The Supposed Role of Ontological Expressions

What is the supposed role of ontological expressions, the role which is supposed to be preserved across alternative languages? Before we can sensibly ask whether different sets of ontological expressions play that role equally well we must be clear on what ontological expressions are supposed to do. “Be used for asking questions about what there is” does not suffice as an answer. (Eklund 2008, 30)

It seems to me that the roles of ontological expressions change considerably across languages. The role of the objectual existential quantifier is (sometimes) to say that a description is true of something without saying what that thing is. The role of the objectual universal quantifier is sometimes to say that a description is true of everything without having to say of each thing individually that the description is true of it. Other times, the role of the objectual universal quantifier is to say that a description is true of everything without having to take a position on what things there are. In the hands of one theorist, the role of the substitutional quantifiers, roughly, is to provide truth-conditions for sentences without saying what (features of) objects make the sentence true. In the hands of another theorist, the role of the substitutional quantifiers is to provide truth-conditions for referentially opaque sentences. The role of the various Meinongian ontological notions surrounding being and objects is, well, to state Meinong’s theory of being and objects.

The uses of ontological expressions differ from language to language and from theorist to theorist. As far as I can tell, the common role for ontological expressions in different languages in the hands of different theorists is just this: to do what they are supposed to do in the language according to the purposes of the theorist. This is not to say that just any expression can be ontological, because just any expression has this sort of role. The category of ontological expressions is not defined by the role its members play. I suggested a way of categorizing existence-like expressions in my last post.

Incidentally, I think what I’ve had to say has been more-or-less in line with Carnap. I don’t think Carnap would say that what ontologists (or, given his antipathy towards ontology so described, he might say “linguistically savvy post-ontological philosopher”) ought to be doing is finding the role that ontological expressions ought to play, and then creating languages in which the ontological expressions best fit that role. He said that theorists choose whole languages according to the uses to which they would like to put them. I think he would have said, if prompted, that there is no one use for language in general. I also think he would have said, if prompted, that, for that reason, there is no one use for the ontological apparatus of language in general.

Existence-Likeness

I would like to take a stab at defining “existence-like” as characterized in Eklund (2008).

An expression is existence-like if it is translated by “exists” in English.

For starters, this handles the cases of disputes about mereology. If L has some formal mereology, with formal criteria for when things have a fusion, and s is the sentence in L stating that there is no fusion that is a table of a certain number of particles "arranged table-wise", then I think we would translate s in English with something such as "There is no table composed of x, y, z particles." The quantifier in L is translated in English with a "there is" equivalent to "exists".

The definition also handles a number of cases related to deviant logics. Consider a schema with branching quantification such as:

For all w there is an x,
(1) such that F(w, x, y, z).*
for all y there is a z,

This might seem to present a problem, since different theorists will translate (1) different ways. Proponents of branching quantification – and especially proponents of branching quantification as a resource for schematizing the logical form of actual English sentences – will translate sentences of this form more-or-less homophonically (perhaps adding some punctuation or inflection marks). Proponents of classical FOL, such as Quine, will probably translate it with a sentence of the form:

(2) For all x there is an f, and for all y there is a g, such that F(x, f(x), y, g(y).

So a potentially existence-like expression, such as the branched existential quantifier in (1), will be translated multiple ways in English, depending on the syntactic and ontological commitments of the translator. But this does not seem actually to be a problem for our definition of “existence-like”, since both the classical logician and the proponent of branching quantification translate the “there is” of (1) with a “there is”. Where they differ is on the range of values of the existentially quantified variables.

Another problem is the theorist who thinks that “there is” and “exists” are not synonymous or equivalent, or that existential quantifications are not existence claims. This view can manifest itself in a number of ways. The most obvious case would be one in which a theorist uses a language in which the “existential” quantifiers are interpreted substitutionally and are intended to help regiment some fragment of English discourse containing “there is”, but no fragment containing “exists”. Given her preferred regimentation, and the existence of the name “Pegasus” in English, she might consider the following true:

(3) There is at least one winged horse.

The classical logician, who prefers to regiment “there is” discourse with objectual quantification alone, has a few options here. She can translate the substitutionally regimented counterpart of (3), and other sentences of similar logical form, just as (3), but with “there is” interpreted objectually. She can treat the translatum as either true or false depending on her preferred theory and interpretation of fictions and empty names in English. She can also employ semantic ascent, translating the substitutionally regimented counterpart of (3) as:

(4) “There is at least one winged horse” is true.

Again, she can evaluate (4) based on her preferred theory of truth. Perhaps she thinks “true” is implicitly relativized to something more precise than English; perhaps she thinks (3) isn’t truth-apt.

