§ 192. Undoubtedly any negative proposition may be exhibited in an
affirmative form, since, by the law of excluded middle, given a pair
of contradictory terms, wherever the one can be asserted, the other
can be denied, and vice versâ. We shall find later on that this
principle gives rise to one of the forms of immediate inference. The
only question then can be, which is the more natural and legitimate
form of expression. It seems simpler to suppose that we assert the
agreement of 'whale' with 'not-fish' by implication only, and that
what we directly do is to predicate a disagreement between 'whale' and
the positive attributes connoted by 'fish.' For since 'not-fish' must
apply to every conceivable object of thought except those which fall
under the positive term 'fish,' to say that a whale is a 'not-fish,'
is to say that we have still to search for 'whale' throughout the
whole universe of being, minus a limited portion; which is only a more
clumsy way of saying that it is not to be found in that portion.
§ 193. Again, the term 'not-fish' must be understood either in its
intension or in its extension. If it be understood in its intension,
what it connotes is simply the absence of the positive qualities which
constitute a fish, a meaning which is equally conveyed by the negative
form of proposition. We gain nothing in simplicity by thus confounding
assertion with denial. If, on the other hand, it is to be taken in
extension, this involves the awkwardness of supposing that the
predicative power of a term resides in its extensive capacity.
§ 194. We therefore recognise predication as being of two
kinds--affirmation and negation--corresponding to which there are two
forms of copula.
§ 195. On the other hand, other logicians have maintained that there
are many kinds of copula, since the copula must vary according to the
various degrees of probability with which we can assert or deny a
predicate of a subject. This view is technically known as the doctrine
of
_The Modality of the Copula._
§ 196. It may plausibly be maintained that the division of
propositions into affirmative and negative is not an exhaustive one,
since the result of an act of judgement is not always to lead the mind
to a clear assertion or a clear denial, but to leave it in more or
less doubt as to whether the predicate applies to the subject or
not. Instead of saying simply A is B, or A is not B, we may be led to
one of the following forms of proposition--
A is possibly B.
A is probably B.
A is certainly B.
The adverbial expression which thus appears to qualify the copula is
known as 'the mode.'
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