ARistotle 
Aristotle recognized
the importance of observation. But his primary concern was still with what one
can rationally infer. This generated a sharp interest in the processes and
patterns of reason itself, and that motivated his systematic mapping of what we
call logic. His ideas suggested a vision of a logical system where all
knowledge is deducible from a set of indubitable axioms. Aristotle’s logic
focused on what we can directly infer from individual assertions (by immediate
inference) and on what we can figure out from pairs of assertion (by using
categorical syllogisms).
I
Aristotle makes room
for the important role that observation plays in thinking—providing data for
our contemplation and raw material for our inferring.
A. His work on
biological taxonomy illustrates this nicely.
B. Alexander the Great
is said to have been so impressed with Aristotle’s interest in observing and
understanding the natural world that he regularly sent samples to his former
teacher.
Ii
But Aristotle’s
primary concern was still with what one can rationally infer.
A. For Aristotle, the
bases of our inferences are observations and generalizations of them, rather
than our memories or intuitions of the Forms.
B. But he is still
working with a vision (that started with Plato and culminates with Descartes)
that all general knowledge is deducible from foundations that are (or nearly
are) indubitable and directly apprehended in one way or another.
Iii
This generated his
sharp interest in the processes and patterns of reasoning itself, and that
motivated his systematic mapping of what we call logic.
A. Logic is not
necessarily a map of how we, in fact, think. It is, rather, a rational
reconstruction of what constitutes reliable thought.
B. The use of logic
presupposes that every statement that we use in our reasoning is either true or
false, never both and never neither, and that the denial of a true statement is
false and the denial of a false statement is true. These “laws of thought” are
often summarized as the Law of Contradiction, the Law of Identity, and the Law
of Excluded Middle.
C. Although we are
confining our attention to logic with two values (true or false), with no
tertium quid available, contemporary logicians have discovered logical systems
that can work with three values or more.
Iv
Aristotle’s logic
focused on what we can directly infer from individual categorical propositions
and on what we can infer from pairs of them in categorical syllogisms.
v
Categorical
propositions declare what is or is not the case.
A. Every categorical
statement has a subject term and a predicate term and asserts something about
the relationship between the sets (categories) named by those terms.
B. A categorical
proposition can be analytic or synthetic. The meaning of the predicate of an
analytic categorical proposition is “contained” in its subject’s meaning. The
meaning of the predicate of a synthetic categorical proposition “adds to” its
subject’s meaning.
C. Categorical
statements with the same subject and predicate terms can differ in quality
(affirmative or negative) and quantity (universal or particular).
D. The standard forms
for categorical propositions are:
Universal
affirmative (called an A proposition): All S are P.
negative (called an
E proposition): No S are P.
Universal Particular
affirmative (called an I proposition):
Some S are P.
Particular negative
(called an O proposition): Some S are
not P.

E. Why are the propositions labeled A, E, I, and O?
1. The A and O
propositions are both affirmative, and the letters A and O are the vowels in
the Latin (and English) word AFFIRM.
2. The E and O
propositions are both negative, and E and O are the vowels in the Latin word
NEGO (meaning “I deny”).
vi
Immediate
inferences from standardform categorical propositions include obversion,
conversion, and contraposition.
A.
Note that the complement of a class name is the name of the class comprised of
everything not in the class named by the term itself. For example, the
complement of the term heroes is nonheroes (not cowards!). Note also that not
is an indicator of a proposition’s quality, but non is part of the class name.
B.
Obversion is changing the quality of a categorical proposition (affirmative to
negative or negative to affirmative) and replacing the predicate term with its
complement. Obversion works reliably for A, E, I, and O propositions.
OBVERSION
A:
All S are P. Obverse: No S are nonP. (reliable)
E:
No S are P. Obverse: All S are nonP. (reliable)
I:
Some S are P. Obverse: Some S are not nonP. (reliable)
O:
Some S are not P. Obverse: Some S are nonP. (reliable)
C. Conversion
amounts to swapping the subject and predicate terms of a categorical
proposition. Conversion works reliably only with E and I propositions.
CONVERSION A: All S are P. Converse: All P are S. (unreliable) E: No S are P.
Converse: No P are S. (reliable) I: Some S are P. Converse: Some P are S.
(reliable) O: Some S are not P. Converse: Some P are not S. (unreliable)
D. Contraposition amounts to replacing the
subject of a categorical proposition with the complement of its predicate and
replacing the predicate with the complement of the subject. Contraposition
works reliably only with A and O propositions.
CONTRAPOSITION
A:
All S are P. Contrapositive:
All nonP are nonS. (reliable)
E:
No S are P. Contrapositive:
No nonP are nonS. (unreliable)
I:
Some S are P. Contrapositive:
Some nonP are nonS. (unreliable)
O:
Some S are not P. Contrapositive:
Some nonP are not nonS. (reliable)

[Courtesy: Professor
James Hall]