Spinoza: ETHICA

Transeo jam ad ea explicanda quæ ex Dei sive Entis æterni et infiniti essentia necessario debuerunt sequi. Non quidem omnia; infinita enim infinitis modis ex ipsa debere sequi propositione 16 partis I demonstravimus sed ea solummodo quæ nos ad mentis humanæ ejusque summæ beatitudinis cognitionem quasi manu ducere possunt.

I now pass on to expound those things which from the essence of God, or of the Eternal and Infinite Being, necessarily ought to follow. Not, indeed, all; for we demonstrated in proposition 16 of part 1 that the infinite must follow from the infinite in infinite ways, but only those things which can, as it were by the hand, lead us to the knowledge of the human mind and of its supreme beatitude.

DEFINITIONES

DEFINITIONS

I. Per corpus intelligo modum qui Dei essentiam quatenus ut res extensa consideratur, certo et determinato modo exprimit; vide corollarium propositionis 25 partis I.

1. By "corpus" I understand the mode which expresses God's essence insofar as it is considered as an extended thing (res extensa), in a certain and determinate manner; see the corollary of proposition 25 of Part 1.

II. Ad essentiam alicujus rei id pertinere dico quo dato res necessario ponitur et quo sublato res necessario tollitur; vel id sine quo res et vice versa id quod sine re nec esse nec concipi potest.

II. To the essence of any thing I say that pertains that whereby, given, the thing is necessarily posited, and whereby, removed, the thing is necessarily taken away; or that without which the thing — and conversely that which without the thing — can neither exist nor be conceived.

III. Per ideam intelligo mentis conceptum quem mens format propterea quod res est cogitans.

III. By idea I understand the concept of the mind which the mind forms, because the thing is a thinking thing.

EXPLICATIO: Dico potius conceptum quam perceptionem quia perceptionis nomen indicare videtur mentem ab objecto pati. At conceptus actionem mentis exprimere videtur.

EXPLICATIO: I say rather "concept" than "perception" because the name "perception" seems to indicate the mind suffering from the object. But "concept" seems to express the action of the mind.

IV. Per ideam adæquatam intelligo ideam quæ quatenus in se sine relatione ad objectum consideratur, omnes veræ ideæ proprietates sive denominationes intrinsecas habet.

4. By an adequate idea I understand an idea which, insofar as it is considered in itself without relation to an object, has all the properties or denominations of true ideas intrinsically.

EXPLICATIO: Dico intrinsecas ut illam secludam quæ extrinseca est nempe convenientiam ideæ cum suo ideato.

EXPLICATIO: I say "intrinsic" so as to exclude that which is extrinsic, namely the congruity of an idea with its own ideate.

V. Duratio est indefinita existendi continuatio.

5. Duration is the indefinite continuation of existence.

EXPLICATIO: Dico indefinitam quia per ipsam rei existentis naturam determinari nequaquam potest neque etiam a causa efficiente quæ scilicet rei existentiam necessario ponit, non autem tollit.

EXPLICATIO: I call it indefinite because by it, through the very nature of the thing's existing, it can in no way be determined, nor yet by the efficient cause which, namely, necessarily posits the existence of the thing, but does not remove it.

VI. Per realitatem et perfectionem idem intelligo.

6. By reality and by perfection I mean the same.

VII. Per res singulares intelligo res quæ finitæ sunt et determinatam habent existentiam. Quod si plura individua in una actione ita concurrant ut omnia simul unius effectus sint causa, eadem omnia eatenus ut unam rem singularem considero.

VII. By "singular things" I understand things which are finite and have a determinate existence. But if several individuals in one action so concur that all together are the cause of one effect, I consider all those same things, insofar as they form one thing, as a single singular thing.

AXIOMATA

AXIOMS

I. Hominis essentia non involvit necessariam existentiam hoc est ex naturæ ordine tam fieri potest ut hic et ille homo existat quam ut non existat.

I. The essence of man does not entail a necessary existence; that is, by the order of nature it can just as well happen that this man and that man exist as that they do not exist.

II. Homo cogitat.

2. Human thinks.

III. Modi cogitandi ut amor, cupiditas vel quicunque nomine affectus animi insigniuntur, non dantur nisi in eodem individuo detur idea rei amatæ, desideratæ etc. At idea dari potest quamvis nullus alius detur cogitandi modus.

III. Modes of thinking — such as amor (love), cupiditas (desire), or whatever by the name affectus animi (affections of the mind) are distinguished — are not given unless in the same individual there is given the idea of the thing loved, desired, etc. Yet an idea may be given although no other mode of thinking is given.

IV. Nos corpus quoddam multis modis affici sentimus.

IV. We feel that a certain body is affected in many ways.

V. Nullas res singulares præter corpora et cogitandi modos sentimus nec percipimus. Postulata vide post 13 propositionem.

5. We perceive and do not apprehend any singular things apart from bodies and modes of thinking. See the postulates after proposition 13.

PROPOSITIO I: Cogitatio attributum Dei est sive Deus est res cogitans.

PROPOSITION 1: Thought is an attribute of God, or God is a thinking thing.

DEMONSTRATIO: Singulares cogitationes sive hæc et illa cogitatio modi sunt qui Dei naturam certo et determinato modo exprimunt (per corollarium propositionis 25 partis I). Competit ergo Deo (per definitionem 5 partis I) attributum cujus conceptum singulares omnes cogitationes involvunt, per quod etiam concipiuntur. Est igitur cogitatio unum ex infinitis Dei attributis quod Dei æternam et infinitam essentiam exprimit (vide definitionem 6 partis I) sive Deus est res cogitans. Q.E.D.

DEMONSTRATION: Singular thoughts, or this and that thought, are modes which express God’s nature in a certain and determinate way (by the corollary of proposition 25 of part 1). It therefore pertains to God (by definition 5 of part 1) an attribute whose concept all singular thoughts involve, by which they are also conceived. Therefore thought is one of the infinite attributes of God which expresses God’s eternal and infinite essence (see definition 6 of part 1), or God is a thinking thing. Q.E.D.

SCHOLIUM: Patet etiam hæc propositio ex hoc quod nos possumus ens cogitans infinitum concipere. Nam quo plura ens cogitans potest cogitare, eo plus realitatis sive perfectionis idem continere concipimus; ergo ens quod infinita infinitis modis cogitare potest, est necessario virtute cogitandi infinitum. Cum itaque ad solam cogitationem attendendo Ens infinitum concipiamus, est necessario (per definitiones 4 et 6 partis I) cogitatio unum ex infinitis Dei attributis, ut volebamus.

SCHOLIUM: This proposition is also clear from the fact that we can conceive an infinite thinking-being (ens cogitans). For the more things a thinking-being can think, the more reality or perfection we conceive that same thing to contain; therefore a being that can think infinite things in infinite modes is necessarily infinite by virtue of its thinking. Since then, by attending to thought alone, we conceive the infinite Being (Ens), it is necessary (by definitions 4 and 6 of Part 1) that thought is one of the infinite attributes of God, as we wished.

PROPOSITIO II: Extensio attributum Dei est sive Deus est res extensa.

PROPOSITION 2: Extension is an attribute of God, or God is a res extensa — a thing extended.

DEMONSTRATIO: Hujus eodem modo procedit ac demonstratio præcedentis propositionis.

DEMONSTRATION: The demonstration of this proceeds in the same manner as the demonstration of the preceding proposition.

PROPOSITIO III: In Deo datur necessario idea tam ejus essentiæ quam omnium quæ ex ipsius essentia necessario sequuntur.

PROPOSITIO 3: In God is necessarily given the idea both of his essence and of all things which necessarily follow from that essence.

DEMONSTRATIO: Deus enim (per propositionem 1 hujus) infinita infinitis modis cogitare sive (quod idem est per propositionem 16 partis I) ideam suæ essentiæ et omnium quæ necessario ex ea sequuntur, formare potest. Atqui omne id quod in Dei potestate est, necessario est (per propositionem 35 partis I); ergo datur necessario talis idea et (per propositionem 15 partis I) non nisi in Deo. Q.E.D.

DEMONSTRATIO: For God (by proposition 1 of this) can think in infinite ways or (which is the same by proposition 16 of Part I) form the idea of his essence and of all that necessarily follows from it. Yet whatever is in God's power is necessary (by proposition 35 of Part I); therefore such an idea is given necessarily and (by proposition 15 of Part I) only in God. Q.E.D.

SCHOLIUM: Vulgus per Dei potentiam intelligit Dei liberam voluntatem et jus in omnia quæ sunt quæque propterea communiter ut contingentia considerantur. Deum enim potestatem omnia destruendi habere dicunt et in nihilum redigendi. Dei porro potentiam cum potentia regum sæpissime comparant.

SCHOLIUM: The common people, by God’s power, understand God’s free will and right over all things, and therefore commonly consider them as contingent. For they say that God has the power to destroy all things and to reduce them into nothing. Moreover they very often compare God’s power with the power of kings.

