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The 4 types of Categorical Syllogisms

As we saw in the last section, there are two quantifiers for the terms (subject and predicate):

AFFIRMO - the Latin for affirmative or positive inclusion
NEGO - the Latin for negative or exclusion

From these two Latin words:

we use the A and I of A ffIrmo for the two inclusion syllogism forms and
we use the E and O of nEgO for the two exclusion syllogism forms.

A-form (UNIVERSAL statement)
	Universal affirmative Total inclusion All X is Y Subject is distributed Predicate is undistributed
A-form Examples: All dinosaurs are extinct. All Norfolk residents are in Virginia.

E-form (UNIVERSAL statement)
	Universal negative Total exclusion All X is not Y Subject is distributed Predicate is distributed
E-form Example: All children are not allowed in the nuclear reactor room. No children are allowed in the nuclear reactor control room.

The E form is most interesting in the debate about whether or not God exists. Atheists exclude the possibility of God because of His being invisible. Thus, they say that God's existence cannot be proven in a scientific laboratory. This illustrates one truth about the universal negative: it cannot be proven. For the atheist this becomes a two-edged sword, where he cannot prove that God does not exist.

Remember that syllogisms are deductive forms of reasoning, where we move logically from a premise to a conclusion through a middle premise. In inductive methods discussed later in argument presentation (debate) and in the reasoning of scientific method, we can look at facts. In the case at hand, the atheist could look at the fact that Jewish scriptures predicted that God would come to earth to suffer and die as a sacrifice for man's sin to be proven in a resurrection from the dead. Now we are out of syllogism and into inductive methods.

I-form (PARTICULAR statement)
	Particular affirmative Partial Inclusion Some X is Y Some X is not Y Subject is undistributed Predicate is undistributed
I-form Example: Some of the high school students are in Algebra I.

O-form (PARTICULAR statement)
	Particular negative Partial Exclusion Some X is not Y Subject is Undistributed Predicate is distributed
O-form Example: Most flowers are not red. Some blondes are not dumb.

The light circle in the Y ellipse is a part of Y but not a part of X in the O-form diagram above.

The cute little circles above are called Euler diagrams after Leonhard Euler, an 18th century Swiss mathematician, who invented this notation.

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