Category: Language, Philosophy of

I grant that logical equivalents not containing 'exist(s)' or cognates can be supplied for all singular and general existentials.  Thus, 'Socrates exists' can be translated, salva veritate, as 'Something is identical to Socrates,' or, in canonical notation,  '(∃x)(x = Socrates).'  Accordingly,

Socrates exists =_df (∃x)(x = Socrates).

But if the definiens preserves the truth of the definiendum, then the definiendum must be true, hence must be meaningful, in which case first-level uses of 'exist(s)' must be meaningful.  Pace Russell, 'Socrates exists' is nothing like 'Socrates is numerous.'

What's more, the definiendum is prior in the order of understanding to the definiens.  If I didn't already understand 'Socrates exists,' then I would not  be able to understand '(∃x)(x = Socrates).'  You couldn't teach me the Quinean translation if I didn't already understand the sentence to be translated.

One conclusion we can draw from this is that if 'exist(s)' is univocal across general and singular existentials, then  existence cannot be instantiation.  For the left-hand side of the definition does not make an instantiation claim.  It is simply nonsense to say of an individual that it is instantiated.  And if the right-hand side makes an instantiation claim, then we need those creatures of darkness, haecceity-properties.

But we don't have to give the RHS a Fressellian reading; we can give it a Quinean-Inwagenian reading.  (We could call this the 'Van' reading.)  Accordingly: There exists an x such that x = Socrates. On the Van reading, in stark contrast to the Fressellian reading,  'exist(s)' can be construed as a first-level predicate, as synonymous to the predicate 'is identical to something.'  Accordingly:

y exists =_df(∃x)(x = y).

On the reasonable assumptions that (i) 'exist(s)' is an admissible first-level predicate and that (ii) there are no nonexistent objects, this last definition is unobjectionable.  If Tom exists, then there exists an object to which he is identical.  And if there exists an object to which Tom is identical, then Tom exists.  No doubt!

The interesting  question, however, is whether any of this affords aid and comfort to the thin theory.  Well, what exactly is the thin theory?  It is the theory that existence is exhaustively understandable in purely logical, indeed purely syntactical, terms.  The thin theory is a deflationary theory that aims  to eliminate existence as a metaphysical topic.  It aims to supplant the metaphysics of existence (of whatever stripe: Thomist, Heideggerian, etc.) with the sober logic of 'exist(s).'  The aim of the thin theory is to show that there is no sense in which existence is a non-logical property of individuals.  The aim is to be able to consign all those tomes of metaphysical rubbish to the flames with a good conscience.

Now glance back at the definition.  Every mark on the RHS  is a bit of logical syntax.  Ignoring the parentheses which in this instance can be dropped, we have the backwards-E, two bound occurrences of the variable 'x,' a free occurrence of the variable 'y,' and the sign for identity.  There are no non-logical expressions such as 'Socrates' or 'philosopher.'  On the LHS, however, we find 'exists' which is not obviously a logical expression.  Indeed,  I claim that it is not a logical expression like 'some' or 'all' or 'not.'  It is a 'content' expression.  What could be more important and contentful than a thing's existing?  If it didn't exist it would be nothing and couldn't have properties or stand in relations.

Surely my sheer be-ing is my most impressive 'feature.'  "To be or not to be, that is the question."

Since there is content on the LHS there has to be content on the RHS.  But how did it get there, given that every expression on the RHS is just a bit of syntax? In only one way: the domain of the bound variables is a domain of existents.  But now it should be clear that the definition gives us no deflationary account of existence.  What it does is presuppose existence by presupposing that the domain of quantification is a domain of existents.  Existence is that which existents have in common and in virtue of which they exist.

In short, I have no objection to the definition read in the 'Van' as opposed to the  'Fressellian' way.  It is perfectly trivial!  My point, however, is that it gives no aid and comfort to the thin theory.  A decent thin theory would have to show how we can dispence with existence entirely by eliminating it  in favor of purely logical concepts.  But that is precisely what we cannot do given that the domain of quantification is a domain of existents.  (Of course, if the domain were populated by Meinongian nonexistent objects, then the definition would be false). 

