Editing Talk:703: Honor Societies
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: While I do understand what you're getting at, you are surprisingly wrong on a few accounts. First, A or not A (i.e. A V ~A) is not always a tautology. I've spent enough painful time around intuitionists to say this whenever I can. | : While I do understand what you're getting at, you are surprisingly wrong on a few accounts. First, A or not A (i.e. A V ~A) is not always a tautology. I've spent enough painful time around intuitionists to say this whenever I can. | ||
:: How is that not a tautology? For any proposition A, if the proposition is true, then A; if not, then ~A. Logic doesn't allow for a proposition to be both true AND false, nor does it allow for a proposition to be neither true NOR false, so the only remaining possibilities are A and ~A; ergo, A v ~A. [[Special:Contributions/108.162.216.38|108.162.216.38]] 16:44, 11 February 2014 (UTC) | :: How is that not a tautology? For any proposition A, if the proposition is true, then A; if not, then ~A. Logic doesn't allow for a proposition to be both true AND false, nor does it allow for a proposition to be neither true NOR false, so the only remaining possibilities are A and ~A; ergo, A v ~A. [[Special:Contributions/108.162.216.38|108.162.216.38]] 16:44, 11 February 2014 (UTC) | ||
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:Unnecessary nitpick aside, then, there are more serious things. I presume the sentence, "It would also be true if there were somehow 1.000.000 members of the group without 1.000.000 people joining it," should be, "It would also '''not''' be true if there were somehow 1.000.000 members of the group without 1.000.000 people joining it." (Otherwise, the "also" is used incorrectly, and the sentence is useless.) Unfortunately, this would make it wrong; a statement of the form "if A then B" is not false if B is true and A isn't. (This is the difficulty of making formal logic: the traditional conditional leads to bizarre, vacuous truths.) Also, more seriously, you say that "if A then A" is a longer way of saying "A", or, more formally, that "A → A" is logically equivalent to "A." Unfortunately, this is not the case. The statement "if A then A" is always true, and hence a tautology. You also assert that "A = A" (or "A ↔ A") is logically equivalent to "A", where "A" is "The first rule of tautology club." This is even more obviously false. Even if "The first rule of tautology club" yields falsehood, it is still equivalent to itself. | :Unnecessary nitpick aside, then, there are more serious things. I presume the sentence, "It would also be true if there were somehow 1.000.000 members of the group without 1.000.000 people joining it," should be, "It would also '''not''' be true if there were somehow 1.000.000 members of the group without 1.000.000 people joining it." (Otherwise, the "also" is used incorrectly, and the sentence is useless.) Unfortunately, this would make it wrong; a statement of the form "if A then B" is not false if B is true and A isn't. (This is the difficulty of making formal logic: the traditional conditional leads to bizarre, vacuous truths.) Also, more seriously, you say that "if A then A" is a longer way of saying "A", or, more formally, that "A → A" is logically equivalent to "A." Unfortunately, this is not the case. The statement "if A then A" is always true, and hence a tautology. You also assert that "A = A" (or "A ↔ A") is logically equivalent to "A", where "A" is "The first rule of tautology club." This is even more obviously false. Even if "The first rule of tautology club" yields falsehood, it is still equivalent to itself. | ||
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The [http://www.xkcd.com/703/info.0.json official transcript] actually identifies him as "a shorter male with glasses that bears a striking resemblance to Jason Fox". I'd say the chances of it being him are a little more than "could be". [[Special:Contributions/173.245.54.38|173.245.54.38]] 07:02, 15 February 2016 (UTC) | The [http://www.xkcd.com/703/info.0.json official transcript] actually identifies him as "a shorter male with glasses that bears a striking resemblance to Jason Fox". I'd say the chances of it being him are a little more than "could be". [[Special:Contributions/173.245.54.38|173.245.54.38]] 07:02, 15 February 2016 (UTC) | ||
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