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Philosophy 103: Introduction to Logic
Syllogistic Fallacies: Four Term Fallacy

Abstract:  The Four Term Fallacy or Fallacy of Equivocation is explained.  Strictly speaking, an argument which commits this fallacy cannot be a syllogism by definition because the argument contains more than three terms.

I.. Consider the following argument:
"A poor lesson is better than a good lesson because a poor lesson is better than nothing, and nothing is better than a good lesson."
A. Note how in the following argument we have an uncomfortable feeling that the argument seems good with true premisses, but the conclusion is obviously false. Often, we smile at arguments like these because we know something is drastically wrong, but it is not initially intuitively obvious what it is. Knowing that a valid argument cannot have true premisses and a false conclusion, and yet the argument appears to be perfectly valid, is a tip-off for the presence of the fallacy of equivocation.
Nothing is better than a good lesson.
A poor lesson is better than nothing.
A poor lesson is better than a good lesson.
B. Obviously, there is something wrong with this syllogism; this is evident from its humorous appearance. When we sketch a diagram, without attending to the meaning of the classes, it is clear that the diagram would appear valid. How is this possible?

poorlesson.gif (2169 bytes)

C. Although the argument does not translate very well into standard form categorical propositions, if we attempt to do so, we can see that the classes do not match. The word "nothing" is being used in two different senses. One attempt at translation yields:
No [lessons] are [things better than good lessons.]
All [poor lessons] are [things better than no lessons at all.]
All [poor lessons] are [things better than good lessons.]
Notice that we have more than three terms--our middle term does not match. Hence, we cannot get a valid diagram: Blank Venn Diagram Relating Four Terms
D. Fallacy of Four Terms occurs when a categorical syllogism contains more than three terms. More commonly, the fallacy of four terms is called from the point of view of informal logic, the fallacy of equivocation.  
1. Rule: A valid standard from categorical syllogism must contain exactly three terms, each of which is used in the same sense throughout the argument.
2. With more than three terms, no connection can be established from which a conclusion can be drawn. Informally, the idea of the syllogism is that two things related to the same thing ought to be related to each other. Diagram of the Mechanism of the Syllogism
3. If, for example, the M term is being used in two different senses, then the M term denotes two different classes and so cannot link together the S and P terms. 

Note:  Not just the middle term is subject to equivocation, as in this example; any of the terms in a syllogism might have be used in two different senses.

Diagram Indicating Different Middle Terms
4.  Before testing any syllogism, be sure to read and understand what is being adduced; otherwise, the four term fallacy could possibly be overlooked.

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11.22.04         2004  Licensed under GFDL

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