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Philosophy 103: Introduction to Logic
Syllogistic Fallacies:
Fallacy of the Illicit Minor Term and Fallacy of the Illicit Major Term

I.  We continue our discussion of the syllogistic fallacies with the third and fourth fallacies on our list.  Consider the following argument.
All [subversives]D are [radicals]U.
No [Republicans]D are [subversives]D.
No [Republicans]D are [radicals]D.
 

A. We can see from the Venn Diagrams corresponding to this argument that this argument is fallacious.

Diagram of AEE-1 Syllogism
B. When we plug in the distribution statuses for the classes in each argument from the chart learned when we studied categorical propositions, we notice something interesting. Diagram of the Mechanism of Fallacy of the Illicit MajorTerm
C. Notice how in the argument, the major term "P-radicals" is undistributed in the major premiss, but is distributed in the conclusion.
1. Since a term is said to be "undistributed" when not every member of the class is being referred to, and a term is said to be "distributed" when each and every member of the class is being referred to, we are reasoning from information about part of a class to information about the whole of the class.
2. When reasoning from a few instances to a conclusion involving all instances, we are, metaphorically speaking, committing the fallacy of converse accident.
That is, in the premiss, we are referring to "some radicals" and then reasoning to "all radicals" in the conclusion.
Another way of looking at this fallacy is to compare the process with subalternation on the Square of Opposition.
We are moving from a subaltern being true (some radicals) to a superaltern being undetermined (all radicals) in truth value .
3. Since this fallacious reasoning involves the major term in the syllogism, the fallacy committed there is termed the Illicit Process of the Major Term or Illicit Major, for short.
D. The Fallacy of the Illicit Major occurs when the major term is undistributed in the premiss but is distributed in the conclusion (but not vice versa!).
E. The second argument is as follows.
All [good citizens]D are [nationalists]U
All [good citizens]
D are [progressives]U
All [progressives]D are [nationalists]U
1. We can see from the Venn Diagram for this argument that it is fallacious. progressives.gif (2058 bytes)
2. When we plug in the distribution statuses for the classes in each argument from the chart learned when we studied categorical propositions, we notice something interesting. Diagram of the Mechanism of Fallacy of the Illicit Minor Term
F. Notice how in the argument, the minor term "S-progressives" is undistributed in the minor premiss, but is distributed in the conclusion.
1. As in the first argument above, we are moving from referring to some of the progressives in the premiss to referring to all of the progressives in the conclusion
3. Since this fallacious reasoning involves the minor term in the syllogism, the fallacy committed there is termed the Illicit Process of the Minor Term or Illicit Minor, for short.
G. The Fallacy of the Illicit Minor occurs when the minor term is undistributed in the premiss but is distributed in the conclusion (but not vice versa).
Rule: In a valid standard form categorical syllogism no term can be distributed in the conclusion unless it is also distributed in the premisses...
Reason: ...otherwise the conclusion would assert more than what is contained in the premisses.

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