From Wikipedia, the free encyclopedia

The logical fallacy of denying the correlative is the opposite of the false dilemma, where an attempt is made at introducing alternatives where there are none. For example:

You say that you have shown that my client must have stolen the money, because no-one else had the opportunity to do so. But what if the money never existed?

Should it be proven that the money never existed, nobody would be accused of the crime of stealing it. However, assuming it's known the money was there, questioning its existence as an alternative to whether a particular person was the thief or not is fallacious.

In determining whether this fallacy is committed, a close look at the context is required. The essence of denying the correlative is introducing a false alternative into a context that logically admits none, but this itself could be taken as a statement (outside of logic) that the context is invalid. For example:

Either all apples are green, or some apples are not green. But what about apples that are both green and red?

The first statement is logically true, but this does not exclude the possibility of questioning whether the statement is appropriate, that is, whether either of "green" or "not green" is supposed to include "green and red" apples as well. Thus denying the correlative should not be confused with questioning definitions.

A counterexample to denying the correlative would be:

You say that either Alice is taller than Bob, or Bob is taller than Alice. But what if they're the same size?

In this case, Alice and Bob being equally tall is a valid alternative, and exposes a false dilemma.

• Correlative based fallacies