§ 197. When we say 'The accused may be guilty' we have a proposition
of very different force from 'The accused is guilty,' and yet the
terms appear to be the same. Wherein then does the difference lie? 'In
the copula' would seem to be the obvious reply. We seem therefore
driven to admit that there are as many different kinds of copula as
there are different degrees of assurance with which a statement may be
made.
§ 198. But there is another way in which modal propositions may be
regarded. Instead of the mode being attached to the copula, it may be
considered as itself constituting the predicate, so that the above
propositions would be analysed thus--
That A is B, is possible.
That A is B, is probable.
That A is B, is certain.
§ 199. The subject here is itself a proposition of which we predicate
various degrees of probability. In this way the division of
propositions into affirmative and negative is rendered exhaustive. For
wherever before we had a doubtful assertion, we have now an assertion
of doubtfulness.
§ 200. If degrees of probability can thus be eliminated from the
copula, much more so can expressions of time, which may always be
regarded as forming part of the predicate. 'The sun will rise
to-morrow' may be analysed into 'The sun is going to rise to-morrow.'
In either case the tense belongs equally to the predicate. It is often
an awkward task so to analyse propositions relative to past or future
time as to bring out the copula under the form 'is' or 'is not': but
fortunately there is no necessity for so doing, since, as has been
said before (§ 188), the material form of the copula is a matter of
indifference to logic. Indeed in affirmative propositions the mere
juxtaposition of the subject and predicate is often sufficient to
indicate their agreement, e.g. 'Most haste, worst speed,' chalepha
tha kala. It is because all propositions are not affirmative that we
require a copula at all. Moreover the awkwardness of expression just
alluded to is a mere accident of language. In Latin we may say with
equal propriety 'Sol orietur cras' or 'Sol est oriturus cras'; while
past time may also be expressed in the analytic form in the case of
deponent verbs, as 'Caesar est in Galliam profectus'--'Caesar is gone
into Gaul.'
§ 201. The copula then may always be regarded as pure, that is, as
indicating mere agreement or disagreement between the two terms of the
proposition.
CHAPTER III.
_Of the Divisions of Propositions_.
§ 202. The most obvious and the most important division of
propositions is into true and false, but with this we are not
concerned. Formal logic can recognise no difference between true and
false propositions. The one is represented by the same symbols as the
other.
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