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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Extra resources for Absolute Generality
Consider the claim that possibly there are more sets than we currently take there to be (∀I[∀x∃I y(y = x) ⊃ ♦∃y∀I x(y = x)]). In order for this to be true, the current quantifier ‘∀x’ over sets must not merely be restricted to sets but to sets of a certain sort, since otherwise there would not be the possibility of the set-quantifier ‘∃y’ having a broader range. But it is then difficult to see why the current interpretation of the quantifier ‘∀x’ should not simply be restricted to sets. For surely we are in possession of an unrestricted concept of a set, not set of such and such a sort but set simpliciter.
A1 ! Thus just as considerations of empirical vicissitude are irrelevant to the question of extendibility, so are considerations of logical form. It should also be fairly clear that it will not be possible to define the relevant notion of necessity by somehow relativizing the notion of logical necessity. The question is whether we can find some condition ϕ such that the necessity of ψ in the relevant sense can be understood as the logical necessity of ϕ ⊃ ψ. But when, intuitively, a domain of quantification is inextendible, we will want ϕ to include the condition ∀x(x = a1 v x = a2 v x = a3 v .
Represented by ‘∀x’ and ‘∃x’. We then seem capable of achieving a new understanding of the quantifier—which we may represent by ‘∀+ x’ and ‘∃+ x’—in which it also ranges over a universal set. Under this new understanding, it is correct to say that there is a universal set relative to the old understanding (∃+ x∀y(y ∈ x)). The question on which I wish to focus is: how do we come to this new understanding of the quantifier on the basis of the initial understanding? It is clear that the condition ∀y(y ∈ x) plays a critical role; since it is by means of this condition that the new understanding is given.
Absolute Generality by Agustín Rayo