Suppose we acquiesce for the space of this post in QuineSpeak. 

Then 'Horses exist' says no more and no less than that 'Something is a horse.'  And 'Harry exists' says no more and no less than that 'Something is Harry.'  But the 'is' does not have the same sense in both translations.  The first is the 'is' of predication while the second is the 'is' of identity.  The difference  is reflected in the standard notation.  The propositional function in the first case is Hx.  The propositional function in the second case is x = h.  Immediate juxtaposition of predicate constant and free variable is the sign for predication.  '=' is the sign for identity.  Different signs for different concepts.  Identity is irreducible to predication which is presumably why first-order predicate logic with identity is so-called.

Those heir to the Fressellian position, such as Quine and his epigoni, dare not fudge the distinction between the two senses of 'is' lately noted. That, surely, is a cardinal tenet of their brand of analysis.

So even along Quinean lines, the strict univocity of 'exist(s)' across all its uses cannot be upheld.  It cannot be upheld across the divide that separates general from singular existentials.

Or have I gone wrong somewhere?

This post continues my examination of Peter van Inwagen's "Being, Existence, and Ontological Commitment."  The first post in this series is here.  There you will find the bibliographical details.

We saw that van Inwagen gives something like the following argument for the univocity of 'exists':

1. Number-words are univocal

2*. 'Exist(s)' is a number-word

Therefore

3*. 'Exist(s)' is univocal.

The second premise is pure Frege.  The question arises: is van Inwagen committed to the Fregean doctrine that 'exists(s)' is a second-level predicate?  He says he isn't. (484)

How should we understand a general existential such as 'Horses exist'?  Frege famously maintained that 'exist(s)' is a second-level predicate: it is never a predicate of objects, but always only  a predicate of concepts.  What the sample sentence says is that the concept horse has instances.  Despite appearances, the sentence is not about horses, but about a non-horse, the concept horse.  The concept horse is not a horse!  (Frege also famously and perplexingly maintains that the concept horse is not a concept, but let's leave that for another occasion.)  And what our general existential says about the concept horse is not that it exists (as we ordinarily understand 'exists') but that it is instantiated.  Van Inwagen, though endorsing Frege's key notion that (as PvI puts it) "existence is closely allied to number" (482) does not follow Frege is in holding that 'exists' is a second-level predicate.

Van Inwagen thus appears to be staking out a middle position between the following extremes:

A. 'Horses exist' predicates existence of individual horses.

B. 'Horses exist' predicates instantiation of the concept horse.

Van Inwagen's view is that 'Horses exist' says that horses, taken plurally, number more than zero.  So 'Horses exist,' contra Frege, is about horses, but not about individually specified horses such as Secretariat and Mr Ed. 'Horses exist' is not about the concept horse or any other abstract object such as a property or a set: it is about concrete horses, but taken plurally.

I am trying to understand this, but I find it obscure.   One thing I do understand is that there are predicates that hold plurally (collectively) but not distributively, but are not, for all that, second-level.  Van Inwagen gives the example:

1. Horses have an interesting evolutionary history.

Obviously, the predicate in (1) is not true of each individual horse.  No individual horse evolves in the sense pertinent to evolutionary theory.  But the predicate  is also not true of the concept horse or the set of horses or the property of being a horse or any other abstract object.  No concept, set, or property evolves in any sense.  So what is the logical subject of (1)?  Horses in the plural, or horses taken collectively.  Or suppose the cops have a building surrounded.  No individual cop has the building surrounded, and of course no abstract object has the building surrounded.  Cops have the building surrounded.  Suppose Manny is one of the cops.  Then the following argument would commit the fallacy of division: (a) The cops have the building surrounded; (b) Manny is one of the cops; ergo (c) Manny has the building surrounded.  What is true of cops in the plural is not true of any cop in the singular.

