Logic is meaningless

Great Debates
1

Logic is a game. It is a game with rules for manipulating symbols. As with other games like “Catch”, “Ring around the Rosie”, and “Parlimentary Democracy” there is no real point (sorry, a little Douglas Adams slipped in there) to it. But logic lays down the syntax and symbols to use in forming little strings of characters, and tells us how we may shift them around.

Logic is the lynchpin of pure thought, is it not? For in principle we do not need anything to confirm or deny its tenets, its manipulation-dogma. In fact, I dare say no matter what happens in this universe, the statement

(P & (P->Q))->Q

remains as before.

The danger does not come from the fact that we may find analogous English constructions which seem to mirror logical ones, such as (in this case), “If [I wake up on time tomorrow] [I will have an egg for breakfast].” The danger comes from stating that these are, in fact, logical statements. It might lead us to think that such a statement is as true as the underlying principle of
(P & P->Q)->Q.

But as we noted,
(P & P->Q)->Q
is true no matter what; that is, under all conditions this is a valid “sentence”.

Clearly, however, I am not compelled in any way to eat eggs tomorrow. I will not violate fundamental laws of the universe should I, in fact, skip breakfast entirely, or have a #3 at McDonalds (as is my usual custom when I eat breakfast at all).

So what’s going on?

I’ll tell you what: logic doesn’t mean anything, so we are quite free to substitute whatever we choose. Any construction we say is logical is only so interpretively; that is, the argument gains nothing from being in a logical form (or more appropriately, being analogous to a logical form, given certain interpretations of symbols) because the power of logic resides in its use as a rule for symbol-games, not as a rule for discussing the world.

For, as my mostest favoritest philosopher noted, the propositions of logic all say the same thing (to wit: nothing). They are all tautologies, each derivable from the same set of propositions, and in fact are just uncanny applications of the same rules over and over again in different permutations. Given this, of course, these “properties”, these “propositions” apply everywhere all the time. And this isn’t to say that they are thus some transcendental conduit to understanding reality (a la some rationalist platform) but rather a set of rules unbound by material existence (which isn’t to imply materialism, it would hold just as true in idealism). The sky is red? No problem, (P & P->Q)->Q. Cows talk? No problem. (P & P->Q)->Q. In fact, nothing that ever happens anywhere at any time will ever stop the statement (P & P->Q)->Q.

So why would anyone say this statement means anything? What could it mean? You could point to anything, anywhere, at any time in the universe; we could be anything, anywhere, at any time and still you could say (P & P->Q)->Q. It is a sign that may be placed in front of every English (or Spanish or whatever) proposition without changing the truth of the proposition.

Some choose to call this absolute truth. I choose to call it meaningless. For what could it mean if I may append it to everything?

2

In the Euclidean plane, the angles of a triangle add up to 180 degrees.

Sure, it’s a tautology, but is it meaningless?

3

Oooooooooh, NOW I get it! Makes perfect sense to me.

4

It’s less of a game and more of a tool. I’m no Spock, but logic can be entirely valuable as my handy computer illustrates. Ultimately I suppose everything can be described as ultimately signifying nothing (ask Shakespear), but some nothings are more equal than others.

DaLovin’ Dj

5

What’s going on is that one of your premises (namely, “P->Q”) clearly doesn’t hold, which certainly explains why the conclusion is false.

From this fact…namely, that false premises lead to false conclusions…you seem to leap to a complete condemnation of all logic. Quite frankly, I don’t see why.

I wish I had more time to hammer this out, but let me ask you this: why not just evaluate logic like any other scientific theory, namely by how well it models reality? Invalid examples like the above one aside, “(P & P->Q) -> Q” certainly seems to describe how the world works in my experience, and I suspect in yours (although clearly I have no evidence of that). If P is true, and P implies Q, then Q is true.

Logic isn’t meaningless if it accurately describes the world around us.

6

Not only does it describe acurately the world around us, it describes the way that the world is not. Simply because we are not forced to eat breakfast given that we get up early enough does not mean that nothing is said at all.

We can eat an egg in the morning if we get up early enough. Equally true is that we could eat pancakes were we to get up early enough. One does not negate the other. They do both make the negative statement that we cannot eat eggs or pancakes if we wake up too late in the morning.

How is that worthless?

7

With words, one can create anything. With thought, one can justify all things. With philosophy one can prove that nothing can be proven, or that nothing can exist. What use is anything then?

8

But Math Geek, (P & P->Q) → Q is already “true” without an appeal to the real world. And, as you say, “…that false premises lead to false conclusions…” No doubt. But then you say the same thing I do: logic is meaningless. The meaning of the implication is not in the logical form of the statements, but the statements themselves. We remove logic, and the meaning is still all there.

