Lexicon of Arguments

 

I 182
Consistency/Bigelow/Pargetter: a way to guarantee that a description is consistent is to show that something meets this description.
>Satisfaction.
Def Principle of instantiation/Bigelow/Pargetter: we can call this the principle of instantiation (instantiation principle).
Contradiction-free/Bigelow/Pargetter: is essential for mathematics, for other areas it is more like housekeeping.
>Instantiation.
Consistency/Hilbert: precedes existence. A mathematical proof exists only if it is non-contradictory.
>Consistency/Hilbert, >Existence/Hilbert, >Mathematics/Hilbert, >Proofs, >Provability.
Consistency/FregeVsFormalism/FregeVsHilbert/Bigelow/Pargetter: Existence precedes the consistency. Consistency requires the existence of a consistently described thing. If it exists, the corresponding description is consistent. If it does not exist, how do we guarantee consistency?
>Existence, >Mathematics.
I 183
Frege/Bigelow/Pargetter: thinks here epistemically, in terms of "guarantees". But his view can be extended: if there is no object, there is no difference between a consistent and a contradictory description.
>G. Frege, >Foundation, >Formalism/Frege, >Truth/Frege,
>Existence/Frege.
Frege/Bigelow/Pargetter: pro Frege: this is the basis for modern mathematics. This is also the reason why quantum theory is so important: it provides examples of everything that mathematicians wish to investigate (at least until recently).
>Sets, >Set theory.