Timeline for Cauchy reals and Dedekind reals satisfy "the same mathematical theorems"
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 18, 2019 at 16:11 | comment | added | Zvonimir Sikic | It ends at the end i.e. everything after the first sentence is quote. | |
| Jul 18, 2019 at 11:34 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
formatting, again
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| Jul 18, 2019 at 11:33 | comment | added | David Roberts♦ | It's not clear now where the quote from the SEP ends, and, checking the source, everything after the first sentence is cut and pasted. I'm going to edit again to make it clear the whole entry is a quote, to avoid any attribution worries. | |
| Jul 17, 2019 at 18:27 | comment | added | Kevin Buzzard | Many thanks for this answer. I was well aware when I wrote the question that this sort of issue would be very well-understood but I had no idea about the history of this sort of concept -- I am not a logician and certainly not a philosopher. | |
| Jul 17, 2019 at 14:32 | comment | added | Zvonimir Sikic | It is even clearer in a letter to Hilbert on January 6, 1900.: “Given that the axioms in special geometries (i.e. special interpretations; my add) are all special cases of general axioms, one can conclude from lack of contradiction in a special geometry (i.e. a special interpretation; my add) to lack of contradiction in the general case, but not to lack of contradiction in another special case (i.e. another special interpretation; my add).” | |
| Jul 17, 2019 at 14:32 | comment | added | Zvonimir Sikic | As you commented earlier “it is not at all easy to insert the correct isomorphisms everywhere” i.e. to translate the proof from one interpretation to another. Frege’s position (in the controversy) is that it is even impossible, as implied by the 3rd paragraph I cited. | |
| Jul 17, 2019 at 14:01 | comment | added | Andrej Bauer | While I think the Frege-Hilbert "controversy" may be somewhat related, I feel the question is more of a "logical engineering" nature, i.e., how to organize mathematics so that certain we can guarantee the validity of certain desirable principles. A hundred years ago such a question would very likely be cast in philosophical and foundational terms, but nowadays there is a clear practical motivation behind the question (how to get a proof assistant to do more work). | |
| Jul 17, 2019 at 12:42 | history | edited | Zvonimir Sikic | CC BY-SA 4.0 |
deleted 1093 characters in body
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| Jul 17, 2019 at 12:35 | history | edited | Zvonimir Sikic | CC BY-SA 4.0 |
deleted 22 characters in body
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| Jul 17, 2019 at 12:34 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
Formatting
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| Jul 17, 2019 at 12:26 | history | answered | Zvonimir Sikic | CC BY-SA 4.0 |