If we use logic to prove that accuracy then the question is begged. If logic doesn’t tell us how to correctly apply it to the real world (as I mistakenly did [quite intentionally]) then in what circumstances can logic mean something? What does it mean? Does P->Q mean “[something] implies [something else] provided we aren’t talking about intention”?

Epimetheus, not much. But that’s a little off topic :wink:

9

Math Geek said that logic is meaningless? Where?

“The meaning of the implication is not in the logical form of the statements, but the statements themselves.”

Please discuss this with respect to my first post in this thread.

10

There’s an unspoken premise in the egg example. It should be:

P1: I wake up on time tomorrow
P2: My appetite for eggs will be the same tomorrow as it is at this moment.
Q: I will eat eggs for breakfast tomorrow.

If P1 and P2; Q.

P1 and P2 are independent. Given the moment-to-moment changes in human appetites, P2 is pretty shaky and by no means likely. Rather than finding a flaw in logic and taking this as evidence that logic is meaningless, you’ve presented a bad example (a false premise) and reached an unsupported conclusion.

11

This same statement could be made about most fields of mathematics, at least after they’ve been re-created axiomatically. Probability theory concerns sets of objects satisfying certain assumptions, such as countable additivity. Even arithmetic can be regarded as a set of elements and relations satisfying Peano’s axioms, rather than a real-world counting system.

12

It seems to me that this is an attempt to use reasoning (i.e. logic) to demonstrate that logic is meaningless.

Not a logical approach, IMO.

13

Nah, that could work. Remember what Gödel did.

14

JThunder, the point is the seperation between what, on the surface, appears as a logical argument (i.e.- a meaningful argument), and its truth or meaning as being partly determined by the structure it has (i.e.- it can be mapped onto logical sentences).

If I was trying to use logic to disprove logic, we’d have a rehash of Godel and I assure you (and ultrafilter, Eris bless him, would vouch for me here) that I am not the man for that job. But the completeness and consistency of the first order predicate logic is already accepted anyway. Still, far from the point.

Consider it like this, if you will. Let us suppose that logic does mean something. Further, let us suppose that propositions of logic are absolutely true. That is, under any and all conceivable conditions they are true (hence, “absolute”). Ask yourself how you would go about explaining these symbols. You could point to anything to represent any symbol, as at all times and points in existence all of logic holds. So how can we distinguish the symbols? —What do they mean?

december, that’s right. That’s right exactly. And what applies to one should not (and, really, cannot) apply to the other. Conceptual confusion.

[This post has subtle links to other threads. In GD, the “absolutes” thread. In the Pit, the thread attacking Justhink, most notably pages 7 and 8. Just thought I’d mention it.]

15

I think I kinda see something related to this.

The fact is, a statement such as (P & (P -> Q)) -> Q doesn’t have the same sort of meaning that we’re used to in everyday life. The symbols really are just placeholders, with no meaning in and of themselves. That doesn’t mean that it’s meaningless, though–it’s a rule of inference, and it does have meaning, as it tells you what you can conclude from a certain set of other statements.

For the purpose of this thread, we would actually be better off restricting ourselves to predicate logic. Truth tables are useless there–in fact, a computer can’t in general decide whether a given statement is a tautology. There, tautologies are meaningful.

And no one uses propositional logic for anything more sophisticated than digital circuit design. It’s the logical equivalent of a paint roller, and most applications call for a quill pen (i.e., the predicate calculus).

16

I should also mention that symbols in predicate logic are even less meaningful than those in the propositional variety. That’s the whole reason we have to dick around with model theory, and there ain’t nothing more weird than that.

17

It is a rule of inference. When may I apply it? And do I have to leave logic to get this meaning?

18

If you’re talking about the Incompleteness Theorem, Gödel didn’t attempt to demonstrate that logic is meaningless. Rather, he used precise mathematical logic to demonstrate that there can be propositions which are TRUE, but not ALGORITHMICALLY PROVABLE.

Obviously, this is quite different from claiming that logic itself is without meaning.

19

Sure, but he was using logic to show its own limitations. Same idea, if a bit grander in scope.

20

It’s not quite accurate to refer to logic as a game. It’s THE game, either higher or lower than all others depending upon how you look at it.

Mathematics is a game. Perhaps not always desirable, but sometimes useful. Such as determining the likely number of opponents you can kill if you launch a projectile in a certain direction, or the extra profit from watering down bar drinks by 20%.

Whether you use these games for good or bad is entirely up to you.