Timeline for What separates mathematics from logic? Can "mathematical" operations be applied to logical systems?
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| when toggle format | what | by | license | comment | |
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| Sep 7, 2020 at 20:12 | vote | accept | mark-antoin9977 | ||
| Sep 3, 2020 at 3:41 | answer | added | RodolfoAP | timeline score: 0 | |
| Sep 2, 2020 at 21:02 | vote | accept | mark-antoin9977 | ||
| Sep 2, 2020 at 21:02 | |||||
| Sep 2, 2020 at 4:36 | answer | added | J D | timeline score: 3 | |
| Sep 1, 2020 at 21:00 | history | tweeted | twitter.com/StackPhilosophy/status/1300901261244596224 | ||
| Sep 1, 2020 at 20:35 | answer | added | Guy Inchbald | timeline score: 0 | |
| Sep 1, 2020 at 19:38 | comment | added | Conifold | @wolf-revo-cats I admittedly have an expansive view of mathematics that does not match the colloquial use, but then general public still often thinks of math as all about geometric shapes and number crunching. So I would say that Hamiltonian dynamics or the formal part of Chomsky's grammar are mathematical parts of physics and linguistics, respectively. I think this is more justifiable philosophically than the haphazard colloquial notion derived from traditional family resemblance. But to the extent that Llullian (or physicist's or linguist's) art is art it is beyond math. | |
| Sep 1, 2020 at 13:59 | comment | added | Nelson Alexander | I know nothing about this area, but questioner might want to read some of the history surrounding Russell and Whitehead's "Principia Mathematica," emphasis on "history surrounding," not necessarily the book itself. | |
| Sep 1, 2020 at 9:56 | answer | added | Speakpigeon | timeline score: 1 | |
| Sep 1, 2020 at 8:37 | comment | added | Mauro ALLEGRANZA | Modern mathematical logic is “mathematical” in two ways: because it is a highly mathematical discipline and because it is used to formalize mathematical theories and study their properties as mathematical objects. | |
| Sep 1, 2020 at 8:35 | comment | added | Mauro ALLEGRANZA | Formal logic was “symbolic” from the start: see Aristotle but a significant symbolization was achieved only after the development of modern algebra, starting with Boole. | |
| Sep 1, 2020 at 6:45 | answer | added | user40843 | timeline score: 0 | |
| Sep 1, 2020 at 3:04 | comment | added | Logikal | You should be told upfront that almost all logical systems fall under MATHEMATICAL LOGIC which is math. Philosophy had the origin of logical systems. The first one was called Aristotelian logic which did not use mathematics nor any symbols as Mathematical logic today uses. Philosophy teaches logic differently. So it is likely confusing to beginners because most people REFUSE to use the correct term for what it is: it is MATHEMATICAL LOGIC. The subject name is NOT LOGIC. There are other logic systems which may differ in rules. ARISTOTELIAN LOGIC still works but used for a different purpose. | |
| Sep 1, 2020 at 0:45 | comment | added | Conifold | @wolf-revo-cats Logic in a narrow sense is just an apparatus for making inferences, even interpreting variables as placeholders for "something" is already semantic interpretation. Such minimal interpretation is often assimilated into logic exactly on account of its boundless vagueness. Once we start putting some meat on the "something" via non-logical axioms we cross over into mathematics. Even then, formal mathematics does not talk about "things" existing or infinity, it only manipulates symbols, one can attach platonic objects to them or treat them as fictions as one wishes. | |
| Aug 31, 2020 at 22:03 | comment | added | Conifold | Mathematical formal systems have non-logical symbols and axioms on top of the underlying system of inference ("logic"). Those introduce operations in particular, but they are not "valid within logical system", one can introduce whatever one wants and then use the logical system as an inference machine. This inference machine can itself be made into a mathematical object and studied, and that is what mathematical logic does, but studying it mathematically is distinct from using it as logic. | |
| Aug 31, 2020 at 20:54 | history | edited | mark-antoin9977 | CC BY-SA 4.0 |
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| Aug 31, 2020 at 20:39 | history | asked | mark-antoin9977 | CC BY-SA 4.0 |