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
What we are provided with is not a new way of seeing how the given domain might have been restricted but with a way of seeing how it might be expanded. We might say that the new domain is understood from ‘above’ under the universalist and restrictionist accounts, in so far as it is understood as the restriction of a possibly broader domain, but that it is understood from ‘below’ under the expansionist account, in that it is understood as the expansion of a possibly narrower domain. Another major difference between the accounts concerns the conditions and consequences of successful reinterpretation.
But the condition ∀y(y ∈ x) picks out all those sets that have all of the objects in the range of ∀y as members, and not just the set that consists solely of these objects. ¹⁶ ¹⁶ One might think that the new object should be defined by the condition: ∃I[∀x∃I y(y = x) & ∀y(y ∈ x ≡ ∃I z(z = y)]. But since the condition is modal, it is of little help in understanding the Relatively Unrestricted Quantification 37 There is a further difficulty, which is a kind of combination of the other two. As we have seen, the required restriction on the quantifier is not just to sets but to sets of such and such a sort.
Thus the present proponent of the modal approach may be regarded as someone who starts out with a notion of possible interpretation that all may agree is relevant to the issue and who then finds good reason not to cash it out in other terms. In this case, the relevance of the notion he has in mind can hardly be doubted. 5 RESTRICTIONISM To better understand the relevant notion of postulational possibility we must understand the notion of interpretation on which it is predicated. Postulational possibilities lie in the possibilities for reinterpreting the domain of quantification.
Absolute Generality by Agustín Rayo