Reliability of mathematical inference
| Autor: | Jeremy Avigad |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Philosophy of science
Correctness 05 social sciences General Social Sciences Inference 06 humanities and the arts 0603 philosophy ethics and religion Mathematical proof 050105 experimental psychology Mathematical practice Philosophy of language Philosophy 060302 philosophy Normative 0501 psychology and cognitive sciences Mathematical economics Axiom |
| Zdroj: | Synthese. 198:7377-7399 |
| ISSN: | 1573-0964 0039-7857 |
| Popis: | Of all the demands that mathematics imposes on its practitioners, one of the most fundamental is that proofs ought to be correct. It has been common since the turn of the twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundation, but then it is hard to see how this normative standard can be met, given the differences between informal proofs and formal derivations, and given the inherent fragility and complexity of the latter. This essay describes some of the ways that mathematical practice makes it possible to reliably and robustly meet the formal standard, preserving the standard normative account while doing justice to epistemically important features of informal mathematical justification. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink