Bauhaus-Universität Weimar

Titel:
Dictionary of philosophy and psychology including many of the principal conceptions of ethics, logics, aesthetics ... and giving a terminology in English, French, German and Italian, vol. 2 [lead-zwing]
Person:
Baldwin, James Mark
PURL:
https://digitalesammlungen.uni-weimar.de/viewer/image/lit29448/384/
PKOPOSITION 
Subject (in logic, 2), which is in certain 
respects different from what follows. 
(C.S.P.-J.M.B.) 
I. The Import of Propositions. It fol¬ 
lows from the definition of the proposition 
that it must consist of at least three dif¬ 
ferent members, two terms (between which 
the relation is said to hold) and another 
word whose function is to express at once 
the nature of the connection between them 
and the asseveration of that connection. (This 
double force of the copula is adverted to by 
Bradley, Prino. of Logic, 22.) In Armies 
conquer countries, we may think of armies 
and countries as the objects of consciousness, 
and of conquer as specifying the nature of the 
relation and at the same time asserting that 
it holds. But such a proposition as A con¬ 
quers B can, if there is any occasion for it, be 
broken up differently, viz. into A is one-of- 
tlie-conquerors-of-B. Whether B or one-of- 
the-conquerors-of-I? be regarded as the second 
of the related objects of consciousness is merely 
a matter of convenience, and will be deter¬ 
mined in any actual case by considering 
whether other propositions, which it is desired 
to combine with this as data towards conclu¬ 
sions, have B or one-of-the-conquerors-of-A 
among their terms. Or, again, we can always 
decide which is for the moment the way in 
which we are regarding the proposition by 
considering whether in its inverted form it is 
the statement B is conquered by A or One of 
those who conquer B is A which interests us. 
To discover the three elements involved in 
A runs, we have, again, simply to invert it, 
One who runs is A. And the fact that there 
is no proposition which cannot be expressed 
in an exactly equivalent inverted form proves 
that this analysis of the proposition into two 
terms and a copulative connecting link is 
justified. 
But there is one particular relation that we 
have by far the most frequently to deal with 
in reasoning-—the relation of b invariably fol¬ 
lowing upon a, or of a as the sufficient antece¬ 
dent of b. This relation is variously expressed 
in words—a is-followed-by-5, a implies b, 
a is-indicative-of b, a is-a-sufficient-condition- 
of b, If a then b, The objects a are-included- 
among the objects b, or All a is & (where a and 
b may themselves be propositions, instead of 
simple terms, without altering the essential 
character, for logic, of the relation). In order 
to hold this relation present in consciousness 
in its purely abstract form, freed from all 
those variations of language which, rich in 
meaning though they may be, are entirely 
inessential to the purposes of logic, it is abso¬ 
lutely necessary to represent it by some 
symbol. Formal logic, as ordinarily treated 
in the books, is only semi-formal. It has 
been agreed, since the time of the earliest 
writers upon the subject, to allow terms to 
enter into propositions shorn of the special 
implications which follow upon their different 
meanings, and to represent them by colourless 
letters of the alphabet ; it is only carrying 
this admirable device for abstracting from 
the inessential a little further if we represent 
the simple copula of All a is b by some symbol. 
We shall make use of the form <^, a modi¬ 
fication of that suggested by Peirce, for this 
purpose, and we shall write a 6 for any 
one of the copulative relations which have just 
been variously put into words. De Morgan 
regard s this relation as sufficiently characterized 
by the fact that it is transitive, but that is 
a statement that needs modification. We shall 
then have for the formal representation of Not 
all a is b (corresponding to the plan of indicat¬ 
ing what is not a by a), the same sign with a 
horizontal mark indicating negation over it, 
as a <5 A It will also add greatly to facility 
of expression if we write 00 and o for the 
Special Teems (q. v.) of logic, everything and 
nothing (or what exists and what does not exist). 
Innovations are difficult to make, and there 
was long and strenuous opposition to the in¬ 
troduction of the special quantity o into arith¬ 
metic and algebra ; but it seems that the time 
has come when these simple aids towards 
extracting the essential from the accidental in 
logic should be used. Cf. Symbolic Logic, 
ad fin., and Teem (negative). 
This view, that the import of the proposi¬ 
tion is to affirm some sort of connection be¬ 
tween two objects of consciousness, dates from 
Aristotle. A favourite view of recent years 
is to maintain that in the simple judgment, 
A is B, there is both an analysis and a syn¬ 
thesis—that A as being B is given first, as an 
integral element of consciousness, and that 
the work of forming the judgment consists in 
first separating the concepts and then re¬ 
uniting them by means of the connecting 
copula (cf. Judgment). This is doubtless 
a correct account of the manner of forming 
# O 
immediate judgments, but it is not correct as 
a description of propositions. The examples 
of the proposition which are usually studied 
by the logicians are so cut and dried that it is 
difficult to detect its real essence ; it is neces¬ 
sary to consider it in the process of being 
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