Timeline for Analytic/synthetic distinction in mathematics besides geometry?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Oct 1, 2021 at 13:16 | comment | added | Robin Saunders | @მამუკაჯიბლაძე I'm still quite new to the subject, but my impression is that a good place to start reading about some of the differences would be early publications, such as this 1991 paper by Martin Hyland: dpmms.cam.ac.uk/~martin/Research/Oldpapers/synthetic91.pdf | |
| Sep 30, 2021 at 12:03 | comment | added | მამუკა ჯიბლაძე | @RobinSaunders Yes, also this. But what would be analytic domain theory? | |
| Sep 30, 2021 at 11:19 | comment | added | Robin Saunders | Abstract Stone Duality (paultaylor.eu/ASD) surely qualifies as synthetic, and indeed the page mentions that it arose from work in synthetic domain theory. Perhaps that will help clarify things, @მამუკაჯიბლაძე? | |
| Sep 29, 2021 at 12:49 | answer | added | Timothy Chow | timeline score: 3 | |
| Sep 29, 2021 at 0:09 | vote | accept | Timothy Chow | ||
| Sep 28, 2021 at 20:59 | comment | added | user44143 | People talk about synthetic approaches to differential geometry too, as in the various examples at mathoverflow.net/a/362006 | |
| Sep 28, 2021 at 16:50 | comment | added | abo | Most philosophers of mathematics take a universalist epistemological approach to mathematics. Mathematics is either all synthetic (see John Stuart Mill) or all analytic (see Frege). So there isn't going to be a distinction of "analytic X" or "synthetic X" within mathematics, at least according to these philosophers. Certainly if you don't follow these philosophers you can make the distinction about a particular area of mathematics, although it would surely be controversial. | |
| Sep 28, 2021 at 15:57 | comment | added | Steven Stadnicki | Can I be vaguely peeved that 'synthetic' refers to a definition that can be used to analyze the thing in question, while 'analytic' refers to a definition that can be used to synthesize the thing in question, or has that ship already sailed? | |
| Sep 28, 2021 at 15:22 | answer | added | Mirco A. Mannucci | timeline score: 7 | |
| Sep 28, 2021 at 14:37 | comment | added | Maxime Ramzi | I guess higher category theory might qualify to some extent ? At least the word "synthetic" makes sense there | |
| Sep 28, 2021 at 13:37 | comment | added | Timothy Chow | @AlexandreEremenko Very interesting. Could you please provide some more details about how (e.g.) the term "analytic geometry" came from philosophy? | |
| Sep 28, 2021 at 12:57 | comment | added | მამუკა ჯიბლაძე | Although I am somehow familiar with Synthetic Domain Theory, I have no idea what would the analytic approach to domains mean. | |
| Sep 28, 2021 at 12:50 | comment | added | Alexandre Eremenko | Dichotomy synthetic/analytic in philosophy is much earlier than Kant; it comes from Aristotle's logic. And it indeed penetrated geometry from philosophy. | |
| Sep 28, 2021 at 12:16 | history | asked | Timothy Chow | CC BY-SA 4.0 |