Timeline for Can we logically analyze mathematical theorems as if-then statements?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 5, 2016 at 15:50 | comment | added | Ovi | Thanks a lot, your last comment (especially the last sentence) helped A LOT! | |
| Jun 5, 2016 at 15:44 | vote | accept | Ovi | ||
| Jun 5, 2016 at 8:14 | history | edited | Mauro ALLEGRANZA | CC BY-SA 3.0 | added 882 characters in body |
| Jun 5, 2016 at 7:36 | comment | added | Mauro ALLEGRANZA | @Ovi - in math usually we are not interested into conditional whatever like "if $0=1$, then the moon is round", but to theorems proved from axioms. Thus, the conditional we are using are like: "if axiom $A$ holds, then theorem $T$ holds also". The fact that the conditional is true also when $A$ is false is a fact than we accept but of course is of no relevance for the mathematical theory we are workin whit. | |
| Jun 4, 2016 at 20:44 | comment | added | Ovi | ...Does it mean that it's not valid to put $p$ and $q$ in a $p \implies q$ relationship? Does it mean it's to put in in $p \implies q$ as long as $q$ as long as $q$ is true? | |
| Jun 4, 2016 at 20:43 | comment | added | Ovi | So my understanding is that when we are given a theorem in math as an $p \implies q$ statement, we are being told "This $p \implies w$ statement is always true, meaning that we can possibly find every combination of $p$ and $q$ except for $p=F$ and $q=T$"? I guess what I'm not really sure I get why my example here (math.stackexchange.com/questions/1793713/…) does not work (would really appreciate it if you could take a look). As an answer to that question, people said $p$ and $q$ were not independent. But what does that mean? | |
| Jun 4, 2016 at 19:08 | history | edited | Mauro ALLEGRANZA | CC BY-SA 3.0 | added 411 characters in body |
| Jun 4, 2016 at 19:02 | history | answered | Mauro ALLEGRANZA | CC BY-SA 3.0 |