logical fallacies

[lilbrattyteen]

In Philosophy 101, we are told about the different logical fallacies - i.e., the slippery slope fallacy, the appeal to authority, the ad hominem argument, etc. All (or most) are listed at http://www.fallacyfiles.orgRead more... )

Comments

[chamcha]

Many logical fallacies can be boiled down to a violation of the principle of noncontradiction (though certainly not all). This states that it cannot be that something both is and is not simultaneously. Many think that is the most fundamental principle of formal logic. I guess it is in a way. But it's more like an axiom. There's no way of proving it, since most proof methods hinge upon it.

The real question is this: how do we know if we have proven something? Why do proofs guarantee the truth of the conclusions? Logic fallacies, then, would simply be mistakes made in the proof strategies that have been developed.

Metalogic is a funny subject, but extremely interesting. You should take some symbolic logic/discrete math courses if you're really interested.

[chamcha]

Touching on something Hollowuvulua mentioned, how would we prove that 2+2=4?

We have to appeal to the Peano Axioms, which are the foundations of our number system. Basically, one of them says that each number is formed by adding 1 to the preceding number. Then we just make up names for each new one, starting with 1.

The point: formal systems (including FOL) require axioms, which cannot be proven, since all proofs in that system (and the system itself) rely on them.

[chamcha]

(This brings up another interesting aspect of metalogic: proving proofs. Ha!)

[lilbrattyteen]

Interesting. It's like a postulate in geometry class - it's obviously true but it can't be proven.
Like, the fact that there is one and only one point through each line is obvious. You don't need a proof.