The manner how speech serveth to the remembrance of the consequence of causes and effects, consisteth in the imposing of names, and the connexion of them.
Names, proper and common.
Of names, some are proper, and singular to one only thing, as Peter, John, this man, this tree; and some are common to many things, man, horse, tree; every of which, though but one name, is nevertheless the name of divers particular things; |Universal.| in respect of all which together, it is called an universal; there being nothing in the world universal but names; for the things named are every one of them individual and singular.
One universal name is imposed on many things, for their similitude in some quality, or other accident; and whereas a proper name bringeth to mind one thing only, universals recall any one of those many.
And of names universal, some are of more, and some of less extent; the larger comprehending the less large; and some again of equal extent, comprehending each other reciprocally. As for example: the name body is of larger signification than the word man, and comprehendeth it; and the names man and rational, are of equal extent, comprehending mutually one another. But here we must take notice, that by a name is not always understood, as in grammar, one only word; but sometimes, by circumlocution, many words together. For all these words, he that in his actions observeth the laws of his country, make but one name, equivalent to this one word, just.
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.
But the use of words in registering our thoughts is in nothing so evident as in numbering. A natural fool that could never learn by heart the order of numeral words, as one, two, and three, may observe every stroke of the clock, and nod to it, or say one, one, one, but can never know what hour it strikes. And it seems, there was a time when those names of number were not in use; and men were fain to apply their fingers of one or both hands, to those things they desired to keep account of; and that thence it proceeded, that now our numeral words are but ten, in any nation, and in some but five; and then they begin again. And he that can tell ten, if he recite them out of order, will lose himself, and not know when he has done. Much less will he be able to add, and subtract, and perform all other operations of arithmetic. So that without words there is no possibility of reckoning of numbers; much less of magnitudes, of swiftness, of force, and other things, the reckonings whereof are necessary to the being, or well-being of mankind.
When two names are joined together into a consequence, or affirmation, as thus, a man is a living creature; or thus, if he be a man, he is a living creature; if the latter name, living creature, signify all that the former name man signifieth, then the affirmation, or consequence, is true; otherwise false. For true and false are attributes of speech, not of things. And where speech is not, there is neither truth nor falsehood; error there may be, as when we expect that which shall not be, or suspect what has not been; but in neither case can a man be charged with untruth.
Necessity of definitions.
Seeing then that truth consisteth in the right ordering of names in our affirmations, a man that seeketh precise truth had need to remember what every name he uses stands for, and to place it accordingly, or else he will find himself entangled in words, as a bird in lime twigs, the more he struggles the more belimed. And therefore in geometry, which is the only science that it hath pleased God hitherto to bestow on mankind, men begin at settling the significations of their words; which settling of significations they call definitions, and place them in the beginning of their reckoning.