1 5 7C a t e g o r i c a l P r o p o s i t i o n sif our logical apparatus could be applied only to propositions with the explicit
forms of A, E, I, and O, then it would apply to few arguments in everyday life.
Fortunately, however, many common statements that are not explicitly in
a categorical form can be translated into a categorical form. For example,
when someone says, “Whales are mammals,” the speaker presumably means
to refer to all whales, so this statement can be translated into “All whales are
mammals,” which is an A proposition. We need to be careful, however. If
someone says, “Whales are found in the North Atlantic,” the speaker prob-
ably does not mean to refer to all whales, because there are many whales in
the Pacific as well. Similarly, if someone says, “A whale is a mammal,” this
can usually be translated as “All whales are mammals,” which is an A prop-
osition, but this translation would be inappropriate for “A whale is stranded
on the beach,” which seems to mean “One whale is stranded on the beach.”
Thus, we can be misled badly if we look only at the surface structure of what
people say. We also need to pay attention to the context when we translate
everyday talk into the basic categorical forms.
Despite these complications, it is possible to give some rough-and-ready
guides to help in translating many common forms of expression into proposi-
tions with the A, E, I, and O forms. Let’s begin with one problem that arises
for all these categorical forms: They all require a class of things as a predicate.
Thus, “All whales are big” and “No whales live on land” should strictly be re-
formulated as “All whales are big things” and “No whales are things that live
on land” or “No whales are land dwellers.” This much is easy.
Things get more complicated when we look at the word “all” in A proposi-
tions. We have already seen that the word “all” is sometimes dropped in eve-
ryday conversation, as in “Whales are mammals.” The word “all” can also be
moved away from the start of a sentence. “Democrats are all liberal” usually
means “All Democrats are liberal,” which is an A proposition. Moreover, other
words can be used in place of “all.” Each of the following claims can, in stand-
ard contexts, be translated into an A proposition with the form “All S is P”:
Every Republican is conservative.
Any investment is risky.
Anyone who is human is mortal.
Each ant is precious to its mother.
To translate such claims, we sometimes need to construct noun phrases out
of adjectives and verbs. These transformations are often straightforward, but
sometimes they require ingenuity, and even then they can seem somewhat
contorted. For example, both “Only a fool would bungee jump” and “No-
body but a fool would bungee jump” can usually be translated into “All peo-
ple who bungee jump are fools.” This translation might not seem as natural
as the originals, but, since the translation has the A form, it explicitly shows
that this claim has the logical properties shared by other A propositions.
With some stretching, it is also possible to translate statements about indi-
viduals into categorical form. The standard method is to translate “Socrates97364_ch07_ptg01_151-176.indd 157 15/11/13 10:29 AM
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