## PHILOSOPHY OF THE HUMAN PERSON

## LOGIC II

## Categorical propositions are claims about classes or categories of things. A categorical proposition affirms or denies that a certain category of things (the subject category) is-whether in whole or in part-included in or excluded from another category of things (the predicate category).

## All categorical propositions are logically equivalent to a proposition in the following STANDARD FORM:

## a QUANTIFIER -- "all" (or "every"), "no," "some," or "some is not" -- followed by

a SUBJECT TERM -- a noun or noun phrase referring to the subject category -- followed by

a COPULA -- "is" or "are" -- followed by

a PREDICATE TERM -- a noun or noun phrase referring to the predicate category.

(Note: "all" with a plural noun is of course equivalent to "every" with a singular noun; when "every" is used instead of "all," the copula should be "is," not "are." )

## For example,

##

All dogs are mammals.

is a categorical proposition in standard form: the quantifier is "all," the subject term is "dogs," the copula is "are" and the predicate term is "mammals."

## Similarly, in

##

Some dogs are not Airedales.

## the subject term and copula are as before, the quantifier is "some is not," and the predicate term is "Airedales."

## Notice that many propositions not in standard form are logically equivalent to standard-form propositions.

## For example,

##

Not every dog is mean.

##

is clearly saying the same thing as the standard-form categorical proposition

Some dogs are not mean animals.

##

Similarly,

##

Anyone who leaves without permission will be fined.

##

## means the same thing as the standard-form proposition

All people who leave without permission are people who will be fined.

(where "people who leave without permission" and "people who will be fined" are the subject and predicate terms, respectively).

## In general, we must rely on context and background information to determine the best standard-form "translation" of a categorical proposition that is not already in standard form. For more details, see the module "Translating Categorical Propositions."

## From now on, whenever we talk about categorical propositions, we will assume that they are in standard form. Further, whenever we use the word "term," without further specification, it will refer to either the subject or the predicate term of a standard-form categorical proposition.

## There are four kinds of standard-form categorical propositions, corresponding to the four kinds of quantifier: "all," "no,", "some," and "some is not."

## Each kind is named by one of the four vowels of the Latin alphabet. Using "S" and "P" to symbolize arbitrarily chosen subject and predicate terms, we can symbolize these four kinds as follows:

## A--All S are P.

E--No S are P.

I--Some S are P.

O--Some S are not P.

## Each of these four kinds of categorical proposition has its own "quantity" and "quality."

## A categorical proposition's quantity is universal or particular, depending on whether it makes a claim about all, or only part, of the subject category.

## Propositions of types A and E are universal; propositions of types I and O are particular.

## A categorical proposition's quality is affirmative or negative, depending on whether it asserts that the subject category is (whether in whole or in part) included in, or excluded from, the predicate category.

## Propositions of types A and I are affirmative; propositions of types E and O are negative.

## These facts are summarized in the following table:

## Type------Quantity------Quality

A----universal-----affirmative

E-------universal-----negative

I----particular----affirmative

O------particular-----negative

## (Incidentally, the types A and I are named from the first two vowels of the Latin verb affirmo, "I assert"; types E and O are named from the first two vowels of the verb nego, "I deny.")

## A term (whether subject term or predicate term) of a categorical proposition is said to be "DISTRIBUTED" when, and only when, it is clear from the proposition's quantifier that the proposition is making a claim about the entire category to which the term in question refers.

## For example, in the proposition

##

All dogs are mammals.

the subject term "dogs" is distributed since, as we can easily see (from the quantifier "all"), this proposition is saying something about the entire category of dogs. On the other hand, in this proposition the predicate term "mammals" is not distributed, because it is not obvious (in fact, it is false!) that this proposition is saying something about the entire category of mammals. All it says about the category of mammals is that at least part of that category is included in the category of dogs. This certainly does not mean that the entire category of mammals is included in the category of dogs! So in this proposition only the subject term is distributed; the predicate term is not.

## Similar arguments can be made for the other three kinds of categorical proposition. The results can be summarized as follows:

## Type-----Subject Term-----Predicate Term

A-----Distributed-----Undistributed

E-------Distributed------Distributed

I----Undistributed----Undistributed

O-----Undistributed-----Distributed

## LOGIC HANDOUT #6

##

## 1. If the E is TRUE, then the I is _____, the A is _____, and the O is
_____.

## 2. If the I is False, then the A is _____, the O is _____, and the E
is _____.

## 3. If the A is TRUE, then the I is _____, the E is _____, and the O is
_____.

## 4. If the O is False, then the A is _____, the I is _____, and the E
is _____.

## 5. If the I is TRUE, then the A is _____, the O is _____, and the E is
_____.

##

## DETERMINE WHETHER THE FOLLOWING ARE TRUE, FALSE OR UNK

##

## 1. If NO X IS Y. is TRUE, Then

## a. All X is Y is _____

## b. Some X is Y is _____

## c. Not all X is Y is _____

## d. No Y is X is _____

## e. All X is NON-Y is _____

##

## 2. If ALL PEOPLE FROM PHILLY ARE FUNNY. is TRUE, Then

## a. No people from Philly are funny is _____

## b. Some people from Philly are funny is _____

## c. All funny people are from Philly is _____

## d. No people from Philly are non-funny is _____

## e. Some people from Minnesota are tall is _____

##

## 3. If SOME CATS ARE GRAY. is TRUE, Then

## a. All cats are gray is _____

## b. Some Cats are non-gray is _____

## c. No cats are gray is _____

## d. Some gray things are cats is _____

## e. Some gray things are not non-cats is _____

## f. No gray things are cats is _____

## g. Some cats are black is _____

##

## 4. If SOME A IS NOT B. is TRUE, Then

## a. All A is not B is _____

## b. No A is B is _____

## c. Every A is B is _____

## d. Some B is A is _____

## e. Some A is NON-B is _____

## f. Not every A is B is _____

## g. Most NON-B is A is _____

## h. Some A is not A is _____