E1P8S2
Scholium — Part I
Latin
Non dubito quin omnibus qui de rebus confuse judicant nec res per primas suas causas noscere consueverunt, difficile sit demonstrationem 7 propositionis concipere; nimirum quia non distinguunt inter modificationes substantiarum et ipsas substantias neque sciunt quomodo res producuntur. Unde fit ut principium quod res naturales habere vident, substantiis affingant; qui enim veras rerum causas ignorant, omnia confundunt et sine ulla mentis repugnantia tam arbores quam homines loquentes fingunt et homines tam ex lapidibus quam ex semine formari et quascunque formas in alias quascunque mutari imaginantur. Sic etiam qui naturam divinam cum humana confundunt, facile Deo affectus humanos tribuunt præsertim quamdiu etiam ignorant quomodo affectus in mente producuntur. Si autem homines ad naturam substantiæ attenderent, minime de veritate 7 propositionis dubitarent; imo hæc propositio omnibus axioma esset et inter notiones communes numeraretur. Nam per substantiam intelligerent id quod in se est et per se concipitur hoc est id cujus cognitio non indiget cognitione alterius rei. Per modificationes autem id quod in alio est et quarum conceptus a conceptu rei in qua sunt, formatur : quocirca modificationum non existentium veras ideas possumus habere quandoquidem quamvis non existant actu extra intellectum, earum tamen essentia ita in alio comprehenditur ut per idem concipi possint. Verum substantiarum veritas extra intellectum non est nisi in se ipsis quia per se concipiuntur. Si quis ergo diceret se claram et distinctam hoc est veram ideam substantiæ habere et nihilominus dubitare num talis substantia existat, idem hercle esset ac si diceret se veram habere ideam et nihilominus dubitare num falsa sit (ut satis attendenti sit manifestum); vel si quis statuat substantiam creari, simul statuit ideam falsam factam esse veram, quo sane nihil absurdius concipi potest adeoque fatendum necessario est substantiæ existentiam sicut ejus essentiam æternam esse veritatem. Atque hinc alio modo concludere possumus non dari nisi unicam ejusdem naturæ, quod hic ostendere operæ pretium esse duxi. Ut autem hoc ordine faciam notandum est I° veram uniuscujusque rei definitionem nihil involvere neque exprimere præter rei definitæ naturam. Ex quo sequitur hoc II° nempe nullam definitionem certum aliquem numerum individuorum involvere neque exprimere quandoquidem nihil aliud exprimit quam naturam rei definitæ. Exempli gratia definitio trianguli nihil aliud exprimit quam simplicem naturam trianguli; at non certum aliquem triangulorum numerum. III° notandum dari necessario uniuscujusque rei existentis certam aliquam causam propter quam existit. IV° denique notandum hanc causam propter quam aliqua res existit, vel debere contineri in ipsa natura et definitione rei existentis (nimirum quod ad ipsius naturam pertinet existere) vel debere extra ipsam dari. His positis sequitur quod si in natura certus aliquis numerus individuorum existat, debeat necessario dari causa cur illa individua et cur non plura nec pauciora existunt. Si exempli gratia in rerum natura 20 homines existant (quos majoris perspicuitatis causa suppono simul existere nec alios antea in natura exstitisse) non satis erit (ut scilicet rationem reddamus cur 20 homines existant) causam naturæ humanæ in genere ostendere sed insuper necesse erit causam ostendere cur non plures nec pauciores quam 20 existant quandoquidem (per III notam) uniuscujusque debet necessario dari causa cur existat. At hæc causa (per notam II et III) non potest in ipsa natura humana contineri quandoquidem vera hominis definitio numerum vicenarium non involvit adeoque (per notam IV) causa cur hi viginti homines existunt et consequenter cur unusquisque existit, debet necessario extra unumquemque dari et propterea absolute concludendum omne id cujus naturæ plura individua existere possunt, debere necessario ut existant causam externam habere. Jam quoniam ad naturam substantiæ (per jam ostensa in hoc scholio) pertinet existere, debet ejus definitio necessariam existentiam involvere et consequenter ex sola ejus definitione debet ipsius existentia concludi. At ex ipsius definitione (ut jam ex nota II et III ostendimus) non potest sequi plurium substantiarum existentia; sequitur ergo ex ea necessario unicam tantum ejusdem naturæ existere, ut proponebatur.
English (Elwes 1883)
No doubt it will be difficult for those who think about things loosely, and have not been accustomed to know them by their primary causes, to comprehend the demonstration of Prop. vii.: for such persons make no distinction between the modifications of substances and the substances themselves, and are ignorant of the manner in which things are produced; hence they may attribute to substances the beginning which they observe in natural objects. Those who are ignorant of true causes, make complete confusion--think that trees might talk just as well as men--that men might be formed from stones as well as from seed; and imagine that any form might be changed into any other. So, also, those who confuse the two natures, divine and human, readily attribute human passions to the deity, especially so long as they do not know how passions originate in the mind. But, if people would consider the nature of substance, they would have no doubt about the truth of Prop. vii. In fact, this proposition would be a universal axiom, and accounted a truism. For, by substance, would be understood that which is in itself, and is conceived through itself--that is, something of which the conception requires not the conception of anything else; whereas modifications exist in something external to themselves, and a conception of them is formed by means of a conception of the thing in which they exist. Therefore, we may have true ideas of non--existent modifications; for, although they may have no actual existence apart from the conceiving intellect, yet their essence is so involved in something external to themselves that they may through it be conceived. Whereas the only truth substances can have, external to the intellect, must consist in their existence, because they are conceived through themselves. Therefore, for a person to say that he has a clear and distinct--that is, a true--idea of a substance, but that he is not sure whether such substance exists, would be the same as if he said that he had a true idea, but was not sure whether or no it was false (a little consideration will make this plain); or if anyone affirmed that substance is created, it would be the same as saying that a false idea was true--in short, the height of absurdity. It must, then, necessarily be admitted that the existence of substance as its essence is an eternal truth. And we can hence conclude by another process of reasoning--that there is but one such substance. I think that this may profitably be done at once; and, in order to proceed regularly with the demonstration, we must premise:----
1. The true definition of a thing neither involves nor expresses anything beyond the nature of the thing defined. From this it follows that----
2. No definition implies or expresses a certain number of individuals, inasmuch as it expresses nothing beyond the nature of the thing defined. For instance, the definition of a triangle expresses nothing beyond the actual nature of a triangle: it does not imply any fixed number of triangles.
