Four Terms (also known by its Latin name quaternio terminorum) refers to the fallacy of using four terms in a categorical syllogism. A categorical syllogism is an argument in which a conclusion is drawn from two premises, with the premises and the conclusion each being of one of the following forms:
- All A are B
- All A are not B (or No A is B)
- Some A are B
- Some A are not B
A and B above are called terms. Only three terms can occur in any valid categorical syllogism (in order to link the premises and conclusion). The following is an example of a valid form (known as Celarent):
- No A is B
- Every C is A
- Therefore no C is B
Example
Instances of this fallacy in real arguments are usually instances of the special case known as equivocation, where the same word is used in two different meanings, disguising the presence of a fourth term.
A note antonyms
A categorical syllogism may appear to contain four terms if an antonym (a word whose meaning is opposite to another) is used. The following argument is of the form given above, but appears to contain four terms because of the antonyms 'rich' and 'poor'.
- No peasant is rich
- Every plowman is a peasant
- Therefore all plowmen are poor
Further reading
For a comprehensive reference on logical fallacies and the principles of good argument, see Attacking Faulty Reasoning: A Practical Guide To Fallacy-Free Arguments:
- Attacking Faulty Reasoning... at Amazon.com
- Attacking Faulty Reasoning... at Amazon.co.uk (for British readers)