Editing Willard Van Orman Quine (section)

====Existence and its contrary====
The [[Empty name|problem of non-referring names]] is an old puzzle in philosophy, which Quine captured when he wrote,

<blockquote>A curious thing about the ontological problem is its simplicity. It can be put into three Anglo-Saxon monosyllables: 'What is there?' It can be answered, moreover, in a word—'Everything'—and everyone will accept this answer as true.<ref name=OWTI>W. V. O. Quine, "[[:s:On What There Is|On What There Is]]", ''The Review of Metaphysics'' '''2'''(5), 1948.</ref></blockquote>

More directly, the controversy goes:
<blockquote>
How can we talk about [[Pegasus]]? To what does the word 'Pegasus' refer? If our answer is, 'Something', then we seem to believe in mystical entities; if our answer is, 'nothing', then we seem to talk about nothing and what sense can be made of this? Certainly when we said that Pegasus was a mythological winged horse we make sense, and moreover we speak the truth! If we speak the truth, this must be truth ''about something''. So we cannot be speaking of nothing.
</blockquote>

Quine resists the temptation to say that non-referring terms are meaningless for reasons made clear above. Instead he tells us that we must first determine whether our terms refer or not before we know the proper way to understand them. However, [[Czesław Lejewski]] criticizes this belief for reducing the matter to empirical discovery when it seems we should have a formal distinction between referring and non-referring terms or elements of our domain. Lejewski writes further:
<blockquote>
This state of affairs does not seem to be very satisfactory. The idea that some of our rules of inference should depend on empirical information, which may not be forthcoming, is so foreign to the character of logical inquiry that a thorough re-examination of the two inferences [existential generalization and universal instantiation] may prove worth our while.
</blockquote>

Lejewski then goes on to offer a description of [[free logic]], which he claims accommodates an answer to the problem.

Lejewski also points out that free logic additionally can handle the problem of the empty set for statements like <math>\forall x\,Fx \rightarrow \exists x\,Fx</math>. Quine had considered the problem of the empty set unrealistic, which left Lejewski unsatisfied.<ref>Czeslaw Lejewski, "Logic and Existence". ''British Journal for the Philosophy of Science'', Vol. 5 (1954–1955), pp. 104–119.</ref>