Interpretar o significado de nomes em termos de objetos deveria satisfazer a de- manda da objetividade ou da transcendência do pensamento e ao mesmo tempo a demanda da liberdade, na medida em que a todo termo singular fosse associado um conteúdo específico. Mas como explicar nomes que nomeiam objetos que não exis- tem e as predicações com eles compostas? Em particular, como explicar sentenças e pensamentos que negam a existência de algo? A aporia dos inexistentes seria a principal evidência em favor da várias posições mantidas pelos pensadores da tradição. Apresento nesta subseção as posições iniciais instáveis de Frege, Russell e Meinong perante o problema dos nomes vazios; posições que tiveram de ser complementadas,
5Nas palavras de Frege (1977, 3):
A correspondence, moreover, can only be perfect if the corresponding things coincide and so are just not different things. (. . . ) It would only be possible to compare an idea with a thing if the thing were an idea too. And then, if the first did correspond perfectly with the second, they would coincide. But this is not at all what people intend when they define truth as the correspondence of an idea with something real. For in this case it is essential precisely that the reality shall be distinct from the idea. But then there can be no complete correspondence, no complete truth. So nothing at all would be true; for what is only half true is untrue. Truth does not admit of more and less.
desenvolvidas ou abandonadas pela tradição para tentar lidar com o problema.
Frege
Frege optou pela sugestão de eliminarmos nomes vazios de nossas teorias. Nomes vazios, afinal, só poderiam ser seriamente usados em ficções, não em teorias. (Essa seria a primeira opção de Frege, como veremos. No último capítulo apresento a solução secundária de Frege, a sugestão de que nomes vazios denotam o número 0 ou o conjunto vazio.)
A logically perfect language (Begriffsschrift) should satisfy the conditions, that every expression grammatically well constructed as a proper name out of signs already introduced shall in fact designate an object, and that no new sign shall be introduced as a proper name without having a referent assured. The logic books contain warnings against logical mistakes arising from the ambiguity of expressions. I regard as no less pertinent a warning against apparent proper names having no referents. The history of mathematics supplies errors which have arisen in this way. This lends itself to demagogic abuse as easily as ambiguity — perhaps more easily. “The will of the people” can serve as an example; for it is easy to establish that there is at any rate no generally accepted referent for this expression. It is therefore by no means unimportant to eliminate the source of these mistakes, at least in science, once and for all.(FREGE, 1960b, 70)
Nomes vazios não precisariam de uma semântica, pois nunca seriam usados intenci- onalmente senão em ficções, que não são feitas para serem levadas a sério.
Names that fail to fulfil the usual role of a proper name, which is to name something, may be called mock proper names. Although the tale of William Tell is a legend and not history, and the name ’William Tell’ is a mock proper name, we cannot deny it a sense. But the sense of the sentence ’William Tell
shot an apple off his son’s head’ is no more true than is that of the sentence ’William Tell did not shoot an apple off his son’s head’. I do not say that this sense is false either, but I characterize it as fictitious. . .
Instead of speaking about fiction we could speak of ’mock thoughts’. Thus, if the sense of an assertoric sentence is not true, it is either false or fictitious, and it will generally be the latter if it contains a mock proper name. (Footnote: We have an exception where a mock proper name occurs within a clause in indirect speech.) Assertions in fiction are not to be taken seriously, they are only mock assertions. Even the thoughts are not to be taken seriously as in the sciences: they are only mock thoughts. If Schiller’s Don Carlos were to be regarded as a piece of history, then to a large extent the drama would be false. But a work of fiction is not meant to be taken seriously in this way at all: it’s all play. . .
The logician does not have to bother with mock thoughts, just as a physicist, who sets out to investigate thunder, will not pay any attention to stage- thunder. When we speak of thoughts in what follows we mean thoughts proper, thoughts that are either true false.(FREGE, 1991, 130)
Meinong
Meinong (1902), por sua vez, é famoso por ter mantido a controversa tese de que há objetos que não existem. Para Meinong, essa conclusão seria uma consequência natural da aporia dos inexistentes, embora a literatura meinongiana insiste que a solução da aporia não é o principal objetivo da teoria dos objetos de Meinong.
If anyone forms the judgment e.g. ’a perpetuum mobile does not exist’, it is clear that the object of which existence (Dasein is here dined, must have properties, and even characteristic properties, for without such the belief in non-existence can have neither sense nor justification; but the possession of properties is as much as to say a manner of being ’Sosein’. This manner
of being, however, does not presuppose any existence, which is rather, and rightly, just what is denied. The same could be shown analogously about knowledge of components. By keeping in general, as has ofter been found helpful, to knowledge of, or the effort to know, how the object under consideration was conceived in two stages, the grasping of the object and the judging about it, it at once becomes evident that one may say: objects are grasped, so to speak, in their manner of being; what is then judged, and eventually assented to, is the being, or a further manner of being, of what is grasped in that manner of being. This manner of being, and through it that which is in this manner, is comprehensible without limitation to existence, as the fact of negative judgments shows; but to that extent our comprehension finds something given about the objects, without respect to how the question of existence or non-existence is decided. In this sense ’there are’ also objects which do not exist, and I have expressed this in a phrase which, while somewhat barbarous, as I fear, is hard to better, as ’externality (Aussersein of the pure object’.(MEINONG, 1983)
Russell
Russell, em 1903, curiosamente, mantinha uma posição muito próxima a de Meinong em 1902 e 1904. Para o Russell de 1903, toda expressão denotativa nomearia um objeto. Ambos, juntamente com Frege, mantiveram uma atitude quase-platonista perante a objetividade do pensamento, atitude que informaria o logicismo de Frege–Russell. A posição de Russell, no entanto, diferia da de Meinong, pois afirmava que objetos inexistentes, não obstante não existirem, teriam ainda privilégio de serem. Meinong e os meinongianos, por sua vez, reconhecem objetos que não são, nem existem. Mas a posição de Russell também, como a de Meinong, também não é propriamente realista, uma vez que não afirma a existência de criaturas fantásticas, números, etc. Pelo contrário. Russell (, 449–550) expõe sua teoria nessa famosa passagem:
Being is that which belongs to every conceivable term, to every possible object of thought—in short to everything that can possible occur in any proposition, true or false, and to all such propositions themselves. Being belongs to whatever can be counted. If A be any term that can be counted as one, it is plain that A is something, and therefore that A is. “A is not” must always be either false or meaningless. For if A were nothing, it could not be said not to be; “A is not” implies that there is a term A whose being is denied, and hence that A is. Thus unless “A is not” be and empty sound, it must be false—whatever A may be, it certainly is. Numbers, the Homeric gods, relations, chimeras and four-dimensional spaces all have being, for if they were not entities of a kind, we could make no propositions about them. Thus being is a general attribute of everything, and to mention anything is to show that it is.
Existence, on the contrary, is the prerogative of some only amongst beings. To exist is to have a specific relation to existence—a relation, by the way, which existence itself does not have. This shows, incidentally, the weakness of the existential theory of judgement—the theory, that ism that every proposition is concerned with something that exists. For if this theory were true, it would still be true that existence itself is an entity, and it must be admitted that existence does not exist. Thus the consideration of existence itself leads to non-existential propositions, and so contradicts the theory. The theory seems, in fact, to have arisen from neglect of the distinction between existence and being. Yet this distinction is essential, if we are ever to deny the existence of anything. For what does not exist must be something, or it would be meaningless to deny its existence; and hence we need the concept of being, as that which belongs even to the non-existent.