- "All dogs are animals, and all cats are mammals, so all dogs are mammals." The four terms are: dogs, animals, cats and mammals. Note: In many cases, the fallacy of four terms is a special case of equivocation. While the same word is used, the word has different meanings, and hence the word is treated as two different terms. Consider the following example:
- "Only man is born free, and no women are men, therefore, no women are born free." The four terms are: man (in the sense of 'humanity'), man (in the sense of 'male'), women and born free.
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Syllogistic Errors
The fallacies in this section are all cases of invalid categorical syllogisms. A categorical syllogism is an argument consisting of exactly three categorical propositions (two premises and a conclusion) in which there appear a total of exactly three categorical terms, each of which is used exactly twice. For example, the classic: (1) All men are mortal. (2) Socrates is a man. Therefore, (3) Socrates is mortal.
The fallacy is committed when a standard form categorical syllogism contains four terms.
Examples:
Proof: Identify the four terms and where necessary state the meaning of each term.
The middle term in the premises of a standard form categorical syllogism never refers to all of the members of the category it describes.
Examples:
- "All Russians were revolutionists, and all anarchists were revolutionist, therefore, all anarchists were Russians." The middle term is 'revolutionist'. While both Russians and anarchists share the common property of being revolutionist, they may be separate groups of revolutionists, and so we cannot conclude that anarchists are otherwise the same as Russians in any way. Example from Copi and Cohen, 208.
- "All trespassers are shot, and someone was shot, therefore, someone was a trespasser." The middle term is 'shot'. While 'someone' and 'trespassers' may share the property of being shot, it doesn't follow that the someone in question was a trespasser; he may have been the victim of a mugging.
Proof: Show how each of the two categories identified in the conclusion could be separate groups even though they share a common property.
The predicate term of the conclusion refers to all members of that category, but the same term in the premises refers only to some members of that category.
Examples:
- "All Texans are Americans, and no Californians are Texans, therefore, no Californians are Americans." The predicate term in the conclusion is 'Americans'. The conclusion refers to all Americans (every American is not a Californian, according to the conclusion). But the premises refer only to some Americans (those that are Texans).
Proof: Show that there may be other members of the predicate category not mentioned in the premises which are contrary to the conclusion. For example, from (i) above, one might argue, "While it's true that all Texans are Americans, it is also true that Ronald Regan is American, but Ronald Regan is Californian, so it is not true that No Californians are Americans."
A standard form categorical syllogism has two negative premises (a negative premise is any premise of the form 'No S are P' or 'Some S is not P').
Examples:
- "No Manitobans are Americans, and no Americans are Canadians, therefore, no Manitobans are Canadians." In fact, since Manitoba is a province of Canada, all Manitobans are Canadians.
Proof: Assume that the premises are true. Find an example which allows the premises to be true but which clearly contradicts the conclusion.
The conclusion of a standard form categorical syllogism is affirmative, but at least one of the premises is negative.
Examples:
- All mice are animals, and some animals are not dangerous, therefore some mice are dangerous.
- No honest people steal, and all honest people pay taxes, so some people who steal pay taxes.
Proof: Assume that the premises are true. Find an example which allows the premises to be true but which clearly contradicts the conclusion.
A standard form categorical syllogism with two universal premises has a particular conclusion. The idea is that some universal properties need not be instantiated. It may be true that 'all trespassers will be shot' even if there are no trespassers. It may be true that 'all brakeless trains are dangerous' even though there are no brakeless trains. That is the point of this fallacy.
Examples:
- All mice are animals, and all animals are dangerous, so some mice are dangerous.
- No honest people steal, and all honest people pay taxes, so some homest people pay taxes.
Proof: Assume that the premises are true, but that there are no instances of the category described. For example, in (i) above, assume there are no mice, and in (ii) above, assume there are no honest people. This shows that the conclusion is false.