ent; for where B
is perdurable, _A_ may co-exist with it at one time and _C_ at another.

Again: _A is to the left of B, B of C; .'. A of C_. This may pass; but it
is not a parallel argument that if _A is north of B and B west of C_,
then _A is north-west of C_: for suppose that A is a mile to the north
of B, and B a yard to the west of C, then A is practically north of C;
at least, its westward position cannot be expressed in terms of the
mariner's compass. In such a case we require to know not only the
directions but the distances of A and C from B; and then the exact
direction of A from C is an affair of mathematical calculation.

Qualitative reasoning concerning position is only applicable to things
in one dimension of space, or in time considered as having one
dimension. Under these conditions we may frame the following
generalisation concerning all Mediate Inferences: Two terms definitely
related to a third, and one of them positively, are related to one
another as the other term is related to the third (that is, positively
or negatively); provided that the relations given are of the same kind
(that is, of Time, or Coinherence, or Likeness, or Equality).

Thus, to illustrate by relations of Time--

B is simultaneous with C;
A is not simultaneous with B:
.'. A is not simultaneous with C.

Here the relations are of the same kind but of different logical
quality, and (as in the syllogism) a negative copula in the premises
leads to a negative conclusion.

An examination in detail of particular cases would show that the above
generalisation concerning all Mediate Inferences is subject to too many
qualifications to be called an Axiom; it stands to the real Axioms (the
_Dictum_, etc.) as the notion of the Uniformity of Nature does to the
definite principles of natural order (_cf._ chap. xiii. Sec. 9).

CHAPTER X

CATEGORICAL SYLLOGISMS

Sec. 1. The type of logical, deductive, mediate, categorical Inference is a
Syllogism directly conformable with the _Dictum_: as--

All carnivores (M) are excitable (P);
Cats (S) are carnivores (M):
.'. Cats (S) are excitable (P).

In this example P is predicated of M, a term distributed; in which term,
M, S is given as included; so that P may be predicated of S.

Many arguments, however, are of a type superficially different from the
above: as--

No wise man (P) fears death (M);
Balbus (S) fears death (M):
.'. Bal