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Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics
| Content Provider | Semantic Scholar |
|---|---|
| Author | Feferman, Solomon |
| Copyright Year | 1992 |
| Abstract | Does science justify any part of mathematics and, if so, what part? These questions are related to the so-called indispensability arguments propounded, among others, by Quine and Putnam; moreover, both were led to accept significant portions of set theory on that basis. However, set theory rests on a strong form of Platonic realism which has been variously criticized as a foundation of mathematics and is at odds with scientific realism. Recent logical results show that it is possible to directly formalize almost all, if not all, scientifically applicable mathematics in a formal system that is justified simply by Peano Arithmetic (via a proof-theoretical reduction). It is argued that this substantially vitiates the indispensability arguments. |
| Starting Page | 442 |
| Ending Page | 455 |
| Page Count | 14 |
| File Format | PDF HTM / HTML |
| DOI | 10.1086/psaprocbienmeetp.1992.2.192856 |
| Alternate Webpage(s) | http://math.stanford.edu/~feferman/papers/psa1992.pdf |
| Alternate Webpage(s) | https://doi.org/10.1086/psaprocbienmeetp.1992.2.192856 |
| Volume Number | 1992 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