Now, in the case of (3), if the translation is interpreted objectually, then I think it is clear that the existential quantifier in the substitutionally regimented counterpart of (3) satisfies our definition of “existence-like”. Even if (3) is viewed as true, but elliptical (as required by certain theories of fiction or empty names), I can’t see how even the fully explicit interpretation could lack the expression “there is”. And if there is a “there is” in the fully explicit version of (3), I don’t see how we could deny that that “there is” is the translation of the existential quantifier in the substitutionally regimented counterpart of (3), as required by our definition of “existence-like”.

If we take the route of semantic ascent, things get a little weirder. After all “there is” does occur in (4), but it is mentioned, not used. Still, my intuition is that “there is” is the translation in (4) of the substitutionalist’s existential quantifier. One might want to say that “‘there is’”, and not “there is” is the translation, but “‘there is’” does not occur in (4), strictly speaking. (There is no close-quotation mark after the “there is” in (4).) Alternatively, assume that, if a word in a sentence is not treated by a translation as elliptical, or as an auxiliary term in a construction-yielding particle phrase, then part of the translation of the sentence is a translation of the word. Then, since the substitutionalist’s existential quantifier is not being treated as elliptical or auxiliary in the translation (4), there must be a translation in (4) of that quantifier. But that translation obviously has to be “there is”.

(Note that we encounter a similar sort of situation when the classical logician translates second-order quantification. If she doesn’t want to translate second-order quantification objectually into set theory, then she will most likely treat it metalinguistically. For instance, she might translate “There is a P and an x such that P(x)” as “There is a “P” such that ‘There is an x such that P(x)’ is true”. The second-order quantification over P becomes metalinguistic quantification over “P”.)

Recall that our substitutionalist distinguishes between “there is” and “exists” as between substitutional and objectual quantification. What happens when she wants to translate from another substitutional language into English? She will translate existential quantification with “there is”, but not with “exists”. We have seen that, in these cases, the classical logician, who treats “there is” and “exists” as equivalent, can use either of these translations. In this case, then, not only is it unclear what translatum sentence to use (which is not necessarily a problem for our definition of “existence-like”), it is also unclear whether the translatum should contain “exists” as the translation of a given non-English expression. Since the questions about whether and when to use substitutional or objectual quantification are fundamental ontological questions, and we are defining “existence-like” in order to help answer these questions, it would be silly to require that we settle the questions about whether and when to use substitutional or objectual quantification in order to apply our definition correctly. I think we need to modify the definition. The only modification I can think of that works (and is also the simplest) is this:

An expression is existence-like if it is translated either by “exists” or “there is” in English.

This solves our problem, since both the substitutionalist and the classical logician satisfy this definition. This also solves a similar problem, which we haven’t explored, for Meinongian non-English languages.

This solution might create a problem of its own, however. The substitutionalist and the Meinongian have sought to create an interesting distinction between “exists” and “there is”. To some extent, our modified definition erases that distinction. We just observed that we don’t want our definition to trivially settle ontological questions. Has our modified definition done just that?

I think not. The point of a definition of existence-likeness is to enable us to survey what meanings it is theoretically possible to assign to “exists” and “there is” when doing ontology. From a Carnapian point of view, we could say that the point was to find out what terms in what languages have semantic rules that we can use to explicate “exists” and “there is” in English. Our definition indicates that we can use (separately) the Meinongian and the substitutional rules for “there is”, as well as other rules. But surely if these rules determine existence-like uses for expressions, and the rules do not prohibit the use of other rules for distinct expressions (such as the Meinongian or objectual “exists”), then our definition does not prohibit the use of both these sorts of expressions to state an ontology. Simply because we could use the Meinongian rules for “there is” to explicate “exists” does not mean that we could not use distinct rules to explicate “exists” a different way in the same language. So our definition is not problematic for that sort of reason.

* - I'm having trouble writing branching quantifiers on Blogger. The two quantifier strings on the different lines are supposed to be on two different branches.

On What There Is and What We Can Perceive

Our knowledge of the physical world depends on our perceptual faculties being just about as sensitive as they are. Consider an ideally rational animal, or ideally rational community of inquirers, with only, say, our auditory and proprioceptive faculties. Call it A. It is hard to imagine how A could develop anything we should consider a complete physics. Perhaps I’m wrong – I’m only going on conceivability here – but it sure seems as if the ontology of the theory A would possess at the end of inquiry just could not be the same as any ontology human beings will reach at the end of inquiry.*

A’s theory and ontology would be, in some sense, inadequate. This is because we have all of the evidence A has and more, and A’s theory is inadequate to account for all of our evidence. My intuition is that this inadequacy has some sort of normative force; that is, in some sense, A should adopt a theory that is able to account for our evidence as well as our own completed physics.