3. There is necessarily for each individual existent thing a cause why it should exist.
4. This cause of existence must either be contained in the nature and definition of the thing defined, or must be postulated apart from such definition.
It therefore follows that, if a given number of individual things exist in nature, there must be some cause for the existence of exactly that number, neither more nor less. For example, if twenty men exist in the universe (for simplicity's sake, I will suppose them existing simultaneously, and to have had no predecessors), and we want to account for the existence of these twenty men, it will not be enough to show the cause of human existence in general; we must also show why there are exactly twenty men, neither more nor less: for a cause must be assigned for the existence of each individual. Now this cause cannot be contained in the actual nature of man, for the true definition of man does not involve any consideration of the number twenty. Consequently, the cause for the existence of these twenty men, and, consequently, of each of them, must necessarily be sought externally to each individual. Hence we may lay down the absolute rule, that everything which may consist of several individuals must have an external cause. And, as it has been shown already that existence appertains to the nature of substance, existence must necessarily be included in its definition; and from its definition alone existence must be deducible. But from its definition (as we have shown, notes ii., iii.), we cannot infer the existence of several substances; therefore it follows that there is only one substance of the same nature. Q.E.D.
Modern English
I do not doubt that for everyone who judges things confusedly and is not accustomed to know them by their primary causes, it will be difficult to grasp the demonstration of (E1P7D), chiefly because they do not distinguish between the modifications of substances and substances themselves, and do not know how things are produced. So it happens that they ascribe to substances the source they see natural things have. Those who are ignorant of the true causes of things confuse everything: with no mental resistance, they imagine trees talking just as men do, men formed from stones as well as from seed, and any form changing into any other. So too those who confuse the divine nature with the human readily attribute human affects to God, especially so long as they remain ignorant of how affects are produced in the mind.
If people attended to the nature of substance, they would not doubt the truth of (E1P7) in the slightest. Rather, this proposition would be an axiom to all and counted among the common notions. For by substance they would understand that which is in itself and is conceived through itself, that is, that whose knowledge does not need the knowledge of another thing. And by modifications they would understand that which is in another, and whose concept is formed from the concept of the thing in which they are. So we can have true ideas of non-existent modifications: although they do not actually exist outside the intellect, their essence is contained in another in such a way that they can be conceived through it. But the truth of substances, outside the intellect, exists only in themselves, because they are conceived through themselves.
So if someone said he has a clear and distinct, that is, a true, idea of substance, and yet doubted whether such a substance exists, it would really be the same as if he said he has a true idea and yet doubted whether it is false (as is plain enough to anyone paying attention); or if someone holds that substance is created, he holds at the same time that a false idea has been made true, than which nothing more absurd can be conceived. So we must necessarily admit that the existence of substance, like its essence, is an eternal truth.
And from this we can conclude in another way that there is only one substance of the same nature, which I have thought worthwhile to show here. To proceed in due order, the following must be noted. First, the true definition of each thing involves and expresses nothing beyond the nature of the thing defined. From which it follows, second, that no definition involves or expresses any particular number of individuals, since it expresses nothing other than the nature of the thing defined. For example, the definition of a triangle expresses nothing other than the simple nature of a triangle, and not any particular number of triangles. Third, it must be noted that for every existing thing there is necessarily some particular cause why it exists. Fourth and finally, that this cause for which a thing exists must either be contained in the very nature and definition of the existing thing (in that existing belongs to its nature), or it must be given outside the thing itself.
With these laid down, it follows that if some particular number of individuals exists in nature, there must necessarily be a cause why those individuals, and not more or fewer, exist. For example, if 20 men exist in nature (whom, for greater clarity, I suppose to exist simultaneously, with no others having previously existed in nature), it will not be enough — to account for why 20 men exist — to show the cause of human nature in general; we must also show the cause why not more or fewer than 20 exist, since (by the third note) there must necessarily be a cause for each one why it exists. But this cause (by notes II and III) cannot be contained in human nature itself, since the true definition of man does not involve the number twenty. And so (by note IV) the cause why these twenty men exist, and consequently why each one exists, must necessarily lie outside each one. So we must conclude absolutely that everything of whose nature several individuals can exist must necessarily have an external cause for its existing.
Now since existing belongs to the nature of substance (by what has just been shown in this scholium), its definition must involve necessary existence, and consequently its existence must be concluded from its definition alone. But from its definition (as we have just shown from notes II and III) the existence of several substances cannot follow. So it follows necessarily from this that only one of the same nature exists, as was proposed.