Timeline for How can the law of the excluded middle possibly be true if we acknowledge that some logical statements are undefined?
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9 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2016 at 18:26 | vote | accept | ApproachingDarknessFish | ||
| Apr 13, 2016 at 15:20 | comment | added | Dan Christensen | Re: 1/0 example. We define division on $R$ as follows: $\forall a,b,c\in R:[b\neq 0 \implies [a/b=c \iff a=cb]]$. Is $1/0=0$? We cannot use this definition to determine if it is true or not. We cannot apply the definition in this case because we have $0$ denominator ($b=0$). In general, we say that any expression with a $0$ denominator is undefined. Nothing mysterious about that. LEM still applies. Being "undefined" is not some kind of third value for logical expressions. It just means that our definition does not handle that case. | |
| Apr 9, 2016 at 21:43 | comment | added | ApproachingDarknessFish | @YuriyS That's an excellent example of the idea I'm getting at. Could you elaborate on what makes this an incorrect application of the LEM in an answer, perhaps? | |
| Apr 9, 2016 at 10:31 | comment | added | Yuriy S | There was a time when I was convinced that since $1/0$ is neither positive nor negative, then it must be zero. Another example of improperly using the LEM | |
| Apr 9, 2016 at 10:05 | comment | added | Asaf Karagila♦ | "Asdafb4562ijsadf;ja...(2134!)" is not a valid statement in English. However all the symbols are part of the English alphabet. How can you even accept the fact that English is a language useful for communication between two beings if you can use the English alphabet to write something which is meaningless? | |
| Apr 9, 2016 at 10:00 | answer | added | joriki | timeline score: 5 | |
| Apr 9, 2016 at 9:24 | comment | added | Git Gud | Not all sequences of words are propositions. You'd have no trouble accepting that "a the supercalifragilisticexpialidocious morning" isn't a proposition. Well, "This proposition is false" isn't a proposition either. That you think of it as being a proposition is a fault of your brain (and most people's - including me at first). It really carries no meaning. | |
| Apr 9, 2016 at 8:49 | comment | added | Patrick Stevens | One way to get around it is that the liar expression is neither true nor false, but malformed and so "not a proposition". This is the "exception-barring" approach in the terminology of Imre Lakatos. | |
| Apr 9, 2016 at 8:24 | history | asked | ApproachingDarknessFish | CC BY-SA 3.0 |