Corcoran-Prentice on Mazur’s semantic problem

John Corcoran and Michael Prentice. 2011. Mazur's Semantic Problem. Bulletin of Symbolic Logic. 17 (2011) 325–6.We discuss the following semantic question—apparently about the denotation of the 9-character expression ‘5 mod 691’ in traditional arithmetic—raised by Harvard mathematician Barry Mazur (page 223 of Gold and Simons 2008). “Is 5 mod 691 to be thought of as a symbol, or as a stand in for any number that has remainder 5 when divided by 691, or should we take the tack that it (i.e., “5 mod 691”) is the equivalence class of all integers that are congruent to 5 mod 691?”Mazur’s is one of the 17 essays in Gold and Simons [2008. Proof and other Dilemmas: Mathematics and Philosophy. Washington DC: Mathematical Association of America] that was not explicitly treated in Corcoran’s review [Mathematical Reviews. MR2435289]CHAT: https://www.academia.edu/s/69d3899ef3?source=linkTEXT: https://www.academia.edu/27754594/CORCORAN_BEMOANS_GOLD-SIMONS From the review: The seventeen essays are reportedly “a sampler of current topics in philosophy of mathematics". As is clear from the number of garbled sentences, misleading and irresponsible assertions, and obvious mistakes, these essays have not been peer-reviewed.