very possibility of coherent fictional discourse! >>Similarly, the initial ‘Stromboli is an island volcano’ is enthymematic for ‘There is an island volcano called ‘Stromboli”, from which we infer the uninformative ‘Stromboli exists’. << Forgive the pedantry, but, by definition, every enthymeme is an argument; 'S. is an island volcano' is not an argument; so 'S. is an island volcano' is not an enthymeme. More fundamentally, I don't see the need for your brand of logical hygiene. It is clear to me at least that context suffices to establish whether our discourse is fictional or factual (i.e., non-fictional). And how this helps with my univocity question escapes me.

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  38. Bill Vallicella Avatar
    Bill Vallicella

    Ed,
    What you say at @6:25 is admirably clear, but the connection between what you demonstrate and my question about univocity of ‘exist(s)’ is unclear to me.
    I suggest we let this thread die a natural death. It’s not bringing me any light.

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  39. David Brightly Avatar
    David Brightly

    Bill,
    One last submission then, if I may.
    >> You seem to be denying the very possibility of coherent fictional discourse!
    How so? In some other possible world ‘Once upon a time there was a philosopher named ‘Socrates” is the beginning of a work of fiction. It’s false, of course.
    I stand corrected on ‘enthymematic’.
    >> I don’t see the need for your brand of logical hygiene.
    Well, it eliminates 99% of the confusion in evidence here, for example. It works for mathematics. What baby goes out with the bathwater?

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  40. Ed from London Avatar
    Ed from London

    >>What you say at @6:25 is admirably clear, but the connection between what you demonstrate and my question about univocity of ‘exist(s)’ is unclear to me.<< OK, laying it on with a trowel (do you Americans have that saying?). C1: {any man at all} C2: {any man besides Socrates} C3: {satisfies C1 but not C2} Then ‘men exists’ is equivalent to ‘C1 is satisfied’. And ‘Socrates exists’ is equivalent to ‘C3 is satisfied’. ‘Exist’ is therefore univocal because in both cases it signifies the satisfaction or instantiation of some concept. The killer argument against univocity is that there is no concept corresponding to ‘Socrates’, which is Frege’s argument. But C3 is such a concept. QED.

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  41. Bill Vallicella Avatar
    Bill Vallicella

    So C3 is the concept: *instantiates *man* but not *man except Socrates**
    (The asterisks are used to mention concepts.)
    Your claim is that C3, which exists, does duty for the haecceity of Socrates which you admit does not exist.
    An ‘A’ for effort, but I don’t think it works. *Man except Socrates* is as objectionable as *man identical to Socrates.* The latter is equivalent to Socrateity. The former, C2, is not an haecceity since it is multiply instantiable. But it is objectionable because it includes within its conceptual content Socrates himself. And so C2 cannot exist unless Socrates exists.
    This implies that C3 cannot exist unless Socrates exists.
    More simply, C3 is the concept *a man but not a man other than Socrates.* But this is equivalent to *a man identical to Socrates* which is equivalent to Socrateity — which you admit is inadmissible.

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  42. London Ed Avatar
    London Ed

    >> Your claim is that C3, which exists, does duty for the haecceity of Socrates which you admit does not exist.<< I agree that there is no such thing as haecceity, i.e. nothing in reality corresponding to the concept *Socrates*. But C3 is a concept, ergo etc. >> More simply, C3 is the concept *a man but not a man other than Socrates.* But this is equivalent to *a man identical to Socrates* which is equivalent to Socrateity<< I shall invoke ‘one man’s modus ponens’ here. Your argument is something like:
    (1) If an expression is an object expression, it is not a concept expression.
    (2) ‘a man identical to Socrates’ is an object expression.
    (3) ‘a man identical to Socrates’ is semantically equivalent to ‘satisfies C1 but not C2’.
    (4) Therefore ‘satisfies C1 but not C2’ is not a concept expression.
    But ‘satisfies C1 but not C2’ clearly is a concept expression, because there is a number corresponding to it. And since we agree it is semantically equivalent to ‘a man identical to Socrates’, it follows that ‘a man identical to Socrates’ is a concept expression. Then applying modus tollens to your (1) above, it follows that ‘a man identical to Socrates’ is not an object expression. Your modus ponens is my modus tollens.
    I suppose you will then object that there cannot be a concept expression to which nothing in reality corresponds. At this point I will involve my argument from fiction, demonstrating that there can be haecceity concepts signified in fiction, to which (because fiction) nothing in reality corresponds, ergo etc. For some reason you have banned the argument from fiction, but you haven’t explained why the argument is not logically valid. (You suggested it was changing the subject, but didn’t explain why).

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