Timeline for Does what happened with the emergence of non-Euclidean geometries deny the existence of axioms in the innate sense?
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Feb 29 at 21:28 | comment | added | Robbie Goodwin | Did you notice how vague that sounds in English? Both in the Question title and in the exposition? | |
| Feb 28 at 17:55 | vote | accept | زكريا حسناوي | ||
| Feb 28 at 12:41 | comment | added | Dan Christensen | The axioms of Euclidean geometry were not shown to be internally inconsistent in the sense of Russell's Paradox. They are still useful in most scientific and engineering applications. Other axioms/assumptions may be more useful in other scientific and engineering applications. If there was any "crisis," it seems to me that it was not in mathematics, but in science. But it is in the very nature of science to deal with such "crises" from time to time by challenging the assumptions of the past. | |
| Feb 27 at 10:46 | answer | added | AnoE | timeline score: 0 | |
| Feb 27 at 7:23 | answer | added | Professor Sushing | timeline score: 2 | |
| Feb 27 at 7:01 | history | became hot network question | |||
| Feb 27 at 6:52 | comment | added | Mauro ALLEGRANZA | "Can the futility of innate intuition really be deduced from the emergence of non-Euclidean geometries?" No, also modern mathematics is based on intution, maybe not innate. | |
| Feb 27 at 6:51 | comment | added | Mauro ALLEGRANZA | "Llobachowski and Riemann did not deal with the straight line with the same concept as Euclid... "not exactly: the they dealt with a more abstract concept od space. "From Euclid's line it can work with different worlds consistently"; yes; the General Relativity showed that a curved space model is more apt to represent physical space. | |
| Feb 27 at 6:49 | comment | added | Mauro ALLEGRANZA | "The crisis of mathematical certainty began with Leibnitz"??? | |
| Feb 27 at 6:48 | comment | added | Mauro ALLEGRANZA | Who are the "Supporters of contemporary mathematics"? We have mathematicians... | |
| Feb 27 at 6:48 | comment | added | Mauro ALLEGRANZA | Parmenides in his poem stated as undubitable the Non Contradiction principle... that were later denied. | |
| Feb 27 at 6:47 | comment | added | Mauro ALLEGRANZA | "axioms in the innate sense"? Axioms are statements assumed as true to build a theory upon it. Euclid assumed the well-known axioms because he cannot prove them, he thinked that they were (most of them) obvious and they were necessary in order to prove the theorems of geometry. Euclidean geometry emerged after a couple of centuries of research, and thus it is hard to assert that its principle were "innate". | |
| Feb 27 at 1:51 | review | Close votes | |||
| Mar 5 at 3:08 | |||||
| Feb 27 at 1:32 | comment | added | Conifold | The "alien philosophy" has been developing very gradually over the course of 19th century in the hands of many people with very different backgrounds, including religious ones. Whatever it was, it was neither alien nor pasted nor atheistic nor materialistic. As to "innate intuition", it was demonstrated to be fallible rather than futile, and subject to habitual biases. The problem was that earlier thinkers confused idealized empirical geometry, to which the intuition applied and still does, with idealized geometry as such, which they purported to consider long before non-Euclidean models. | |
| Feb 26 at 23:56 | answer | added | niels nielsen | timeline score: 0 | |
| Feb 26 at 23:42 | answer | added | Davius | timeline score: 3 | |
| Feb 26 at 23:30 | answer | added | Jo Wehler | timeline score: 5 | |
| Feb 26 at 22:52 | history | asked | زكريا حسناوي | CC BY-SA 4.0 |