Maverick Philosopher

By now all of us should be fairly familiar with two recurring themes in Bill’s posts about the topic of singular existence: (A) The thin’s theory of singular existence (henceforth, TSE) relying upon identifying singular existence with the existential quantifier is inevitably circular; (B) The question “What it is for a particular contingently existing individual to exist?” is meaningful, has a robust answer, and that the thin’s TSE cannot give an informative and a non-viciously circular answer to this question.

In this post I wish to address these two concerns Bill has from a point of view that is sympathetic to a thin TSE. I shall be using ‘TSE’ to stand for any theory or conception of singular existence. So in this sense, the “thick” conception is a TSE, but so is the “thin” conception, an eliminativist conception, a reductive conception, etc. Some of the material presented here has been already posted on other threads. I shall try to bring them together and knit a coherent integrated position from which we can address issues A and B above. I apologize in advance for the length of this post.

II. Setting up the problem: What types of TSE are possible?

Well, there are several different TSEs possible:

(a) Eliminativist: The colloquial expression ‘. . . exists,’ and its variants are meaningless; they should be replaced with some other expressions. Note: This view is similar to Churchland’s view about mental concepts.

BV: Yes, when 'exist(s)' and cognates are employed as first-level predicates. And then we get a position close to Frege and Russell. But no one is out to eliminate second-level uses of 'exist(s)' not that Peter thinks otherwise.

(b) Reductive: Reductivism about TSE can take two forms:

(b1) Definitional: The expression, concept, *exists* or any of its colloquial cognates can be defined in more basic terms. Thus expressions or propositions of the form ‘. . . exists’ can be systematically coupled with expressions or propositions in which the term ‘exist’ does not appear. All expressions in which the term ‘…exists…’ occur can be translated into expressions in which this term or its cognates do not occur.

(b2) Non-Definitional: Singular (contingent) existence is *reducible* to more fundamental facts by means of certain law-like correlations between singular existence and these more basic facts.

Note: Bill frequently complains that the thins link singular existence to a species of general existence. Such a view, whether it is a correct description of the thin’s conception, is a non-definitional reduction of singular existence to a more fundamental fact, namely, general existence.

(c) The *Thick* or *robust* TSE: according to this view TSE will have the form of a *substantive correlation* between singular existence and some *stuff*; a property, a trait, a part, a mode or whatever, such that the *stuff* necessarily holds in all and only cases of singular existence. Call this the singular existence stuff or *SE-stuff*. While every contingently existing entity features SE-stuff, there are significant differences between Socrates’ SE-stuff, for instance, and the moon’s SE-stuff. Moreover, the difference between each of these contingently existing objects and a contingently non-existent one such as Pegasus is that while the former two enjoy similar SE-stuff, Pegasus fails to enjoy the same kind of SE-stuff. Note: Bill holds, I believe, something like this view.

BV: 'Stuff' is not a word I would choose, but if Peter holds a gun to my head and forces me to express myself in 'stuff' terms, I would say: Socrates, a contingent individual, is a singular existent composed of existence-stuff and essence, the latter term used very broadly to encompass all quidditative determinations, i.e., all properties monadic and relational, accidental and essential, all properties pertaining to WHAT a thing is, in a very broad sense of 'what.' But since 'stuff' adds nothing except misleading connotations, I will just say that Socrates is composed of existence and essence. Since existence is not matter, I don't call it stuff. The main point is that there is a real distinction (distinctio realis) between an individual and its existence. On my theory, the existence of Socrates is not a spatial, temporal, or even ontological part of him: it is the unity of his ontological parts or constituents. But since this unity is distinct from that which it unifies, one could say that Socrates is composed of both existence and essence.

Note the asymmetry: The existence of Socrates is not reducible to the instantiation of any property; but the nonexistence of Pegasus is just the non-instantiation of a certain property.

