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
Some philosophers have suggested that we get round this difficulty by adopting a schematic approach. Let us use r(I) for the interpretation obtained by applying the Russell device to a given interpretation I. Then what the limitavist wishes to commit himself to, on this view, is the scheme: (ES) ∃r(I) y∀I x ∼ (x = y) (something under the Russell interpretation is not an object under the given interpretation). ⁸ The difficulty with this view is to see how it might be coherently maintained. We have an understanding of what it is to be committed to a scheme; it is to be committed to the truth of each of its instances.
There are various standard set-theoretic grounds upon which the transition to (R) might be questioned, but none is truly convincing. It has been suggested, for example, that no set can be ‘too big’, of the same size as the universe, and that it is this that prevents the formation of the universal or the Russell set. Now it may well be that no understanding of the quantifier that is subject to reasonable set-theoretical principles will include sets that are too big within its range. But this has no bearing on the question of whether, given such an understanding of the quantifier, we may come to an understanding of the quantifier that ranges over sets that would have been too big relative to the original understanding of the quantifier.
What remains? I believe that our difficulties stem from adopting an unduly narrow conception of what might constitute an interpretation of the quantifier. To understand better what alternative conceptions there might be, we need to reconsider the Russell jump and how it might be capable of effecting a change in the interpretation of the quantifier. As I have remarked, the change in the interpretation of the domain of quantification is somehow given by the condition ∀y(y ∈ x). But rather than thinking of that condition as serving to define a new predicate by which the quantifier is to be restricted, we should think of it as serving to indicate how the range of the quantifier is to be extended.
Absolute Generality by Agustín Rayo