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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If there is a case to be made against absolutely unrestricted quantification, then it will rest here, upon logical considerations of extendibility, rather than upon the nature of understanding or the metaphysics of identity. 1 T H E E X T E N D I B I L I T Y A RG U M E N T Let us begin by reviewing the classic argument from indefinite extendibility. I am inclined to think that the argument is cogent and that the intelligibility of absolutely unrestricted quantification should therefore be rejected.
I am grateful to Timothy Williamson for pressing this question upon me. Relatively Unrestricted Quantification 35 is indeed sufficient to show that the given narrower interpretation is not absolutely unrestricted. For suppose someone proposes an interpretation of the quantifier and I then attempt to do a ‘Russell’ on him. Everyone can agree that if I succeed in coming up with a broader interpretation, then this shows the original interpretation not to have been absolutely unrestricted. Suppose now that no one in fact does do a Russell on him.
But the intent is that there is no more fundamental understanding of what the new domain should be except as the domain that might be reached from the given domain by adding an object in conformity with the condition. x∀y(y ∈ x) serves as a positive injunction on how the domain is to be extended rather than as a negative constraint on how it is to be restricted. It might be wondered why the present account of how the domain is to be extended is not subject to a form of the objection that we previously posed against the restrictionist account.