Quine and Carnap on Ontology

This is rather rambling, and what I say about Quine is speculative and probably not entirely correct, but I'm posting anyway.

After complaining about Quine's "On What There is" being diametrically opposed to Carnap's "Empiricism, Semantics and Ontology" (and I was thinking of it as the third in a triumvirate of Quinean oppositions to the core of Carnap's philosophy, the other two being the analytic/synthetic distinction and modal logic) the words "Ontological Relativity" popped up in my head, by way of reference to a contribution of Quine's in this area which I have never actually seen.

I searched my little philosophical library and discovered that I really did not have a copy, and decided to have a look when next I visit the British Library.
(and also to get Code from PGRICE, no longer readable on google books, and the journal in which Grice on Aristotle appears).


However, notwithstanding my never having read the paper, just the sight of a few lines of commentary suffices to change my perception of Quine on this topic.  It seems that though "On What there is" seems contrary to Carnap, "Ontological Relativity", apart from being naturalistic rather than formalistic, is on the same lines as Carnap, i.e. it is relativistic; ontology is relative to language.  That also makes it broadly similar I would guess, to Grice, for he had a relaxed liberal attitude to ontology, and one might perhaps think he allowed relativity to context not just language (which I'm sure the other two could be stretched to as well).

It may be worth exploring this a little further for we are here saying something about absolute metaphysics, i.e. that ontology is not a part of it, ontological claims are supposed to be relative rather than absolute.

"On What there is" is perhaps ambivalent, rather than clearly opposite to the later paper (which I haven't read, still).
It certainly seems antithetical to Carnap, because it is about "ontological commitment" and it is easy to think that that is exactly what Carnap denies when he distinguishes between internal and external questions and holds that a positive answer to an internal ontological question should not be confused with assent to the apparently relevant but actually meaningless external question.
But if we read it in this way then Quine the logical empiricist almost comes out as a Platonist.

My feeling is that the origins of this paper come from his analysis of Russell's "no class theory".  Russell introduced the idea of "incomplete symbol" which appears in his theory of descriptions (in "On Denoting") but which applies also to his notation for classes in Principia Mathematica.  Quine provides, in his "Set Theory and Its Logic" an analysis of exactly how much mathematics you can achieve by the use of "incomplete symbols" to talk as if classes exist without actually assuming the existence of classes.  The disadvantage of this technique if you take it seriously is that, by hypothesis, these things that look like classes as far as the notation is concerned don't actually exist, and therefore are not in the range of bound variables (after all, existence, in modern logic, is just a quantifier, the things which exist are just the things in the range of the existential quantifier).  In this context Quine is using the question whether or not you want the "class" to be in the range of quantification as a test for whether it can properly be called a virtual class or incomplete symbol.  He is investigating what can be done with few things in the range of quantification.

Quine conducts this analysis in the context of set theory, and its relevance to Principia Mathematics remains to be established.  It is now generally accepted that Russell's no-class theory does not eliminate classes in the way that they would be eliminated if only virtual classes were admitted in set theory.
This is because Russell's theory of types does have a complete hierachy of types of propositional functions, which, apart from not being extensional, are logically similar to sets.  Russell's incomplete symbols in this case allow classes to be eliminated in favour of propositional functions, rather than eliminated altogether.  So Russell's ontology is almost as rich as zermelo set theory, but it just happens that the things in it are mostly functions not sets.
The effect is that the limitations Quine illustrates on what can be done with virtual classes in set theory do not apply to their use in Russell's theory of types.

Russell's ontological parsimony (at roundabout the time of Principia) was not limited to the "no class" theory.  He followed up with his philosophy of logical atomism, which is more explicitly metaphysical.  As well as the distinction between real classes and virtual classes, Russell talks about logical fictions.
When he considers how to apply modern logic to science a key idea is the idea of a "logical construction". So the idea is that complex objects are logical constructions from atomic entities of some kind (perhaps material atoms, perhaps sense data).  These logical constructions yield logical fictions, but this does not mean that we do not need to have them in the range of the quantifiers.
So incomplete symbols might possibly count as logical fictions, but they don't by any means exhaust the logical fictions, many of which (like propositional functions in general) are in the range of quantifiers.

If we read Quine here as criticising Russell's beliefs about what can be achieved with incomplete symbols, then the criticism fails in two ways.  Firstly because what you can do with incomplete symbols is not independent of context, Russell could manage without classes in the context of his type theory, even though Quine could not in a first order set theory (because he has no alternative ontology).  Secondly, we may observe that Russell no more than Carnap believes that the range of the quantifiers has the metaphysical significance which Quine seems to suggest.  Russell is happy to quantify over logical fictions, and presumably does not think that logical fictions are "real".  Carnap goes one step further in denying that the metaphysical question is meaningful (let alone relevant).

Carnap's step here is widely misunderstood, but I think should be regarded as possibly his most important contribution to metaphysics, for I know of no previous philosopher who considered it metaphysical even to allow that the questions (e.g. absolute, external. questions about existence) have an answer.

This connects us with Carnap's "Principle of Tolerance".
In "On What there Is", the alleged ontological commitment involved (let us suppose) in the use of a language, means that someone can be accused of inconsistency for using two languages whose ontological commitments are incompatible.  It is this kind of accusation of inconsistency which, according to Carnap, provoked his principle of tolerance.

As a graduate student he recalls discussions with friends in which he would use (say) materialistic or idealistic language depending on who he was talking to.  He was then criticised by some for inconsistency.  The idea is that you either are a materialist or an idealist.  Whichever you are you must not use the language of the other, for that entails assent to multiple incompatible metaphysical ontologies.

Carnap's principle of tolerance is just the rejection of this point of view, the relativisation of metaphysics (which of course, once relativised may no longer be called metaphysics, and of course is not counted as metaphysics by Carnap, because it is just a working out of the semantics of the language and hence of necessity de dicto rather than de re).


As to "The City of Eternal Truth", where are these to be found in ontology.
After all this relativisation what room do we have for ontological absolutes, are there any necessary truths in ontology?
Well, the obvious candidates is questions of consistency.
Even if any ontology were possible, not every description of an ontology is consistent.
The natural context in which the most difficult questions of this kind are addressed is set theory, where the relative consistency of large cardinals is considered.
This is just the preferred language in which such questions are considered, and questions about the consistency of arbitrary logical systems (and their underlying ontologies) are generally answered by reduction to set theory.
If we argue that such questions are "absolute" in some sense, does that make them metaphysics rather than just logic?

RBJ