Fallacy of Exclusive Premises

Exclusive premises fallacy is a formal fallacy that covers up the problem when reasoning is based on one of the three fallacies of Agrippa's trilemma. Whenever a logical fallacy is committed, the fallacy has its roots in Agrippa's trilemma. All human thought (without Divine revelation) is based on one of three unhappy possibilities. These three possibilities are infinite regress, circular reasoning, or axiomatic thinking. This problem is known as Agrippa's trilemma. Some have claimed that only logic and math can be known without Divine revelation; however, that is not true. There is no reason to trust either logic or math without Divine revelation. Science is also limited to the pragmatic because of the weakness on human reasoning, which is known as Agrippa's trilemma.

The Fallacy of Exclusive Premises occurs when a syllogism has two negative premises. Only one premise can be negative if the conclusion is negative. With two negative premises, you cannot support a negative conclusion or a positive conclusion. If both of the premises are positive, you cannot support a negative concluson. If the conclusion is positive, both premises must be positive. If the conclusion is negative, one of the premises must be negative and the other premise must be positive.

Invalid Form

"No A are B.

Some B are not C.

Therefore, some C are not A."

 or

"No A are B.

No B are C.

Therefore, no C are A."

Examples of the Fallacy of Exclusive Premises

"No followers of Christ are following their own way.

Some who are following their own way are not Atheists.

Therefore, some Atheists are not followers of Christ."

No categorical syllogism that contains two negative premises, as this one does, has sound reasoning--even if both premises and the conclusion are all true.

"No creation scientists are evolutionists.

No evolutionists are convinced by evidence.

Therefore, no one who is convinced by evidence is a creation scientist."

No categorical syllogism that contains two negative premises, as this one does, has sound reasoning.

"No Christians are Atheists.

Some Atheists are not Evolutionists.

Therefore, some Evolutionists are not Christians."

The conclusion may be true, and the premises may be true, but the logic is not sound. In other words, by this logic, the conclusion cannot be known to be true.