Here’s my question: What reason do we have, if any, not to believe that, for all we know, we are in A’s position? More precisely, what reason do we have, if any, not to believe that, for all we know, there is some (perhaps uninstantiated) perceptual faculty, such that our theories should account for the evidence this faculty would furnish for us, were we to have it, in the same sense that A’s theory should account for the evidence furnished by our visual faculties? To be sure, we have pretty good evidence to suspect that none of the animals on Earth have such a perceptual faculty. The question is whether, for all we know, something could have such a faculty, with the world and its contents remaining otherwise entirely as they are.

The only reason I can think of – if it is true – would be furnished by a certain sort of “instrumentalist” meta-ontology. I take instrumentalism to be the view that ontology O is to be preferred over ontology P just in case O is better suited to our purposes than P. Once we have all the evidence in hand, we answer these sorts of “big picture” ontological questions (Carnap might have called them external questions) by recourse to our purposes in theorizing. Suppose our purposes are just to develop a theory with all of the virtues of descriptive adequacy, explanatory power, and simplicity that accounts as well as possible for all of the way things appear to us.** In that case, it is clear that no such troublesome perceptual faculty could exist, because no perceptual faculties other than our own can have any normative bearing on our choice of ontology. Note that this sort of meta-ontology makes it difficult to hold on to the initial intuition I had about A’s epistemic situation – namely, that A should adopt a theory that is able to account for evidence outside of her own perceptual purview. If we think that ontologies are beholden, at last, only to the way things appear to the community of inquiry, then the percepts of outsiders, real or imagined, can have no rational bearing on what exists, in our language.

It’s not clear which I like more – this version of instrumentalism or the offending intuition. Is there some adjudicating evidence that I’ve left out of court? Can anyone point me in the direction of some relevant literature?
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* - I’m assuming here that neither we nor A ever experience any sort of divine revelation or anything like that.
** - This description of “our” purposes is really unsatisfactory to me, but I can’t do any better yet. For what it’s worth, it probably beats Carnap in ESO, where he suggests that the purpose for which he uses the language of serious theory is “the purpose of communicating factual knowledge.”

Is Existence a First-Order Property?

I think I’ve found a not-so-bad argument for construing existence as a first-order property. Here goes:

Begin with the principle that first-order properties are those things in virtue of which a sentence of the form “x is not identical to y” is true, for some substitution of individual-symbols for “x” and “y”. So existence is a first-order property if some such statement is true solely in virtue of the truth of a corresponding sentence of the form “x exists” or “x does not exist” – or, if you like, corresponding sentences of the form “there is a z, such that x = z” and “there is no z, such that x = z.” Let c1 =def the bottom tennis ball in a certain canister that can contain as many as three tennis balls; let c2 =def the middle tennis ball in that same canister; let c3 =def the ball immediately above c1 in the canister. Now suppose that there are actually only two balls in the canister. Then c3 is above c1, but c2 is not, since c2 does not exist. It seems that ~(c2 = c3).

I would suggest that this is the case just because c2 does not exist. Supporting this contention is the apparent fact that if c2 did exist (i.e. if there were some ball, such that that ball is the middle ball in the canister; if there were some ball, such that that ball is c2), then it would be the case that c2 = c3. But if ~(c2 = c3) just because c2 does not exist, then by our initial principle about first-order properties, existence is a first-order property.

Does this work? Am I missing something? I don’t really understand the necessity of identity. Is some abuse of that principle at work here? Or is my beginning principle about first-order properties false? Or is it actually not the case that ~(c2 = c3) – say, because “~(c2 = c3)” lacks a truth-value?
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Update:

In a comment at the Maverick's, Ockham, writes: "You cannot say 'c2 =def the middle tennis ball in that same canister' and then say 'but c2 does not exist'" Here's my response, which is too long and too irrelevant to the discussion of the Maverick's post to leave on his blog.

I suppose that, in classic FOL, you can't introduce a term through a definite description that doesn't refer. FOL aside, though, do you mean to say that this is incoherent in natural English? "The middle ball in that same canister doesn't exist" does sound strange to me. Admittedly, it sounds more natural to say "There is no middle ball in the canister," which we might formalize "~(Ex)(Middle ball in the canister(x))." It doesn’t sound unnatural to introduce a proper name through that definite description, however. Nor does it sound unnatural to me to say “c2 doesn’t exist” (even though “the middle ball in the canister” is the definition of “c2”), just the same way it doesn’t sound unnatural to say that “Pegasus doesn’t exist.” The big difference between “c2” and “Pegasus” seems to be that “c2” was obviously introduced by a definite description, whereas “Pegasus” was not obviously so introduced. I’m not sure that this difference is enough to make “c2 doesn’t exist” incoherent and “Pegasus doesn’t exist” coherent. Still, we might imagine situations in which a term like "c2" is introduced – say, by a group of people who believe, incorrectly, that there are three balls in the canister – otherwise than by the definite description “the middle ball in the canister.” (Briefly: maybe the group could use a function from canisters to the middle ball in the canister. Maybe they could just start using “c2” to (try to) refer to what they believe to be the middle ball by stating facts that would be true of such a ball, were it to exist.) In any event, I’m not sure that “c2 doesn’t exist” is incoherent, and if it is, we can use other stories about how something like “c2” comes to have a certain meaning, and then tell a story similar to the one I tell about ~(c2 = c3).

