A non-sequitur (lit. "doesn't follow") is a logical fallacy in which the premises do not 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.
A problem with the logical structure of this non sequitur is that it assumes a conditional statement's ("If A, then B") converse ("If B, then A"; See http://www2.edc.org/makingmath/mathtools/conditional/conditional.asp for a more in-depth description of this) is always true. But this is only the case for definitions, where the conditional statement is true. Furthermore, 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 sequitur is this:
- If A is true, then B is true.
- A is not true.
- Therefore, B is not true.
A problem with the logical structure of this non sequitur is that it assumes a conditional statement's inverse ("If not A, then not B") of a conditional statement is always true.
Here's an example:
- If I am in my bedroom, then I'm at home.
- I'm not in my bedroom.
- Therefore, I'm not at home.
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 have been valid and non-fallacious but still unsound.
The above examples are the two main types of non sequitur, 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 soundness.
A good example of a non-sequitur commonly used by Creationists is the following:
- No one knows what caused the Big Bang.
- God must've done it.
Obviously the premise doesn't support the conclusion. In order for this argument to be used the Creationist must first show that the universe couldn't've always existed/come from another collapsed universe/etc, then they must show that science will never solve the problem of the cause of the Big Bang, then they must show that no other god or goddess ever worshipped in human history caused it, then they must prove that the Christian god exists, and finally they must prove that he caused the Big Bang. Of course, no Creationist would ever take on such a prodigiously difficult task.