Logic

Hello. How do you prove that a certain logical fallacy is a fallacy indeed? Are there "fallacies" about which there is a controversy if it is a fallacy or not? And if in the future, a new fallacy will be discovered, what will be the outline of the proof that one will have to use to prove that it exists? (Just an application of the first question.)

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From the point of view of deductive logic, your question is very easily answered: a fallacy is an argument form in which the premises may all be true, but the conclusion false. To prove this, one provides what is called a "counterexample," which is simply a substitution instance that has the above characteristics.

For example, take a fairly common deductive fallacy, called affirming the consequent:

(1) If p, then q.
(2) q.
Therefore,
(3) p.

Here is a counterexample:

If 2+2=5 (p), then 5>3 (q)
5>3.
Therefore, 2+2=5.

In inductive logic, however, fallacies may be controversial, because there can be some unclarity about how to calculate or assign probabilities. An example of this kind of problem (to be brief) can be found in the philosophy of religion. For example, some philosophers have claimed that probability arguments can be used to show that it is more likely than not that our world was created by an intelligent designer, because the likelihood of this world coming to exist without a designer is so small. The problem here is trying to assign the relevant probabilities: the probability that there was an intelligent designer, and the probability of our world coming to exist without a designer. Without a way to fix in a determinate way the relevant probabilities, whether an argument is fallacious may be controversial.

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