Sed hoc in corollario I et II propositionis 32 partis I refutavimus et propositione 16 partis I ostendimus Deum eadem necessitate agere qua seipsum intelligit hoc est sicuti ex necessitate divinæ naturæ sequitur (sicut omnes uno ore statuunt) ut Deus seipsum intelligat, eadem etiam necessitate sequitur ut Deus infinita infinitis modis agat. Deinde propositione 34 partis I ostendimus Dei potentiam nihil esse præterquam Dei actuosam essentiam adeoque tam nobis impossibile est concipere Deum non agere quam Deum non esse. Porro si hæc ulterius persequi liberet, possem hic etiam ostendere potentiam illam quam vulgus Deo affingit, non tantum humanam esse (quod ostendit Deum hominem vel instar hominis a vulgo concipi) sed etiam impotentiam involvere.

But this we refuted in corollaries 1 and 2 of proposition 32 of Part 1, and by proposition 16 of Part 1 we showed that God acts with the same necessity with which He understands Himself — that is, as follows from the necessity of the divine nature (as all with one mouth declare) that God understands Himself — it likewise follows with the same necessity that God acts infinitely in infinite modes. Then by proposition 34 of Part 1 we showed that God’s power is nothing other than God’s actuating essence, and accordingly it is as impossible for us to conceive God not acting as to conceive God not being. Moreover, if it were permitted to pursue these things further, I could here also show that that power which the vulgus attributes to God is not only human (which shows that God is conceived by the common people as a man or in the likeness of a man) but also involves impotence.

Sed nolo de eadem re toties sermonem instituere. Lectorem solummodo iterum atque iterum rogo ut quæ in prima parte ex propositione 16 usque ad finem de hac re dicta sunt, semel atque iterum perpendat. Nam nemo ea quæ volo percipere recte poterit nisi magnopere caveat ne Dei potentiam cum humana regum potentia vel jure confundat.

I do not wish to set up discourse about the same matter so often. I only ask the reader again and again to weigh what in the first part, from proposition 16 to the end, was said about this matter, once and again. For no one will be able rightly to apprehend the things I desire unless he take great care not to confuse the power of God with the human power or right of kings.

PROPOSITIO IV: Idea Dei ex qua infinita infinitis modis sequuntur, unica tantum esse potest.

PROPOSITION 4: The idea of God, from which infinite things follow in infinitely many modes, can be only one.

DEMONSTRATIO: Intellectus infinitus nihil præter Dei attributa ejusque affectiones comprehendit (per propositionem 30 partis I). Atqui Deus est unicus (per corollarium I propositionis 14 partis I). Ergo idea Dei ex qua infinita infinitis modis sequuntur, unica tantum esse potest. Q.E.D.

DEMONSTRATION: An infinite intellect comprehends nothing save the attributes of God and their affections (by Proposition 30 of Part I). Moreover God is one (by the Corollary to Proposition 14 of Part I). Therefore the idea of God, from which the infinite follow in infinite modes, can be only one. Q.E.D.

PROPOSITIO V: Esse formale idearum Deum quatenus tantum ut res cogitans consideratur, pro causa agnoscit et non quatenus alio attributo explicatur. Hoc est tam Dei attributorum quam rerum singularium ideæ non ipsa ideata sive res perceptas pro causa efficiente agnoscunt sed ipsum Deum quatenus est res cogitans.

PROPOSITIO V: The formal being of ideas recognizes God, insofar as only he is considered as a thinking thing, as cause, and not insofar as he is explained by any other attribute. That is, the ideas both of God’s attributes and of singular things do not recognize the things themselves ideated or the perceived things as efficient causes, but recognize God himself insofar as he is a thinking thing.

DEMONSTRATIO: Patet quidem ex propositione 3 hujus. Ibi enim concludebamus Deum ideam suæ essentiæ et omnium quæ ex ea necessario sequuntur, formare posse ex hoc solo nempe quod Deus est res cogitans et non ex eo quod sit suæ ideæ objectum. Quare esse formale idearum Deum quatenus est res cogitans, pro causa agnoscit.

DEMONSTRATIO: It is indeed clear from proposition 3 of this. For there we concluded that God could form the idea of his essence and of all things which necessarily follow from it from this alone, namely that God is a thinking thing, and not from the fact that he is the object of his idea. Therefore God, insofar as he is a thinking thing, knows the formal being of ideas as cause.

Sed aliter hoc modo demonstratur. Esse formale idearum modus est cogitandi (ut per se notum) hoc est (per corollarium propositionis 25 partis I) modus qui Dei naturam quatenus est res cogitans, certo modo exprimit adeoque (per propositionem 10 partis I) nullius alterius attributi Dei conceptum involvit et consequenter (per axioma 4 partis I) nullius alterius attributi nisi cogitationis est effectus adeoque esse formale idearum Deum quatenus tantum ut res cogitans consideratur etc. Q.E.D.

But this is shown in another manner. The formal being of the ideas is a mode of thinking (as is self-evident), that is (by the corollary of Proposition 25 of Part I) the mode which expresses God's nature insofar as He is a thinking thing in a determinate way and therefore (by Proposition 10 of Part I) involves the concept of no other attribute of God, and consequently (by Axiom 4 of Part I) is the effect of no other attribute except thought; and therefore the formal being of the ideas recognizes God insofar only as He is considered a thinking thing, etc. Q.E.D.

PROPOSITIO VI: Cujuscunque attributi modi Deum quatenus tantum sub illo attributo cujus modi sunt et non quatenus sub ullo alio consideratur, pro causa habent.

PROPOSITION 6: The modes of whatever attribute have God for a cause only insofar as he is considered under that attribute to which those modes belong, and not insofar as he is considered under any other.

DEMONSTRATIO: Unumquodque enim attributum per se absque alio concipitur (per propositionem 10 partis I). Quare uniuscujusque attributi modi conceptum sui attributi, non autem alterius involvunt adeoque (per axioma 4 partis I) Deum quatenus tantum sub illo attributo cujus modi sunt et non quatenus sub ullo alio consideratur, pro causa habent. Q.E.D.

DEMONSTRATIO: For each attribute is conceived by itself without another (by proposition 10 of Part 1). Therefore the modes of any one attribute involve the concept of their own attribute, not of another, and consequently (by axiom 4 of Part 1) have for a cause God considered only insofar as under that attribute whose modes they are, and not insofar as under any other. Q.E.D.

COROLLARIUM: Hinc sequitur quod esse formale rerum quæ modi non sunt cogitandi, non sequitur ideo ex divina natura quia res prius cognovit sed eodem modo eademque necessitate res ideatæ ex suis attributis consequuntur et concluduntur ac ideas ex attributo cogitationis consequi ostendimus.

COROLLARIUM: Hence it follows that the formal esse of things (res) whose modes are not modes of thinking does not therefore proceed from the divine nature because God previously knew the things; but in the same manner and by the same necessity the ideate things follow and are concluded from their attributes, and we have shown that ideas follow from the attribute of cogitation (thought).

PROPOSITIO VII: ordo et connexio idearum idem est ac ordo et connexio rerum.

PROPOSITION 7: the order and connection of ideas is the same as the order and connection of things.

DEMONSTRATIO: Patet ex axiomate 4 partis I. Nam cujuscunque causati idea a cognitione causæ cujus est effectus, dependet.

DEMONSTRATIO: It is evident from axiom 4 of part 1. For the idea of any caused thing depends on the cognition of the cause of which it is the effect.

COROLLARIUM: Hinc sequitur quod Dei cogitandi potentia æqualis est ipsius actuali agendi potentiæ. Hoc est quicquid ex infinita Dei natura sequitur formaliter, id omne ex Dei idea eodem ordine eademque connexione sequitur in Deo objective.

COROLLARIUM: Hence it follows that the potency of cogitation in God is equal to his actual potency of acting. That is, whatever formally follows from the infinite nature of God, all of it follows from God’s idea in the same order and with the same connexion, objectively in God.

SCHOLIUM: Hic antequam ulterius pergamus, revocandum nobis in memoriam est id quod supra ostendimus nempe quod quicquid ab infinito intellectu percipi potest tanquam substantiæ essentiam constituens, id omne ad unicam tantum substantiam pertinet et consequenter quod substantia cogitans et substantia extensa una eademque est substantia quæ jam sub hoc jam sub illo attributo comprehenditur. Sic etiam modus extensionis et idea illius modi una eademque est res sed duobus modis expressa, quod quidam Hebræorum quasi per nebulam vidisse videntur, qui scilicet statuunt Deum, Dei intellectum resque ab ipso intellectas unum et idem esse. Exempli gratia circulus in natura existens et idea circuli existentis quæ etiam in Deo est, una eademque est res quæ per diversa attributa explicatur et ideo sive naturam sub attributo extensionis sive sub attributo cogitationis sive sub alio quocunque concipiamus, unum eundemque ordinem sive unam eandemque causarum connexionem hoc est easdem res invicem sequi reperiemus.

