ARISTOTLE AND THE EARLIER PERIPATETICS vol.I by Eduard Zeller, B.F.C.Costelloe 1897

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LOGIC 235
Aristotle pays as little attention as to the Hypothetical
and Disjunctive Syllogisms.
himself admits {Anal. Pr. i. 3,
25, a, 37; De Interpr. c. 13, 22,
b, 29 ; of. Metapli. ix. 2 init. c. 5,
1048, a, 4, c. 8, 1050, b, 30 sqq.)
with regard to the forces of
nature (Swi/jeis) which only act
in one direction, that the necessary
also may be called a possible
(Swot!)!'), and that, allowing this,
universal negative possible-propositions
can be converted simply,
and that we may conclude from
necessity to possibility—but he
also adds that this is not true as
to Ms own concept of the possible.—Two
further points of
dispute, on which Alexander
wrote a work (Alex. Anal. 40, b,
83, a), arose between Aristotle
and his pupils upon the question
about the mood of conclusions in
syllogisms, the premisses of
which are in different moods.
Aristotle says that where one
premiss is a possible- and the
other an actual-proposition, a
perfect syllogism can only be had
in the case where the major proposition
is a possible-proposition
if, however, it is the minor, we
get, first of all, an imperfect
syllogism, i.e. one in which the
conclusion is only obtained by
a deduetio ad aiswdum and not
immediately from the given premisses,
and secondly, in the case
of a negative syllogism (more
correctly : in all cases), the possibility
in the conclusion must be
taken in the improper sense (i.e.
not as confined to that which
both can and cannot be) (Anal.
Pr. i. 15). Theophrastus and
Eudemus, on the contrary, were
of opinion that even in this case
Only in what he
there was a perfect possiblesyllogism
(Alex. loo. cit. 56, b).
Both sides are right, according to
their concepts of the possible.
If we understand by ' possible '
everything that can be, including
also the necessary, the syllogisms
are quite correct and simple
'
Every B is A, every C can be B,
therefore every G can be A';
'
No B is A, every C can be B,
therefore it is possible that no C
is A,' If, on the other hand, we
take possible ' ' to mean only that
of which the contrary is likewise
possible, we cannot make such
syllogisms, because in this supposition
the minor, ' every C can
be B,' includes the negative proposition,
every C can be not-B.'
'
And also, as Theophrastus and
Budemns merely adhered to the
principle that the modality of
the conclusion is conformed to
the weaker premiss (Alex, ibid.'),
they asserted, on the same principle,
that when one premiss
is assertorial and the other
apodeictic, \the conclusion is
4ymliiilio (Alex. ibid. 40, a, 42, J
b, and from him Philop. Schol.
in Arist. 158, b, 18, 159, a, 6),
whilst, according to Aristotle
(Anal. Pr. i. 9 sqq.) it is apodeictic
when the major is so. In
this case also, according to the
meaning which we attach to the
modality of propositions, both
assertions may be made. If the
propositions 'B must be A,' B
'
cannot be A,' are supposed to
express that between B and A
there is (or is not) not a contingent,
but a necessary connection,
it follows that between every-
L>36 ARISTOTLE
says of contradictory opposition ' do we find the kernel of
the late doctrine of disjunctive judgments. On the
other hand, he is copious in his treatment of the Conversion
of Propositions, 2 laying down the well-known
rules, 3 but he treats it solely in connection with his
theory of the Syllogism.
This theory of the Syllogism was expounded by
Aristotle at full length, and it may truly be called his
most original discovery. 4 As he was the first to introduce
the name of the Syllogism into the scientific
vocabulary, 5 so he was also the first to remark that all
connections and all advances in our thought depend
upon the syllogistic combination of judgments. A
'
Syllogism ' is a chain of thoughts, in which, from certain
matters assumed, and by virtue of these alone, there issues
of necessity some further matter different from them. 6
thing contained in B and A, by
the same necessity, there is,, or
is not, a connection (if all living
beings, by reason of a necessity
of nature, are mortal, the same
is also true of every kind of
living beings, e.g. of men), as
Aristotle, loo. tit. 30, a, 21 sqq.
shows quite clearly. If, on the
other hand, these propositions
are meant to state that we are
obliged to think A connected or
not connected with B, the proposition,
' C must (or cannot) be
'
A can only be deduced from
the proposition B must ' (or
cannot) be A,' when we are
obliged to consider C implied in
B. If, however, we only know
as a fact (assertorially) that
C is B, then we only know as a
fact, likewise, that C is or is not
that which we are obliged to
think connected or not connected
with B.
1
Vid. supr. p. 230.
' Anal. Pr. i. 2, 3, cf. c. 13,
32, a, 29 sqq. c. 17, 36, b, 15
sqq. ii. 1, 53, a, 3 sqq.
3
Simple conversion of universal
negative and particular
affirmative judgments, particular
conversion (later so-called conrersio
per aecidens) of universal
affirmative, and no conversion at
all of particular negative judgments
— for the nonversio per
oontrapontionem was not as yet
known to him.
4
As he himself says, Soph. M.
c. 34, 183, b, 34, 184, b, 1.
6 Cf. Pbantl, Gescli. d.
Log. i. 264.
6
Anal. Pr. i. 24. b, 18
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