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.
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:
[nonpolluting power plants] are [safe devices].
combustion engines] are [nonpolluting power plants].
combustion engines] are [safe devices].
1. The Venn diagram shows this
argument to be invalid.
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.
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.
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
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.