(d) The *Thin* or *deflationary* TSE: according to this view, TSE includes a Tarski-like truth theory for a fragment of a language such as English involving the word ‘exists’ and its cognates. Call this the T-theory component of TSE. The T-theory includes the typical resources of first-order quantification theory plus (absolute) identity. It may be supplemented as needed by additional resources such as the apparatus of some modal logic, free logic, etc. A substitutional version may be explored in this regard. In addition TSE will include at least one more component, a bridge-theory, that will map certain elements of the T-theory onto expressions of the language that include the word ‘exists’, ‘there are some’, and their cognates. Call this the B-theory.

(di) Now, the T-theory entails consequences of the form:

(T*) ‘(Ex)(…x…)’ is true iff S

where ‘S’ is a place holder for a *set-theoretical* construction that will look (very roughly and in a simplified form) as follows: a is a member of a certain set (e.g., the domain of the quantifiers) such that ….; where ‘a’ is among the constants of the T-theory.

Note: (T*) nowhere includes the word ‘exists’ or any of its cognates.

BV: Here Peter owes us an illustration. Perhaps he means something like the following. Let D be a domain consisting of exactly three individuals, a, b, and c. Suppose each of these individuals is F. We can think of D as a mathematical set. Then a, b, and c are elements of D. We can then say that '(Ex)Fx' is true in D iff Fa v Fb v Fc. E.g., 'Someone is fat' iff Al is fat or Beatrice is fat or Carl is fat.

(dii) The B-theory in turn will entail consequences such as:

(B*) S iff Socrates exists;

i.e., a is a member of a certain set such that… iff Socrates exists. Note 1: (B*)’s left-hand-side (LHS) contains the very same set theoretical construction as we have encountered in (T*)’s right-hand-side (RHS), namely, ‘S’. So (B*) includes the word ‘exists’ or one of its cognates only on the RHS.

BV: This is less than clear. Is S a proposition? It would have to be since (B*) is a proposition. But earlier you said that S is a set-theoretical construction, and thus a set. But no proposition is a set and no set is a proposition. Yes, I know that David Lewis and others hold that propositions are sets of possible worlds, but that is an absurd view, and I hope it is not yours.

Note 2: The T-theory contains an interpretation (or valuation) function that maps each constant to an element of its domain, each predicate to a set of such elements, etc. The B-theory imports these valuations and uses them to entail consequences such as (B*). Hence, we are assuming here that the T-theory’s valuation function assigned the constant ‘a’ to Socrates. Hence, B* is true.

(diii) The T-theory (featuring consequences such as T*)jointly with the B-theory (featuring consequences such as B*) entail sentences of the form (E-equivalences):

(E) (Ex)(x=Socrates) iff Socrates exists;

(div) Now, the E-equivalence of Bill’s McCain sentence will look as follows: (E-McCain) (Ex)(x=a) iff McCain exists

where McCain is a member of the set that serves as the domain of the quantifiers of T* and ‘a’ is among the constants of the T-theory assigned by the latter’s valuation function to McCain.

(dv) The following positions characterize a thin TSE:

(i) Singular existence sentences are perfectly meaningful; hence, an eliminativist TSE is false.
(ii) Singular existence sentences are not definable in more basic terms and singular existence is not reducible to conceptually more basic facts; hence, any reductive TSE is false.
(iii) There is no SE-stuff; hence, a thick TSE is false.

III. The “ideology” of a thin or deflationary TSE

(a) A thin or deflationary TSE is a substantive theory of singular existence. While a thin TSE does not appeal to a reductive analysis of singular existence to more basic terms, for there are none, and it does not posit an SE-stuff, for no such stuff exists, a thin TSE offers a *structural explication* of singular existence. Such a theory is substantive because it contains resources that entail a truth-functionally equivalent proposition for each singular existence proposition such that this truth-functionally equivalent proposition is drawn from a pool of resources that are common to all other propositions. In other words, while each consequence of the theory is *thin*, the theory as a whole is *thick* in substance because it contains resources rich enough to entail equivalences for each proposition, including all singular existence propositions. So unlike the *thick* conception of TSE which aspires to purchase a substantive explanation by means of assigning something, SE-stuff, to each singular existence of an object, the *thin* conception is substantive because it contains rich explanatory resources that suffice to explain all cases even though they are thinly distributed in each individual case.

