E2P40S2
Scholium — Part II
Latin
Ex omnibus supra dictis clare apparet nos multa percipere et notiones universales formare I° ex singularibus nobis per sensus mutilate, confuse et sine ordine ad intellectum repræsentatis (vide corollarium propositionis 29 hujus) et ideo tales perceptiones cognitionem ab experientia vaga vocare consuevi. II° ex signis exempli gratia ex eo quod auditis aut lectis quibusdam verbis rerum recordemur et earum quasdam ideas formemus similes iis per quas res imaginamur (vide scholium propositionis 18 hujus). Utrumque hunc res contemplandi modum cognitionem primi generis, opinionem vel imaginationem in posterum vocabo. III° denique ex eo quod notiones communes rerumque proprietatum ideas adæquatas habemus (vide corollarium propositionis 38 et propositionem 39 cum ejus corollario et propositionem 40 hujus) atque hunc rationem et secundi generis cognitionem vocabo. Præter hæc duo cognitionis genera datur, ut in sequentibus ostendam, aliud tertium quod scientiam intuitivam vocabimus. Atque hoc cognoscendi genus procedit ab adæquata idea essentiæ formalis quorundam Dei attributorum ad adæquatam cognitionem essentiæ rerum. Hæc omnia unius rei exemplo explicabo. Dantur exempli gratia tres numeri ad quartum obtinendum qui sit ad tertium ut secundus ad primum. Non dubitant mercatores secundum in tertium ducere et productum per primum dividere quia scilicet ea quæ a magistro absque ulla demonstratione audiverunt, nondum tradiderunt oblivioni vel quia id sæpe in numeris simplicissimis experti sunt vel ex vi demonstrationis propositionis 19 libri 7 Euclidis nempe ex communi proprietate proportionalium. At in numeris simplicissimis nihil horum opus est. Exempli gratia datis numeris 1, 2, 3, nemo non videt quartum numerum proportionalem esse 6 atque hoc multo clarius quia ex ipsa ratione quam primum ad secundum habere uno intuitu videmus, ipsum quartum concludimus.
English (Elwes 1883)
From all that has been said above it is clear, that we, in many cases, perceive and form our general notions:--(1.) From particular things represented to our intellect fragmentarily, confusedly, and without order through our senses (II. xxix. Coroll.); I have settled to call such perceptions by the name of knowledge from the mere suggestions of experience.[4]
[4] A Baconian phrase. Nov. Org. Aph. 100. [Pollock, p. 126, n.]
(2.) From symbols, e.g., from the fact of having read or heard certain words we remember things and form certain ideas concerning them, similar to those through which we imagine things (II. xviii. note). I shall call both these ways of regarding things knowledge of the first kind, opinion, or imagination. (3.) From the fact that we have notions common to all men, and adequate ideas of the properties of things (II. xxxviii. Coroll., xxxix. and Coroll. and xl.); this I call reason and knowledge of the second kind. Besides these two kinds of knowledge, there is, as I will hereafter show, a third kind of knowledge, which we will call intuition. This kind of knowledge proceeds from an adequate idea of the absolute essence of certain attributes of God to the adequate knowledge of the essence of things. I will illustrate all three kinds of knowledge by a single example. Three numbers are given for finding a fourth, which shall be to the third as the second is to the first. Tradesmen without hesitation multiply the second by the third, and divide the product by the first; either because they have not forgotten the rule which they received from a master without any proof, or because they have often made trial of it with simple numbers, or by virtue of the proof of the nineteenth proposition of the seventh book of Euclid, namely, in virtue of the general property of proportionals.
But with very simple numbers there is no need of this. For instance, one, two, three, being given, everyone can see that the fourth proportional is six; and this is much clearer, because we infer the fourth number from an intuitive grasping of the ratio, which the first bears to the second.
Modern English
From everything said above it is clear that we perceive many things and form universal notions in the following ways.
First, from particular things represented to our intellect by the senses in a fragmentary, confused, and unordered way (E2P29C). I have been accustomed to call such perceptions knowledge from random experience.
Second, from signs, for instance from having heard or read certain words, we remember things and form certain ideas of them, similar to those through which we imagine things (E2P18S). Both of these ways of considering things I will from now on call knowledge of the first kind, opinion, or imagination.
Third, from the fact that we have common notions and adequate ideas of the properties of things (E2P38C) (E2P39) (E2P40). This I will call reason and knowledge of the second kind.
Besides these two kinds of knowledge there is, as I will show later, a third kind, which we will call intuitive knowledge. This kind of knowledge proceeds from an adequate idea of the formal essence of certain attributes of God to adequate knowledge of the essence of things.
I will illustrate all three kinds with a single example. Suppose three numbers are given and a fourth is to be found that stands to the third as the second stands to the first. Merchants perform this without hesitation: they multiply the second by the third and divide the result by the first, either because they have not yet forgotten the rule they received from a teacher without any demonstration, or because they have often tried it with very simple numbers, or by virtue of the proof of Proposition 19 of Book 7 of Euclid, namely from the general property of proportionals.
With very simple numbers, none of this is needed. Given the numbers 1, 2, 3, anyone can see that the fourth proportional is 6, and this is much clearer still, because from the very ratio that we see in a single glance the first bears to the second, we draw the conclusion about the fourth number itself.