An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

156
MEDIATE INFERENCE
expression, was called by post-Aristotelian logicians a
Sorites (crwpen-?/?, acervus). According to the order,
in which the premises follow one another, it is usual to
distinguish
"
"
The Aristotelian
1
the Aristotelian and the Goclenian Sorites.
form is : A is B, B is C, C is D, D is
E, hence A is E. It progresses from terms of narrower
to those of wider extent ; and (in addition to the con
clusions) the minor premise of every syllogism except
the first is not expressed. The Goclenian form is : D
is E, C is D, B is C, A is B ; hence A is D. It pro
gresses from terms of wider to those of narrower extent
i.e., D, C, B, A; and the major premise of every
syllogism except
the first is omitted.
For the sake of clearness we add an analysis of the two
forms.
.A
Aristotelian Sorites. Goclenian Sorites.
A is B,
B is C,
C is D ;
.
C is D,
B is C,
.-. A is D.
is D. A is B ;
Analysis. Analysis.
(1) (A is B (minor). (i) f C is D (major).
\B is C (major). \B is C (minor).
A is C (conclusion). B is D (conclusion).
(2) rA is C (minor). (2) JB is D (major).
|C is D (major). \A is B (minor).
A is D (conclusion). A is D (conclusion).
In both forms the procedure is synthetic or progressive.
In these examples the syllogisms are all in i.
fig. Dr
Keynes has shown that Sorites are possible in which
each syllogism is of the second figure, and also in which
each syllogism is of the third figure ; but these are only
1 The "Goclenian" form is so called because it was suggested by
a German logician of the sixteenth century, Goclenius.