If I have understood PvI, he is saying that 'exists' functions like the predicate in (1), and like the predicate in 'The cops have the building surrounded.'   But this strikes me as problematic.  Consider these two arguments:

Horses have evolved
Secretariat is a horse
ergo
Secretariat has evolved.

Horses exist
Secretariat is a horse
ergo
Secretariat exists.

The first argument is invalid, committing as it does the fallacy of division.  The second argument is perfectly in order.

So it seems, contra Van Iwagen, that  'Horses exist' is importantly disanalogous to 'Horses have evolved' and 'The cops have the building surrounded.'  'Exists' is predicable of specified individuals, individuals in the singular.  'Evolved' is not predicable of specified individuals, individuals in the singular, but only of individuals in the plural.

I take van Inwagen to be saying that the logical subject of 'Horses exist' is not the concept horse, but horses, horses in the plural, and what it says of them is that they number more than zero.  What I am having trouble understanding is how 'more than zero' can attach to a plurality as a plurality, as opposed  to a  one-over-many such as a concept (which has an extension) or a set (which has a membership).

A plurality as a plurality is not one item, but a mere manifold of items: there is simply nothing there to serve as logical subject of the predicate 'more than zero.' 

"But look, Bill, it is the horses that are more than zero; so there is a logical subject of the predicate."

Response: You can't say what you want to say grammatically.  If there IS a logical subject of the predicate, then it is not a mere manyness. But if there ARE many subjects of predication, then 'more than zero' applies to each horse which is not what you want to say.   There must be something that makes the particulars you are calling horses horses, and that would have to be something like the concept horse; otherwise you have an unintelligible plurality of bare particulars.  But then when you say that the horses are more than zero you are saying that the concept horse has more than one instance, and number-words become second-level predicates.

My suspicion is that van Inwagen's middle path is unviable and that his position collapses into the full-throated Fregean position according to which (a) "existence is allied to number" and (b) number-words are second-level predicates. 

This is a response to a post of the same name by London Ed.  I am much in his debt for his copious and relentless commentary.  My responses are in blue.

After reading some of Maverick’s other posts on the subject, and reading some material he sent me, it  is clear I have misrepresented his argument. Although I am still some way from understanding it, I think it is this.

Suppose there is only one American philosopher, and suppose that it is Vallicella. Then the sentence ‘an American philosopher exists’ is true because Vallicella (qua American philosopher) exists. Now we can translate ‘an American philosopher exists’ into ‘some philosopher is American’, which reduces the verb ‘exists’ to the copula ‘is’. But we can’t translate ‘Vallicella exists’ in the same way. Thus general existential statements presuppose the truth of singular existential statements (or a disjunction or conjunction of singular existential statements). But we cannot analyse away ‘exists’ from singular existential statements. Therefore there is circularity: the same word appears on the right and left hand side of the definition. An American philosopher exists if and only if Vallicella exists.

That is not quite what I say, but it is a fair approximation.

But there is an obvious route out of this problem. What actually makes ‘some philosopher is American’ true is ‘Vallicella is an American philosopher’, which does not use the word ‘exist’. Vallicella may object that ‘Vallicella exists’ has to be true for that to work. Certainly, but we can reply in two ways. We could suppose that empty proper names are meaningless, and that ‘Vallicella’ is only meaningful because it names something. I.e. if it names something, it must name an existing something. ‘Vallicella exists’ is therefore true in virtue of the meaning of the proper name ‘Vallicella’. Or we could allow that empty proper names are meaningful, and that they have a sense but not a reference. Then we can appeal to the idea of instantiation, as with general concepts. ‘Vallicella exists’ means that the sense of ‘Vallicella’ has a referent or instance. ‘An American philosopher exists’ means that the sense of ‘American philosopher’ has an instance.