(b) Thus, while no particular proposition of a thin TSE provides a full explication of the singular existence of an object, the theory as a whole achieves a level of explication of singular existence as thoroughly as possible for any theory to achieve (more on this later). However, if one wants a slogan in order to represent the thin’s ideology of singular existence; here is a proposal that captures, I believe, the core of the theory:

Thin’s Slogan: To exist is to be a member of a set that can serve as the domain of the quantifiers.

(c) Notice the division of labor between the T-theory and the B-theory. The former is a theory of truth conditions and in this sense it is not specifically a TSE. But it contains wffs that give truth conditions to sentences or propositions that include the existential quantifier. In this sense it entails the truth conditions of all existentially quantified sentences or propositions that are later on (in the B-theory) exploited for the purpose of explicating singular existence sentences or propositions.

(c) Note also that the semantics given in the T-theory involves only set theoretic constructions. Thus, the ontology of the T-theory is sets. T*, for instance, does not involve a translation into colloquial English or whatever; the RHS of T* refers to a set. Nor can we view T* as identifying or translating statements about the existence of some individual into quantificational language. The word ‘exists’ does not occur in T* nor in ANY part of the T-theory. So the T-theory alone is not a theory of existence, singular or otherwise.

BV: I don't understand how the RHS of T* can refer to a set. 'Iff' connects propositions, and no set is a proposition as I have already said.

(d) The B-theory alone cannot be viewed as a complete TSE either. While it entails biconditionals that feature on their RHS the expression ‘exists’, these biconditionals cannot be viewed as translating or reducing singular existence to anything. Moreover, in order to discern that biconditionals such as B* are in fact true we need to glean into the valuation function of the T–theory in order to verify that the constant appearing on the LHS of B* is indeed assigned to the correct individual object.

IV. Bill’s Circularity Objections to the thin TSE A

(a) Bill has been arguing that a thin TSE is viciously circular. What is his argument? Bill’s argument, roughly, is that a thin TSE (any thin TSE including the one I have just proposed above) presupposes at one point or another the existence of the very objects which the theory aims to explain. Take for instance Socrates. The version of the thin TSE I have proposed will be viciously circular, according to Bill, because it must recall Socrates as a member of the set that serves as the domain of the quantifiers of the T-theory. Hence, Bill argues, he is told by the proponents of a thin TSE that the explanation of what it is for Socrates to exist is given by the fact that Socrates is a member of a certain set. But in order for Socrates to be a member of a certain set, Socrates must exist. Hence, the explanation of what it is for Socrates to exist is given by appealing to Socrates’ existence; not a very informative way of explaining anything: such a theory, Bill protests, is “Trivial”; “Boring”; “Uninformative”.

(b) Indeed! Bill would be right provided the question “What is it for a contingently existing individual such as Socrates to exist?” would have had a *thick* content and a *thick* answer would have been possible without being viciously circular; neither of which, I submit, is possible.

BV: I don't see that Peter has shown that a thick theory must be viciously circular, nor that existence has no thick content. These are key differences between us. On these two points I think Peter is long on assertion and short on argument. But even if I am wrong on both of these points, Peter's theory is still viciously circular! The situation may be this: no thick theory is possible, and Peter's quasi-Quinean theory is also a nonstarter. It might be that the correct theory is a thin theory along Fregean lines as Frege is interpreted by C. J. F. Williams — our man 'Ockham's' teacher — in his important book, What is Existence? Roughly, Williams argues that Quine falls back into the very fallacy unmasked by Frege, the fallacy of thinking of existence as belonging to individuals. This will be the topic of a separate post.

(c) What is the *thick* presupposition behind the question Bill asks? The question assumes that the contingent existence of an object has a unique quality or feature, an SE-stuff, that is unique to each contingent existent and yet shared by all contingently existing beings so as to distinguish them from other things that do not partake in this SE-stuff (Pegasus, for instance, does not share in the SE-stuff, but might feature some other type of quality shared by, lets say, fictional characters). But, what could this SE-stuff be other than, well, the fact that they all share in contingent existence?

