Timeline for Why do people say Gödel's sentence is true when it is true in some models but false in others?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 11, 2021 at 0:14 | comment | added | Stilez | I had in mind that OP, being a self.declared beginner, said "g can't be a logical consequence of the axioms, which means there are models of the system that make g false." I had in mind that, as they acknowledge the axioms dont allow g to be decidable, they might have in mind, logical extensions of the system, which would 1) be consistent with the existing system and 2) allow g to be clearly false, and wouldn't this contradict the whole idea. Thats a common beginner error, so its one I was addressing, why it wouldn't work that way, in simple terms. | |
| Oct 10, 2021 at 21:13 | comment | added | Andreas Blass | @Stilez About item 2) in your comment: I didn't see anything in the question that "in effect says you can add an axiom". | |
| Oct 10, 2021 at 8:58 | comment | added | Stilez | "am a beginner, so this question may be naive" ..... 1) Not everyone understands the technicalities of axiomatic mathemetical/logic theory. But many have heard of Godels jncompleteness, even if not fully understanding it. There is a place for a simple explanation among the complex more accurate ones. 2) The OP in effect says you can add an axiom, whereby its no longer undecidable. A typical error, because that of course changes the axioms, and some other proposition will be undecidable, rather than the original. Typical error. This in simple terms explains that error, and why its so. | |
| Oct 10, 2021 at 8:13 | comment | added | user44143 | I downvoted the vagueness about which “logic systems” have these properties, the lack of examples, and the mischaracterization of the question: the question does not ask about “adding an axiom to make the sentence true or false”, but rather about different models in which it might be true or false. | |
| S Oct 10, 2021 at 6:52 | review | First answers | |||
| Oct 10, 2021 at 9:45 | |||||
| S Oct 10, 2021 at 6:52 | history | answered | Stilez | CC BY-SA 4.0 |