(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.