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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 with examples.

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 because the top part of the area of the diagram where “internal combustion engines” and “safe devices” overlap is empty of markings. This indicates no information is available about the relation of those two classes.

2. Note also that both premisses are negative. As most people are intuitively aware, knowledge about what a thing is not, does not carry much information about what that thing is. For example, if I say I am thinking of something that is not a tree, you would not know very much about what I am thinking.[1]

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 relatable to the same thing should be somehow relatable (positively or negatively) to each other, if at least one of them is.

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 in the diagram on the right.

B. Our 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; the premisses entail no specific relationship exists between the S and the P class.

3. Note that you can detect the fallacy of Exclusive Premisses merely by inspecting the first two statement-names of the mood of the syllogism.

Test yourself on the following examples by noticing E or I premises in the initial two letters of the following mood and figure syllogisms:

EOI-2 AAA-2
OOI-3 OEO-1
IEO2 EEE-2

### Notes

1. Each premiss gives negative information about the relation between the middle term and the major and minor terms.

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