# Talk:703: Honor Societies

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Granted; the statements hold enough implied information that we will agree that they are true in a trivial sense, and they are much more fun than 'either there are 1.000.000 people in this group or there aren't 1.000.000 people in this group' and 'either this is the first rule of the tautology club or it isn't' [[Special:Contributions/193.88.197.67|193.88.197.67]] 22:15, 2 September 2013 (UTC) | Granted; the statements hold enough implied information that we will agree that they are true in a trivial sense, and they are much more fun than 'either there are 1.000.000 people in this group or there aren't 1.000.000 people in this group' and 'either this is the first rule of the tautology club or it isn't' [[Special:Contributions/193.88.197.67|193.88.197.67]] 22:15, 2 September 2013 (UTC) | ||

: 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) | ||

: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. |

## Revision as of 16:44, 11 February 2014

A tautology is a statement that is always true and that doesn't convey any information. A classic example is 'A or not A', which is true if A is true, but also if A isn't true. 'Either it rains or it doesn't rain' is true, no matter what weather it is.

"If 1.000.000 people join this group, it will have 1.000.000 people in it" is, strictly speaking, not a tautology, since it wouldn't be true if - somehow - 1.000.000 people were able to join the group without it having 1.000.000 people in it (I don't know - maybe if people leave the group before the counter hit 1.000.000?). It would also be true if there were somehow 1.000.000 members of the group without 1.000.000 people joining it. It is of the form 'if A then A' which is pretty much a much longer version of just 'A'. It's true if it's true, and it isn't if it isn't - so it isn't a tautology.

The same goes for 'The first rule of the tautology club is the first rule of the tautology club' - It's just a long way of saying "This is the first rule of the tautology club' - which can be true or false.

- No, it's saying that, whatever the first rule of the club is at any given moment, that's the first rule of the club. Which cannot be false. 108.162.216.38 16:39, 11 February 2014 (UTC)

Granted; the statements hold enough implied information that we will agree that they are true in a trivial sense, and they are much more fun than 'either there are 1.000.000 people in this group or there aren't 1.000.000 people in this group' and 'either this is the first rule of the tautology club or it isn't' 193.88.197.67 22:15, 2 September 2013 (UTC)

- 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. 108.162.216.38 16:44, 11 February 2014 (UTC)

- 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.

- Serious issues aside, I do agree with your sentiment that "[i]f 1.000.000 people join this group, it will have 1.000.000 people in it" is not necessarily a tautology, but removing the ambiguities (did they all join at the same time? did anyone leave?), which would necessarily be done in any formalization of the statement, would yield the tautological "A → A." -- Quicksilver (talk)
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Why does this comic have the Philosophy category? Am I missing something? GameZone (talk) 08:27, 6 September 2013 (UTC)

- Logic is technically philosophy, or at least they're closely connected. Sciepsilon (talk) 20:23, 30 December 2013 (UTC)

It is worth noting that this comic is Randall's commentary on certain honor societies, who don't do anything except for selecting new members. Feynman once made a remark to that effect, and may be Randall's influence on the matter. (Or not.) Regardless, this explanation is missing the viewpoint. 108.162.215.74 20:53, 28 November 2013 (UTC)

I see that nobody's pointed out that the third figure from the left in the third panel appears to be Jason Fox (see 824: Guest Week: Bill Amend (FoxTrot))- known to be one of those nerdy types who would join a tautology club. He is (to my knowledge) perpetually in the fifth grade, though, which does make me a little suspicious. --173.245.56.24 00:03, 2 January 2014 (UTC)