The Generalizations which respectively affirm that all the angles of a triangle are equal to two right angles, or that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, rest upon an entirely different basis of proof from those upon which the Generalizations rest which respectively assert that water is composed of certain chemical constituents combined in certain proportions, or that the nerves are the instruments of sensation and of motion. The former are irresistible conclusions of the human mind, because, from the nature of the intellect, they cannot be conceived of as being otherwise. The Laws of Thought are such, that we are unable to think a triangle whose angles will _not_ be equal to two right angles, or a right-angled one, the square of whose hypothenuse will _not_ be equal to the squares of the other two sides. So long, therefore, as man is constituted as he now is--unless the human organization becomes radically changed, these geometrical Laws cannot be conceived as being otherwise than as they are. All men must apprehend them alike if they apprehend them at all. So long as man lives and thinks they remain unalterable verities, about which there can be no shadow of doubt, no possibility of error. The doctrine that water is composed of certain definite chemical constituents in certain definite proportions, or the theory that the nerves are the instruments of sensation and of motion, rests upon no such foundation. Whenever water has been analyzed, it has yielded the same separate elements in the same proportions; and whenever these elements are put together in the same quantitative ratio they have produced water; so that the conviction is proximately established in the minds of all that water is invariably the product of these elements in certain proportions. But this proof does not establish the generalization as _inevitably true, nor show that it is impossible for it to be otherwise_. It is _possible_, in the nature of things, for us to conceive that the fluid which we call water may be produced from other constituents than oxygen or hydrogen, or that such a fluid may even now exist undiscovered, the product of elements altogether unknown. So in regard to the nerves. Observation and experiment have established to the general satisfaction, that they are the instruments of sensation and motion; but we are not _absolutely sure_ that this is the fact, nor can we _know_ that a human being may not be born in whom no trace of nerves can be detected, and who will nevertheless experience sensation and exhibit motion. We may be as well satisfied, for all practical purposes, of the nature of water and of the office of the nerves as of the nature of a triangle; but the character of the evidence, on which the convincement is based, is essentially different; being, in the one case, incontrovertible and infallible; and, in the other, indecisive and _possibly_ fallacious.