SCHOLIUM: Before we proceed further, we must recall to our memory what we showed above, namely that whatever can be perceived by the infinite intellect as constituting the essence of a substance, all of that pertains to one and only one substance; and consequently that thinking substance and extended substance are one and the same substance, which is now comprehended under this attribute now under that attribute. Thus likewise the mode of extension and the idea of that mode are one and the same thing, but expressed under two attributes, which some of the Hebrews seem to have seen as it were through a mist, who, namely, assert that God, God’s intellect, and the things perceived by that intellect are one and the same. For example, a circle existing in nature and the idea of the circle existing—which also is in God—are one and the same thing, explained through diverse attributes; and therefore whether we conceive the nature under the attribute of extension or under the attribute of thought or under any other attribute, we shall find one and the same order, that is one and the same connexion of causes, that is the same things following one another.

Nec ulla alia de causa dixi quod Deus sit causa ideæ exempli gratia circuli quatenus tantum est res cogitans et circuli quatenus tantum est res extensa nisi quia esse formale ideæ circuli non nisi per alium cogitandi modum tanquam causam proximam et ille iterum per alium et sic in infinitum, potest percipi ita ut quamdiu res ut cogitandi modi considerantur, ordinem totius naturæ sive causarum connexionem per solum cogitationis attributum explicare debemus et quatenus ut modi extensionis considerantur, ordo etiam totius naturæ per solum extensionis attributum explicari debet et idem de aliis attributis intelligo. Quare rerum ut in se sunt, Deus revera est causa quatenus infinitis constat attributis nec impræsentiarum hæc clarius possum explicare.

Nor did I say for any other reason that God is the cause of the idea — for example, of the circle insofar as it is only a thinking thing, and of the circle insofar as it is only an extended thing — except because the formal being of the idea of the circle, only through one mode of thinking as the proximate cause, and that again through another, and so to infinity, can be conceived so that, so long as things are considered as modes of thinking, we must explain the order of the whole of nature or the connexion of causes by the attribute of Thought alone; and insofar as they are considered as modes of extension, the order likewise of the whole of nature must be explained by the attribute of Extension alone — and I mean the same of the other attributes. Wherefore, with respect to things as they are in themselves, God truly is the cause insofar as He consists of infinite attributes; nor at present can I explain these things more clearly.

PROPOSITIO VIII: Ideæ rerum singularium sive modorum non existentium ita debent comprehendi in Dei infinita idea ac rerum singularium sive modorum essentiæ formales in Dei attributis continentur.

PROPOSITIO 8: The ideas of singular things or of modes not existing ought thus to be comprehended in the infinite idea of God, and the formal essences of singular things or of modes are contained in God’s attributes.

DEMONSTRATIO: Hæc propositio patet ex præcedenti sed intelligitur clarius ex præcedenti scholio.

DEMONSTRATION: This proposition is evident from the preceding, but is understood more clearly from the preceding scholium.

COROLLARIUM: Hinc sequitur quod quamdiu res singulares non existunt nisi quatenus in Dei attributis comprehenduntur, earum esse objectivum sive ideæ non existunt nisi quatenus infinita Dei idea existit et ubi res singulares dicuntur existere non tantum quatenus in Dei attributis comprehenduntur sed quatenus etiam durare dicuntur, earum ideæ etiam existentiam per quam durare dicuntur, involvent.

COROLLARIUM: Hence it follows that so long as singular things do not exist except insofar as they are comprehended in God's attributes, their objective being or ideas do not exist except insofar as the infinite idea of God exists; and where singular things are said to exist not only insofar as they are comprehended in God's attributes but also insofar as they are said to endure, their ideas also involve the existence by which they are said to endure.

SCHOLIUM: Si quis ad uberiorem hujus rei explicationem exemplum desideret, nullum sane dare potero quod rem de qua hic loquor, utpote unicam adæquate explicet; conabor tamen rem ut fieri potest, illustrare. Nempe circulus talis est naturæ ut omnium linearum rectarum in eodem sese invicem secantium rectangula sub segmentis sint inter se æqualia; quare in circulo infinita inter se æqualia rectangula continentur : attamen nullum eorum potest dici existere nisi quatenus circulus existit nec etiam alicujus horum rectangulorum idea potest dici existere nisi quatenus in circuli idea comprehenditur. Concipiantur jam ex infinitis illis duo tantum nempe E et D existere.

SCHOLIUM: If anyone desires an example for a fuller explication of this matter, I certainly cannot give any that adequately explains the thing I speak of as the one unique instance; I will nevertheless try, as far as possible, to illustrate the matter. For a circle is of such a nature that the rectangles formed by all straight lines cutting one another in the same [circle] under the segments are equal among themselves; therefore in the circle infinitely many mutually equal rectangles are contained: yet none of them can be said to exist except insofar as the circle exists, nor can the idea of any one of those rectangles be said to exist except insofar as it is comprehended in the idea of the circle. Now let it be conceived that of those infinites two only, namely E and D, exist.

Sane eorum etiam ideæ jam non tantum existunt quatenus solummodo in circuli idea comprehenduntur sed etiam quatenus illorum rectangulorum existentiam involvunt, quo fit ut a reliquis reliquorum rectangulorum ideis distinguantur.

Certainly their ideas too now exist not only insofar as they are merely comprehended in the idea of the circle, but also insofar as they involve the existence of those rectangles, whereby they are distinguished from the remaining ideas of the other rectangles.

PROPOSITIO IX: Idea rei singularis actu existentis Deum pro causa habet non quatenus infinitus est sed quatenus alia rei singularis actu existentis idea affectus consideratur cujus etiam Deus est causa quatenus alia tertia affectus est et sic in infinitum.

PROPOSITIO 9: The idea of a singular thing actually existing has God for its cause not insofar as He is infinite but insofar as the idea of another singular thing actually existing is considered as an affect, of which God is likewise cause insofar as a third is affected, and so on to infinity.

DEMONSTRATIO: Idea rei singularis actu existentis modus singularis cogitandi est et a reliquis distinctus (per corollarium et scholium propositionis 8 hujus) adeoque (per propositionem 6 hujus) Deum quatenus est tantum res cogitans, pro causa habet. At non (per propositionem 28 partis I) quatenus est res absolute cogitans sed quatenus alio cogitandi modo affectus consideratur et hujus etiam Deus est causa quatenus alio cogitandi modo affectus est et sic in infinitum. Atqui ordo et connexio idearum (per propositionem 7 hujus) idem est ac ordo et connexio causarum; ergo unius singularis ideæ alia idea sive Deus quatenus alia idea affectus consideratur, est causa et hujus etiam quatenus alia affectus est et sic in infinitum.

DEMONSTRATIO: The idea of a singular thing actually existing is a singular mode of thinking and is distinct from the rest (by the corollary and scholium of proposition 8 of this), and therefore (by proposition 6 of this) has God, insofar as He is only a thinking thing, as its cause. But not (by proposition 28 of part 1) insofar as He is absolutely a thinking thing, but insofar as He is considered as affected in another mode of thinking; and of this also God is the cause insofar as He is affected in another mode of thinking, and so to infinity. Moreover the order and connection of ideas (by proposition 7 of this) is the same as the order and connection of causes; therefore of one singular idea another idea — or God, insofar as He is considered as affected by another idea — is the cause, and of this likewise insofar as He is affected by another, and so to infinity.

Q.E.D.

Which was to be demonstrated.

COROLLARIUM: Quicquid in singulari cujuscunque ideæ objecto contingit, ejus datur in Deo cognitio quatenus tantum ejusdem objecti ideam habet.

COROLLARIUM: Whatever occurs in the singular object of any idea, knowledge of it is given in God insofar as He has only the idea of that same object.

DEMONSTRATIO: Quicquid in objecto cujuscunque ideæ contingit, ejus datur in Deo idea (per propositionem 3 hujus) non quatenus infinitus est sed quatenus alia rei singularis idea affectus consideratur (per præcedentem propositionem) sed (per propositionem 7 hujus) ordo et connexio idearum idem est ac ordo et connexio rerum; erit ergo cognitio ejus quod in singulari aliquo objecto contingit, in Deo quatenus tantum ejusdem objecti habet ideam. Q.E.D.

DEMONSTRATION: Whatever in the object of any idea occurs, its idea is given in God (by proposition 3 of this work) not insofar as the Infinite is but insofar as the affect of the idea of another single thing is considered (by the preceding proposition); but (by proposition 7 of this work) the order and connection of ideas is the same as the order and connection of things; therefore the cognition of that which occurs in any singular object is in God insofar as He has the idea of that same object. Q.E.D.

PROPOSITIO X: Ad essentiam hominis non pertinet esse substantiæ sive substantia formam hominis non constituit.

PROPOSITION 10: To the essence of man it does not pertain to be a substance, nor does substance constitute the form of man.

DEMONSTRATIO: Esse enim substantiæ involvit necessariam existentiam (per propositionem 7 partis I). Si igitur ad hominis essentiam pertineret esse substantiæ, data ergo substantia, daretur necessario homo (per definitionem 2 hujus) et consequenter homo necessario existeret, quod (per axioma 1 hujus) est absurdum. Ergo etc. Q.E.D.

