absolute axiom _is_--and,
consequently, that any subsequent proposition which shall conflict with
this one primarily advanced, must be either a falsity in itself--that is
to say no axiom--or, if admitted axiomatic, must at once neutralize both
itself and its predecessor.

"And now, by the logic of their own propounder, let us proceed to test
any one of the axioms propounded. Let us give Mr. Mill the fairest of
play. We will bring the point to no ordinary issue. We will select for
investigation no common-place axiom--no axiom of what, not the less
preposterously because only impliedly, he terms his secondary class--as
if a positive truth by definition could be either more or less
positively a truth:--we will select, I say, no axiom of an
unquestionability so questionable as is to be found in Euclid. We will
not talk, for example, about such propositions as that two straight
lines cannot enclose a space, or that the whole is greater than any one
of its parts. We will afford the logician _every_ advantage. We will
come at once to a proposition which he regards as the acme of the
unquestionable--as the quintessence of axiomatic undeniability. Here it
is:--'Contradictions cannot _both_ be true--that is, cannot coeexist in
nature.' Here Mr. Mill means, for instance,--and I give the most forcible
instance conceivable--that a tree must be either a tree or _not_ a
tree--that it cannot be at the same time a tree _and_ not a tree:--all
which is quite reasonable of itself and will answer remarkably well as
an axiom, until we bring it into collation with an axiom insisted upon a
few pages before--in other words--words which I have previously
employed--until we test it by the logic of its own propounder. 'A tree,'
Mr. Mill asserts, 'must be either a tree or _not_ a tree.' Very
well:--and now let me ask him, _why_. To this little query there is but
one response:--I defy any man living to invent a second. The sole answer
is this:--'Because we find it _impossible to conceive_ that a tree can be
any thing else than a tree or not a tree.' This, I repeat, is Mr. Mill's
sole answer:--he will not _pretend_ to suggest another:--and yet, by his
own showing, his answer is clearly no answer at all; for has he not
already required us to admit, _as an axiom_, that ability or inability
to conceive is _in no case_ to be taken as a criterion of axiomatic
truth? Thus all--absolutely _all_ his argumentation is at sea without a
rudder. Let it not be urg