BV: I have been somewhat coy about showing my hand, though I show it plainly enough in my book A Paradigm Theory of Existence. I want to throw the issues and problems into relief and show the deficiencies of thin theories. That is Job One. For only if thin theories are unacceptable is there any rational motive to adopt a thick theory. If thin theories are rationally acceptable, then the metaphysics of existence is out of business, Analogy: if naturalism can explain everything, then God and the soul are out of business.

I want to make it clear that I do not take a Meinongian line. For me, as for Quine, everything exists. It is just that for me, this is a substantive thesis, not a thesis that is either logically or definitionally true.

(d) The presupposition behind Bill’s question that in addition to the fact that a given object actually exists or that it could actually exist in some possible world there is some other hidden quality or stuff that applies uniquely to these objects only and that philosophers need to uncover is simply false. For let me remind you that Bill is not interested in giving a causal or scientific account of Socrates’ existence. Bill’s question is not about the causal antecedents of Socrates’ existence. Nor is it about the qualities Socrates enjoys. The question rather is about something that is necessarily identical to the existence of contingently existing individuals but is not their existence. Well, I submit, that the only thing that is necessarily identical to the existence of contingently existing individuals is, what else, their existence.

BV: Peter is now simply making gratuitous assertions when he is not making assertions to which I can attach no meaning. He writes, "The question rather is about something that is necessarily identical to the existence of contingently existing individuals but is not their existence." That's gibberish. I am concerned precisely with the real (extramental) existence of contingent individuals and nothing else. My point is that this existence cannot be denied in an eliminativist manner or reduced to something else such as the instantiation of a property, no matter how exotic. Furthermore, theories like Peter's, despite all the fancy footwork and rigmarole displayed above, in the end simply presuppose that there are existing individuals. He gave his answer above in the form of a slogan:

It is true that I am not concerned with empirical-causal explanations of contingent existents. I am concerned with the logically prior question of the existence of the causal relata without which there would be no causal relations and thus no causal explanations.

(e) For let us suppose otherwise. Suppose that it is necessarily the case that SE-stuff is present if and only if the property of contingent existence is present, but these are not the same property. But how can that be? If the presence of these properties necessarily coincides, then how can they be distinct? What would count in favor of distinguishing them despite the fact that they must coincide jointly? And if Bill cannot cite what distinguishes them under these conditions, then isn’t this simply admitting that the property, quality, mode or whatever that makes up SE-stuff just is the contingent existence of an object? And admitting this much is admitting that the *thick* presupposition behind Bill’s question is false; that there cannot be another property, quality, mode, or “stuff” that is necessarily like the contingent existence of objects but is somehow distinct from it.

BV: These objections are simply artifacts of Peter's illicit introduction of this 'stuff' talk which has little to do with anything I have actually said. See my above remarks.

V. Bill’s Circularity Objection to the Thin TSE B

(a) Bill’s circularity objection has a bite against the thin conception only on the assumption that his question “What is it for a contingently existing individual such as Socrates to exist?” has a meaningful *thick* content and, hence, a substantive *thick* answer. But, both of these assumptions are false. A *thick* answer is impossible to this question for reasons cited above.

BV: What reasons were those? You gave no reasons that I can see; you simply made assertions.

(b) If this is correct, then in what sense can there be any substantive theory of singular existence, thick or thin or whatever? Well, in order to see how a TSE can be substantive we must first let go of the aspiration that a *thick* theory is possible. Then we must come to terms with the fact that there is a sense in which the concept of the “singular existence of contingent objects” is philosophically primitive. The fact that the existence of Socrates as a singular contingently existing object is philosophically primitive does not mean that interesting questions cannot be asked in this regard. One can ask about the causal antecedents of Socrates’ existence, or ask about what are his essential properties. One can even inquire whether it is possible for two numerically distinct objects to share all of their properties. There are many interesting question, philosophical or otherwise, that can be asked even if we give up on the *thick* project. And we can ask the question of whether there can be a theory which describes the structure of existence without eliminating, reducing, or finding a necessary substitute for it. I submit that the best shot at this question is the *thin* TSE.

BV: Although I see no reason to accept a thin theory of existence, I want to thank Peter for his contribution which helps us all see the issues more clearly.