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Aristotle's Logic
ARISTOTLE'S influence, which was very great in many dif-
ferent fields, was greatest of all in logic. In late antiquity,
when Plato was still supreme in metaphysics, Aristotle was
the recognized authority in logic, and he retained this position
throughout the Middle ages. It was not till the thirteenth century
that ' Christian philosophers accorded him supremacy in the field of
metaphysics. This supremacy was largely lost after the Renaissance,
but his supremacy in logic survived Even at the present day, all
Catholic teachers of philosophy and many others still obstinately
reject the discoveries of modern logic, and adhere with a strange
tenacity to a system which is as definitely antiquated as Ptolemaic
astronomy. This makes it difficult to do historical justice to Aristotle.
His present-day influence is so inimical to clear thinking that it is
hard to remember how great an advance he made upon all his prede-
cessors (including Plato), or how admirable his logical work would
still seem if it had been a stage in a continual progress, instead of
being (as in fact it was) a dead end, followed by over two thousand
years of stagnation. In dealing with the predecessors of Aristotle, it
is not necessary to remind the reader that they are not verbally in-
spired; one can therefore praise them for their ability without being
supposed to subscribe to all their doctrines. Aristotle, on the con-
trary, is still, especially in logic, a battle-ground, and cannot be
treated in a purely historical spirit.
Aristotle's most important work in logic is the doctrine of the
syllogism. A syllogism is an argument consisting of three parts, a
major premiss, a minor premiss, and a conclusion. Syllogisms are of
a number of different kinds, each of which has a name, given by the
scholastics. the most familiar is the kind called "Barbara":
All men are mortal (Major premiss).
Socrates is a man (Minor premiss).
Therefore: Socrates is mortal (Conclusion).
Or: All men are mortal
All Greeks are men
Therefore: All Greeks are mortal.
(Aristotle does not distinguish between these two forms; this, as we
shall see later, is a mistake.)
Other forms are: No fishes are rational, all sharks are fishes, there-
fore no sharks are rational. (This is called "Celarent.")
All men are rational, some animals are men, therefore some animals are rational
(This is called "Darii")
No Greeks are black some men are Greek, therefore some men
are not black. (This is called "Ferio")
These four make up the "First figure"; Aristotle adds a second
and third figure, and the Schulman added a fourth. It is shown that the
three later figures can be reduced to the first by various devices.
There are some inferences dot can be made hem a single premiss.
From "some men are mortal" we can infer that "some mortals are
men." According to Aristotle, this can also be inferred from "all men
are mortal". From "no gods are mortal" we can infer "no mortals are
gods," but from "some men are not Greeks" it does not, follow that
"some Greeks are not men"
Apart from such inferences as the above, Aristotle and his fol-
lowers thought that all deductive inference, when strictly stated, is
syllogistic. By setting forth all the valid kinds of syllogism, and setting
out any suggested argument in syllogistic form, it should therefore
be possible to avoid all fallacies.
This system was the beginning of formal logic, and, as such, was
both important and admirable. But considered as the end, not the
beginning, of formal logic, it is open to three kinds of criticism:
(1) Formal defects within the system itself
(2) Over-estimation of the syllogism, as compared to other forms
of deductive argument.
(3) Over-estimation of deduction as a form of argument
On each of these three, something must be said.
(1) Formal defects. Let us begin with the two statements "Socrates
is a man" and "all Greeks are men." It is necessary to make a sharp
distinction between these two, which is not done in Aristotelian logic.
The statement "all Greeks are men" is commonly interpreted as
implying that there are Greeks, without this implication, some of
Aristotle's syllogisms are not valid. Take for instance-
"All Greeks are men, all Greeks are white, therefore some men
are white." This is valid if there are Greeks, but not otherwise. If
I were to say-:
"All golden mountains are mountains, all golden mountains are
golden, therefore some mountains are golden." my conclusion would
be false, though in some sense my premisses would be true. If we are
to be explicit, we must therefore divide the one statement "all Greeks
are men" into two, one saying "there are Greeks," and the other
saying "if anything is a Greek, it is a man." The latter statement is
purely hypothetical, and does not imply that there are Greeks.
The statement "all Greeks are men" is thus much more complex
in form than the statement "Socrates is a man." "Socrates is a man"
has 'Socrates" for its subject, but "all Greeks are men" does not have
"all Greeks" for its subject, for there is nothing about "all Greeks"
either in the statement "there are Greeks" or in the statement "if any-
thing is a Greek it is a man."
This purely formal error was a source of errors in metaphysics and
theory of knowledge. Consider the state of our knowledge in regard
to the two propositions "Socrates is mortal" and "all men are mortal."
In order to know the truth of "Socrates is mortal," most of us are
content to rely upon testimony; but if testimony is to be reliable,
it must lead us back to some one who knew Socrates and saw him
dead. The one perceived fact - the dead body of Socrates -together
with the knowledge that this was called "Socrates," was enough to
assure us of the mortality of Socrates. But when it comes to "all
men are mortal," the matter is different. The question of our knowl-
edge of such general propositions is a very difficult one. Sometimes
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