# Illicit Conversion

**Taxonomy:** Logical Fallacy > Formal Fallacy > Quantificational Fallacy > 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.

Forms | |
---|---|

All P are Q.
Therefore, all Q are P. |
Some P are not Q.
Therefore, some Q are not 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:

Illicit conversion does not refer to unlawful changing of religion. Rather, "conversion" is the name given in the logic of categorical propositions to the switching of the subject and predicate terms. The table below shows the four traditional categorical propositions, together with their conversions, and whether the original proposition is logically equivalent to its converse.

Type | Form | Converse | Equivalent? |
---|---|---|---|

A | All S is P. | All P is S. | No |

E | No S is P. | No P is S. | Yes |

I | Some S is P. | Some P is S. | Yes |

O | Some S is not P. | Some P is not S. | No |

As can be seen from the table, the E- and I-type propositions are equivalent to their converses, which means that conversion is a validating form of immediate inference for E- and I-type categorical propositions. In contrast, conversion is non-validating for the A- and O-type propositions. Hence, to commit the traditional fallacy of Illicit Conversion is to convert an A- or O-type proposition.

### Source:

Paul Edwards (Editor in Chief), The Encyclopedia of Philosophy, (Macmillan, 1972), Volume 3, pp. 170-1 and Volume 5, p. 37.

### Exposure:

Originally, as explained in the Exposition above, illicit conversion was considered a fallacy in the Aristotelian logic of categorical propositions. However, there is no reason why the fallacy shouldn't be extended to quantified statements that go beyond the original four. For this reason, I classify this as a fallacy of quantificational logic rather than one of categorical logic, since the traditional logic of categorical statements is subsumed within quantificational logic.

For example, consider the statement: "Every man loves some woman", which is not an A-type statement―though it looks superficially like one―because it contains two quantifiers. Nonetheless, it is not equivalent to its converse: "Everyone who loves some woman is a man." Thus, it would be just as much an illicit conversion to reason from the former to the latter.

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

- We like the beautiful, therefore what we like is beautiful.
- 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.

**Source:** Howard Pospesel, Introduction to Logic: Predicate Logic (1976), p. 176.