1 5 8C H A P T E R 7 ■ C a t e g o r i c a l L o g i cis a man” as the A proposition “All things that are Socrates are men.” Simi-
larly, “The cannon is about to go off” in a typical context must not be trans-
lated as the I proposition “Some cannon is about to go off,” because the
original statement is about a particular cannon. Instead, the original state-
ment should be translated as the A proposition “All things that are that can-
non are about to go off.” These translations might seem stilted, but they are
necessary in order to apply syllogistic logic to everyday forms of expression.
Similar difficulties arise with the other basic propositional forms. If a
woman says, “I am looking for a man who is not attached,” and a friend
responds, “All of the men in my church are not attached,” then this response
should probably be translated as “No men in my church are attached,” which
is an E proposition. In contrast, “All ocean dwellers are not fish” should usu-
ally be translated not as the E proposition “No ocean dwellers are fish” but
rather as “Not all ocean dwellers are fish.” This means “Some ocean dwellers
are not fish,” which is an O proposition. Thus, some statements with the form
“All S are not P” should be translated as E propositions, but others should be
translated as O propositions. (This ambiguity in the form “All S are not P”
explains why it is standard to give E propositions in the less ambiguous form
“No S is P.”) Other sentences should also be translated as E propositions even
though they do not explicitly contain the word “no.” “Underground cables
are not easy to repair” and “If a cable is underground, it is not easy to repair”
and “There aren’t any underground cables that are easy to repair” can all be
translated as the E proposition “No underground cables are easy to repair.”
Similar complications also arise for I and O propositions. We already saw
that “Whales are found in the North Atlantic” should be translated as the
I proposition “Some whales are found in the North Atlantic.” In addition,
some common forms of expression can be translated as O propositions even
though they do not contain either the word “not” or the word “some.” For
example, “There are desserts without chocolate” can be translated as “Some
desserts are not chocolate,” which is an O proposition.
Because of such complications, there is no mechanical procedure for translat-
ing common English sentences into A, E, I, and O propositions. To find the cor-
rect translation, you need to think carefully about the sentence and its context.Translate each of the following sentences into an A, E, I, or O proposition. Be
sure that the subjects and predicates in your translations use nouns that refer
to classes of things (rather than adjectives or verbs). If the sentence can be
translated into different forms in different contexts, give each translation and
specify a context in which it seems natural.- Real men eat ants.
- Bats are not birds.
3. The hippo is charging.
4. The hippo is a noble beast.
Exercise II97364_ch07_ptg01_151-176.indd 158 15/11/13 10:29 AM
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