A non-sequitur (lit. "doesn't follow") is a logical fallacy in which the premises don't support the conclusion in any way. Thus, the conclusion doesn't follow from the premises.
Construction of a Non-Sequitur
Non-sequiturs typically take the following forms:
- If A is true, B is true.
- B is stated to be true.
- Therefore, A is true.
Even if the both premises and the conclusion are true, the argument is still logically bad since the premises don't support the conclusion. For example:
- If I am human, then I'm a mammal.
- I am a mammal.
- Therefore, I'm human.
Even though both the premises and the conclusion are true, the argument is still a fallacy since the premises don't support the conclusion.
Another common non-sequiter is this:
- If A is true, then B is true.
- A is not true.
- Therefore, B is not true.
Here's an example:
- If I am at home, then I'm in my bedroom.
- I'm not at home.
- Therefore, I'm not in my bedroom.
Again, the premises don't support the conclusion.
It's worth noting that if either of the above examples had said "If and only if A is true, then B is true" as their first premise, they would've been valid and non-fallacious but still unsound.
The above examples are the two main types of non-sequiter, however there are many other less common types. An everyday example would be "If I wear my new shirt, all the girls will think I'm sexy." However, not all girls will think that the same shirt looks sexy so there really isn't a connection between the two. This type of non-sequitur is commonly seen in advertising.
The two main premises above are good representations of the difference between validity and truth.