Willard Van Orman Quine

“ Thus it is that the great mediaeval controversy over universals has flared up anew in the modern philosophy of mathematics. The issue is clearer now than of old, because we now have a more explicit standard whereby to decide what ontology a given theory or form of discourse is committed to: a theory is committed to those and only those entities to which the bound variables of the theory must be capable of referring in order that the affirmations made in the theory be true. ”

“ Conceptualism holds that there are universals but they are mind-made. Intuitionism, espoused in modern times in one form or another by Poincaré, Brouwer, Weyl, and others, countenances the use of bound variables to refer to abstract entities only when those entities are capable of being cooked up individually from ingredients specified in advance. As Fraenkel has put it, logicism holds that classes are discovered while intuitionism holds that they are invented—a fair statement indeed of the old opposition between realism and conceptualism. ”

“ Are no two possible things alike? Is this the same as saying that it is impossible for two things to be alike? Or, finally, is the concept of identity simply inapplicable to unactualized possibles? But what sense can be found in talking of entities which cannot meaningfully be said to be identical with themselves and distinct from one another? These elements are well-nigh incorrigible. By a Fregean therapy of individual concepts, [2] some effort might be made at rehabilitation; but I feel we’d do better simply to clear Wyman’s slum and be done with it. ”

“ Our acceptance of an ontology is, I think, similar in principle to our acceptance of a scientific theory, say a system of physics: we adopt, at least insofar as we are reasonable, the simplest conceptual scheme into which the disordered fragments of raw experience can be fitted and arranged. Our ontology is determined once we have fixed upon the over-all conceptual scheme which is to accommodate science in the broadest sense ”

“ A platonistic ontology of this sort is, from the point of view of a strictly physicalistic conceptual scheme, as much a myth as that physicalistic conceptual scheme itself is for phenomenalism. This higher myth is a good and useful one, in turn, in so far as it simplifies our account of physics. Since mathematics is an integral part of this higher myth, the utility of this myth for physical science is evident enough. In speaking of it nevertheless as a myth, I echo that philosophy of mathematics to which I alluded earlier under the name of formalism. ”

“ If spatio-temporal reference is lacking when we affirm the existence of the cube root of 27, this is simply because a cube root is not a spatio-temporal kind of thing, and not because we are being ambiguous in our use of ‘exist’. [1] However, Wyman, in an ill-conceived effort to appear agreeable, genially grants us the nonexistence of Pegasus and then, contrary to what we meant by nonexistence of Pegasus, insists that Pegasus is. Existence is one thing, he says, and subsistence is another. The only way I know of coping with this obfuscation of issues is to give Wyman the word ‘exist’. ”

“ But we do not commit ourselves to an ontology containing Pegasus or the author of Waverley or the round square cupola on Berkeley College when we say that Pegasus or the author of Waverley or the cupola in question is not. We need no longer labor under the delusion that the meaningfulness of a statement containing a singular term presupposes an entity named by the term. A singular term need not name to be significant. ”

“ Judged in another conceptual scheme, an ontological statement which is axiomatic to McX’s mind may, with equal immediacy and triviality, be adjudged false. One may admit that there are red houses, roses, and sunsets, but deny, except as a popular and misleading manner of speaking, that they have anything in common. The words ‘houses’, ‘roses’, and ‘sunsets’ are true of sundry individual entities which are houses and roses and sunsets, and the word ‘red’ or ‘red object’ is true of each of sundry individual entities which are red houses, red roses, red sunsets ”

“ The useful ways in which people ordinarily talk or seem to talk about meanings boil down to two: the having of meanings, which is significance, and sameness of meaning, or synonymy. What is called giving the meaning of an utterance is simply the uttering of a synonym, couched, ordinarily, in clearer language than the original. ”

“ For we have seen that being a name of something is a much more special feature than being meaningful. He cannot even charge us—at least not by that argument—with having posited an attribute of pegasizing by our adoption of the predicate ‘pegasizes’.
However, McX hits upon a different strategem. “Let us grant,” he says, “this distinction between meaning and naming of which you make so much. Let us even grant that ‘is red’, ‘pegasizes’, etc., are not names of attributes. Still, you admit they have meanings. ”

“ This opposition is no mere quibble; it makes an essential difference in the amount of classical mathematics to which one is willing to subscribe. Logicists, or realists, are able on their assumptions to get Cantor’s ascending orders of infinity; intuitionists are compelled to stop with the lowest order of infinity, and, as an indirect consequence, to abandon even some of the classical laws of real numbers. [8] The modern controversy between logicism and intuitionism arose, in fact, from disagreements over infinity. ”

“ Wyman’s overpopulated universe is in many ways unlovely. It offends the aesthetic sense of us who have a taste for desert landscapes, but this is not the worst of it. ”

“ Similarly, from a phenomenalistic point, of view, the conceptual scheme of physical objects is a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part. ”

“ Moreover, the doctrine of meaninglessness of contradictions has the severe methodological drawback that it makes it impossible, in principle, ever to devise an effective test of what is meaningful and what is not. It would be forever impossible for us to devise systematic ways of deciding whether a string of signs made sense—even to us individually, let alone other people—or not. ”

“ For an adequate basis for agreement among mathematicians can be found simply in the rules which govern the manipulation of the notations—these syntactical rules being, unlike the notations themselves, quite significant and intelligible. [9]
I have argued that the sort of ontology we adopt can be consequential—notably in connection with mathematics, although this is only an example. Now how are we to adjudicate among rival ontologies? Certainly the answer is not provided by the semantical formula “To be is to be the value of a variable” ”

“ The unanalyzed statement ‘The author of Waverley was a poet’ contains a part, ‘the author of Waverley’, which is wrongly supposed by McX and Wyman to demand objective reference in order to be meaningful at all. But in Russell’s translation, ‘Something wrote Waverley and was a poet and nothing else wrote Waverley’, the burden of objective reference which had been put upon the descriptive phrase is now taken over by words of the kind that logicians call bound variables, variables of quantification, namely, words like ‘something’, ‘nothing’, ‘everything’. ”

“ Whatever we say with the help of names can be said in a language which shuns names altogether. To be assumed as an entity is, purely and simply, to be reckoned as the value of a variable. In terms of the categories of traditional grammar, this amounts roughly to saying that to be is to be in the range of reference of a pronoun. ”

“ The rule of simplicity is indeed our guiding maxim in assigning sense data to objects: we associate an earlier and a later round sensum with the same so-called penny, or with two different so-called pennies, in obedience to the demands of maximum simplicity in our total world-picture. ”

“ Possibility, along with the other modalities of necessity and impossibility and contingency, raises problems upon which I do not mean to imply that we should turn our backs. But we can at least limit modalities to whole statements. ”

“ Nonbeing must in some sense be, otherwise what is it that there is not? This tangled doctrine might be nicknamed Plato’s beard; historically it has proved tough, frequently dulling the edge of Occam’s razor. ”

“ How many possible men are there in that doorway? ”

“ A curious thing about the ontological problem is its simplicity. It can be put in three Anglo-Saxon monosyllables: ‘What is there?’ It can be answered, moreover, in a word—‘Everything’—and everyone will accept this answer as true. ”