Timeline for So after all, what is this thing about topos theory and non-binary truth?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 12, 2021 at 23:55 | comment | added | dohmatob | @AndrejBauer Thanks for the clarification. | |
| Mar 12, 2021 at 21:26 | comment | added | Andrej Bauer | But to answer your question: in this topos we always use pair of truth values. As far as the topos is concerned, "truth" is $(\mathrm{true}, \mathrm{true})$ and "falsehood" is $(\mathrm{false}, \mathrm{false})$. If you ask "Is $(\mathrm{true}, \mathrm{false})$ equal to $\mathrm{true}, \mathrm{true})$?" the answer is "$(\mathrm{true}, \mathrm{false})$". Given any truth value $(p_1, p_2)$, the value of $\neg (p_1, p_2) \land \neg\neg (p_1, p_2)$ (whose meaning is "$(p_1, p_2)$ is neither true nor false") is $(\mathrm{false}, \mathrm{false})$. | |
| Mar 12, 2021 at 21:25 | comment | added | Andrej Bauer | @dohmatob: it is quite impossible for anyone to define precisely all the details of the logic in a topos in an answer on MO, so you should give a great deal of leeway to the answer. It is just trying to illustrate a point, it's not a precise definition. | |
| Mar 12, 2021 at 18:08 | comment | added | dohmatob | Thanks for the input (upvoted). i'm not sure I follow (first paragraph). What do you mean by "are neither true nor false" when you've only defined what it means for a statement to be "true" ? In this system, what does it mean to say something is "false" ? (This is classically defined to mean "not true", via excluded middle principle / axiom, I guess. But how to go about that here ?). | |
| Mar 12, 2021 at 17:41 | history | edited | Matthias Hutzler | CC BY-SA 4.0 |
added 140 characters in body
|
| Mar 12, 2021 at 17:31 | history | answered | Matthias Hutzler | CC BY-SA 4.0 |