Taxonomy of the Fallacy of Illicit Conversion Alias: False Conversion

Example:

We like the beautiful and don't like the ugly; therefore, what we like is beautiful, and what we don't like ugly….

Source: Charles Ives, Essays Before a Sonata, The Majority, and Other Writings, ed. by Howard Boatwright (New York: W. W. Norton & Co., Inc., 1962), p. 77.

Analysis

Forms
All P are Q.
Therefore, all Q are P.
Some P are not Q.
Therefore, some Q are not P.
Similar Validating Forms
No P are Q.
Therefore, no Q are P.
Some P are Q.
Therefore, some Q are P.
Examples
All communists are atheists.
Therefore, all atheists are communists.
Some dogs are not pets.
Therefore, some pets are not dogs.
Counter-Examples
All dogs are mammals.
Therefore, all mammals are dogs.
Some mammals are not cats.
Therefore, some cats are not mammals.

Exposition:

Conversion is a validating form of immediate inference for E- and I-type categorical propositions. To convert such a proposition is to switch the subject and predicate terms of the proposition, which is non-validating for the A- and O-type propositions. Hence, the fallacy of Illicit Conversion is converting an A- or O-type proposition.

Source:

Paul Edwards (Editor in Chief), The Encyclopedia of Philosophy, (Macmillan, 1972), Volume 3, pp. 170-1.


Analysis of the Example: This is really two arguments, both of which have the same general form, packed into one:

  1. We like the beautiful, therefore what we like is beautiful.
  2. We don't like the ugly, therefore what we don't like is ugly.

"We like the beautiful" means that whatever is beautiful we like. In other, more stilted, words: all beautiful things are things that we like. In contrast, "what we like is beautiful" means that whatever we like is beautiful, that is, all things that we like are beautiful things. So, the first argument reworded is:

All beautiful things are things that we like.
Therefore, all things that we like are beautiful things.

Clearly, this argument commits an illicit conversion. The invalidity of the argument may have been concealed from Ives by the confusingly similar wording of the premiss and conclusion. Analogous considerations apply to the second argument.

Acknowledgment: The example is taken from: Howard Pospesel, Introduction to Logic: Predicate Logic (1976), p. 176.


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