Is logic ignorant?

[Boojatta]

Logic: To speak of an axiom as being "true" is to reveal ignorance.

Boojatta: Do you agree that if there exists even one instance of a rule of inference that involves an assumption that is true and a conclusion that is false, then that rule of inference is faulty?

Logic: Yes, of course. You can rely on me.

Boojatta: Is it possible for an instance of a rule of inference to involve an assumption that is an axiom of standard mathematics?"

Logic: Yes, of course. Otherwise, the axioms of standard mathematics would be cut off from everything else. You would be unable to use the axioms to prove any theorems.

Boojatta: Okay, let's put that together now, shall we? Suppose that there exists at least one instance of a rule of inference that involves a true assumption that is an axiom of standard mathematics and that involves a false conclusion. Is such a rule of inference faulty?

Logic: Yes, so what?

Boojatta: "Yes" isn't good enough. Please say it as your own utterance. I, Logic, do solemnly believe...

Logic: Very well, but as a Quaker I refuse to take the oath. Suppose that there exists at least one instance of a rule of inference that involves a true assumption that is an axiom and that involves a false conclusion. Then that particular rule of inference is faulty.

Boojatta: Are you just saying that to be agreeable?

Logic: No, I meant it.

Boojatta: You spoke of an axiom as being true. You have revealed your ignorance.

[BlooInBloo]

1. Sigh.

[On the Road]

2. Logic is Never Reliable

because terms can never be defined and applied consistently to future possibilities.

Induction is the opposite of logic, and is faulty, but has a better track record.

In the sphere of political discourse, those who consistenly bring up what "logic would dictate" tend to be conservative populists without a whole lot of experience beyond their neighborhood.

[xchrom]

3. can't logic be informed by fact and science?

you sound more like you're describing common sense than logic.

[TreasonousBastard]

4. Of course logic is ignorant-- it is...

merely a tool and has no more knowledge or wisdom than a hammer or computer. It does precisely what it is instructed to do and any "knowledge" or "truth" is external to it.

(Being slick with the definition of "axiom" doesn't change that one bit.)


Treasonous the Logician

[Boojatta]

5. I agree with you.

Somebody can accuse a fellow message board participant of "ignorance" and chalk that up as one point won by the side of the debate from which the ad hominem attack originated. A similar attack against logic unfortunately doesn't even make sense. Perhaps I should have capitalized the word "logic" in the title of this thread to identify it with the personification of logic named "Logic" who has a role in the Original Post of this thread.

The Original Post is designed to display not a potential problem with logic, but a potential problem with the opening statement in the dialog ("To speak of an axiom as being 'true' is to reveal ignorance"). However, staunch advocates of the opening statement in the dialog are predisposed to think of the opening statement as an unquestionable principle of logic. It is their logic and not logic itself that is the target of gentle mockery.

[Boojatta]

6. Kick

[Boojatta]

7. Kick

[Salviati]

8. Any interesting logical system is either incomplete or inconsistant...

http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems


Either there exist true statements that cannot be proven from the axioms as given, or if every true statement can be proven, then the axioms will invariably also show that some false statements are also true.

[Boojatta]

9. Are you simply indicating that you aren't interested in first-order logic?

I presume that you are aware that Kurt Gödel proved the completeness of first-order logic in 1929, which was before he proved the incompleteness of any recursively enumerable axiomatization of number theory.

If you examine the Original Post carefully, you should observe that it deals with matters that are much more general than number theory.

Consider an analogy. There is a concept of the "boundary" of any subset of a topological space. There's also a concept of a "boundary" of a manifold in an ordinary, finite-dimension Euclidean space. However, until you invent some concept of the "boundary" of an arbitrary set, the word "boundary" has no meaning in that general context.

Similarly, until you can define the concepts of formal number theory using just the resources available in the dialog of the Original Post, you aren't in a position to invoke Gödel's incompleteness theorem in an attempt to resolve the problem posed by the Original Post. Of course, there's no problem to be resolved if you don't insist that it's meaningless to speak of an axiom as being true.

[Boojatta]

10. Kick

[Boojatta]

11. Kick

[pfloydguy7750]

12. no. stupid question

[Boojatta]

13. Welcome to Democratic Underground, pfloydguy7750.

Could you share with readers of this thread any information about the criteria that you use? I mean the criteria that you use to decide whether a question is correctly classified as "stupid" or correctly classified as not necessarily "stupid".

Note: I formulated things above using the term "correctly classified" because you expressed your judgment without making any explicit reference to yourself. Imagine that you had written something like the following: "I, pfloydguy7750, have contemplated the question and it wasn't thought-provoking, and the asking of the question violates some principle of clearness and simplicity that I personally respect and adhere to." In that case, you would have carried some load in the conversation. In a sense, you would be meeting me half-way, and making it easy for me or anyone else interested in this thread to respond to you.

After all, if a question can be stupid, then why can't the personification of logic identified in the dialog as Logic be ignorant?

[Boojatta]

14. Kick

[bananas]

15. For you

http://www.democraticunderground.com/discuss/duboard.php?az=view_all&address=228x56934

[Boojatta]

16. Kick

[Boojatta]

17. Kick

[Fumesucker]

18. If Boojatta was a drug...

How might one go about ingesting this delightful substance?