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
true, is impossible. The latter is a doubly 
compound proposition. 
III. The Existence of Terms. Do universal 
propositions imply the existence of their 
subjects? From All a is b, are we safe in 
concluding that a’s exist ? The answer to 
this question is that in the statements of real 
life there is no general rule. For the most 
part we should regard it as waste of time to 
speak much about things which do not exist, 
yet we can say All disobedience is punished 
without in the least asserting that dis¬ 
obedience ever occurs. But in formal logic, 
where terms have become a and b and we 
know nothing about the meanings of our 
concepts, it is necessary to adopt some fixed 
convention in this matter ; if any implications 
of this sort are made by propositions in 
general, we must know exactly what they 
are and be able to state them explicitly. 
The convention which many logicians accept 
is this : Some a is b, since it affirms the 
existence of a which is b, must be taken 
as implying the separate existence of both 
a and b. But in the case of No a is b, there is 
no difficulty whatever in admitting that one 
way in which it may become a valid state¬ 
ment is by our knowing that a or b (one or 
the other) does not exist at all. Moreover, 
it is indispensable that we should have in 
logic propositions that are the exact denials 
of each other; and hence if Some a is b is 
taken as meaning Some a is b, and a and b 
both exist, we must mean, in full, by No a is b 
that No a is b or else a or b is non-existent. 
It follows that No a is b cannot be taken as 
asserting the existence of either a or b. It is, 
however, an error to say that it makes no 
implication of existence ; if there is no a 
which is b, then everything must be either 
non-a or else non-b (unless we are taking 
account of that imaginary universe in which 
nothing exists), and hence certainly either 
non-a or else non-& must exist. So in the 
proposition All that is non-a is b, we do 
not assert the existence of non-a, it is true ; 
but the proposition is exactly equivalent to 
All but a is b, and this certainly affirms that 
a or b, one or the other, exists. On the other 
hand, the immediate denial of this last, Not 
all but a is b, though a particular proposition, 
makes no affirmation in regard to the terms 
that explicitly enter it ; but it is equivalent 
to Some non-a is non-b, and hence it does 
affirm, by a necessary implication, the exis¬ 
tence of both non-a and non-&. Hence the 
rule that is sometimes stated—particular 
propositions imply the existence of their 
terms, universal propositions make no impli¬ 
cation in regard to the existence of their 
terms—is not correct. If it is said, for 
instance, that all is vanity, things that are 
vanity are certainly affirmed to exist (if 
anything exists). If the rule is limited to 
subjects—i. e. that particulars imply, while 
universals do not imply, the existence of 
their subjects—then it is true except in the 
case of two of the particular propositions of the 
complete scheme, Not all but a is b and Some 
besides a is b ; but it does not give us all the 
information in regard to existence that we 
have the right to demand of the logician. 
The complete rule is this : Express every 
universal proposition in the equivalent form, 
All but x is y, and every particular p>roposi- 
tion in the equivalent form, Some x is y ; then 
the particular proposition affirms the existence 
of both x and y, and the universal proposition 
affirms the existence of either x or y. With 
this convention it is to be noted that Some a 
is b does not follow from All a is b, except 
with the aid of the explicitly stated minor 
premise, There is some a. [In most cases, 
however, the existence is not ‘asserted’ ex¬ 
plicitly, but rather taken for granted. It 
should be added, also, that on another view, 
there is absolutely no difference between 
universal and particular propositions in the 
matter of their reference to existence ; and 
much may be said for such a view.—j.m.b.] 
A large amount of bad reasoning has been 
expended upon the question of the existence 
of terms, mostly due, of course, to the non¬ 
comprehension of what those who uphold the 
above doctrine mean by existence. The word 
is unfortunately chosen, for it has unavoidable 
metaphysical and psychological implications 
which invite confusion ; existence in the sense 
of being something that we are capable of 
thinking about must of course belong to 
every term that is an element of a compre¬ 
hensible statement, but that is not the sort 
of existence that the logician has in mind. 
It would be better to substitute for it the 
word occurrence, meaning occurrence within 
that field of thought which the speaker is 
talking about (see Universe oe Discourse) ; 
when we say Nothing has happened, we do 
not mean to assert that nothing has happened 
within the planet Mars, nor that nothing has 
happened among the microbes. The word 
occurrence has the additional reason for its 
use that nothing else is possible in speaking 
of compound propositions (to which the above


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