By Agustín Rayo
Este libro reune ensayos de los más grandes especialistas en el tema de l. a. 'cuantificación common' abordado desde todas sus dimensiones. Ellos no sólo se limitan a hablar sobre el tema sino que después del análisis que realizan, presentan avesadas tesis de cara a los problemas que se sucitan.
Lo recomiendo, pues, creo que si todavía no lo es, en el futuro se convertirá en un clásico.
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Additional resources for Absolute Generality
For not every object can be postulated into existence. x∀y(y admires x)). And likewise, we cannot postulate an object which stands in the membership relationship to pre-existing objects. But this means that, once a universal set for a given domain has been introduced, no further objects that might be introduced can be among its members. Thus the membership—and hence identity—of the set will be fixed ‘for all time’, once it has been introduced. ¹⁸ Under the universalist account, the old and new domains are to be understood as restrictions; and these restrictions, in turn, are to be understood as restrictions on an absolutely unrestricted domain.
Thus far from presupposing that the all-in-one principle is true, we presuppose that it is false! Of course, there is some mystery as to how we arrive at this new understanding of the quantifier. What is the extraordinary mental feat by which we generate a new object, as it were, merely from an understanding of the quantifier that does not already presuppose that there is such an object? I shall later have something to say on this question. But it seems undeniable that we can achieve such an understanding even if there is some difficulty in saying how we bring it off.
Then it is logically possible that these are not all of the objects (♦∃x∼(x = a1 v x = a2 v x = a3 v . ) ), since there can be no logical guarantee that any particular objects are all of the objects that there are. This is especially clear if there are infinitely many objects a1 , a2 , a3 , . . For if it were logically impossible that some object was not one of a1 , a2 , a3 , . . , then it would be logically impossible that some object was not one of a2 , a3 , . . , since the logical form of the existential proposition in the two cases is the same.
Absolute Generality by Agustín Rayo