y with the argument _a fortiori_,

A > B > C .'. (much more) A > C.

This also is said to contain four terms: (1) A, (2) greater than B, (3)
B, (4) greater than C. Such inferences are nevertheless intuitively
sound, may be verified by trial (within the limits of sense-perception),
and are generalised in appropriate axioms of their own, corresponding to
the _Dictum_ of the syllogism; as 'Things equal to the same thing are
equal to one another,' etc.

Now, surely, this is an erroneous application of the usual logical
analysis of propositions. Both Logic and Mathematics treat of the
_relations_ of terms; but whilst Mathematics employs the sign = for only
one kind of relation, and for that relation exclusive of the terms;
Logic employs the same signs (_is_ or _is not_) for all relations,
recognising only a difference of quality in predication, and treating
every other difference of relation as belonging to one of the terms
related. Thus Logicians read _A--is--equal to B_: as if _equal to B_
could possibly be a term co-relative with A. Whence it follows that the
argument _A = B = C .'. A = C_ contains four terms; though everybody sees
that there are only three.

In fact (as observed in chap. ii. Sec. 2) the sign of logical relation
(_is_ or _is not_), whilst usually adequate for class-reasoning
(coinherence) and sometimes extensible to causation (because a cause
implies a class of events), should never be stretched to include other
relations in such a way as to sacrifice intelligence to formalism. And,
besides mathematical or quantitative relations, there are others
(usually considered qualitative because indefinite) which cannot be
justly expressed by the logical copula. We ought to read propositions
expressing time-relations (and inferences drawn accordingly) thus:

B--is before--C;
A--is before--B:
.'. A--is before--C.

And in like manner _A--is simultaneous with--B; etc._ Such arguments (as
well as the mathematical) are intuitively sound and verifiable, and
might be generalised in axioms if it were worth while: but it is not,
because no method could be founded on such axioms.

The customary use of relative terms justifies some Mediate Inferences,
as, _The father of a father is a grand-father_.

Some cases, however, that at first seem obvious, are really delusive
unless further data be supplied. Thus _A co-exists with B, B with C; .'. A
with C_--is not sound unless _B_ is an instantaneous ev