In 1, what is called a "fallacy" is a type of argument, so "fallacy" in this sense is a type of mistaken reasoning. In 2, it is a specific argument that is "fallacy", so that in this sense a "fallacy" is an argument which uses bad reasoning. Not just any type of mistake in reasoning counts as a logical fallacy. To be a fallacy, a type of reasoning must be potentially deceptive, it must be likely to fool at least some of the people some of the time. Moreover, in order for a fallacy to be worth identifying and naming, it must be a common type of logical error.
FORMAL FALLACY (Deductive Fallacies)
Philosophers distinguish between two types of argument: deductive and inductive. For each type, there is a different understanding of what counts as a fallacy.
Deductive arguments are supposed to be water-tight. For a deductive argument to be a good one (to be “valid”) it must be absolutely impossible for both its premises to be true and its conclusion to be false. With a good deductive argument, that simply cannot happen; the truth of the premises entails the truth of the conclusion.The classic example of a deductively valid argument is:
(1) All men are mortal.
(2) Socrates is a man. Therefore:
(3) Socrates is mortal.
It is simply not possible that both (1) and (2) are true and (3) is false, so this argument is deductively valid. Any deductive argument that fails to meet this (very high) standard commits a logical error, and so, technically, is fallacious. This