I was asked by a commenter what motivates the thin theory of existence. One motivation is
. . . the old Platonic riddle of nonbeing. 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. (Willard Van Orman Quine, "On What There Is" in From a Logical Point of View, Harper Torchbook ed., 1963, pp. 1-2)
As I see it, here is how the paradox arises.
1) 'Pegasus does not exist' is true. Therefore:
2) The sentence in question has meaning. (Only meaningful sentences have a truth value.)
3) If a sentence has meaning, then so do its (sentential and sub-sentential) parts. (Compositionality of meaning.) Therefore:
4) 'Pegasus' has meaning. Therefore:
5) Something is such that 'Pegasus' refers to it. ('Pegasus' is a proper name, and the meaning of a proper name is its referent, that to which it refers.) Therefore:
6) 'Pegasus' refers to something that exists. (Everything exists; there are no nonexistent objects; one cannot refer to what does not exist for it is not there to be referred to.) Therefore:
7) Pegasus must exist for it to be true that Pegasus does not exist. Paradox!
None of the first four propositions is plausibly denied. To avoid the conclusion, we must deny either (5) or (6) and the assumptions that generate them. Now Quine is no Meinongian/Wymanian. Quine advocates a Russellian solution which amounts to rejecting (5) by rejecting the assumption that the meaning of a proper name is exhausted by its reference. For Russell, ordinary proper names are definite descriptions in disguise. This allows them to have meaning or sense without reference. Thus 'Pegasus' is elliptical for 'the winged horse of Greek mythology.' This allows the following contextual paraphrase of 'Pegasus does not exist':
It is not the case that there exists an x such x is the winged horse of Greek mythology
which is free of paradox. What the paraphrase says is that the definite description which gives the sense of 'Pegasus' is not satisfied. Equivalently, it says that the concept winged horse of Greek mythology is not instantiated. Thus the original sentence, which appeared to be about something that does not exist but which, if it existed, would be an animal, is really about about a description or concept which does exist and which is assuredly not an animal.
It is a brilliant solution, prima vista. It works for negative general existentials as well. 'Unicorns do not exist,' despite its surface grammar, cannot be about unicorns -- after all, there aren't any -- it is about the concept unicorn and predicates of it the property of not being instantiated. Extending the analysis to affirmative general existentials, we can say that 'Horses exist,' for example, is not about horses -- after all, which horses would it be about? -- it is about the concept horse and predicates of it the property of being instantiated.
What about singular affirmative existentials such as 'Harry exists'? Quine maintains that, in a pinch, one can turn a name into a verb and say, with truth, 'Nothing pegasizes' thereby avoiding both Plato's Beard and Meinong's Jungle so as to enjoy, clean-shaven, the desert landscape bathed in lambent light. So what's to stop us from saying 'Something Harry-sizes'? (Quite a bit, actually, but I won't go into that in this post, having beaten it to death in numerous other entries. Briefly, there are no haecceity-concepts: there is no such concept Harry-ness that (i) can exist uninstantiated; (ii) if instantiated is instantiated by Harry and Harry alone in the actual world; (iii) is not instantiated by anything distinct from Harry in any possible world.)
Let us now pause to appreciate what the Russellian (or rather 'Fressellian') approach accomplishes in the eyes of its advocates. It untangles Plato's Beard. It avoids Meinong's jungle. It preserves the existence-nonexistence contrast by situating it at the second level, that of descriptions, concepts, propositional functions, properties, as the contrast between satisfaction-nonsatisfaction (for descriptions), instantiation-noninstantiation (for concepts and properties), and having a value-not having a value for propositional functions, or as Russell puts it, being sometimes true or the opposite.
What's more, it diagnoses the failure of certain versions of the ontological argument. Descartes' Meditation Five version has it that God exists because God has all perfections and existence is a perfection. But if Frege and Russell are right, existence is not even a property of God let alone a perfection of him inasmuch as '. . .exist(s)' has no legitimate use as a first-level predicate and can be be properly deployed only as a second-level predicate. (God is an individual.)
Last, but not least, the Fressellian analysis consigns entire libraries of school metaphysics to he flames, the books in which drone on endlessly about Being and Existence and the distinctio realis, and the analogia entis, and ipsum esse subsistens, ad nauseam. Swept aside are all the hoary and endlessly protracted debates about the relation of essence and existence in individuals: is it a real distinction, and what could that mean? Is it a formal distinction, and what could that mean? Etc. On the Frege-Russell approach there simply is no existence of individuals.
And now you know why the thin theory is called 'thin.' It could also be called 'shallow' in that it eliminates existence as a deep and mysterious topic. The thin theory disposes of existence as a metaphysical topic, reducing it to a merely logical topic. As Quine famously says in an essay other than the one cited above, "Existence is what existential quantification expresses." Thus 'Cats exist' says no more and no less than 'For some x, x is a cat.' You will note that the analysans makes no mention of existence. It features only the word 'cat' and some logical machinery. Existence drops out as a metaphysical topic.
Of course, I don't accept the thin theory; but as you can see, I appreciate what motivates it in the minds of its adherents.
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