# 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:** 20\ **Page:** 3
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [November 19, 2002, 8:36pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/41 "2002-11-19T20:36:00Z")
Yes, **MAth Geek** … so you’re saying that (P & (P -\> Q)) -\> Q is only true so long as you don’t [have and not have breakfast]? Interesting. ---
**Author:** ![Orbifold](https://avatars.discourse-cdn.com/v4/letter/o/779978/32.png) [@Orbifold](https://boards.straightdope.com/u/Orbifold)\ **Post date:** [November 19, 2002, 8:37pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/42 "2002-11-19T20:37:42Z")
> [@](#): > > \*Originally posted by Math Geek \* > **Just the truth as (P & (P-\>Q))-\>Q, _once I substitute actual propositions for P and Q_, is a measure of the value of logic, and is the “meaning” of logic.** Yeesh. I don’t mind the occasional spelling mistake, but I should at least form meaningful sentances. That should read “Just _as_ the truth _of_ (P & (P-\>Q))-\>Q…” ---
**Author:** ![JaKiri](https://avatars.discourse-cdn.com/v4/letter/j/a8b319/32.png) [@JaKiri](https://boards.straightdope.com/u/JaKiri)\ **Post date:** [November 19, 2002, 8:38pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/43 "2002-11-19T20:38:16Z")
Bertrand Russell. > [@](#): > > \*Originally posted by ultrafilter \*\*\* > As for your claim that logic doesn’t deal in truth–that’s just odd. Where did you get that notion? \*\* Bertrand Russell. > [@](#): > > \*Originally posted by ultrafilter \* > **False premises, true conclusion. It’s also a valid argument, by vacuous implication.** > [@](#): > > \*Originally posted by JaKiri \* > To refer to the first example, the statement used is logically valid, but the statements that lead to the conclusion are not all true, therefore the conclusion is not true \*\*by that logic. \*\* The statement 2+2=4 does not follow from your previous argument. ---
**Author:** ![Orbifold](https://avatars.discourse-cdn.com/v4/letter/o/779978/32.png) [@Orbifold](https://boards.straightdope.com/u/Orbifold)\ **Post date:** [November 19, 2002, 8:43pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/44 "2002-11-19T20:43:52Z")
**erislover** : That’s a slight rephrasing, but essentially correct, yes. > [@](#): > > \*Originally posted by JaKiri \* > \*\* > \ What the buffoon lessons, the four years at clown college? > \ I’ll thank you not to refer to Princeton that way. \*\* You aren’t exactly blinding me with the light of your reason either, bub. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [November 19, 2002, 8:45pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/45 "2002-11-19T20:45:38Z")
> [@](#): > > \*Originally posted by JaKiri \* > \*\*If an argument does not obey logical constructs, it cannot be valid. That does not mean that it is valid if it is, which is where the problem in this thread arises. \*\* So? What do you mean by valid? One definition would simply be that something is valid when it obeys certain principles of logic. Okay, fine – but now your argument is circular. Does the concept of validity involve being an accurate representation of the way the world works? Let’s say it does – but then we can’t just make the claim that obeying logical principles makes a statement valid. Either your definition is circular, in which case no one is particularly interested, or you’re making a fundamental claim about the nature of reality by linking properties together with a single word, in which case I’d like to see an actual argument in favor of the position. ---
**Author:** ![JaKiri](https://avatars.discourse-cdn.com/v4/letter/j/a8b319/32.png) [@JaKiri](https://boards.straightdope.com/u/JaKiri)\ **Post date:** [November 19, 2002, 8:45pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/46 "2002-11-19T20:45:49Z")
> [@](#): > > \*Originally posted by Math Geek \* > \*\*You aren’t exactly blinding me with the light of your reason either, bub. \*\* It’s a simpsons quote. And I’m right you know. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [November 19, 2002, 8:45pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/47 "2002-11-19T20:45:57Z")
> [@](#): > > \*Originally posted by JaKiri \* > \*\*The statement 2+2=4 does not follow from your previous argument. \*\* But it’s true, and the premises are false. Relevance is irrelevant here. btw, logic has changed quite a bit since the days of Russell. You may wish to check with a current textbook–I recommend Mendelson’s book, or Barwise & Etchmenedy for a slightly less advanced exposition. ---
**Author:** ![JaKiri](https://avatars.discourse-cdn.com/v4/letter/j/a8b319/32.png) [@JaKiri](https://boards.straightdope.com/u/JaKiri)\ **Post date:** [November 19, 2002, 8:57pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/48 "2002-11-19T20:57:00Z")
> [@](#): > > \*Originally posted by ultrafilter \* > **But it’s true, and the premises are false. Relevance is irrelevant here.** The statement does not logically follow though, so its not a valid argument. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [November 19, 2002, 9:00pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/49 "2002-11-19T21:00:42Z")