DEMONSTRATIO: For the esse of a substance involves necessary existence (by proposition 7 of Part I). If therefore the esse of a substance belonged to the essence of man, given the substance a man would be given necessarily (by definition 2 of this) and consequently a man would exist necessarily, which (by axiom 1 of this) is absurd. Ergo etc. Q.E.D.

SCHOLIUM: Demonstratur etiam hæc propositio ex propositione 5 partis I nempe quod duæ ejusdem naturæ substantiæ non dentur. Cum autem plures homines existere possint, ergo id quod hominis formam constituit, non est esse substantiæ. Patet præterea hæc propositio ex reliquis substantiæ proprietatibus videlicet quod substantia sit sua natura infinita, immutabilis, indivisibilis etc. ut facile unusquisque videre potest.

SCHOLIUM: This proposition is also demonstrated from proposition 5 of Part I, namely that two substances of the same nature are not given. But since several men can exist, therefore that which constitutes the form of a man is not the being of a substance. Furthermore this proposition is plain from the remaining properties of substance, namely that substance by its nature is infinite, immutable, indivisible, etc., as anyone can easily see.

COROLLARIUM: Hinc sequitur essentiam hominis constitui a certis Dei attributorum modificationibus.

COROLLARIUM: Hence it follows that the essence of man is constituted by certain modifications of God’s attributes.

DEMONSTRATIO: Nam esse substantiæ (per propositionem præcedentem) ad essentiam hominis non pertinet. Est ergo (per propositionem 15 partis I) aliquid quod in Deo est et quod sine Deo nec esse nec concipi potest sive (per corollarium propositionis 25 partis I) affectio sive modus qui Dei naturam certo et determinato modo exprimit.

DEMONSTRATIO: For the being of substance (by the preceding proposition) does not pertain to the essence of man. Therefore (by proposition 15 of Part I) there is something which is in God and which without God can be neither—existence nor be conceived, or (by the corollary of proposition 25 of Part I) an affection or mode which expresses God’s nature in a certain and determinate way.

SCHOLIUM: Omnes sane concedere debent nihil sine Deo esse neque concipi posse. Nam apud omnes in confesso est quod Deus omnium rerum tam earum essentiæ quam earum existentiæ unica est causa hoc est Deus non tantum est causa rerum secundum fieri ut aiunt sed etiam secundum esse. At interim plerique id ad essentiam alicujus rei pertinere dicunt sine quo res nec esse nec concipi potest adeoque vel naturam Dei ad essentiam rerum creatarum pertinere vel res creatas sine Deo vel esse vel concipi posse credunt vel quod certius est, sibi non satis constant.

SCHOLIUM: All certainly ought to concede that nothing can be or be conceived without God. For with all it is confessed that God is the sole cause of all things, both of their essences and of their existences; that is, God is not only the cause of things with respect to becoming, as they say, but also with respect to being. Yet meanwhile many say that this belongs to the essence of some thing without which the thing can neither be nor be conceived, and accordingly either they hold that the nature of God pertains to the essence of created things, or that created things without God can neither be nor be conceived, or, which is more certain, they are not sufficiently settled in their view.

Cujus rei causam fuisse credo quod ordinem philosophandi non tenuerint. Nam naturam divinam quam ante omnia contemplari debebant quia tam cognitione quam natura prior est, ordine cognitionis ultimam et res quæ sensuum objecta vocantur, omnibus priores esse crediderunt; unde factum est ut dum res naturales contemplati sunt, de nulla re minus cogitaverint quam de divina natura et cum postea animum ad divinam naturam contemplandum appulerint, de nulla re minus cogitare potuerint quam de primis suis figmentis quibus rerum naturalium cognitionem superstruxerant; utpote quæ ad cognitionem divinæ naturæ nihil juvare poterant adeoque nihil mirum si sibi passim contradixerint. Sed hoc mitto.

I believe the cause of this was that they did not observe the order of philosophizing. For the divine nature, which they ought to have contemplated above all because it is prior both in cognition and in nature, they judged to be last in the order of cognition, and that the things called objects of the senses were prior to all; whence it came about that, while they contemplated natural things, of nothing did they think less than of the divine nature, and when afterwards they steered the mind to contemplate the divine nature, of nothing could they think less than of their first figments with which they had superimposed the cognition of natural things — things that could in no way aid the cognition of the divine nature, and therefore no wonder if they contradicted themselves everywhere. But I pass over this.

Nam meum intentum hic tantum fuit causam reddere cur non dixerim id ad essentiam alicujus rei pertinere sine quo res nec esse nec concipi potest; nimirum quia res singulares non possunt sine Deo esse nec concipi et tamen Deus ad earum essentiam non pertinet sed id necessario essentiam alicujus rei constituere dixi quo dato, res ponitur et quo sublato, res tollitur vel id sine quo res et vice versa id quod sine re nec esse nec concipi potest.

For my intent here was only to render the cause why I did not say that this pertains to the essence of any thing, without which a thing can neither be nor be conceived; namely, because singular things cannot be without God nor be conceived, and yet God does not pertain to their essence; but I said that what necessarily constitutes the essence of any thing is that by which, given, the thing is posited, and by which, removed, the thing is taken away — or that without which a thing, and conversely that which without the thing can neither be nor be conceived.

PROPOSITIO XI: Primum quod actuale mentis humanæ esse constituit, nihil aliud est quam idea rei alicujus singularis actu existentis.

PROPOSITIO 11: The first thing that constitutes the actuality of the human mind is nothing other than the idea of some singular thing actually existing.

DEMONSTRATIO: Essentia hominis (per corollarium præcedentis propositionis) a certis Dei attributorum modis constituitur nempe (per axioma 2 hujus) a modis cogitandi quorum omnium (per axioma 3 hujus) idea natura prior est et ea data reliqui modi (quibus scilicet idea natura prior est) in eodem debent esse individuo (per axioma 3 hujus). Atque adeo idea primum est quod humanæ mentis esse constituit. At non idea rei non existentis. Nam tum (per corollarium propositionis 8 hujus) ipsa idea non potest dici existere; erit ergo idea rei actu existentis.

DEMONSTRATIO: The essence of man (by the corollary of the preceding proposition) is constituted from certain modes of the attributes of God, namely (by axiom 2 of this) from modes of thinking, the idea of all of which is prior by nature (by axiom 3 of this) and, the idea being prior by nature given, the remaining modes (in which, namely, the idea is prior by nature) must be in the same individual (by axiom 3 of this). And thus the idea is first that which constitutes the being of the human mind. But not the idea of a thing not existing. For then (by the corollary of proposition 8 of this) that very idea cannot be said to exist; therefore it will be the idea of a thing actually existing.

At non rei infinitæ. Res namque infinita (per propositiones 21 et 22 partis I) debet semper necessario existere; atqui hoc (per axioma 1 hujus) est absurdum; ergo primum quod esse humanæ mentis actuale constituit, est idea rei singularis actu existentis. Q.E.D.

But not of an infinite thing. For an infinite thing (by propositions 21 and 22 of Part 1) must always necessarily exist; and yet this (by axiom 1 of this) is absurd; therefore the first thing that constitutes the actual being of the human mind is the idea of a singular thing actually existing. Q.E.D.

COROLLARIUM: Hinc sequitur mentem humanam partem esse infiniti intellectus Dei ac proinde cum dicimus mentem humanam hoc vel illud percipere, nihil aliud dicimus quam quod Deus non quatenus infinitus est sed quatenus per naturam humanæ mentis explicatur sive quatenus humanæ mentis essentiam constituit, hanc vel illam habet ideam et cum dicimus Deum hanc vel illam ideam habere non tantum quatenus naturam humanæ mentis constituit sed quatenus simul cum mente humana alterius rei etiam habet ideam, tum dicimus mentem humanam rem ex parte sive inadæquate percipere.

COROLLARIUM: Hence it follows that the human mind is a part of the infinite intellect of God and therefore when we say the human mind perceives this or that, we say nothing else than that God, not insofar as He is infinite but insofar as He is expressed through the nature of the human mind or insofar as He constitutes the essence of the human mind, has this or that idea; and when we say that God has this or that idea not only insofar as He constitutes the nature of the human mind but insofar as, together with the human mind, He also has the idea of another thing, then we say that the human mind perceives the thing in part or inadequately.

SCHOLIUM: Hic sine dubio lectores hærebunt multaque comminiscentur quæ moram injiciant et hac de causa ipsos rogo ut lento gradu mecum pergant nec de his judicium ferant donec omnia perlegerint.

SCHOLIUM: Here without doubt readers will cling and will commix many things which will cast in delay, and for this reason I ask them to proceed with me at a slow pace and not to pass judgment on these matters until they have read everything through.

PROPOSITIO XII: Quicquid in objecto ideæ humanam mentem constituentis contingit, id ab humana mente debet percipi sive ejus rei dabitur in mente necessario idea hoc est si objectum ideæ humanam mentem constituentis sit corpus, nihil in eo corpore poterit contingere quod a mente non percipiatur.

