“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 cöexist 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 urged that an exception from the general rule is to be made, in cases where the ‘impossibility to conceive’ is so peculiarly great as when we are called upon to conceive a tree _both_ a tree and _not_ a tree. Let no attempt, I say, be made at urging this sotticism; for, in the first place, there are no _degrees_ of ‘impossibility,’ and thus no one impossible conception can be _more_ peculiarly impossible than another impossible conception:—in the second place, Mr. Mill himself, no doubt after thorough deliberation, has most distinctly, and most rationally, excluded all opportunity for exception, by the emphasis of his proposition, that, _in no case_, is ability or inability to conceive, to be taken as a criterion of axiomatic truth:—in the third place, even were exceptions admissible at all, it