Not Reinventing the Triangle

Hobbes ( Leviathan Publisher: Penguin Classics , 1.4) argues that speech enables us generalize and so to avoid the labor that would come if we had to analyze and assess every new object of knowledge individually:

“a man that hath no use of Speech at all, (such, as is born and remains perfectly deafe 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 equall to those two right angles that stand by it. But if another triangle be shewn him different in shape from the former, he cannot know without a new labour, whether the three angles of that also be equall 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 onely 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 generall termes, Every Triangle Hath Its Three Angles Equall To Two Right Angles . And thus the consequence found in one particular, comes to be registred and remembred, as a Universall rule; and discharges our mentall 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 .”