PROPOSITION 12: Whatever in the object of an idea constituting the human mind happens, that must be perceived by the human mind, or the idea of that thing will be given in the mind necessarily — that is, if the object of the idea constituting the human mind is a body, nothing in that body can happen which is not perceived by the mind.

DEMONSTRATIO: Quicquid enim in objecto cujuscunque ideæ contingit, ejus rei datur necessario in Deo cognitio (per corollarium propositionis 9 hujus) quatenus ejusdem objecti idea affectus consideratur hoc est (per propositionem 11 hujus) quatenus mentem alicujus rei constituit. Quicquid igitur in objecto ideæ humanam mentem constituentis contingit, ejus datur necessario in Deo cognitio quatenus naturam humanæ mentis constituit hoc est (per corollarium propositionis 11 hujus) ejus rei cognitio erit necessario in mente sive mens id percipit. Q.E.D.

DEMONSTRATION: For whatever occurs in the object of any idea, knowledge of that thing is necessarily given in God (by the corollary of proposition 9 of this) insofar as the idea of that same object is considered an affect, that is (by proposition 11 of this) insofar as it constitutes the mind of a thing. Therefore whatever occurs in the object of the idea that constitutes the human mind, knowledge of it is necessarily given in God insofar as it constitutes the nature of the human mind; that is (by the corollary of proposition 11 of this) the knowledge of that thing will necessarily be in the mind, or the mind perceives it. Q.E.D.

SCHOLIUM: Hæc propositio patet etiam et clarius intelligitur ex scholio propositionis 7 hujus, quod vide.

SCHOLIUM: This proposition is also plain and is understood more clearly from the scholium of proposition 7 of this work, which see.

PROPOSITIO XIII: Objectum ideæ humanam mentem constituentis est corpus sive certus extensionis modus actu existens et nihil aliud.

PROPOSITION 13: The object of the idea constituting the human mind is a body, or a certain mode of extension actually existing, and nothing else.

DEMONSTRATIO: Si enim corpus non esset humanæ mentis objectum, ideæ affectionum corporis non essent in Deo (per corollarium propositionis 9 hujus) quatenus mentem nostram sed quatenus alterius rei mentem constitueret hoc est (per corollarium propositionis 11 hujus) ideæ affectionum corporis non essent in nostra mente; atqui (per axioma 4 hujus) ideas affectionum corporis habemus. Ergo objectum ideæ humanam mentem constituentis est corpus idque (per propositionem 11 hujus) actu existens. Deinde si præter corpus etiam aliud esset mentis objectum, cum nihil (per propositionem 36 partis I) existat ex quo aliquis effectus non sequatur, deberet (per propositionem 12 hujus) necessario alicujus ejus effectus idea in mente nostra dari; atqui (per axioma 5 hujus) nulla ejus idea datur.

DEMONSTRATIO: For if body were not the object of the human mind, the ideas of the affections of body would not be in God (by the corollary of proposition 9 of this), insofar as they would constitute not our mind but the mind of some other thing, that is (by the corollary of proposition 11 of this) the ideas of the affections of body would not be in our mind; yet (by axiom 4 of this) we have ideas of the affections of body. Therefore the object of the idea that constitutes the human mind is body, and this (by proposition 11 of this) exists actually. Further, if besides body something else were also the object of the mind, since nothing (by proposition 36 of part 1) exists from which some effect does not follow, it would be necessary (by proposition 12 of this) that some idea of its effect be given in our mind; yet (by axiom 5 of this) no such idea is given.

Ergo objectum nostræ mentis est corpus existens et nihil aliud. Q.E.D.

Therefore the object of our mind is a body existing and nothing else. Q.E.D.

COROLLARIUM: Hinc sequitur hominem mente et corpore constare et corpus humanum prout ipsum sentimus existere.

COROLLARIUM: From this it follows that man consists of mind and body, and that the human body, as we perceive it, exists.

SCHOLIUM: Ex his non tantum intelligimus mentem humanam unitam esse corpori sed etiam quid per mentis et corporis unionem intelligendum sit. Verum ipsam adæquate sive distincte intelligere nemo poterit nisi prius nostri corporis naturam adæquate cognoscat. Nam ea quæ hucusque ostendimus, admodum communia sunt nec magis ad homines quam ad reliqua individua pertinent, quæ omnia quamvis diversis gradibus animata tamen sunt.

SCHOLIUM: From these things we understand not only that the human mind is united to the body but also what is to be understood by the union of mind and body. But no one will be able to apprehend the mind itself adequately or distinctly unless first he adequately knows the nature of our body. For those things which we have hitherto shown are most common and pertain no more to men than to the other individuated beings, which all, although animated in different degrees, nevertheless are.

Nam cujuscunque rei datur necessario in Deo idea cujus Deus est causa eodem modo ac humani corporis ideæ atque adeo quicquid de idea humani corporis diximus, id de cujuscunque rei idea necessario dicendum est. Attamen nec etiam negare possumus ideas inter se ut ipsa objecta differre unamque alia præstantiorem esse plusque realitatis continere prout objectum unius objecto alterius præstantius est plusque realitatis continet ac propterea ad determinandum quid mens humana reliquis intersit quidque reliquis præstet, necesse nobis est ejus objecti ut diximus hoc est corporis humani naturam cognoscere. Eam autem hic explicare nec possum nec id ad ea quæ demonstrare volo, necesse est.

For to whatever thing an idea is necessarily given in God, of which God is the cause, in the same way as the ideas of the human body — and therefore whatever we said about the idea of the human body must necessarily be said about the idea of any thing. Yet we cannot even deny that ideas differ among themselves as the objects themselves differ, and that one is more pre-eminent than another and contains more of reality, insofar as the object of one is more excellent than the object of another and contains more reality; and therefore, to determine in what the human mind differs from the rest and in what it excels the rest, it is necessary for us to know the nature of that object, as we said, that is, the nature of the human body. But to explain that here I cannot, nor is it necessary for the matters I wish to demonstrate.

Hoc tamen in genere dico quo corpus aliquod reliquis aptius est ad plura simul agendum vel patiendum, eo ejus mens reliquis aptior est ad plura simul percipiendum et quo unius corporis actiones magis ab ipso solo pendent et quo minus alia corpora cum eodem in agendo concurrunt, eo ejus mens aptior est ad distincte intelligendum. Atque ex his præstantiam unius mentis præ aliis cognoscere possumus, deinde causam etiam videre cur nostri corporis non nisi admodum confusam habeamus cognitionem et alia plura quæ in sequentibus ex his deducam. Qua de causa operæ pretium esse duxi hæc ipsa accuratius explicare et demonstrare, ad quod necesse est pauca de natura corporum præmittere.

In this respect, however, I say: insofar as any body is more apt than the rest to do or to suffer many things simultaneously, so much the more apt is its mind than the others to perceive many things at once; and the more the actions of a single body depend upon it alone, and the less other bodies concur with it in acting, the more apt is its mind for distinct understanding. From these considerations we can recognize the pre-eminence of one mind above others, and then also see the cause why our knowledge of our body is only very confused, and many other matters which I will deduce in what follows. For this reason I have judged it worth the trouble to explain and demonstrate these very points more accurately, for which it is necessary to preface a few things about the nature of bodies.

AXIOMA I: Omnia corpora vel moventur vel quiescunt.

AXIOM I: All bodies either move or are at rest.

AXIOMA II: Unumquodque corpus jam tardius jam celerius movetur.

AXIOMA II: Each body is moved now more slowly, now more swiftly.

LEMMA I: Corpora ratione motus et quietis, celeritatis et tarditatis et non ratione substantiæ ab invicem distinguuntur.

LEMMA 1: Bodies are distinguished from one another by reason of motion and rest, of celerity and tardiness, and not by reason of substance.

DEMONSTRATIO: Primam partem hujus per se notam suppono. At quod ratione substantiæ non distinguantur corpora, patet tam ex propositione 5 quam 8 partis I sed clarius ex iis quæ in scholio propositionis 15 partis I dicta sunt.

DEMONSTRATIO: I suppose the first part of this to be self-evident. But that bodies are not distinguished from one another by the nature of substance is evident both from proposition 5 and 8 of PART I, yet more clearly from those things which are said in the scholium of proposition 15 of PART I.

LEMMA II: Omnia corpora in quibusdam conveniunt.

LEMMA II: All bodies agree in certain respects.

DEMONSTRATIO: In his enim omnia corpora conveniunt quod unius ejusdemque attributi conceptum involvunt (per definitionem 1 hujus), deinde quod jam tardius jam celerius et absolute jam moveri jam quiescere possunt.

DEMONSTRATIO: In these things all bodies agree in that they involve the concept of one and the same attribute (by definition 1 of this), and likewise in that they can now be moved more slowly, now more quickly, and absolutely now be movable, now be at rest.

LEMMA III: Corpus motum vel quiescens ad motum vel quietem determinari debuit ab alio corpore quod etiam ad motum vel quietem determinatum fuit ab alio et illud iterum ab alio et sic in infinitum.

