On the Dangers of "Is and Is Not Not"

• June 10, 2007
• James Skemp
• article, philosophy

Logically speaking, the rule of Double Negation tells us that p :: ~~p. In order words, if something is blue, it is not not blue. Unfortunately, this is one of the rules for sentential logic that is philosophically troubling.

There's a simple example to show this; happy. We then have the following:

happy :: not not happy

or

I am happy :: I am not not happy

or

I am happy :: I am not unhappy

Now, if we are in fact declaring that we are happy, there is no problem with double negation in this case. Yet, if the declaration is the other way, it's not so easy to double negate.

In this case, it may be more because there is a third option; I am neither happy nor unhappy. In states of affairs in which there are only two options, double negation will serve us well. If something is blue, then it's not not blue. If I'm unhappy, then I'm not happy.

It's therefore important to realize cases in which there are not merely two options, but potentially three or more. In such cases, double negation will do us little good.

• double negation
• sentential logic