Generalizations
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Explanation
By this imposition of names, some of larger, some of stricter signification, we turn the reckoning of the consequences of things imagined in the mind into a reckoning of the consequences of appellations. For example, a man that hath no use of speech at all, (such as is born and remains perfectly deaf and dumb), if he set before his eyes a triangle, and by it two right angles (such as are the corners of a square figure), he may by meditation compare and find that the three angles of that triangle are equal to those two right angles that stand by it. But if another triangle be shown him different in shape from the former, he cannot know without a new labour whether the three angles of that also be equal to the same. But he that hath the use of words, when he observes that such equality was consequent, not to the length of the sides, nor to any other particular thing in his triangle; but only to this, that the sides were straight, and the angles three, and that that was all, for which he named it a triangle; will boldly conclude universally that such equality of angles is in all triangles whatsoever, and register his invention in these general terms: Every triangle hath its three angles equal to two right angles. And thus the consequence found in one particular comes to be registered and remembered as a universal rule; and discharges our mental reckoning of time and place, and delivers us from all labour of the mind, saving the first; and makes that which was found true here, and now, to be true in all times and places.
Hobbes, Lev IV 9
Argument
Generalizations are either true or nonsense.
But when we reason in words of general signification, and fall upon a general inference which is false; though it be commonly called error, it is indeed an absurdity, or senseless speech. For error is but a deception, in presuming that somewhat is past, or to come; of which, though it were not past, or not to come, yet there was no impossibility discoverable. But when we make a general assertion, unless it be a true one, the possibility of it is inconceivable. And words whereby we conceive nothing but the sound are those we call absurd, insignificant, and nonsense. And therefore if a man should talk to me of a round quadrangle; or accidents of bread in cheese; or immaterial substances; or of a free subject; a free will; or any free but free from being hindered by opposition; I should not say he were in an error, but that his words were without meaning; that is to say, absurd.
Hobbes, Lev V 5
