## Philosophy Lexicon of Arguments | |||

Consistency, philosophy, logic: within a system, consistency may be demonstrated, but not beyond the boundaries of this system, since the use of the symbols and the set of possible objects are only defined for this system.Within mathematics, and only there applies that the mathematical objects, which are mentioned in consistent formulas, exist (Hilbert, Über das Unendliche, 1926). See also falsification, verification, existence, well-formed. | |||

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Books on Amazon |
I 182 Consistency/Bigelow/Pargetter: a way to guarantee that a description is consistent is to show that something meets this description. Definition 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. Consistency/Hilbert: precedes existence. A mathematical proof exists only if it is non-contradictory. 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? --- 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. 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). |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |

> Counter arguments against **Bigelow**

> Counter arguments in relation to **Consistency**

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Ed. Martin Schulz, access date 2017-05-26