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
Thus suppose that the initial quantifier ∀x is implicitly restricted to objects satisfying the condition θ(x), so that to say ∀xϕ(x) is tantamount to saying ∀x[θ(x): ϕ(x)] (every θ-object is a ϕ-object). The effect of considering the condition ∀y(y ∈ x) is then to weaken the initial restrictive condition θ(x) to θ(x) ∨ ∀y(y ∈ x), so that to say ∀+ xϕ(x) is tantamount to saying ∀x[θ(x) ∨ ∀y(y ∈ x): ϕ(x)]. Unfortunately, this proposal does not deliver the right results. Intuitively, we wanted the quantifier ∀+ x to include one new object in its domain, the set of all those objects that are in the range of ∀y.
J(I ⊂ J). Then one formulation of the limitavist position is: (L) ∀IE(I). But as thorough-going limitavists, we are likely to think that, whatever interpretation our opponent might come up with, it will be possible to come up with an interpretation that extends it. e. ∀I♦∃J(I ⊂ J)). It should be noted that there is now no longer any need to use a primitive notion of being absolutely unrestricted (UR) in the formulation of the limitavist’s position. The theses (L) and (L)+ are intended to apply when different delimitations on the range of the quantifier may be in force.
That there are swans, for example, is a postulational necessity but it is not something that, intuitively, must be the case. Thus it is entirely compatible with the current ‘modal’ approach that it is not merely considerations of metaphysical modality, but genuine considerations of modality in general, that are irrelevant to questions of extendibility. The postulational modalities concern not a possible variation in circumstance but in interpretation. The possibility that there are more sets, for example, depends upon a reinterpretation in what it is for there to be a set.
Absolute Generality by Agustín Rayo