## Friday, 3 April 2015

### On Quine's Arguments Against QML, Part 3: Ontology

The second objection that Quine levels against quantified modal logic in [1] is that its ontology is “curiously idealistic” and “repudiates material objects” [1, p. 43]. This consideration arises from the same starting point as the objection discussed in the previous subsection: The problem of quantifying into an intensional context

Consider the following:

(6) ∃x(x is red ∧ M(x is round))

Quine says that in order to interpret this sentence, we need supplementary criteria, and suggests one potential criterion:

(ii) An existential quantification holds if there is a constant whose substitution for the variable of quantification would render the matrix true [1, p. 46],

where a ‘matrix’ is simply “an expression which has the form of a statement but contains a free variable” [2, p. 126]. This criterion, he argues has the consequence that

there are no concrete objects (men, planets, etc.), but rather that there are only, corresponding to each supposed concrete object, a multitude of distinguishable entities (perhaps ‘individual concepts’, in Church’s phrase) [1, p. 47].

Thus, instead of having concrete objects such as Venus, Mars, and Pluto in our ontology, we have instead things such as Venus-concept, Evening-Star-concept, Morning-Star-concept, etc. Let us spell out his argument for this conclusion.

Suppose that Venus, Evening Star, and Morning Star are all constants in our language suitable for use in criterion (ii). Each of these constants bears a certain relationship to itself and to the other in virtue of the empirical data; Quine calls this relation ‘congruence’. The question is what these constants are names of; if they pick out concrete objects in the domain, then they should all pick out the same concrete object, namely, a planet. But we shall see that truths about congruence prevent us from taking as the values of these constants concrete objects.

Let C represent the relation of congruence; we have the following two truths:

(7) Morning Star C Evening Star ∧ L(Morning Star C Morning Star)

(8) Evening Star C Evening Star ∧ ¬L(Morning Star C Evening Star)

From these along with (ii), we can conclude that there are at least two distinct objects in the ontology which are congruent with ‘Evening Star’:

(9) ∃x(x C Evening Star ∧ L(x C Morning Star)

(10) ∃x(x C Evening Star ∧ ¬L(x C Morning Star)

But since there is but one planet Venus, it must be the case that the ontology is not made up of planets and other concrete objects, but rather concepts of planets, for only then could we find constants whose substitution for the variable would make (9) and (10) true.

A strange ontology this may be, but it does not immediately follow from this that QML is incoherent or that expressions involving quantification into modal contexts are nonsense. For let us recall what Quine’s modal logic is a modal logic of: Not logical necessity, not physical necessity, but analytic necessity. As discussed above, the notion of analyticity is defined in terms of synonymy. Synonymy—sameness of meaning or sameness of intension—is itself a notion concerning concepts, not objects. Therefore, in a modal logic designed to explicate a notion based on concepts rather than objects, we should not be surprised that the ontology of that logic is populated with concepts, rather than objects. What is surprising is that Quine does not apparently recognize this, despite the fact that he says, elsewhere, that “being necessarily or possibly thus and so is in general not a trait of the object concerned, but depends on the manner of referring to the object” [3, p. 148, emphasis added]. If the logic of necessity is thus not about properties of actual objects but of ways that objects are described, then we should in fact expect that the ontology of the logic to not be populated by actual objects, but rather by ways that objects can be described, i.e., by concepts.

#### References

• [1] W. V. Quine. The problem of interpreting modal logic. Journal of Symbolic Logic, 12(2):43–48, 1947.
• [2] Willard V. Quine. Notes on existence and necessity. Journal of Philosophy, 40(5):113–127, 1943.
• [3] W. V. O. Quine. From a Logical Point of View. Harper & Row, 2nd edition, 1961.

1. Again (I commented on the last post), I'm happy to see some posts on these issues. Some criticisms:

'Each of these constants bears a certain relationship to itself and to the other in virtue of the empirical data; Quine calls this relation ‘congruence’.'

It looks like you've made an interpretative mistake here and a use-mention slip, but my main comment is just that I'm confused by this and the surrounding text. Quine is talking about a relation between heavenly bodies (or a heavenly body), not between linguistic expressions ('constants'): he says he uses 'C' 'to express the relation which Venus, the Evening Star, and the Morning Star, e.g., bear to themselves and, according to empirical evidence, to one another'. And this is borne out by the examples: 'C' gets flanked by terms referring to Venus, not constants.

So there's certainly, I think, a misattribution in what you say, but maybe *you're* intentionally *using* 'Morning Star' etc. as expressions standing for expressions... in any case, I'm very confused as to what's going on here.

2. Sara, I think your (8) should have "~L(Evening star C Morning star)" instead of "~L(Morning star C Evening star)". cf., Quine's 1947 original, page 47, line 18. Then your (8) will be the result of substituting "Evening star" for both occurrences of "x" in the matrix of your (10).

Jeff

1. You're absolutely right; thanks for catching!