Bauhaus-Universität Weimar

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]
Baldwin, James Mark
denoted thing has some essential or accidental 
aspect. Such is ‘ white/ which means ‘ having 
Denominative term : a Name (q. v.). 
[Designate term (and designation) : a term 
which is used to indicate merely a particular 
object or class of objects ; the application of 
such a term is ‘ designation.’—J.m.b.] 
Discrete term : a term which denotes one 
sole individual, hut this may be an individual 
collection, or system. 
Exponible term : a syncategorematic word 
making a proposition exponible, that is, ex¬ 
ceptive, exclusive, reduplicative, inceptive, 
comparative, &c. (c.S.p.) 
Negative term’, any portion of experience 
(whether complicated or not) can be conceived 
of as a single term a ; all of what is other 
than it is then regarded as the negative of 
that term, and is repi-esented by non-a (or by 
a). The negative has, therefore, two pro¬ 
perties : (2) it fills up the whole of the rest 
of the field of thought (whether that be abso¬ 
lutely all that is conceivable or merely the 
immediate subject of discussion), and (1) it 
is in some essential respect distinct from its 
positive, so that there can be no object which 
is at once a and d; in other words, (1) 
nothing is both, and (2) everything is one or 
the other. If, following the grammatical de¬ 
vice by which we say large round table for 
a thing which is at once large and l’ound and 
a table, we write a b for things which are at 
once a and b, and if we wi'ite a + b for things 
which are a or b ; if, moreover, we write o 
and 00 for nothing and everything respectively, 
and < for is, or implies, we may express 
these two elements of the definition of the 
negative thus : 
(1) ad-^o, (2) 00 a + d. 
The second is commonly called the principle 
of no tertium quid or of the excluded middle ; 
the first, the principle of contradiction. But 
a and d are called contradictory terms (and 
in the case of propositions p and p are said 
to exactly contradict each another) ; it is a 
pity, therefore, to give the name of principle 
of contradiction to one only of the two con¬ 
ditions which they must satisfy. It would be 
much better to call (1) the property of exclu¬ 
sion (or mutual exclusion), and (2) the property 
of exhaustion (or conjoint exhaustion). These 
two properties of being mutually exclusive 
and conjointly exhaustive may be possessed 
by any number of parts of a whole; thus 
equal to, greater than, and less than exhaust 
the relation of relative size and exclude each 
othei’—they may be regarded as a contradic¬ 
tory triplet. When we abstract from all 
other properties of objects and think of them 
simply under the aspect of quantity (that is, 
in mathematics), we state these two properties 
at once in the form of a so-called axiom; 
(3) the whole is equal to the sum of its parts ; 
that is, is not greater than (there is no 
overlapping) and is not less than (there is no 
falling short, no unoccupied space, no tertium 
quid) its parts when put together. But as 
thus stated, this axiom is tautologous ; what 
is the meaning of its parts, if not the two 
properties restated in the axiom ? It would 
be better to substitute for this axiom a 
postulate: things can be separated up into 
parts which are distinct and constitutive, that 
is, which do not overlap and which together 
fully make up the whole, or which are exclu¬ 
sive and exhaustive. And as thus stated the 
postulate applies to the concepts or terms of 
logic as well as to the quantities of mathe¬ 
Every term has a negative unless it fills 
up the whole universe, in which case its 
negative is non-existent : 00 a is the same 
thing as d 0. It can be proved that to 
a given term there is only one negative 
(Grassmann; Whitehouse, Universal Algebra, 
i. 36). What is the negative of a term which 
is itself a negative 1 It must be all of that 
which is other than that negative, but this 
takes us back to the original positive term, 
or the relation of ‘ being a negative of ’ a 
term is a reciprocal relation ; that is, a = a. 
This last is, therefore, not, as Sigwart thinks, 
another axiom, or postulate, but a derived 
proposition. (c.l.f.) 
Terminism and Terminists : see Occam - 
Terminology. [The various sections of 
this article are supplementary to the termino¬ 
logical matter of the Dictionary. The sec¬ 
tions are arranged by languages, and in each 
the terms are in alphabetical order. Cross-; 
references from one of these lists to another 
always have the word ‘ above ’ or ‘ below ’ to 
distinguish them from cross-references to the 
main topics of the work. In cases in which 
the recommendation supplements or modifies 
that made under a leading topic, a cross-refer¬ 
ence is made to that topic. The terms in¬ 
cluded here are indexed in the general Indexes 
to vol. ii, along with the matter of the 
Dictionary generally, so that the entries in 
those Indexes suffice for the whole text.— 


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