By Agustín Rayo
Este libro reune ensayos de los más grandes especialistas en el tema de los angeles '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 info for Absolute Generality
But if postulational possibility is a form of interpretational possibility, then why does the postulational possibility of a proposition not simply consist in the existence of an interpretation for which the proposition is true? It is here that considerations of extendibility force our hand. For from among the interpretations that there are is one that is maximal. ¹³ Nor can we plausibly take the postulational possibility of a proposition to consist in the metaphysical possibility of our specifying an interpretation under which the proposition is true.
Given (6), (7) implies: (8) UR(M0 ) ⊃ ∃I[Max(I)]. And so (3G)′ above yields: (9) ∼ UR(M0 ). ⁵ In this proof, we have helped ourselves to the reasoning by which we showed the universalist’s first-order quantifier not to be absolutely unrestricted. But it may be shown, quite regardless of how (5G) might have been established, that its truth is not compatible with its quantifier being absolutely unrestricted. For it may plausibly be maintained that if a second-order interpretation M is absolutely unrestricted then so is any first-order interpretation that is maximal with respect to M (or, at least, if the notion is taken in a purely extensional sense).
For the quantifier is already restricted to a sort, viz. set, and so we have as good a conception as we might hope to have of which kind of objects are in question. To insist upon a further restriction of the quantifier is like thinking that we cannot properly quantify over swans but only over black swans, say, or English swans. There is another difficulty with the model. Any satisfactory view must account for the act of reinterpretation that is involved in the Russell jump. In making the Russell jump, we go from one interpretation of the quantifier to another; and we need to provide a satisfactory account of how this is done.