1 6 1C a t e g o r i c a l P r o p o s i t i o n sExistential Commitment
It might also seem that an A proposition (with the form “All S is P”) implies
the corresponding I proposition (with the form “Some S is P”). This, how-
ever, raises a difficult problem that logicians have not fully settled. Usually
when we make a statement, we are talking about certain specific things. If
someone claims that all whales are mammals, that person is talking about
whales and mammals and stating a relationship between them. In making
this statement, the person seems to be taking the existence of whales and
mammals for granted. The remark seems to involve what logicians call exis-
tential commitment to the things referred to in the subject and predicate terms.
In the same way, stating an E proposition often seems to commit the speaker
to the existence of things in the subject and predicate classes and, thus, to
imply an O proposition. For example, someone who says, “No whales are
fish” seems committed to “Some whales are not fish.”
In other contexts, however, we seem to use universal (A and E) proposi-
tions without committing ourselves to the existence of the things referred to
in the subject and predicate terms. For example, if we say, “All trespassers
will be fined,” we are not committing ourselves to the existence of any tres-
passers or to any actual fines for trespassing; we are only saying, “If there
are trespassers, then they will be fined.” Similarly, if we tell a sleepy child,
“No ghosts are under your bed,” we are not committing ourselves to the ex-
istence of ghosts or anything under the bed. Finally, when Newton said, “All
bodies that are acted on by no forces are at rest,” he did not commit himself
to the existence of bodies that are acted on by no forces. Given these exam-
ples of A and E propositions that carry no commitment to the things referred
to, it is easy to think of many others.
The question then arises whether we should include existential commit-
ment in our treatment of universal propositions or not. Once more, we must
make a decision. (Remember that we had to make decisions concerning the
truth-table definitions of both disjunction and conditionals in Chapter 6.)
Classical logic was developed on the assumption that universal (A and E)
propositions carry existential commitment. Modern logic makes the opposite
decision, treating the claim “All men are mortal” as equivalent to “If some-
one is a man, then that person is mortal,” and the claim “No men are islands”
as equivalent to “If someone is a man, then that person is not an island.” This
way of speaking carries no commitment to the existence of any men.
Which approach should we adopt? The modern approach is simpler and
has proved more powerful in the long run. For these reasons, we will adopt
the modern approach and not assign existential commitment to universal
(A and E) propositions, so these propositions do not imply particular (I and
O) propositions. All the same, there is something beautiful about the classical
approach, it has a long and celebrated history, and it does seem appropriate
in some contexts, so it is worth exploring in its own right. Still, for the sake of
simplicity, we will not develop the classical theory here.97364_ch07_ptg01_151-176.indd 161 15/11/13 10:29 AM
some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materiallyCopyright 201^3 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights,
affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.