Absolute Generality by Agustín Rayo

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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What is to prevent the new object from containing members besides those in the range of y? relevant sense of . Also, there would appear to be something viciously circular about specifying an interpretation in this way, since the application of within such conditions must be understood by reference to the very interpretations it is being used to specify. At the very least, it is hard to see how such interpretations could be legitimate unless their application could be grounded in interpretations of an ordinary, nonmodal kind.

But surely we can intelligibly suppose that there is something, be what it may, that has all of the previously given objects as its members (in a sense that conservatively extends our previous understanding of membership). Thus the standard considerations in support of ZF or the like do nothing to undermine the argument from extendibility. Their value lies not in showing how the argument might be resisted but in showing how one might develop a consistent and powerful set theory within a given domain, without regard for whether that domain might reasonably be taken to be unrestricted.

7): to quantify over certain objects is to presuppose that those objects constitute a ‘collection’ or a ‘completed collection’—some one thing of which those objects are members. Now one might indeed argue for extendibility on the basis of the all-in-one principle. But this is not how our own argument went. We did not argue that our understanding of the quantifier ∀ presupposes that there is some one thing of which the objects in the range of ∀ are members (∃+ y∀x(x ∈ y)). For this would mean that the quantifier ∀ was to be understood in terms of the quantifier ∀+ .

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