Categorical Propositions

There are four kinds of categorical proposition. Examples corresponding to each kind are as follows:

All men are pigs.
No women are servants.
Some guys are jerks.
Some people are not believers.

A categorical proposition has four components. Two of these components determine the content of the proposition and two determine the kind.
 Subject Term:
The class, category or concept which the proposition is about. In the above examples "men", "women", "guys" and "people" are each a subject term. The subject term helps determine the content of a proposition.
Predicate Term:
The class, category or concept which is related by the proposition to the subject term. In the above examples "pigs", "servants", "jerks" and "believers" are each a predicate term. The predicate term helps to determine the content of a proposition.
Quality (copula):
The relation of inclusion or exclusion is determined by the copula or the copula plus a negative. When the relation is inclusion, the proposition is called affirmative, and when the relation is exclusion the proposition is called negative. The copula is always some form of the verb "to be". In the examples above, the first and third are affirmative; the copula does not work with any negating word. The second and fourth examples are negative; in the second the copula works with the word "No" to indicate exclusion; in the fourth the copula works with the word "not". The quality helps to determine the kind of categorical the proposition is.
The proportion of the subject term about which the proposition makes a claim. Only two proportions matter in categorical logic: all and less than all. If the whole subject class is referred to, the statement is called universal; if less than the whole is referred to, it is called particular. In the examples above,  the first and second are universal (typically indicated by words like "all", "every", "no" and "none", but not always). The third and fourth examples above are particular (typically indicated by the word "some", but not always).

The four kinds of categorical proposition have been given names for convenience:
  In ordinary language propositions are not always in standard form. The following considerations will be useful for translating ordinary propositions into standard form.
  1. The grammatical predicate of a sentence does not always literally include a class or concept. For example, "Rabbits run fast." does not actually have a predicate term. But these can be easily translated so that their predicate term is explicit. For example: "Rabbits are fast runners." reveals that the predicate term for the above sentence would be the class of fast runners.
  2. While the copula is always some form of the verb "to be" (e.g.. "is", "are", "was", "were", "will be"), tense is not important to the logic of what is being claimed.
  3. Usually the subject term occurs first in a proposition. On occasion the subject and predicate may be switched as for example: "Tender is the night." The subject term is what the proposition is about. The forgoing statement is not about tenderness; it is about the night. "The night is tender." is closer to standard form.
  4. When the subject term is explicitly singular, as in the case of proper names and definite descriptions, one should treat it as a class of one, which means that the whole class is being referred to; so singular propositions are treated as universals. For example, "Bryan Wiebe is not a mother." should be considered equivalent to "None of the class of Bryan Wiebe is a mother." (an E form proposition) in standard form.
  5. Often nonstandard quantifiers or no quantifiers are used.
    1. When no quantifier is used one must judge from the context what is being claimed. For example, "Lions are carnivores." would be a universal proposition about all lions while "Lions are circus animals." would be a particular proposition making a claim about some lions.
    2. Any proposition of the form "All S are not P" (S refers to the subject term and P to the predicate term) is ambiguous. It may be translated into either an E form or an O form proposition. For example, "All fish are not warm blooded." would mean "No fish are warm blooded." But, "All fish are not salmon." would mean "Some fish are not salmon." Some judgement is required.
    3. In logic the word "some" always means "at least one". Words such as "few", "several", "many" and "most" must all be translated as some, because the logic here cares only about whether the claim is about the whole class or less than the whole class.

Warning: Web Page Notes are not intended as a substitute for attending lectures.

For further information see Garth Kemerling's Web Page on Categorical Propositions