This proposition is followed by an important demonstration and an extremely long and significant scholium. The demonstration is important because it connects ideation with causality. Since the order and connection of ideas is the same as the order and connection of things, this is important. The causal connection is not from God insofar as God is infinite or insofar as God is affect of other ideas, but only insofar as it is rooted in the singular mode of the thinking attribute.
The scholium goes on to delineate what this is. Spinoza begins with common notions as the root of the adequate idea. Common notions are ideas such as motion and rest that are experienced commonly in the attribute of extension. These common notions are distinguished from transcendental ones which appear to be commonly held but, in fact, are so mutilated and distorted as to appear common. Instead, the imagination pares down characteristics into a summary form so that commonalities exists. Here Spinoza takes on the position of medieval nominalism or modern statistics where summaries are at risk of a loss of meaning.
Quæcunque ideæ in mente sequuntur ex ideis quæ in ipsa sunt adæquatæ, sunt etiam adæquatæ.
Whatsoever ideas follow in the mind from ideas which are adequate in themselves, are also adequate.
DEMONSTRATIO: Patet. Nam cum dicimus in mente humana ideam sequi ex ideis quæ in ipsa sunt adæquatæ, nihil aliud dicimus (per corollarium propositionis 11 hujus) quam quod in ipso divino intellectu detur idea cujus Deus est causa, non quatenus infinitus est nec quatenus plurimarum rerum singularium ideis affectus est sed quatenus tantum humanæ mentis essentiam constituit.
It is evident. For when we say that an idea in the human mind from ideas which are adequate in themselves, we say nothing other (by IIP11C) than what exists in the divine intellect itself the idea of which God is the cause, not insofar as it is infinite and not insofar it is the affect for ideas of more singular things but insofar as it constitutes the essence of the human mind.
SCHOLIUM I: His causam notionum quæ communes vocantur quæque ratiocinii nostri fundamenta sunt, explicui. Sed aliæ quorundam axiomatum sive notionum causæ dantur quas hac nostra methodo explicare e re foret; ex iis namque constaret quænam notiones præ reliquis utiliores, quænam vero vix ullius usus essent. Deinde quænam communes et quænam iis tantum qui præjudiciis non laborant, claræ et distinctæ et quænam denique male fundatæ sint. Præterea constaret unde notiones illæ quas secundas vocant et consequenter axiomata quæ in iisdem fundantur suam duxerunt originem et alia quæ circa hæc aliquando meditatus sum. Sed quoniam hæc alii dicavi tractatui et etiam ne propter nimiam hujus rei prolixitatem fastidium crearem, hac re hic supersedere decrevi. Attamen ne quid horum omittam quod scitu necessarium sit, causas breviter addam ex quibus termini transcendentales dicti suam duxerunt originem ut Ens, Res, Aliquid. Hi termini ex hoc oriuntur quod scilicet humanum corpus quandoquidem limitatum est, tantum est capax certi imaginum numeri (quid imago sit explicui in scholio propositionis 17 hujus) in se distincte simul formandi, qui si excedatur, hæ imagines confundi incipient et si hic imaginum numerus quarum corpus est capax ut eas in se simul distincte formet, longe excedatur, omnes inter se plane confundentur. Cum hoc ita se habeat, patet ex corollario propositionis 17 et propositione 18 hujus quod mens humana tot corpora distincte simul imaginari poterit quot in ipsius corpore imagines possunt simul formari. At ubi imagines in corpore plane confunduntur, mens etiam omnia corpora confuse sine ulla distinctione imaginabitur et quasi sub uno attributo comprehendet nempe sub attributo entis, rei etc. Potest hoc etiam ex eo deduci quod imagines non semper æque vigeant et ex aliis causis his analogis quas hic explicare non est opus nam ad nostrum ad quem collimamus scopum, unam tantum sufficit considerare. Nam omnes huc redeunt quod hi termini ideas significent summo gradu confusas. Ex similibus deinde causis ortæ sunt notiones illæ quas universales vocant ut Homo, Equus, Canis etc. videlicet quia in corpore humano tot imagines exempli gratia hominum formantur simul ut vim imaginandi, non quidem penitus sed eo usque tamen superent ut singulorum parvas differentias (videlicet uniuscujusque colorem, magnitudinem etc.) eorumque determinatum numerum mens imaginari nequeat et id tantum in quo omnes quatenus corpus ab iisdem afficitur, conveniunt, distincte imaginetur nam ab eo corpus maxime scilicet ab unoquoque singulari affectum fuit atque hoc nomine hominis exprimit hocque de infinitis singularibus prædicat. Nam singularium determinatum numerum ut diximus imaginari nequit. Sed notandum has notiones non ab omnibus eodem modo formari sed apud unumquemque variare pro ratione rei a qua corpus affectum sæpius fuit quamque facilius mens imaginatur vel recordatur. Exempli gratia qui sæpius cum admiratione hominum staturam contemplati sunt, sub nomine hominis intelligent animal erectæ staturæ; qui vero aliud assueti sunt contemplari, aliam hominum communem imaginem formabunt nempe hominem esse animal risibile, animal bipes sine plumis, animal rationale et sic de reliquis unusquisque pro dispositione sui corporis rerum universales imagines formabit. Quare non mirum est quod inter philosophos qui res naturales per solas rerum imagines explicare voluerunt, tot sint ortæ controversiæ.
