Non sequitur (logic)

A non sequitur (Latin for "it does not follow"), in formal logic, is an invalid argument. In a non sequitur, the conclusion could be either true or false (because there is a disconnect between the premises and the conclusion), but the argument nonetheless asserts the conclusion to be true and is thus fallacious. While a logical argument is a non sequitur if, and only if, it is invalid (and so, technically, the terms 'invalid argument' and 'non sequitur' are equivalent), the word 'non sequitur' is typically used to refer to those types of invalid arguments which do not constitute covered by particular terms (e.g. affirming the consequent). In other words, in practice, 'non sequitur' is used to refer to an unnamed logical fallacy. Often, in fact, 'non sequitur' is used when an irrelevancy is showing up in the conclusion. The term has special applicability in law, having a formal legal definition.

Any argument that takes the following form is a non sequitur

Even if the premise and conclusion are all true, the conclusion is not a necessary consequence of the premise. This sort of non sequitur is also called affirming the consequent.

An example of affirming the consequent would be:

While the conclusion may be true, it does not follow from the premise:

The truth of the conclusion is independent of the truth of its premise – it is a 'non sequitur', since Jackson might be a mammal without being human. He might be, say, an elephant.

Affirming the consequent is essentially the same as the fallacy of the undistributed middle, but using propositions rather than set membership.

Another common non sequitur is this:

While B can indeed be false, this cannot be linked to the premise since the statement is a non sequitur. This is called denying the antecedent.

An example of denying the antecedent would be:

While the conclusion may be true, it does not follow from the premise. For all the reader knows, the declarant of the statement could be Asian, but for example Chinese, in which case the premise would be true but the conclusion false. This argument is still a fallacy even if the conclusion is true.

Affirming a disjunct is a fallacy when in the following form:

The conclusion does not follow from the premise as it could be the case that A and B are both true. This fallacy stems from the stated definition of or in propositional logic to be inclusive.

An example of affirming a disjunct would be:

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