root of minus one is in many instances the necessary result of correct mathematical operations, nay further, where would mathematics higher or lower be if one were forbidden to operate with the square root of minus one.
Mathematics itself enters the realm of the dialectic and significantly enough it was a dialectic philosopher, Descartes, who introduced this progressiveness into mathematics. As is the relation of the mathematics of variable magnitudes to that of invariable quantities, so is the relation of the dialectic method of thought to the metaphysical. This does not prevent the great majority of mathematicians from only recognising the dialectic in the realms of mathematics, a condition of things satisfactory to those who operate in the antiquated, limited, metaphysical fashion by methods attained by means of the dialectic.
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(Duehring having made an attack upon Marx's "Capital" because of its reliance upon the dialectic, and having indulged in the epithets to which he is too prone with respect to this work, Engels takes up its defence in that respect as follows):
It is not our business to concern ourselves at this point with the correctness or incorrectness of the investigations of Marx as regards economics, but only with the application which he makes of the dialectic method. So much is certain, that it is only now that the readers of "Capital" will by the aid of Herr Duehring understand what they have read properly, and among them Herr Duehring himself, who in the year 1867 was still in a position, as far as possible to a man of his calibre, to review the book rationally. He did not then, it may be noted, first translate the arguments of Marx into Duehringese, as now seems indispensable to him. Even if he at that
