Timeline for True, false and meaningless statements in math.
Current License: CC BY-SA 3.0
11 events
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| Feb 10, 2014 at 17:10 | comment | added | Mauro ALLEGRANZA | @randomatlabuser - You are right: I've improved my answer, in order to avoid the previous sloppiness. Instead of "meaningless", we have to appeal to semantics for first-order logic. In defining truth of a sentence in a model, we require that every name occurring in the sentence has a denotation. Moreover, function signs are taken always to represent operations everywhere defined in the domain: there is no place in standard semantics for "non-denoting" terms in the sentences involved [this is different for free logic]. | |
| Feb 10, 2014 at 16:02 | history | edited | Mauro ALLEGRANZA | CC BY-SA 3.0 |
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| Feb 10, 2014 at 10:16 | history | edited | Mauro ALLEGRANZA | CC BY-SA 3.0 |
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| Feb 10, 2014 at 9:19 | history | edited | Mauro ALLEGRANZA | CC BY-SA 3.0 |
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| Feb 8, 2014 at 19:14 | comment | added | randomatlabuser | Actually I agree that if "$\sqrt{-1}$" is not defined then any sentence containing "$\sqrt{-1}$" is meaningless, unless it is about the meaninglessness of that object. "$\sqrt{-1}$ does not mean anything", "$\sqrt{-1}$ does not make any sense", "$\sqrt{-1}$ is not defined", "I do not understand what you mean by $\sqrt{-1}$", "$\sqrt{-1}$ is meaningless", "$\sqrt{-1}$ needs to be defined", etc. | |
| Feb 8, 2014 at 18:18 | history | edited | Mauro ALLEGRANZA | CC BY-SA 3.0 |
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| Feb 8, 2014 at 17:15 | comment | added | Mauro ALLEGRANZA | @nkoreli - You are right; following Carl perfect answer, I should have written : "Assuming that the statement ... is false ...". | |
| Feb 8, 2014 at 17:09 | comment | added | Carl Mummert | The issue with this is that there is not likely to be any "SQRT" function symbol; there is not one in the normal language of fields, for example. | |
| Feb 8, 2014 at 17:08 | comment | added | nkoreli | Mauro, thanks for the answer. But, I cannot get how one statement be with meaning, and the negation be meaningless?? Do you have other examples of such statements? | |
| Feb 8, 2014 at 17:07 | comment | added | amWhy | We can still say, because of the non-definition of the square root, that $\sqrt{-1} \neq 1$...This is indeed true. | |
| Feb 8, 2014 at 17:05 | history | answered | Mauro ALLEGRANZA | CC BY-SA 3.0 |