Complete Essays, Literary Criticism, Cryptography, Autography, Translations & Letters. Эдгар Аллан По
The simple truth is, that the Aristotelians erected their castles upon a basis far less reliable than air; for no such things as axioms ever existed or can possibly exist at all. This they must have been very blind indeed not to see, or at least to suspect; for, even in their own day, many of their long-admitted ‘axioms’ had been abandoned: ‘ex nihilo nihil fit,’ for example, and a ‘thing cannot act where it is not,’ and ‘there cannot be antipodes,’ and ‘darkness cannot proceed from light.’ These and numerous similar propositions formerly accepted, without hesitation, as axioms, or undeniable truths, were, even at the period of which I speak, seen to be altogether untenable. How absurd in these people, then, to persist in relying upon a basis, as immutable, whose mutability had become so repeatedly manifest!
“But, even through evidence afforded by themselves against themselves, it is easy to convict these a priori reasoners of the grossest unreason; it is easy to show the futility, the impalpability, of their axioms in general. I have now lying before me” — it will be observed that we still proceed with the letter — “I have now lying before me a book printed about a thousand years ago. Pundit assures me that it is decidedly the cleverest ancient work on its topic, which is ‘Logic.’ The author, who was much esteemed in his day, was one Miller, or Mill; and we find it recorded of him, as a point of some importance, that he rode a mill-horse whom he called Jeremy Bentham; — but let us glance at the volume itself.
“Ah! — ‘Ability or inability to conceive,’ says Mr. Mill, very properly, ‘is in no case to be received as a criterion of axiomatic truth.’ Now, that this is a palpable truism no one in his senses will deny. Not to admit the proposition, is to insinuate a charge of variability in Truth itself, whose very title is a synonym of the Steadfast. If ability to conceive be taken as a criterion of Truth, then a truth to David Hume would very seldom be a truth to Joe; and ninety-nine hundredths of what is undeniable in Heaven would be demonstrable falsity upon Earth. The proposition of Mr. Mill, then, is sustained. I will not grant it to be an axiom; and this merely because I am showing that no axioms exist; but, with a distinction which could not have been cavilled at even by Mr. Mill himself, I am ready to grant that, if an axiom there be, then the proposition of which we speak has the fullest right to be considered an axiom — that no more 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 commonplace 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 coexist 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 anything 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 remains to be shown how any exception is admissible here. That a tree can be both a tree and not a tree, is an idea which the angels, or the devils, may entertain, and which no doubt many an earthly Bedlamite, or Transcendentalist, does.
“Now I do not quarrel with these ancients,” continues the letter-writer, “so much on account of the transparent frivolity of their logic — which, to be plain, was baseless, worthless, and fantastic altogether — as on account of their pompous and infatuate proscription of all other roads to Truth than the two narrow and crooked paths — the one of creeping and the other of crawling — to which, in their ignorant perversity, they have dared to confine the Soul — the Soul which loves nothing so well as to soar in those regions of illimitable intuition which are utterly incognizant of ‘path.’
“By the bye, my dear friend, is it not an evidence of the mental slavery entailed upon those bigoted people by their Hogs and Rams, that, in spite of the eternal prating of their savants about roads to Truth, none of them fell, even by accident, into what we now so distinctly perceive to be the broadest, the straightest, and most available of all mere roads — the great thoroughfare — the majestic highway of the Consistent? Is it not wonderful that they should have failed to deduce from the works of God the vitally momentous consideration that a perfect consistency can be nothing but an absolute truth? How plain — how rapid our progress since the late announcement of this proposition! By its means, investigation has been taken out of the hands of the ground moles, and given as a duty, rather than as a task, to the true, to the only true thinkers — to the generally educated men of ardent imagination. These latter — our Keplers, our Laplaces — ‘speculate’ — ‘theorize’ — these are the terms; can you not fancy the shout of scorn with which they would be received by our progenitors, were it possible for them to be looking over my shoulders as I write? The Keplers, I repeat, speculate — theorize — and their theories are merely corrected — reduced — sifted — cleared, little by little, of their chaff of inconsistency — until at length there stands apparent an unencumbered Consistency — a consistency which the most stolid admit, because it is a consistency, to be an absolute and unquestionable Truth.
“I have often thought, my friend, that it must have puzzled these dogmaticians of a thousand years ago to determine, even, by which of their two boasted roads it is that the cryptographist attains the solution of the more complicated cyphers; or by which of them Champollion guided mankind to those important and innumerable truths which, for so many centuries, have lain entombed amid the phonetical hieroglyphics of Egypt. In especial, would it not have given these bigots some trouble to determine by which of their two roads was reached the most momentous and sublime of all their truths — the truth, the fact, of gravitation? Newton deduced it from the laws of Kepler. Kepler admitted that these laws he guessed — these laws whose investigation disclosed to the greatest of British astronomers that principle, the basis of all (existing) physical principle, in going behind which we enter at once the nebulous kingdom of Metaphysics. Yes! these vital laws