Does the Possibility of Discovering Novel Experiences Have Serious Meta-Ontological Consequences?

It sure seems to me as if we can discover new sui generis properties, and that this has some important consequences for the approach to ontology, which I am very sympathetic to, outlined in Carnap’s “Empiricism, Semantics, and Ontology.” Some examples of discoveries of new sui generis properties: that feeling I had when I was writing the verses of Sophie thinking about Alyssa; Dennett's example (from “Quining Qualia”) of discovering that the sound of the open E on a guitar is, in part, composed of the sound of the E harmonic at the 12th fret might also work (especially if "sounds like open E" was a sui generis property before, and so the structure of my linguistic framework is more severely changed around by the introduction of "sounds like the E harmonic at the 12th fret"); also, the first time one tries any really distinctive kind of food, esp. a raw ingredient. Really, any time we use demonstratives like “this experience” because other words just wouldn’t do the trick. (One thing: how do I know the properties are sui generis right off the bat? Well, I don't, especially since I take calling them "sui generis" to amount to a claim about the place of the predicate for the property in the L-structure [i.e., undefined and probably also undefinable]. But I discover them and add them at least to the model at once [even if I only pick out the properties demonstratively], and I can try to reassure myself that they are sui generis later.)

What exactly do I mean by "discover"? I discover a property when I acquire a concept of or else actually refer to a property that was not previously in my ontology, in the model of the language I was using. This property is introduced all at once, not after subtle reflection and meta-reflection on previous experience and theory. It is precisely because it is all at once that I do not know that the property is sui generis, though I think I have my suspicions from the get-go.

What exactly are the consequences? Well, that the changes to an L-structure that we can effect are sometimes completely determined by what seem to be universally adopted methodological norms. It seems like, just in the face of these novel experiences, I have to add the new property to the model of my linguistic framework. There is no room for conceptual engineering at this point (though that can come later - perhaps "sounds like E-12th fret harmonic" later becomes a defined term). Also, a sort of realism about properties - not that we need to quantify over predicate symbols, but that (at least some sui generis) properties are in some sense "out there". They are not necessarily "out there" in that our norms should be such that the property should have been in the model all along; this is not a claim about the inadequacy of our norms, but about the sensitivity of linguistic change to extra-linguistic forces.

At least that’s what I want to say the consequences are, but maybe I’m wrong. In ESO, Carnap says only that in a “linguistic framework” the use of existential quantifiers must be rule-governed. But my discovery of these new properties of my experience (if it was as I describe it) was quite rule-governed, in the sense that I did not violate or change any rules of English semantics in pronouncing it. Perhaps adding a property to a model does not change the rules of a language. It seems to depend on what counts as a “linguistic framework.” If numerically identical frameworks can have different universes of discourse (perhaps relative to a single context) or words (say, predicates coined ad hoc to pick out newly discovered property), then I do not necessarily adopt a new linguistic framework whenever I denote new sui generis properties. I have been thinking of linguistic frameworks as interpreted L-structures, but perhaps this is too rigid. Perhaps we might conceive of linguistic frameworks in such a way that they might be constituted, in whole or in part, by rules for introducing new terms, or even new “kinds” of terms.

I guess I still don’t really have an answer to the question, at first a bit inchoate, that motivated this post: Does the apparent fact that, in our linguistic framework – scientific English? –, we can denote (what we sometimes correctly take to be) entirely new sui generis properties somehow entail that ontology is not guided by the convenient choice of a linguistic framework?

In other words: sometimes we introduce altogether new (sometimes sui generis) properties into our ontology by a process that apparently does not necessitate commitment to any sort of heavy background theory. The introduction, and the need for the introduction, presses on us with a feeling of utter immediacy. Clearly, we are following some norm here – both in feeling the need for the introduction, and in actually executing it (an act perhaps beyond our control). This norm, whatever it is, is meta-ontological. It dictates how and when to introduce new kinds of terms and objects. The question is: can this norm be stated within or somehow compassed by the meta-ontology of ESO, say as a peculiar fact about the rules that constitute the linguistic framework of present-day scientific English? It seems hard to square the utter non-verbalness of the need to follow the norm and ESO’s (perhaps deceptive) appearance of making all ontological norms essentially semantical rules, and meta-ontological norms reasons for changing semantical rules. It all seems to depend on the nature of linguistic rules and linguistic frameworks.