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.
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.
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.
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
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.
A: Universal Affirmative
(E.g. All men are pigs.)
Negative (E.g. No women are servants.)
Particular Affirmative (E.g. Some guys are jerks.)
Negative (E.g. Some people are not believers.)
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
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.
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.
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.
Often nonstandard quantifiers or no quantifiers are used.
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.
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.
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