Validity has nothing to do with relevance. If the premises are false, then an argument is automatically valid. If the premises are true, then the argument is valid whenever that implies that the conclusion must be true. Look it up in any modern logic textbook if you don’t believe me. There was a controversy in the early 20th century brought about by some people who wanted to bring in rules of relevance, but they never came up with a very good system to replace the standard predicate calculus. And that’s the one we use. ---
**Author:** ![Cervaise](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cervaise/32/16693_2.png) [@Cervaise](https://boards.straightdope.com/u/Cervaise)\ **Post date:** [November 19, 2002, 9:14pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/50 "2002-11-19T21:14:19Z")
What does a hammer mean? ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [November 19, 2002, 9:19pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/51 "2002-11-19T21:19:06Z")
Hmm… I was actually expecting something different here. I agree with Eris that logic is meaningless, but for a different reason. Logic is meaningless because its primary Axiom, A=A, is a tautology: it is true regardless of the values of its variables. Moreover, it seems this thread is destined to branch out all over the place. An argument is valid if all its premises follow logically from one another. It is sound if all its premises are true. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [November 19, 2002, 9:21pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/52 "2002-11-19T21:21:26Z")
Not all tautologies are meaningless, and the axiom of reflexivity is nowhere near a primary axiom: in fact, it doesn’t even exist in first-order predicate calculus. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [November 19, 2002, 9:28pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/53 "2002-11-19T21:28:15Z")
> [@](#): > > \*Originally posted by Cervaise \* > \*\*What does a hammer mean? \*\* It depends on whose head it’s buried in. ---
**Author:** ![Orbifold](https://avatars.discourse-cdn.com/v4/letter/o/779978/32.png) [@Orbifold](https://boards.straightdope.com/u/Orbifold)\ **Post date:** [November 19, 2002, 9:37pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/54 "2002-11-19T21:37:25Z")
**Cervaise** : ah, but logic is more than a tool. It’s also a language for describing the world around us. Thus, I would argue that “What is the meaning of logic?” is as valid a question as “What is the meaning of art?” or “What is the meaning of science?”, as both art and science are also in part languages for describing reality. **Libertarian** : out of curiousity, in what sense do you consider “A=A” (or any other axiom) to be true? Logically? Empirically? Something else? (I’m guessing that you’ve thought about this question before, since I’ve seen you post about epistemology on other occasions…) ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [November 19, 2002, 9:40pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/55 "2002-11-19T21:40:27Z")
> [@](#): > > \*Originally posted by ultrafilter \* > \*\*Not all tautologies are meaningless, and the axiom of reflexivity is nowhere near a primary axiom: in fact, it doesn’t even exist in first-order predicate calculus. \*\* Of _course_ every tautology is meaningless. It is proved by everything. It is a mistake to assume that first order logic is, merely because of its name, the basis for all other logic. In fact, it is derived from more general symbolic logics of the broader logical calculus. It’s not the case that other logics are built from the fifteen axioms and two rules of inference of first order logic, but rather merely that those axioms and rules are constituent formulas built from the manipulation of variables by operators that are derived from higher logic’s wiffs. Keep in mind that propositional logic, with two fewer axioms, is simpler even than first order predicate. ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [November 19, 2002, 9:46pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/56 "2002-11-19T21:46:00Z")
Math Geek wrote: > [@](#): > > Libertarian: out of curiousity, in what sense do you consider “A=A” (or any other axiom) to be true? Logically? Empirically? Something else? (I’m guessing that you’ve thought about this question before, since I’ve seen you post about epistemology on other occasions…) In general, I subscribe to the Deflationary Theory of truth. Of course, you would expect that that is my theory of choice since I believe that the universe is an illusion. And as I said elsewhere, that’s why logic models the universe so well. It, too, is a house of cards. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [November 19, 2002, 9:46pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/57 "2002-11-19T21:46:30Z")
