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Plural Grundgesetze

“…To this sort of limitation, the Fregean, in fact, may likely object that, given the Platonist existence of concepts, there is no obvious reason why a concept should not be specified through quantification over the domain it belongs to. In what follows, I will endorse a claim by [9] and [10] in order to get the appropriate justification for holding a predicativist view of concepts, which is also compatible with Frege's view.…”

“…9 From a Fregean perspective, concepts platonistically exist. Thus, as predicativism is usually taken to be unmotivated from a Platonist viewpoint, 10 the limitation on the domain of concepts in PG seems rather unFregean.…”

“…According to [9] and [10], the possibility of directly referring, at least ideally, to any object of a Universe of Discourse is presupposed both by logical and mathematical reasoning, also when non-denumerable domains are concerned. As a consequence, quantification itself logically presupposes the ideal possibility of referring to each and every element of a domain, before we consider those elements through generalisation.…”

“…As a consequence, quantification itself logically presupposes the ideal possibility of referring to each and every element of a domain, before we consider those elements through generalisation. [9] and [10] call this claim the Thesis of Ideal Reference (TIR). 11 Such a possibility of direct reference is very well expressed by the crucial role arbitrary reference plays both in logical and mathematical reasoning.…”

“…Thus, though 'a' refers to any individual, it has to refer to a well-defined individual. See [9] and [10].…”