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Sometimes there are statements about logic e.g. "That's not logical" and I can neither prove nor disprove a statement about logic with no definition for logic itself. It's just a negation and it's also like a metalogic - logic about logic and how can I know something about saying something is "illogical" ? A consequence should not be able to be illogical since then it wouldn't be a consequence would it?

I don't have a definition for logic itself so I don't consider that I can tell whether something is logical or illogical or in this case actually "not logical" so I don't even know if I can make to leap to "not logical" = "illogical"

A statement such as "A causes B" could be false and still be logic just that the statement is false. And if it's a statement that claims any logic shouldn't it be gödelnumberable and could we include just a negation and a negation about logic itself to logic?

I don't have a problem with a statement such as "The statement A is false." and the statement A could still be "logical" and false.

Maybe this is more about how people use the expressions "logical" and "not logical" without any definition of either?

Even if we had a non sequitur, how is it "not logical"?

Why do people say "not logical" and not even "illogical"?

Thanks for any response

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closed as off-topic by Macavity, Eric Stucky, Grigory M, Did, Davide Giraudo Dec 26 '13 at 10:34

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I do not recall in any place to have seen this use of the word "logical". I'm not even sure what it means that is something is "logic" or "logical". –  Asaf Karagila Aug 17 '11 at 1:35
This seems to be an english question not a math question. To say something is not logical means that it goes against common sense. –  Joe Aug 17 '11 at 1:48
The common understanding is that arguments are logical if they are valid and illogical otherwise. Specific claims are deemed illogical (in informal discussion) when the presumed reasoning behind them is illogical, but this always tied to context. (I suppose one might also say a proposition is "logical" if it is well-structured according to some predefined set of rules for formal expression and truth evaluation.) –  anon Aug 17 '11 at 1:54
@Niklos R: I'm talking about the understanding of the word "logical" by the average person. Now philosophers have probably invented many, many different variants of the word "rational" - warranted, justified true, properly basic, etc. - so (a) there would be no single answer to your question, (b) the technical meanings would diverge from what most people conceive of and (c) philosophers themselves might argue over the various meanings without standard usage. At any rate, this is essentially a question of semantics, so is probably more appropriate for a different SE site. –  anon Aug 17 '11 at 2:12
@Niklas: The news media is just not a place for logic, sorry. Also you seem to be going on an unrelated, albeit still semantics based, tangent. –  anon Aug 17 '11 at 2:14

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