## Philosophy Lexicon of Arguments | |||

Author | Item | Excerpt | Meta data |
---|---|---|---|

Bigelow, John Books on Amazon |
Consistency | 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 2017-04-30