"I dispute the availability, and thus the value, of that reason which is cultivated in any especial form other than the abstractly logical. I dispute, in particular, the reason educed by mathematical study. The mathematics are the science of form and quantity; mathematical reasoning is merely logic applied to observation upon form and quantity. The great error lies in supposing that even the truths of what is called _pure_ algebra are abstract or general truths. And this error is so egregious that I am confounded at the universality with which it has been received. Mathematical axioms are _not_ axioms of general truth. What is true of _relation_--of form and quantity--is often grossly false in regard to morals, for example. In this latter science it is very usually _un_true that the aggregated parts are equal to the whole. In chemistry also the axiom fails. In the consideration of motive it fails; for two motives, each of a given value, have not, necessarily, a value when united, equal to the sum of their values apart. There are numerous other mathematical truths which are only truths within the limits of _relation_. But the mathematician argues, from his _finite truths_, through habit, as if they were of an absolutely general applicability--as the world indeed imagines them to be. Bryant, in his very learned 'Mythology,' mentions an analogous source of error, when he says that 'although the Pagan fables are not believed, yet we forget ourselves continually, and make inferences from them as existing realities.' With the algebraists, however, who are Pagans themselves, the 'Pagan fables' _are_ believed, and the inferences are made, not so much through lapse of memory, as through an unaccountable addling of the brains. In short, I neyer yet encountered the mere mathematician who could be trusted out of equal roots, or one who did not clandestinely hold it as a point of his faith that _x²+px_ was absolutely and unconditionally equal to _q_. Say to one of these gentlemen, by way of experiment, if you please, that you believe occasions may occur where _x²+px_ is _not_ altogether equal to _q_, and, having made him understand what you mean, get out of his reach as speedily as convenient, for, beyond doubt, he will endeavor to knock you down.