LEMMA 3: A body, moving or quiescent, must have been determined to motion or to rest by another body which likewise was determined to motion or rest by another, and that again by another, and so on to infinity.

DEMONSTRATIO: Corpora (per definitionem 1 hujus) res singulares sunt quæ (per lemma 1) ratione motus et quietis ab invicem distinguuntur adeoque (per propositionem 28 partis I) unumquodque ad motum vel quietem necessario determinari debuit ab alia re singulari nempe (per propositionem 6 hujus) ab alio corpore quod (per axioma 1) etiam vel movetur vel quiescit. At hoc etiam (per eandem rationem) moveri vel quiescere non potuit nisi ab alio ad motum vel quietem determinatum fuisset et hoc iterum (per eandem rationem) ab alio et sic in infinitum. Q.E.D.

DEMONSTRATIO: Bodies (by definition 1 of this) are singular things which (by lemma 1) are distinguished from one another by reason of motion and rest and therefore (by proposition 28 of part 1) each one had necessarily to be determined to motion or rest by another singular thing, namely (by proposition 6 of this) by another body which (by axiom 1) either moves or rests. But this also (by the same reasoning) could not be moved or rest except insofar as it had been determined to motion or rest by another, and this again (by the same reasoning) by another, and so to infinity. Q.E.D.

COROLLARIUM: Hinc sequitur corpus motum tamdiu moveri donec ab alio corpore ad quiescendum determinetur et corpus quiescens tamdiu etiam quiescere donec ab alio ad motum determinetur. Quod etiam per se notum est. Nam cum suppono corpus exempli gratia A quiescere nec ad alia corpora mota attendo, nihil de corpore A dicere potero nisi quod quiescat.

COROLLARY: Hence it follows that a moving body will continue to move so long as it is not determined by another body to rest, and a resting body will likewise continue to rest so long as it is not determined by another to motion. This is also self-evident. For when I suppose, for example, the body A to be at rest and pay no attention to other bodies being moved, I can say nothing about body A except that it rests.

Quod si postea contingat ut corpus A moveatur, id sane evenire non potuit ex eo quod quiescebat; ex eo enim nil aliud sequi poterat quam ut corpus A quiesceret. Si contra supponatur A moveri, quotiescunque ad A tantum attendimus, nihil de eodem affirmare poterimus nisi quod moveatur. Quod si postea contingat ut A quiescat, id sane evenire etiam non potuit ex motu quem habebat; ex motu enim nihil aliud sequi poterat quam ut A moveretur : contingit itaque a re quæ non erat in A nempe a causa externa a qua ad quiescendum determinatum fuit.

But if afterwards it should happen that body A is moved, that certainly could not have come from the fact that it was at rest; for from that nothing else could have followed than that body A was at rest. If, on the contrary, it is supposed that A is moving, whenever we attend to A alone we can assert nothing about it except that it is moving. If afterwards it should happen that A is at rest, that likewise certainly could not have come from the motion it had; for from motion nothing else could have followed than that A be moved: it therefore happens from a thing which was not in A, namely from an external cause by which it was determined to rest.

AXIOMA I: Omnes modi quibus corpus aliquod ab alio afficitur corpore, ex natura corporis affecti et simul ex natura corporis afficientis sequuntur ita ut unum idemque corpus diversimode moveatur pro diversitate naturæ corporum moventium et contra ut diversa corpora ab uno eodemque corpore diversimode moveantur.

AXIOMA 1: All the modes by which any body is affected by another body follow from the nature of the body affected and likewise from the nature of the affecting body, so that one and the same body is moved diversely because of the diversity of the natures of the moving bodies, and conversely that different bodies are moved diversely by one and the same body.

AXIOMA II: Cum corpus motum alteri quiescenti quod dimovere nequit, impingit, reflectitur ut moveri pergat et angulus lineæ motus reflectionis cum plano corporis quiescentis cui impegit, æqualis erit angulo quem linea motus incidentiæ cum eodem plano efficit. Atque hæc de corporibus simplicissimis quæ scilicet solo motu et quiete, celeritate et tarditate ab invicem distinguuntur : jam ad composita ascendamus.

AXIOMA II: When a moving body strikes a resting body which it cannot displace, it is reflected so as to continue to be moved, and the angle of the line of motion of the reflection with the plane of the resting body which it struck will be equal to the angle which the line of the incident motion with the same plane makes. And this concerns the most simple bodies which, namely, are distinguished from one another only by motion and rest, by swiftness and slowness: now let us ascend to composites.

DEFINITIO: Cum corpora aliquot ejusdem aut diversæ magnitudinis a reliquis ita coercentur ut invicem incumbant vel si eodem aut diversis celeritatis gradibus moventur ut motus suos invicem certa quadam ratione communicent, illa corpora invicem unita dicemus et omnia simul unum corpus sive individuum componere quod a reliquis per hanc corporum unionem distinguitur.

DEFINITIO: When several bodies of the same or of different magnitude are restrained from the others so that they press upon one another, or when they are moved with the same or different degrees of celerity so that they communicate their motions to one another according to a certain rule, those bodies we shall call united to one another, and all together compose one body or individuum which is distinguished from the rest by this union of bodies.

AXIOMA III: Quo partes individui vel corporis compositi secundum majores vel minores superficies sibi invicem incumbunt, eo difficilius vel facilius cogi possunt ut situm suum mutent et consequenter eo difficilius vel facilius effici potest ut ipsum individuum aliam figuram induat. Atque hinc corpora quorum partes secundum magnas superficies invicem incumbunt, dura, quorum autem partes secundum parvas, mollia et quorum denique partes inter se moventur, fluida vocabo.

AXIOM III: The more the parts of an individual or of a composite body rest upon one another according to larger or smaller surfaces, the more difficult or easier they can be compelled to change their position, and consequently the more difficult or easier it can be to cause that individual itself to assume another figure. And hence I will call bodies whose parts rest upon one another by large surfaces hard; those whose parts rest by small surfaces soft; and those whose parts finally move among themselves fluid.

LEMMA IV: Si corporis sive individui quod ex pluribus corporibus componitur, quædam corpora segregentur et simul totidem alia ejusdem naturæ eorum loco succedant, retinebit individuum suam naturam uti antea absque ulla ejus formæ mutatione.

LEMMA 4: If a body or individual which is composed of several bodies has certain bodies separated and at the same time just as many other bodies of the same nature succeed them in their place, the individual will retain its nature as before without any change of its form.

DEMONSTRATIO: Corpora enim (per lemma 1) ratione substantiæ non distinguuntur; id autem quod formam individui constituit, in corporum unione (per definitionem præcedentem) consistit; atqui hæc (per hypothesin) tametsi corporum continua fiat mutatio, retinetur : retinebit ergo individuum tam ratione substantiæ quam modi suam naturam uti ante. Q.E.D.

DEMONSTRATION: For bodies (by lemma 1) are not distinguished with respect to substance; and that which constitutes the form of the individual consists in the union of bodies (by the preceding definition); moreover these (by hypothesis), although a continuous change of bodies takes place, are retained: therefore the individual will retain both with respect to substance and to mode its nature as before. Q.E.D.

LEMMA V : Si partes individuum componentes majores minoresve evadant, ea tamen proportione ut omnes eandem ut antea ad invicem motus et quietis rationem servent, retinebit itidem individuum suam naturam ut antea absque ulla formæ mutatione.

LEMMA V : If the parts composing an individuum become greater or smaller, yet in such proportion that all preserve toward one another the same relation of motion and rest as before, the individuum will likewise retain its nature as before without any change of form.

DEMONSTRATIO: Hujus eadem est ac præcedentis lemmatis.

DEMONSTRATIO: The demonstration of this is the same as that of the preceding lemma.

LEMMA VI: Si corpora quædam individuum componentia motum quem versus unam partem habent, aliam versus flectere cogantur at ita ut motus suos continuare possint atque invicem eadem qua antea ratione communicare, retinebit itidem individuum suam naturam absque ulla formæ mutatione.

LEMMA 6: If certain bodies composing an individual, which have motion toward one part, are compelled to bend that motion toward another, and yet so that they can continue their motions and communicate with one another in the same manner as before, the individual likewise will retain its nature without any change of form.

DEMONSTRATIO: Per se patet. Id enim omne retinere supponitur quod in ejusdem definitione formam ipsius constituere diximus.

DEMONSTRATIO: It is evident in itself. For all that is supposed to be retained is what, in its very definition, we said constitutes its form.

LEMMA VII: Retinet præterea individuum sic compositum suam naturam sive id secundum totum moveatur sive quiescat sive versus hanc sive versus illam partem moveatur dummodo unaquæque pars motum suum retineat eumque uti antea reliquis communicet.

LEMMA 7: Moreover the individual thus composed retains its nature whether it be moved as a whole or rest, or be moved toward this or toward that part, provided each part retains its motion and communicates it to the others as before.

DEMONSTRATIO: Patet ex ipsius definitione, quam vide ante lemma 4.

