Deductive fallacy

A deductive fallacy is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion. Thus, a deductive fallacy is a fallacy where deduction goes wrong, and is no longer a logical process.

The standard Aristotelian logical fallacies are:

Other logical fallacies include:

In philosophy, the term logical fallacy properly refers to a formal fallacy—a flaw in the structure of a deductive argument, which renders the argument invalid.

However, it is often used more generally in informal discourse to mean an argument that is problematic for any reason, and thus encompasses informal fallacies as well as formal fallacies—valid but unsound claims or poor non-deductive argumentation.

The presence of a formal fallacy in a deductive argument does not imply anything about the argument's premises or its conclusion (see fallacy fallacy). Both may actually be true, or even more probable as a result of the argument (e.g. appeal to authority), but the deductive argument is still invalid because the conclusion does not follow from the premises in the manner described. By extension, an argument can contain a formal fallacy even if the argument is not a deductive one; for instance an inductive argument that incorrectly applies principles of probability or causality can be said to commit a formal fallacy.

In the strictest sense, a logical fallacy is the incorrect application of a valid logical principle or an application of a nonexistent principle:

This is fallacious. And so is this:

Indeed, there is no logical principle that states:

An easy way to show the above inference as invalid is by using Venn diagrams. In logical parlance, the inference is invalid, since under at least one interpretation of the predicates it is not validity preserving.

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