# Logic is meaningless **URL:** \ **Category:** Great Debates\ **Created:** [November 19, 2002, 5:15pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554 "2002-11-19T17:15:01Z")\ **Posts on this page:** 7\ **Page:** 13
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [December 4, 2002, 6:02pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/241 "2002-12-04T18:02:36Z")
That’s what I love most about Spiritus. He makes people think. ---
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [December 4, 2002, 8:06pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/242 "2002-12-04T20:06:30Z")
**Spiritus** , I am looking over your step 2, A-\>A with necessitation as a justification, but I don’t think it applies there as you’ve written it. Necessitation only shows that what we prove _a priori_ is necessary (and when you think about it, one would hope so). That A is the case doesn’t make it necessary. But, I admit, I cannot think of how else to do it without asserting A -\> \<\>A in the first place, after which (as we have shown) it is trivial. ---
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [December 4, 2002, 11:03pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/243 "2002-12-04T23:03:54Z")
1. A -\> ~~A 2. (A -\> ~~A) 3. A -\> ~~A 4. A -\> ~~~~ A 5. A -\> ~\<\>~A 😕 I have been trying this off and on all day and I can get all kinds of possibles, but there’s always a stupid negation I can’t eliminate. 5 is interesting though. It seems that, just like \<\> can be defined as ~~, can be defined as ~\<\>~. The symmetry surprised me, though I don’t know why. ---
**Author:** ![Spiritus\_Mundi](https://avatars.discourse-cdn.com/v4/letter/s/c68b51/32.png) [@Spiritus\_Mundi](https://boards.straightdope.com/u/Spiritus_Mundi)\ **Post date:** [December 4, 2002, 11:21pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/244 "2002-12-04T23:21:09Z")
**erl** Hmmmm . . . you might be right. I would have to include classical quantifiers to get that application of necessity. Actually, I might be able to since we start with “the principles of propositional logic”, but that strikes me as a bit dodgy since I know there is great disagreement over how to apply and read the classical quantifiers in modal contexts. Hmmmm . . . I might be right. Damn, I told you I was no expert. It really should be trivially derivable in just T. Maybe including an existential quntifier is the right way to go, but I get the feeling I am overlooking something else: something outrageously obvious. ---
**Author:** ![Spiritus\_Mundi](https://avatars.discourse-cdn.com/v4/letter/s/c68b51/32.png) [@Spiritus\_Mundi](https://boards.straightdope.com/u/Spiritus_Mundi)\ **Post date:** [December 4, 2002, 11:31pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/245 "2002-12-04T23:31:39Z")
Yes, the symmetry is implicit in the definitional relationship. You can start with either or \<\> as the primitive. (Well, except for some modal forms designed to model actualism, which require both to be primitive: no symmetry, no elegance, no implication of necessary existence.) ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [December 4, 2002, 11:35pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/246 "2002-12-04T23:35:10Z")
Eris wrote: > [@](#): > > It seems that, just like \<\> can be defined as ~~, can be defined as ~\<\>~. That is the exact definition of , if I recall. ---
**Author:** ![Spiritus\_Mundi](https://avatars.discourse-cdn.com/v4/letter/s/c68b51/32.png) [@Spiritus\_Mundi](https://boards.straightdope.com/u/Spiritus_Mundi)\ **Post date:** [December 5, 2002, 2:54am UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/247 "2002-12-05T02:54:53Z")
Well, either one can be defined in terms of the other. Usually, I believe, is taken as the primitive with \<\> = ~~ by definition. But the of th relationship is easily demonstrated: \<\>A = ~~A \<\>~A = ~~~A \<\>~A = ~A ~\<\>~A = ~~A ~\<\>~A = A (Of course, **erl** had already given a derivation above, but I wanted to actually solve a trivial derivation for once.) [Previous page](https://boards.straightdope.com/t/logic-is-meaningless/137554.md?page=12)