Other posters have already explained, from a variety of angles, WHY this “logical argument” that you presented is flawed.
In other words, the problem is not due to a failure in the nature of logic. The problem is due to one person’s failure to apply logic correctly. One should not use a hammer or a saw to build a computer, but does this mean that carpentry is itself meaningless?
Not the same idea at all. There’s a tremendous difference between demonstrating the limitations of logic (or more specifically, predicate logic) and claiming that logic is meaningless. If anything, the scope of Godel’s claim was far LESS grand than the one which erislover is presenting.
But JT, logic applies everywhere. Nothing that can happen can contradict it. Its truth, its rules, stand independent of justification. Thus there is no way to “apply it incorrectly”; it cannot be applied at all. It attaches to every point of reality unreservedly… or, if you prefer, it attaches to none of them.
Nothing supports it or contradicts it. What meaning can it have?
It’s a valid logical construct if and only if all the statements are true. Here, Q is not true because you choose not to have eggs for breakfast.
Godel’s Incompleteness theorem states that (in normal english) ‘All consistent axiomic formulations of number theory include undecidable propositions’. ie. Not that logic is inconsistent, just taken from first principles there are areas that you can neither prove nor disprove by logical means.
I agree with your last sentence. And I still maintain that a logical system can be turned in on itself and show itself meaningless, and that it may be the same rough idea as Godel’s work. We haven’t seen it done, so experience doesn’t help, and we both know how useful intuition is in higher mathematics.
Logic is correct, according to its axioms.
Logic isn’t necessarily a useful guide to the way that the world works (although it’s better than everything else that has ever been tried AFAIK).
There’s no particular reason to think that the world would operate according to logic (and in some senses, it clearly doesn’t).
Alternatively, we might use the term ‘logic’ to refer to a class of systems derived from fundamental principles, some of which might be useful to describe the universe – assuming that the universe is derived from and can understood as sets of basic principles.
What do you mean when you say that something is meaningless? What does it take for something to be meaningful?
The statement is still true, regardless of the truth values of its constituents. That’s what makes it a tautology. It’s also valid, as the truth of the premises necessarily entails the truth of the conclusion.
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.
Also, if the meaningfulness of a statement is determined only by its truth values, I should substitue (A & B) V (~A & B) V (~A & ~B) for A -> B whenever I see it without affecting the meaningfulness of the larger statement.
The statement is not true if its constituents are not true. It is merely logically valid. For a statement to be true, it must be both valid and all the premises must be correct.
Replace “should” in my last post with “should be able to”.
JaKiri: Nope, that’s soundness. Truth value is determined only by truth tables, and you can’t find an assignment of truth values that makes that statement false.
If I may. . .
erislover, it sounds to me that your argument proceeds from the assumption that “logic applies everywhere”. That is, it has no limits – and thus no external referents against which its accuracy can be measured, and therefore affords no means of independent verification of the “truth” it purports to describe.
While JThunder et al. seem to be saying that logic does indeed have demonstrable limits, but the things outside those limits any less true or real simply because logic fails to prove them.
Is this a fair, if overly simplistic, re-statement of the positions?
Logic is only used for defining the validity of statements/arguments. In that capactiy, it is the be all and end all. Outside that, logic is meaningless.
What the fucking hell are you talking about?
A statement may be logically valid.
If all the statements leading to the conclusion are true, then if the statement is logically valid, the conclusion is valid.
Logic does NOT deal in truth. Simply because something is logically valid does not make it true. It is simply defining whether the statement ‘works’. 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.
Jerevan, that is a fair call. But it is one part of a two-part attack on logic. The second half is that an argument’s merit is not based on how closely it maps to a sentence of logic given arbitrary rules of variable substitution (which, of course, aren’t located in logic). The truth of non-logical statements (statements made in a symbol-set not contained or described in logic) is not discernable by creating an arbitrary map to logical symbols (it certainly isn’t a logical map!).
If meaning is in a logical English sentence, it is not because the sentence was logical. If we may remove the logic and keep the meaning, then logic has no meaning. By saying this I am not using logic to disprove itself since I am contesting the very notion of treating “if - then” statements as P->Q statements.
And that is my last statement in the matter.
There’s no way you can know that for a certainty. It’s entirely conceivable that tomorrow, the following three statements will be true: that I will wake up, that if I wake up then I will have eggs for breakfast, and that I will not have eggs for breakfast. I won’t hold my breath waiting for it to happen, and the possible consequences of such an occurence would be largely unimaginable, but it’s conceivable that it will happen. And if it does, then logic will not apply in my kitchen tomorrow.
All we can say is that nothing has happened which contradicts logic. The truths predicted by logic do not stand independant of justification; always we must ask, “does this agree with our perception”? It’s exactly the same standard we apply to any other scientific theory. It’s just that in the case of logic, we’d be much more suprised if the theory turns out to be false.
Reality either supports it or contradicts it.
This relates to your earlier reply:
The statement is true without appeal to the real world, but only until we substitute actual propositions for P and Q. Once I say “let P=`I wake up’ and Q=‘I have eggs’”, then the meaning of the statement ceases to be solely a matter of logic, and starts to be a matter of empirical fact. The “meaning of logic”, rougly, is as follows: that the truth-value predicted by the “game” agrees with the truth-value observed in reality, both in this example and in every previously observed example.
But this is not a tautology, any more than it is a tautology that the sun will rise tomorrow. “The sun will rise tomorrow” is not guaranteed, it is a prediction, and the fact that the prediction is likely to be true is a measure of the value of the current state of physics, and is the “meaning” of physics. 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.
**
Fortunately, we don’t. We use empirical observation, as discussed above.
JaKiri: This isn’t the Pit. Could you please mind your language?
Watch your language, please.
Wrong. An argument is valid iff whenever the premises are true, the conclusion is true. A statement is neither valid nor invalid.
(P & (P -> Q)) -> Q
That’s a statement.
Q
That’s an argument. And a valid one to boot.
A sound argument is a valid argument with true premises.
**
[quoteLogic does NOT deal in truth. Simply because something is logically valid does not make it true. It is simply defining whether the statement ‘works’. 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. **[/QUOTE]
Wrong again. Consider the following:
If it rains, I will go to the movies. If it doesn’t rain, I will go to the movies. I will not go to the movies. Therefore, 2 + 2 = 4.
False premises, true conclusion. It’s also a valid argument, by vacuous implication.
As for your claim that logic doesn’t deal in truth–that’s just odd. Where did you get that notion?
Although I’m going to have one off topic post:
'Math Geek
Member
Registered: Oct 2000
Location: Princeton, NJ, USA
Posts: 359’
<Bob> What the buffoon lessons, the four years at clown college?
<Cecil> I’ll thank you not to refer to Princeton that way.
I thought it would be censored. Obviously not.