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Appendix A: Sources
Aristotle: On Interpretation
Chapter 1
{1} Words spoken are symbols or signs of affections or impressions
of the soul; written words are the signs of words spoken. As
writing, so also is speech not the same for all races of men.
But the mental affections themselves, of which these words
are primarily signs, are the same for the whole of mankind,
as are also the objects of which those affections are
representations or likenesses, images, copies.
Aristotle: Prior Analytics
Book 1 Chapter 4
{1} When three terms are so related to one another that the last
is wholly contained in the middle and the middle is wholly
contained in or excluded from the first, the extremes must admit
of perfect syllogism. By 'middle term' I mean that which both is
contained in another and contains another in itself, and which is
the middle by its position also; and by 'extremes' (a) that which
is contained in another, and (b) that in which another is
contained. For if A is predicated of all B, and B of all C,
A must necessarily be predicated of all C. ... I call this kind
of figure the First.
Chapter 5
{2} When the same term applies to all of one subject and to none
of the other, or to all or none of both, I call this kind of
figure the Second; and in it by the middle term I mean that which
is predicated of both subjects; by the extreme terms, the subjects
of which the middle is predicated; by the major term, that which
comes next to the middle; and by the minor that which is more
distant from it. The middle is placed outside the extreme terms,
and is first by position.
Chapter 6
{3} If one of the terms applies to all and the other to none of
the same subject, or if both terms apply to all or none of it,
I call this kind of figure the Third; and in it by the middle I
mean that of which both the predications are made; by extremes
the predicates; by the major term that which is [further from?]
the middle; and by the minor that which is nearer to it. The
middle is placed outside the extremes, and is last by position.
Book 2 Chapter 21
{1} Similarly too with the theory in the Meno that learning is
recollection. For in no case do we find that we have previous
knowledge of the individual, but we do find that in the process
of induction we acquire knowledge of particular things just as
though we could remember them; for there are some things which we
know immediately: e.g., if we know that X is a triangle we know
that the sum of its angles is equal to two right angles.
Similarly too in all other cases.
{2} Thus whereas we observe particular things by universal
knowledge, we do not know them by the knowledge peculiar to them.
Hence it is possible to be mistaken about them, not because we
have contrary knowledge about them, but because, although we have
universal knowledge of them, we are mistaken in our particular
knowledge.
Book 2 Chapter 23
{1} Induction (epagoge), or inductive reasoning, consists in
establishing a relation between one extreme term and the middle
term by means of the other extreme; e.g., if B is the middle term
of A and C, in proving by means of C that A applies to B; for this
is how we effect inductions. E.g., let A stand for 'long-lived',
B for 'that which has no bile' and C for the long-lived
individuals such as man and horse and mule. Then A applies to the
whole of C, for every bileless animal is long-lived. But B, 'not
having bile', also applies to all C. Then if C is convertible
with B, i.e., if the middle term is not wider in extension,
A must apply to B.
{2} This kind of syllogism is concerned with the first or
immediate premiss. Where there is a middle term, the syllogism
proceeds by means of the middle; where there is not, it proceeds
by induction. There is a sense in which induction is opposed to
syllogism, for the latter shows by the middle term that the major
extreme applies to the third, while the former shows by means of
the third that the major extreme applies to the middle. Thus by
nature the syllogism by means of the middle is prior and more
knowable; but syllogism by induction is more apparent to us.
Book 2 Chapter 24
{1} We have an Example (paradeigma) when the major extreme is shown
to be applicable to the middle term by means of a term similar to
the third. It must be known both that the middle applies to the
third term and that the first applies to the term similar to the
third. E.g., let A be 'bad', B 'to make war on neighbors',
C 'Athens against Thebes' and D 'Thebes against Phocis'. Then
if we require to prove that war against Thebes is bad, we must be
satisfied that war against neighbors is bad. Evidence of this can
be drawn from similar examples, e.g., that war by Thebes against
Phocis is bad. Then since war against neighbors is bad, and war
against Thebes is against neighbors, it is evident that war
against Thebes is bad. Now it is evident that B applies to C
and D (for they are both examples of making war on neighbors),
and A to D (since the war against Phocis did Thebes no good); but
that A applies to B will be proved by means of D. ...
{2} Thus it is evident that an example represents the relation,
not of part to whole or of whole to part, but of one part to
another, where both are subordinate to the same general term,
and one of them is known. It differs from induction in that the
latter, as we saw, shows from an examination of all the individual
cases that the [major] extreme applies to the middle, and does not
connect the conclusion with the [minor] extreme; whereas the
example does connect it and does not use all the individual cases
for its proof.
Book 2 Chapter 25
{1} We have Reduction (apagoge) (a) when it is obvious that the
first term applies to the middle, but that the middle applies to
the last term is not obvious, yet nevertheless is more probable or
not less probable than the conclusion; or (b) if there are not
many intermediate terms between the last and the middle; for in
all such cases the effect is to bring us nearer to knowledge.
{2} (a) E.g., let A stand for 'that which can be taught', B for
'knowledge' and C for 'morality'. Then that knowledge can be
taught is evident; but whether virtue is knowledge is not clear.
Then if BC is not less probable or is more probable than AC, we
have reduction; for we are nearer to knowledge for having
introduced an additional term, whereas before we had no knowledge
that AC is true.
{3} (b) Or again we have reduction if there are not many
intermediate terms between B and C; for in this case too we are
brought nearer to knowledge. E.g., suppose that D is 'to square',
E 'rectilinear figure' and F 'circle'. Assuming that between
E and F there is only one intermediate term - that the circle
becomes equal to a rectilinear figure by means of lunules -
we should approximate to knowledge.
{4} When, however, BC is not more probable than AC, or there are
several intermediate terms, I do not use the expression
'reduction'; nor when the proposition BC is immediate; for such
a statement implies knowledge.
Book 2 Chapter 27
{1} A probability (eikos) is not the same as a sign (semeion). The
former is a generally accepted premiss; for that which people know
to happen or not to happen, or to be or not to be, usually in a
particular way, is a probability: e.g., that the envious are
malevolent or that those who are loved are affectionate. A sign,
however, means a demonstrative premiss which is necessary or
generally accepted. That which coexists with something else,
or before or after whose happening something else has happened,
is a sign of that something's having happened or being.
{2} An enthymeme is a syllogism from probabilities or signs; and
a sign can be taken in three ways - in just as many ways as there
are of taking the middle term in the several figures ...
{3} We must either classify signs in this way, and regard their
middle term as an index (tekmerion) (for the name 'index' is given
to that which causes us to know, and the middle term is especially
of this nature), or describe the arguments drawn from the extremes
as 'signs', and that which is drawn from the middle as an 'index'.
For the conclusion which is reached through the first figure is
most generally accepted and most true.
Aristotle: The Art of Rhetoric
Book 1 Chapter 2
{1} But for purposes of demonstration, real or apparent, just as
Dialectic possesses two modes of argument, induction and the
syllogism, real or apparent, the same is the case in Rhetoric;
for the example is induction, and the enthymeme a syllogism, and
the apparent enthymeme an apparent syllogism. Accordingly I call
an enthymeme a rhetorical syllogism, and an example rhetorical
induction.
{2} But since few of the propositions of the rhetorical syllogism
are necessary, ... it is evident that the materials from which
enthymemes are derived will be sometimes necessary, but for the
most part only generally true; and these materials being
probabilities and signs, it follows that these two elements must
correspond to these two kinds of propositions, each to each. ...
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