DEMONSTRATIO: It is clear from its own definition, which see before lemma 4.

SCHOLIUM: His itaque videmus qua ratione individuum compositum possit multis modis affici, ejus nihilominus natura servata. Atque hucusque individuum concepimus quod non nisi ex corporibus quæ solo motu et quiete, celeritate et tarditate inter se distinguuntur hoc est quod ex corporibus simplicissimis componitur. Quod si jam aliud concipiamus ex pluribus diversæ naturæ individuis compositum, idem pluribus aliis modis posse affici reperiemus, ipsius nihilominus natura servata.

SCHOLIUM: Thus we see by what reasoning an individuum compositum can be affected in many ways, its natura nevertheless preserved. And hitherto we conceive an individuum which is composed only of bodies that are distinguished among themselves by motion and rest, by celerity and tardiness — that is, which is composed from the most simple bodies. But if now we conceive another made up of several individuals of diverse natures, we shall find that the same can be affected in many other modes, its natura nevertheless preserved.

Nam quandoquidem ejus unaquæque pars ex pluribus corporibus est composita, poterit ergo (per lemma præcedens) unaquæque pars absque ulla ipsius naturæ mutatione jam tardius jam celerius moveri et consequenter motus suos citius vel tardius reliquis communicare. Quod si præterea tertium individuorum genus ex his secundis compositum concipiamus, idem multis aliis modis affici posse reperiemus absque ulla ejus formæ mutatione. Et si sic porro in infinitum pergamus, facile concipiemus totam naturam unum esse Individuum cujus partes hoc est omnia corpora infinitis modis variant absque ulla totius Individui mutatione.

For since each of its parts is composed of several bodies, therefore (by the preceding lemma) each part will be able, without any change of its nature, now to move more slowly, now more quickly, and consequently to communicate its motions more swiftly or more slowly to the rest. And if moreover we conceive a third kind of individuals composed of these secondary ones, we shall find that the same can be affected in many other ways without any alteration of its form. And if thus we proceed onward to infinity, we shall easily conceive the whole of nature to be one Individual whose parts—that is, all bodies—vary in infinite ways without any change of the whole Individual.

Atque hæc, si animus fuisset de corpore ex professo agere, prolixius explicare et demonstrare debuissem. Sed jam dixi me aliud velle nec alia de causa hæc adferre quam quia ex ipsis ea quæ demonstrare constitui, facile possum deducere.

And these things, had my purpose been to treat of the body professedly, I ought to have explained and demonstrated at greater length. But I have already said that I desire something else, and I bring these matters for no other reason than that from those very things which I have resolved to demonstrate I can easily deduce them.

POSTULATA

POSTULATES

I. Corpus humanum componitur ex plurimis (diversæ naturæ) individuis quorum unumquodque valde compositum est.

1. The human body is composed of very many individuals (of diverse nature), each one of which is highly composite.

II. Individuorum ex quibus corpus humanum componitur quædam fluida, quædam mollia et quædam denique dura sunt.

2. Some of the individuals out of which the human body is composed are fluid, some soft, and some, finally, hard.

III. Individua corpus humanum componentia et consequenter ipsum humanum corpus a corporibus externis plurimis modis afficitur.

3. Individuals composing the human body, and consequently the human body itself, are affected by numerous external bodies in a great many ways.

IV. Corpus humanum indiget ut conservetur plurimis aliis corporibus a quibus continuo quasi regeneratur.

4. The human body needs, in order to be preserved, very many other bodies, from which it is continuously, as it were, regenerated.

V. Cum corporis humani pars fluida a corpore externo determinatur ut in aliam mollem sæpe impingat, ejus planum mutat et veluti quædam corporis externi impellentis vestigia eidem imprimit.

5. When a fluid part of the human body is directed by an external body so that it often strikes into another soft one, it changes its plane and, as it were, impresses upon it certain vestiges of the external body that is impelling.

VI. Corpus humanum potest corpora externa plurimis modis movere plurimisque modis disponere.

6. The human body is able to move external bodies in very many ways and to dispose of/arrange them in very many ways.

PROPOSITIO XIV: Mens humana apta est ad plurima percipiendum et eo aptior quo ejus corpus pluribus modis disponi potest.

PROPOSITIO 14: The human mind is apt to perceive very many things, and is all the more apt insofar as its body can be disposed in more numerous ways.

DEMONSTRATIO: Corpus enim humanum (per postulata 3 et 6) plurimis modis a corporibus externis afficitur disponiturque ad corpora externa plurimis modis afficiendum. At omnia quæ in corpore humano contingunt (per propositionem 12 hujus) mens humana percipere debet; est ergo mens humana apta ad plurima percipiendum et eo aptior etc. Q.E.D.

DEMONSTRATIO: For the human body (by postulates 3 and 6) is affected in very many ways by external bodies and is disposed so as to be affected by external bodies in very many ways. But all things that occur in the human body (by proposition 12 of this) the human mind ought to perceive; therefore the human mind is apt to perceive very many things, and all the more apt in proportion as its body can be disposed in more ways. Q.E.D.

PROPOSITIO XV: Idea quæ esse formale humanæ mentis constituit non est simplex sed ex plurimis ideis composita.

PROPOSITION 15: The idea which constitutes the formal being of the human mind is not simple but composed of many ideas.

DEMONSTRATIO: Idea quæ esse formale humanæ mentis constituit, est idea corporis (per propositionem 13 hujus) quod (per postulatum 1) ex plurimis valde compositis individuis componitur. At cujuscunque individui corpus componentis datur necessario (per corollarium propositionis 8 hujus) in Deo idea; ergo (per propositionem 7 hujus) idea corporis humani ex plurimis hisce partium componentium ideis est composita. Q.E.D.

DEMONSTRATIO: The idea which constitutes the formal being of the human mind is the idea of a body (by proposition 13 of this), which (by postulate 1) is composed of very many highly composite individuals. But to each individual composing that body an idea is necessarily given (by the corollary of proposition 8 of this) in God; therefore (by proposition 7 of this) the idea of the human body is composed of many of these component-part ideas. Q.E.D.

PROPOSITIO XVI : Idea cujuscunque modi quo corpus humanum a corporibus externis afficitur, involvere debet naturam corporis humani et simul naturam corporis externi.

PROPOSITIO 16 : The idea of whatever manner by which the human body is affected by external bodies ought to involve the nature of the human body and at the same time the nature of the external body.

DEMONSTRATIO: Omnes enim modi quibus corpus aliquod afficitur ex natura corporis affecti et simul ex natura corporis afficientis sequuntur (per axioma 1 post corollarium lemmatis 3) : quare eorum idea (per axioma 4 partis I) utriusque corporis naturam necessario involvet adeoque idea cujuscunque modi quo corpus humanum a corpore externo afficitur, corporis humani et corporis externi naturam involvit. Q.E.D.

DEMONSTRATION: For all the modes by which any body is affected follow from the nature of the affected body and at the same time from the nature of the affecting body (by axiom 1 after the corollary of lemma 3): therefore their idea (by axiom 4 of Part I) will necessarily involve the nature of both bodies and hence the idea of any mode by which the human body is affected by an external body involves the nature of the human body and of the external body. Q.E.D.

COROLLARIUM I: Hinc sequitur primo mentem humanam plurimorum corporum naturam una cum sui corporis natura percipere.

COROLLARIUM I: Hence it follows, in the first place, that the human mind perceives the nature of very many bodies together with the nature of its own body.

COROLLARIUM II: Sequitur secundo quod ideæ quas corporum externorum habemus, magis nostri corporis constitutionem quam corporum externorum naturam indicant; quod in appendice partis primæ multis exemplis explicui.

COROLLARIUM II: It follows secondly that the ideas which we have of external bodies signify more the constitution of our own body than the nature of external bodies; which I have explained in the appendix of the first part with many examples.

PROPOSITIO XVII: Si humanum corpus affectum est modo qui naturam corporis alicujus externi involvit, mens humana idem corpus externum ut actu existens vel ut sibi præsens contemplabitur donec corpus afficiatur affectu qui ejusdem corporis existentiam vel præsentiam secludat.

PROPOSITION 17: If a human body is affected in a manner that involves the nature of some external body, the human mind will contemplate that same external body as actually existing or as present to it, until the body is affected by an affection which excludes the existence or presence of that same body.

DEMONSTRATIO: Patet. Nam quamdiu corpus humanum sic affectum est tamdiu mens humana (per propositionem 12 hujus) hanc corporis affectionem contemplabitur hoc est (per propositionem præcedentem) ideam habebit modi actu existentis quæ naturam corporis externi involvit hoc est ideam quæ existentiam vel præsentiam naturæ corporis externi non secludit sed ponit adeoque mens (per corollarium I præcedentis) corpus externum ut actu existens vel ut præsens contemplabitur donec afficiatur etc. Q.E.D.