That is, either common names and proper names fall into different logical categories, in which case we don’t need to use the word ‘exists’ in singular sentences at all. Or they fall into the same category, in which case we can analyse singular existential statements exactly as we analyse general existential statements. In neither case is the definition of ‘exists’ circular.

The second alternative is available only if there are haecceity properties to serve as the Fregean senses of proper names.  Now I have argued many times in these pages and in print against such properties.  It follows that we cannot analyze 'Vallicella exists' in the same as as 'American philosophers exist.'  This leaves the first alternative, according to which the meaning of 'Vallicella' is its referent, an existing individual.  Ed claims that on this alternative "‘Vallicella exists’ is therefore true in virtue of the meaning of the proper name ‘Vallicella’."

I would say that Ed has it precisely backwards.  What he should say is that 'Vallicella' has meaning in virtue of the truth of 'Vallicella exists.'  What Ed says illustrates the linguistic idealism that I have more than once criticized him for.  V.'s existence does not depend on his name or on its meaning.  The point is clearer in terms of a non-human example.  So consider Stromboli, the island volcano.  Presumably Stromboli existed long before the emergence of language.  So what we should say is that 'Strromboli' has meaning in virtue of the fact that Stromboli extralinguistically and extramentally exists, and not vice versa.

Ed and I agree that 'Island volcanos exist' is logically equivalent to 'Some volcano is an island.'  This equivalence, however, rests on the assumption that the domain of quantification is a domain of existing individuals.  (If the domain were populated by Meinongian nonexistent objects, then the equivalence would fail.)   The attempted reduction of existence to someness is therefore circular.  For when we think it through we come to realize that the general existence expressed by sentences like 'Some volcano is an island' presupposes the  singular existence of the individuals in the domain of quantification.  This singular existence, obviously enough, precisely because it is singular, cannot be understood in terms of the logical quantity, someness.  So we move in a circle: from existence to someness and then back to existence.

The same argument can be couched in terms of instantiation.  'Island volcanos exist' is logically equivalent to the second-level predication  'The concept island volcano is instantiated.'  But if a first-level concept is instantiated, it is instaniated by at least one individual.  Obviously, this individual must exist.  (If it were a nonexistent individual, the link between existence and instantiation would be broken.)  So again we move in an explanatory circle,from existence to instantiation and back to existence again.  It follows that existence cannot be reduced to instantiation.

Pace Quine, existence is NOT what 'existential' (i.e., particular) quantification expresses.  What the particular quantifier expresses is instantiation, and instantiation is not existence. 

Here are some general existentials:

An island volcano exists.
There are uninhabited planets.
Faithful husbands exist.
Unicorns do not exist.
There aren't many chess players in Bagdad, Arizona.

Each of these is expressible salva significatione et veritate (without loss of meaning or truth) by a corresponding instantiation claim:

The concept island volcano is instantiated. 
The concept uninhabited planet is instantiated.
The property of being a faithful husband is exemplified.
The property of being a unicorn is not exemplified.
The concept Bagdad, Arizona chess player has only a few instances.

Should we conclude that every general existential is expressible as an instantiation claim?  No.  'Everything exists' is a true general existential.  It affirms existence and is not singular.  But it does not make an instantiation claim.  If you think it does, tell me which property it says is instantiated. 

Please note that it cannot be the property of existence.  For there is no first-level property of existence, and the whole point of translations such as the above is to disabuse people of the very notion that existence is a first-level property.

Addendum, 4:40 PM.  The problem arises also for 'Something exists,' 'Something does not exist,' and 'Nothing exists.'  Consider the latter.  It is not true but it is (narrowly-logically) possibly true.  In any case it is meaningful.  Can it be expressed as an instantiation claim?  If I want to deny the existence of unicorns I say that the concept unicorn has no instances.  What if I want to deny the existence of everything?  Which concept is it whose non-instantiation is the nonexistence of everything?