Non sequitur

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:

1. If A is true, B is true.
2. B is stated to be true.
3. 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:

1. If I am human, then I'm a mammal.
2. I am a mammal.
3. 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:

1. If A is true, then B is true.
2. A is not true.
3. Therefore, B is not true.

Here's an example:

1. If I am at home, then I'm in my bedroom.
2. I'm not at home.
3. 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.