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Philosophy 103: Introduction to Logic
Syllogistic Fallacies: Exclusive Premisses

Abstract:  The Fallacy of Two Negative Premisses or Exclusive Premisses is illustrated and explained.

I. We continue our study of fallacies with a fifth fallacy. Consider the following argument.
"No internal combustion engines are nonpolluting power plants, and no nonpolluting power plants are safe devices. Therefore, no internal combustion engines are safe devices."
A. First, let's put the argument in standard form:
M P
No [nonpolluting power plants] are [safe devices].
S M
No [internal combustion engines] are [nonpolluting power plants].
S P
No [internal combustion engines] are [safe devices].
1. The Venn diagram shows this argument to be invalid. Diagram of EEE-1 syllogism
2. Note that both premisses are negative. As most people are intuitively aware, about what a thing is not, do not carry much information about what that thing is. If I say I am thinking of something that is not a tree, you would not know very much about what I am thinking.
3. By referring to the mnemonic of the mechanism of the syllogism sketched here, we can surmise that the basis of the syllogism is captured by noting that two things related to the same thing should be somehow related to each other, if at least one of them is totally related. Diagram of the Mechanism of a Syllogism
4. However, when both premisses are negative, our mnemonic shows the classes are not related in some way to each other, and this information is of no use to see how the terms in the conclusion are related. This state of affairs can be illustrated as follows. Diagram Illustrating the Fallacy of Exclusive Premisses
B. This Rule of Quality states that no standard form syllogism with two negative premisses is valid.
1. The fallacy is called either the Fallacy of Exclusive Premisses or the Fallacy of Two Negative Premisses.
2. Reason: When a syllogism has exclusive premisses, all that is being asserted is that S is wholly or partially excluded from part or all of the M class, likewise for the P class; but since this statement is true for every possible syllogism, the premisses entail no information.
3. Note that you can detect the fallacy of Exclusive Premisses merely by inspecting the mood of the syllogism. Test yourself on the following examples.
EOI-2 AAA-2
OOI-3 OEO-1
IEO2 EEE-2

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