Every other science than Logic is the science of certain concrete
relations. Arithmetic, for example, is the science of the relations of
number—Geometry, of the relations of form—Mathematics in general, of the
relations of quantity in general—of whatever can be increased or
diminished. Logic, however, is the science of Relation in the
abstract—of absolute Relation—of Relation considered solely in itself.
An axiom in any particular science other than Logic is, thus, merely a
proposition announcing certain concrete relations which seem to be too
obvious for dispute—as when we say, for instance, that the whole is
greater than its part:—and, thus again, the principle of the _Logical_
axiom—in other words, of an axiom in the abstract—is, simply,
_obviousness of relation_. Now, it is clear, not only that what is
obvious to one mind may not be obvious to another, but that what is
obvious to one mind at one epoch, may be anything but obvious, at
another epoch, to the same mind. It is clear, moreover, that what,
to-day, is obvious even to the majority of mankind, or to the majority
of the best intellects of mankind, may to-morrow be, to either majority,
more or less obvious, or in no respect obvious at all. It is seen, then,
that the _axiomatic principle_ itself is susceptible of variation, and
of course that axioms are susceptible of similar change. Being mutable,
the “truths” which grow out of them are necessarily mutable too; or, in
other words, are never to be positively depended upon as truths at
all—since Truth and Immutability are one.
It will now be readily understood that no axiomatic idea—no idea founded
in the fluctuating principle, obviousness of relation—can possibly be so
secure—so reliable a basis for any structure erected by the Reason, as
_that_ idea—(whatever it is, wherever we can find it, or _if_ it be
practicable to find it anywhere)—which is _ir_relative altogether—which
not only presents to the understanding _no obviousness_ of relation,
either greater or less, to be considered, but subjects the intellect,
not in the slightest degree, to the necessity of even looking at _any
relation at all_. If such an idea be not what we too heedlessly term “an
axiom,” it is at least preferable, as a Logical basis, to any axiom ever
propounded, or to all imaginable axioms combined:—and such, precisely,
is the idea with which my deductive process, so thoroughly corroborated
by induction, commences. My _particle proper_ is but _absolute
Irrelation_. To sum up what has been here advanced:—As a starting point
I have taken it for granted, simply, that the Beginning had nothing
behind it or before it—that it was a Beginning in fact—that it was a
beginning and nothing different from a beginning—in short that this
Beginning was——_that which it was_. If this be a “mere assumption” then
a “mere assumption” let it be.
Public-domain text, read in full here on John Shaqi.
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