LAWS OF THOUGHT 
relations of the three principles to forms of 
syllogism. They have even been called Die 
Principien des Schliessens, and have often 
been so regarded. Some points in reference 
to the meanings they have borne in such 
discussions require mention. Many writers 
have failed to distinguish sufficiently between 
reasoning and the logical forms of inference. 
The distinction may be brought out by com¬ 
paring the moods Camestres and Cesare 
(see Mood, in logic). Formally, these are 
essentially different. The form of Camestres 
is as follows : 
Every P is an M, 
Every S is other than every M ; 
.•. Every S is other than every P. 
This form does not depend upon either clause 
of the definition of ‘ not ’ or ‘ other than.’ For 
if any other relative term, such as ‘ lover of,’ 
be substituted for ‘ other than,’ the inference 
will be equally valid. The form of Cesare is 
as follows : 
Every P is other than every M, 
Every S is an M ; 
.•. Every S is other than every P. 
This depends upon the equiparance of ‘ other 
than.’ For if we substitute an ordinary rela¬ 
tive, such as loves, for ‘ other than ’ in the 
premise, the conclusion will be 
Every S is loved by every P. 
(See De Morgan’s fourth memoir on the 
syllogism, Cambridge Philos. Trans., x. (i860) 
354.) The two forms are thus widely distinct 
in logic; and yet when a man actually per¬ 
forms an inference, it would be impossible to 
determine that he ‘ reasons in ’ one of these 
moods rather than in the other. Either 
statement is incorrect. He does not, in strict 
accuracy, reason in any form of syllogism. 
For his reasoning moves in first intentions, 
while the forms of logic are constructions of 
second intentions. They are diagrammatic 
representations of the intellectual relation 
between the facts from which he reasons and 
the fact which he infers, this diagram neces¬ 
sarily making use of a particular system of 
symbols—a perfectly regular and very limited 
kind of language. It may be a part of a 
logician’s duty to show how ordinary ways of 
speaking and of thinking are to be translated 
into that symbolism of formal logic ; but it is 
no part of syllogistic itself. Logical prin¬ 
ciples of inference are merely rules for the 
illative transformation of the symbols of the 
particular system employed. If the system is 
essentially changed, they will be quite diffe¬ 
rent. As the Boolians represent Cesare and 
Camestres, they appear, after literally trans¬ 
lating the algebraic signs of those logicians into 
words, as follows : 
A that is B is nothing, 
C that is not B is nothing ; 
A that is C is nothing. 
The two moods are here absolutely indis¬ 
tinguishable. 
From the time of Scotus down to Kant 
more and more was made of a principle 
agreeing in enunciation, often exactly, 
in other places approximately, with our 
principle of contradiction, and in the later 
of those ages usually called by that name, 
although earlier more often principium pri- 
mum, p>rimum cognitum, principium identi- 
tatis, dignitas dignitatum, &c. It would best 
be called the Principle of Consistency. Atten¬ 
tion was called to it in the fourth book of 
Aristotle’s Metaphysics. The meaning of this, 
which was altogether different, at least in 
post-scholastic times, from our principle of 
contradiction, is stated in the so-called Monado¬ 
logie of Leibnitz (§31) to be that principle 
by virtue of which we judge that to be false 
which involves a contradiction, and the denial 
of the contradiction to be true. The latter 
clause involves an appeal to the principle of 
excluded middle as much as the former clause 
does to the formal principle of contradiction. 
And so the ‘principle of contradiction ’ was for¬ 
merly frequently stated. But, in fact, neither is 
appealed to ; for Leibnitz does not say that the 
contradiction is to be made explicit, but only 
that it is to be recognized as an inconsistency. 
Interpreted too strictly, the passage would 
seem to mean that all demonstrative reasoning 
is by the reductio ad absurdum ; but this 
cannot be intended. All that is meant is 
that we draw that conclusion the denial of 
which would involve an absurdity—in short, 
that which consistency requires. This is a 
description, however imperfect, of the proce¬ 
dure of demonstrative Beasoning (q. v.), and 
deos not relate to logical forms. It deals with 
first, not second, intentions. (c.s.p.) 
It is unfortunate that ‘contradictory’ and 
‘ principle of contradiction ’ are terms used 
with incongruent significations. If a and ß 
are statements, they are mutually contra¬ 
dictory, provided that one or the other of 
them must be true and that both cannot be 
true ; these are the two marks (essential and 
sufficient) of contradiction, or precise denial, as 
it might better be called. If a and b are 
terms, b is the precise negative of a (or the 
contradictory term to a), provided it takes in 
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