Are You Playing the Fool?
Part 3
posted almost 14 years ago
Formal Logic
Syllogistic Fallacies
Covered previously
- Undistributed Middle. Two common examples:
All A are B. All C are B. All A are C.
All A are B. Some B are C. Some A are C. - Affirming the Consequent:
If P, then Q. Q, therefore P. - Denying the Antecedent:
If P, then Q. Not P, therefore not Q.
3 More Syllogistic Fallacies
1. Fallacy of Four Terms
All A is B.
All C is D.
Therefore, All A is D.
The missing premise is All B is C. If this is not true, then the conclusion is unreliable (note that it is not necessarily false. It can still be true if SOME B is C (as long as it's the part including all A). However, if no B is C, then the conclusion is false.
Example:
Example:
All cars are vehicles.
All airplanes fly.
Therefore, All cars fly.
The missing term is All vehicles are airplanes. But this is false, so the conclusion is not reliable.
A similar fallacy is known as the Fallacy of Equivocation:
The missing term is All vehicles are airplanes. But this is false, so the conclusion is not reliable.
A similar fallacy is known as the Fallacy of Equivocation:
All beautiful women are young.
All young people are unemployed.
Therefore, all beautiful women are unemployed.
The fallacy, ignoring the false premise, lies in ambiguity about the definition of ''young.'' It's being used in two different senses. A similar example, about the definition of ''man,'' is:
All men are intelligent creatures.
No women are men.
Therefore, no women are intelligent creatures.
This is a common fallacy that can be avoided if the people arguing agree beforehand on the definitions of terms that they will use. If they assume that words mean different things, then there will be confusion when they attempt to prove things to one another, as seen above. A word is being used in a different sense in the minor premise, which means that the major premise and conclusion are not connected without importing a fourth premise that connects the two senses of ''man'' together.
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As a last example of Four Terms, take this:
All dogs are mammals.
All fish are animals.
Therefore, all dogs are animals.
This is true, but not proven by the premises. The premise all mammals are animals is needed, which actually makes the third premise irrelevant in proving the conclusion. Of course, all mammals are fish would make the argument into a valid format, with a true conclusion. However, the premise is wrong, and thus the conclusion has not been proved in the argument, despite being true.
The fallacy is called of Four Terms because there are 4 terms: A, B, C, and D, whereas there are only 3 propositions in a syllogistic argument. There needs to be at least as many propositions as there are terms in order to make it possible to have a logically connected sequence of thought.
The fallacy, ignoring the false premise, lies in ambiguity about the definition of ''young.'' It's being used in two different senses. A similar example, about the definition of ''man,'' is:
All men are intelligent creatures.
No women are men.
Therefore, no women are intelligent creatures.
This is a common fallacy that can be avoided if the people arguing agree beforehand on the definitions of terms that they will use. If they assume that words mean different things, then there will be confusion when they attempt to prove things to one another, as seen above. A word is being used in a different sense in the minor premise, which means that the major premise and conclusion are not connected without importing a fourth premise that connects the two senses of ''man'' together.
----------
As a last example of Four Terms, take this:
All dogs are mammals.
All fish are animals.
Therefore, all dogs are animals.
This is true, but not proven by the premises. The premise all mammals are animals is needed, which actually makes the third premise irrelevant in proving the conclusion. Of course, all mammals are fish would make the argument into a valid format, with a true conclusion. However, the premise is wrong, and thus the conclusion has not been proved in the argument, despite being true.
The fallacy is called of Four Terms because there are 4 terms: A, B, C, and D, whereas there are only 3 propositions in a syllogistic argument. There needs to be at least as many propositions as there are terms in order to make it possible to have a logically connected sequence of thought.
2. Illicit Major
This, and the next fallacy, each have an unspoken assumption in a categorical syllogistic argument.
All X are Y.
No P (P is a subset of Y) are X.
Therefore, no P are Y.
Unspoken assumption: All Y are X.
Proof by analogy:
All Brits are European.
No Frenchmen are Brits.
Therefore, no Frenchmen are Europeans.
It's a fallacy because the assumption is made that all of what X is part of is also part of X. Imagine a diagram where one circle is completely inside a larger circle. The smaller circle is X, the larger circle is Y, and P is anywhere inside Y, which could place it only in Y, completely in X, or partly only in Y and partly also in X.
It's called illicit Major because the fallacy lies in mistaking the major premise to be reversible (that if all X are Y, then all Y are also X).
3. Illicit Minor
In contrast, illicit Minor is a mistake in thinking the minor premise to be reversible.
All X are Y.
All X are P.
Therefore, All P are Y.
Unspoken assumption: all P are X.
Proof by analogy:
All supermodels are attractive.
All supermodels are people.
Therefore, all people are attractive.
(obviously, though perhaps sadly, not true. Not all people are supermodels.)
(edited almost 14 years ago)