“In the Euclidean plane, the angles of every triangle add up to 180 degrees” That’s a tautology. Is it meaningless? First-order predicate logic is, IMHO, more properly viewed as a subset of higher-order logics. But that’s not my area of expertise. I need to do more reading on that. ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [November 19, 2002, 9:58pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/58 "2002-11-19T21:58:32Z")
Math Geek I guess really I should answer your question more directly. A = A is true if A = A is true. It’s an anaphoric dependence. * * * Ultrafilter You’re right that first order logic is a subset of higher logic. That’s what I meant to say, only you said it more clearly. And yes, “triangle = 180 degrees” is meaningless. Another name for tautologies is “definitions”. And the obvious problem with them is their recursion. The words that comprise them themselves have definitions, which have words that have definitions, which have words that have definitions, and so on ad infinitum. Eventually, it circles back to itself. Logic rests on air. There is no foundation, i.e., nothing absolute upon which all of it stands. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [November 19, 2002, 10:02pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/59 "2002-11-19T22:02:25Z")
That’s no definition. It’s a theorem, following from other theorems about parallel lines. It’s not hard to prove, but it’s not trivial to your average high-school geometry student. In fact, a definition has no truth value. Definitions are equivalent to function letters in the predicate calculus. They’re just names. Personally, I think that it might be interesting to define the information content of a theorem as the length of its shortest proof, and see where you go with that. ---
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [November 19, 2002, 10:04pm UTC](https://boards.straightdope.com/t/logic-is-meaningless/137554/60 "2002-11-19T22:04:37Z")
> [@](#): > > \*Originally posted by Math Geek \* > …once I substitute actual propositions for P and Q, is a measure of the value of logic, and is the “meaning” of logic. Of course. But that’s my point. The meaning of logic isn’t there; its the meaning of the sentences we use. But those had meaning already. They don’t _gain_ meaning by showing that there is an analogous construction in logic. **Everyone** My motivation for this attack is founded on my continued rereading of Wittgenstein. Specifically, his Tractutus Logico-Philosophicus. Not the best book to read in search of an exhaustive treatment of _meaning_, but logic itself is the target of this work, and it has influenced my thoughts appreciably. It is a difficult book to read, but no one should ever be satisfied by reading summaries of the man’s work. Much controversy still exists regarding the points he made. Similarly, one wouldn’t go to a Catholic priest to get word on the final interpretation of the Bible… you’d read it yourself. However, barring that… [**ultrafilter** , this quote is especially relevant to your point about some tautologies not being meaningless] [http://plato.stanford.edu/entries/wittgenstein/](http://plato.stanford.edu/entries/wittgenstein/) > [@](#): > > There are, first, the propositions of logic. These do not represent states of affairs, and the logical constants do not stand for objects. “My fundamental thought is that the logical constants do not represent. That the logic of the facts cannot be represented” (TLP 4.0312). This is not a happenstance thought; it is fundamental precisely because the limits of sense rest on logic. Tautologies and contradictions, the propositions of logic, are the limits of language and thought, and thereby the limits of the world. Obviously, then, they do not picture anything and do not, therefore, have sense. They are, in Wittgenstein’s terms, senseless (sinnlos). Propositions which do have sense are bipolar; they range within the truth-conditions drawn by the propositions of logic. But the propositions of logic themselves are neither true nor false “for the one allows every possible state of affairs, the other none” [**erl’s** note: this last quote remarks on tautologies and contradictions, the only things constructable with logical symbols so that should be implicit but it makes the sentence easier to read with this in mind] (TLP 4.462). I am not trying to rehash his arguments; however, I may use some quotes from sources about this work (and from the work itself) to aid my points. No sense in reinventing the wheel. To continue… > [@](#): > > …but logic is more than a tool. It’s also a language for describing the world around us. What am I describing here: (P & (P-\>Q))-\>Q ? English is a language for describing the real world. In fact, we teach it by pointing to the real world, and pointing to behaviors of other being (people) in this world (among other ways which are outside the scope of this thread). The reference is implicit. What do we point to for the logical statement? And if two English sentences have the same logical statement, are they the same sentence? Why not? [Previous page](https://boards.straightdope.com/t/logic-is-meaningless/137554.md?page=2) [Next page](https://boards.straightdope.com/t/logic-is-meaningless/137554.md?page=4)