Timeline for intuitionistic interpretation of classical logic
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 1, 2015 at 20:08 | answer | added | user76671 | timeline score: 1 | |
| S Dec 15, 2014 at 18:46 | history | suggested | Incnis Mrsi | CC BY-SA 3.0 |
(intuitionism), normalization of typography
|
| Dec 15, 2014 at 18:25 | review | Suggested edits | |||
| S Dec 15, 2014 at 18:46 | |||||
| Dec 4, 2014 at 15:29 | comment | added | Emil Jeřábek | Actually, there are infinitely many intuitionistically nonequivalent formulas in just one propositional variable. Search for Rieger–Nishimura lattice. | |
| Dec 9, 2009 at 22:25 | history | edited | user577 | CC BY-SA 2.5 |
added a reference to a comment
|
| Dec 9, 2009 at 18:52 | comment | added | Reid Barton | @davidk01: that's how you can interpret the first statement; the second statement can be interpreted as "Every theorem of intuitionistic logic is a theorem of classical logic, but not conversely." Maybe a better way of capturing your idea is the observation that given n variables, there are more intuitionistically nonequivalent formulas in those variables (but still finitely many!) than there are classically nonequivalent formulas (2^2^n). | |
| Dec 9, 2009 at 16:18 | comment | added | Neel Krishnaswami | davidk01: you can convert intuitionistic logic into classical modal logic using the Godel translation. Basically you introduce a modality "provable", and view intuitionistic $A \to B$ as classical $provable(A) \to B$. So intuitionistic implications are weaker than classical ones, since their assumptions are stronger, but its conclusions are stronger than classical ones, since you get actual existence proofs. This contravariance makes comparing it to classical logic hard, and show why there are constructively legit principles that are false classically. (E.g., all functions are continuous.) | |
| Dec 9, 2009 at 7:15 | comment | added | Andrew Critch | Upvote for showing me an awesome theorem in the question :) Can you provide a reference for it? | |
| Dec 9, 2009 at 5:34 | answer | added | Dan Piponi | timeline score: 6 | |
| Dec 9, 2009 at 5:21 | comment | added | Reid Barton | "More" is a tricky word, and both "there are more theorems in intuitionistic logic than in classical logic" and "there are more theorems in classical logic than in intuitionistic logic" have natural true interpretations. | |
| Dec 9, 2009 at 5:19 | history | edited | user577 | CC BY-SA 2.5 |
added 139 characters in body
|
| Dec 9, 2009 at 5:01 | history | edited | user577 | CC BY-SA 2.5 |
added some clarifying remarks.; added 154 characters in body
|
| Dec 9, 2009 at 4:23 | answer | added | Joel David Hamkins | timeline score: 11 | |
| Dec 9, 2009 at 4:20 | vote | accept | CommunityBot | moved from User.Id=577 by developer User.Id=69903 | |
| Dec 9, 2009 at 4:11 | answer | added | LSpice | timeline score: 6 | |
| Dec 9, 2009 at 3:51 | history | asked | user577 | CC BY-SA 2.5 |