Avançando em alguns temas que já me interessavam desde o início das pesquisas para o doutorado, encontrei o bom artigo de Markus Gabriel sobre The Meaning of “Existence” and the Contingency of Sense.
Ao comentar a posição fregeana, Gabriel apresenta um interessante argumento, a partir da própria posição de Frege, contra a posição de que a Existência seria a propriedade de conceitos terem extensão maior que zero:
Frege ties the notion of existence as a higher-order predicate to his notion of reference. The extension of a concept constitutes the, in principle, countable range of objects falling under it. In this way, his notion of existence squares with his attempt to build mathematics on formal semantics (in the sense of a Begriffsschrift), to the extent that number theory can be based on set theory and set theory is tied to formal semantics. Existence thus turns from mysterious metaphysical Being into the existential quantifier. This idea culminates in Quine’s oft-quoted dictum “to be is to be the value of a bound variable.”
Prima facie there seems to be nothing wrong with this move. However, it ultimately neglects the dimension of sense, which is constitutive for the distinction between sense and reference. As Frege himself points out, we have no way to access reference (and hence to assert existence) without sense. Yet, his disregard of sense in his theory of existence, that is, in his ontology, leads him to identify existence with quantifiability.