From these [propositions] I have explained the cause of notions which we call common which are the fundamentals of our thinking. But other causes of certain axioms or notions exist which might be in accord with the matter to explain in this our method; for from these [causes] it might stand together that certain notions are more useful than the remaining, that certain [notions] are, in truth, scarcely of any use. Then, certain [notions] are common, certain [notions] are only, for those who do not work with prejudices, clear and distinct, and finally certain [notions] might be established poorly. Meanwhile, it might stand together from where those notions which they call secondary and consequently axioms which are founded on the same [notions] which have guided their origin and other things which I have meditated on about these things now and then. But since I have stated these [causes] for another tractatus and of course lest I create disgust on account of too much duration of this matter, I have decided to restrain here on this matter. Nevertheless, lest I omit something of these [causes] which is necessary for learning, I add briefly the causes from which the terms called transcendental have guided their origin such as Being, Matter, Somethingness. These terms arise from this - that, of course, the human body since it is limited, to a degree is capable of forming a certain number of images (I have explained what an image is in IIP17S) at the same time distinctly in itself, which if it is exceeded, these images begin to be confused and if this number of images, of which the body is capable as it forms these distinctly in itself at the same time, is exceeded by far, everything might be completely confused within itself. Because this has itself in this way, it is clear from IIP17C and IIP18 that the human mind will be able to imagine so many bodies distinctly at the same time as many images as it is able to form at the same time in its own body. But when the images are completely confused in the body, the mind also will imagine all bodies confusedly without any distinction and will comprehend as if under one attribute namely under the attribute of Being, Matter etc. This is also able to be deduced from this that images are not equally strong and from other causes by these similarities which it is not the work to explain here for our scope which we glance at sideways, this one thing is sufficient to consider. For everything returns to this - that these terms signify ideas confused to the highest degree. From similar causes, then, arise those notions which are called universals, such as Man, Horse, Dog, etc. that is to say, since in the human body so many images, for example, of the human body are formed, so that the power of imagining not, of course, deeply but nevertheless they overcome so that the mind can imagine neither small differences of individuals, (that is to say of color or size of each and everyone) nor the determinate number of them and imagines distinctly what so far in which everything agrees insofar as the body is affected by the same things; for from this the body, greatly of course, has been affected by whatever singular thing and expresses by this name of man and declares by this about infinite singulars. For he is unable, as we said, to imagine the determinate number of singular individuals. But it must be noted that these notions are not formed in the same way by all but vary among each individual on account of the way of each thing by which the body has more often been affected more the more easily the mind imagines or records. For example, those who have frequently contemplated with admiration the stature of humans, then under the name of man, they understand an animal of erect stature; those who in truth have been accustomed to contemplate something else, they will certainly form another image common to humans that a man is a laughing animal, that man is two-footed without feathers, that man is rational and thus will form universal images of things in accord with the disposition of his own body concerning every other remaining trait. Therefore it is not surprising that there are, among philosophers who wish to explain natural things by common images of things, so many controversies arising.
SCHOLIUM II: 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.
From everything said above it is perfectly clear that we perceive many things and form universal notions 1) from singular things represented to understanding by us through senses mutilated, confused and without order, (see IIP29C) and to such an extent I am accustomed to call such perceptions understanding from wandering experience, 2) from signs, for example, from which by hearing or reading certain words of things we record and form certain ideas of things similar to those by which things we imagine (see IIP18S). Each of these things for contemplating I will call a mode of thinking of the first kind, opinion or imagination from now on, 3) finally from which we have adequate ideas which are common notions and properties of things (see IIP38C and IIP39 and IIP39C and IIP40). and I will call this reason and thinking of the second kind. Beyond these two kinds of thinking existing, as I will show in the following, another third [kind of thinking] which we will call intuitive knowledge. And this kind of understanding proceeds from the adequate idea of the formal essence of whatever attributes of God to the adequate thinking of the essence of things. These things I will explain by the example of one thing. For example, three numbers exist for finding the fourth which is to the third as to the second as to the first. Merchants do not hesitate to follow the second into the third and divide that product by the first because of course they have heard things which from their teacher and by any demonstration, not yet have they surrendered to oblivion or because they have often found this in the simplest of numbers or by the force of the demonstration of proposition 19 book 7 of Euclid, namely, from the common property of proportions. But in the simplest of numbers none of these are work. For example, given the numbers 1, 2, 3, no one does not see that the fourth proportional number is 6 and by much more clearly because from reason itself which we see by one intuition has the first to the second, we conclude the fourth itself.
