Aristotle wrote six works that were later grouped together
as the Organon, which means “instrument.” These
works are the Prior Analytics, Posterior Analytics, On Interpretation,
Topics, Sophistical Refutations, and Categories. These
texts are considered the body of Aristotle’s work on logic, though
there is a great deal in the Organon that we would
not consider logic, and many of Aristotle’s other works, most notably
the Metaphysics, deal to some extent with logic.
These six works have a common interest not primarily in saying what
is true but in investigating the structure of truth and the structure
of the things that we can say such that they can be true. Broadly
speaking, the Organon provides a series of guidelines
on how to make sense of things.
Our discussion of the Organon is divided
into two parts. The first discusses the syllogism, the main weapon
in Aristotle’s logical arsenal, which he treats primarily in Prior
Analytics and On Interpretation. The second
discusses Aristotle’s more general remarks on the structure of being,
knowledge, and argument, covered primarily in the four other works
that constitute the Organon.
Summary
Aristotle’s most famous contribution to logic is the syllogism,
which he discusses primarily in the Prior Analytics. A
syllogism is a three-step argument containing three different terms.
A simple example is “All men are mortal; Socrates is a man; therefore,
Socrates is mortal.” This three-step argument contains three assertions
consisting of the three terms Socrates, man,
and mortal. The first two assertions are called premises and
the last assertion is called the conclusion; in
a logically valid syllogism, such as the one just presented, the conclusion
follows necessarily from the premises. That is, if you know that
both of the premises are true, you know that the conclusion must
also be true.
Aristotle uses the following terminology to label the
different parts of the syllogism: the premise whose subject features
in the conclusion is called the minor premise and
the premise whose predicate features in the conclusion is called
the major premise. In the example, “All men are
mortal” is the major premise, and since mortal is also
the predicate of the conclusion, it is called the major
term. Socrates” is called the minor
term because it is the subject of both the minor premise
and the conclusion, and man, which features in both
premises but not in the conclusion, is called the middle
term.
In analyzing the syllogism, Aristotle registers the important
distinction between particulars and universals. Socrates is
a particular term, meaning that the word Socrates names
a particular person. By contrast, man and mortal are
universal terms, meaning that they name general categories or qualities
that might be true of many particulars. Socrates is
one of billions of particular terms that falls under the universal man.
Universals can be either the subject or the predicate of a sentence,
whereas particulars can only be subjects.
Aristotle identifies four kinds of “categorical sentences”
that can be constructed from sentences that have universals for
their subjects. When universals are subjects, they must be preceded
by every, some, or no.
To return to the example of a syllogism, the first of the three
terms was not just “men are mortal,” but rather “all men are mortal.”
The contrary of “all men are mortal” is “some men are not mortal,”
because one and only one of these claims is true: they cannot both
be true or both be false. Similarly, the contrary of “no men are
mortal” is “some men are mortal.” Aristotle identifies sentences of
these four forms—“All X is Y,” “Some X is not Y,” “No X is Y,” and
“Some X is Y”—as the four categorical sentences and claims that
all assertions can be analyzed into categorical sentences. That means
that all assertions we make can be reinterpreted as categorical
sentences and so can be fit into syllogisms. If all our assertions can
be read as premises or conclusions to various syllogisms, it follows
that the syllogism is the framework of all reasoning. Any valid argument
must take the form of a syllogism, so Aristotle’s work in analyzing
syllogisms provides a basis for analyzing all arguments. Aristotle
analyzes all forty-eight possible kinds of syllogisms that can be
constructed from categorical sentences and shows that fourteen of
them are valid.