DEMONSTRATIO: It is manifest. For as long as the human body is so affected, so long the human mind (by proposition 12 of this) will contemplate this bodily affection, that is (by the preceding proposition) will have the idea of a mode actually existing which involves the nature of the external body, that is the idea which does not exclude but posits the existence or presence of the nature of the external body; and therefore the mind (by corollary 1 of the preceding) will contemplate the external body as actually existing or as present until it be affected etc. Q.E.D.

COROLLARIUM: Mens corpora externa a quibus corpus humanum semel affectum fuit, quamvis non existant nec præsentia sint, contemplari tamen poterit velut præsentia essent.

COROLLARIUM: The mind can contemplate external bodies by which the human body was once affected, even though they do not exist nor are present, yet as if they were present.

DEMONSTRATIO: Dum corpora externa corporis humani partes fluidas ita determinant ut in molliores sæpe impingant, earum plana (per postulatum 5) mutant, unde fit (vide axioma 2 post corollarium lemmatis 3) ut inde alio modo reflectantur quam antea solebant et ut etiam postea iisdem novis planis spontaneo suo motu occurrendo eodem modo reflectantur ac cum a corporibus externis versus illa plana impulsæ sunt et consequenter ut corpus humanum dum sic reflexæ moveri pergunt, eodem modo afficiant, de quo mens (per propositionem 12 hujus) iterum cogitabit hoc est (per propositionem 17 hujus) mens iterum corpus externum ut præsens contemplabitur et hoc toties quoties corporis humani partes fluidæ spontaneo suo motu iisdem planis occurrent. Quare quamvis corpora externa a quibus corpus humanum affectum semel fuit, non existant, mens tamen eadem toties ut præsentia contemplabitur quoties hæc corporis actio repetetur. Q.E.D.

DEMONSTRATIO: While the external bodies determine the fluid parts of the human body so as often to impinge upon softer ones, their planes (by postulate 5) change, whence it happens (see axiom 2 after corollary of lemma 3) that from thence they are reflected in a different manner than they formerly were wont, and that afterwards likewise by their encountering those same new planes by their own spontaneous motion they are reflected in the same way as when they were urged by the external bodies toward those planes; and consequently that the human body, while thus reflected parts continue to move, will be affected in the same manner, about which the mind (by proposition 12 of this work) will think again, that is (by proposition 17 of this work) the mind will again contemplate the external body as present; and this as many times as the fluid parts of the human body by their own spontaneous motion shall run against those same planes. Wherefore although the external bodies by which the human body was once affected do not exist, yet the same mind will contemplate them as present as many times as this action of the body is repeated. Q.E.D.

SCHOLIUM: Videmus itaque qui fieri potest ut ea quæ non sunt veluti præsentia contemplemur, ut sæpe fit. Et fieri potest ut hoc aliis de causis contingat sed mihi hic sufficit ostendisse unam per quam rem sic possim explicare ac si ipsam per veram causam ostendissem nec tamen credo me a vera longe aberrare quandoquidem omnia illa quæ sumpsi postulata, vix quicquam continent quod non constet experientia de qua nobis non licet dubitare postquam ostendimus corpus humanum prout ipsum sentimus, existere (vide corollarium post propositionem 13 hujus). Præterea (ex corollario præcedentis et corollario II propositionis 16 hujus) clare intelligimus quænam sit differentia inter ideam exempli gratia Petri quæ essentiam mentis ipsius Petri constituit et inter ideam ipsius Petri quæ in alio homine, puta in Paulo, est. Illa enim essentiam corporis ipsius Petri directe explicat nec existentiam involvit nisi quamdiu Petrus existit; hæc autem magis constitutionem corporis Pauli quam Petri naturam indicat et ideo durante illa corporis Pauli constitutione mens Pauli quamvis Petrus non existat, ipsum tamen ut sibi præsentem contemplabitur.

SCHOLIUM: We see therefore how it can be that those things which are not can be contemplated as if present, as often happens. And it can happen for other reasons, but it suffices me here to have shown one by which I can thus explain the matter as if I had shown it by the true cause; nor do I think I have wandered far from the truth, since all those things which I have taken as postulata scarcely contain anything not established by experience, about which we may not doubt after we have shown that the human body, as we feel it, exists (see corollary after proposition 13 of this). Moreover (from the corollary of the preceding and corollary II of proposition 16 of this) we clearly understand what the difference is between the idea, for example, of Peter which constitutes the essence of Peter’s very mind and the idea of Peter which is in another man, say in Paul. For the former directly explains the essence of Peter’s body and involves existence only so long as Peter exists; the latter rather indicates the constitution of Paul’s body than the nature of Peter, and therefore during that constitution of Paul’s body the mind of Paul, although Peter does not exist, will nevertheless contemplate him as present to itself.

Porro ut verba usitata retineamus, corporis humani affectiones quarum ideæ corpora externa velut nobis præsentia repræsentant, rerum imagines vocabimus tametsi rerum figuras non referunt. Et cum mens hac ratione contemplatur corpora, eandem imaginari dicemus. Atque hic ut quid sit error indicare incipiam, notetis velim mentis imaginationes in se spectatas nihil erroris continere sive mentem ex eo quod imaginatur, non errare sed tantum quatenus consideratur carere idea quæ existentiam illarum rerum quas sibi præsentes imaginatur, secludat.

Furthermore, that we may retain customary words, we will call the affections of the human body—whose ideas represent external bodies to us as if present—images of things, although they do not correspond to the very figures of those things. And when the mind contemplates bodies in this way, we shall say that it imagines them. And here, to show what error is, I will begin: note, I wish, that the imaginations of the mind, when viewed in themselves, contain no error; whether the mind, from what it imagines, does not err, but only insofar as, when it is considered to lack the idea that would indicate the existence of those things which it imagines as present to itself, it is deprived (and so mistaken).

Nam si mens dum res non existentes ut sibi præsentes imaginatur, simul sciret res illas revera non existere, hanc sane imaginandi potentiam virtuti suæ naturæ, non vitio tribueret præsertim si hæc imaginandi facultas a sola sua natura penderet hoc est (per definitionem 7 partis I) si hæc mentis imaginandi facultas libera esset.

For if the mind, while it imagines things not existing as present to itself, at the same time knew that those things in reality do not exist, it would surely ascribe this power of imagining to the virtue of its nature, not to a fault, especially if this faculty of imagining depended on its nature alone — that is (by definition 7 of Part I) if this faculty of the mind for imagining were free.

PROPOSITIO XVIII: Si corpus humanum a duobus vel pluribus corporibus simul affectum fuerit semel, ubi mens postea eorum aliquod imaginabitur, statim et aliorum recordabitur.

PROPOSITIO 18: Si the human body has once been affected simultaneously by two or more bodies, whenever the mind afterwards imagines any one of them, it will immediately recall the others.

DEMONSTRATIO: Mens (per corollarium præcedentis) corpus aliquod ea de causa imaginatur quia scilicet humanum corpus a corporis externi vestigiis eodem modo afficitur disponiturque ac affectum est cum quædam ejus partes ab ipso corpore externo fuerunt impulsæ sed (per hypothesin) corpus tum ita fuit dispositum ut mens duo simul corpora imaginaretur; ergo jam etiam duo simul imaginabitur atque mens ubi alterutrum imaginabitur, statim et alterius recordabitur. Q.E.D.

DEMONSTRATIO: The mind (by the corollary of the preceding) imagines some body for this reason, namely that the human body is affected and disposed in the same manner by the traces of an external body, and certain of its parts were impelled by that very external body; but (by hypothesis) the body was then so disposed that the mind would imagine two bodies simultaneously; therefore now it will also imagine two simultaneously, and whenever the mind imagines one or the other, immediately it will recollect the other. Q.E.D.

SCHOLIUM: Hinc clare intelligimus quid sit memoria. Est enim nihil aliud quam quædam concatenatio idearum naturam rerum quæ extra corpus humanum sunt involventium quæ in mente fit secundum ordinem et concatenationem affectionum corporis humani. Dico primo concatenationem esse illarum tantum idearum quæ naturam rerum quæ extra corpus humanum sunt, involvunt, non autem idearum quæ earundem rerum naturam explicant.

SCHOLIUM: From this we clearly understand what memory is. For it is nothing else than a certain concatenation of ideas of the nature of things that are outside the human body, which is formed in the mind according to the order and concatenation of the affections of the human body. I say first that the concatenation consists only of those ideas which involve the nature of things outside the human body, and not of the ideas which explain the nature of those same things.

Sunt enim revera (per propositionem 16 hujus) ideæ affectionum corporis humani quæ tam hujus quam corporum externorum naturam involvunt. Dico secundo hanc concatenationem fieri secundum ordinem et concatenationem affectionum corporis humani ut ipsam distinguerem a concatenatione idearum quæ fit secundum ordinem intellectus quo res per primas suas causas mens percipit et qui in omnibus hominibus idem est. Atque hinc porro clare intelligimus cur mens ex cogitatione unius rei statim in alterius rei cogitationem incidat quæ nullam cum priore habet similitudinem; ut exempli gratia ex cogitatione vocis pomi homo romanus statim in cogitationem fructus incidet qui nullam cum articulato illo sono habet similitudinem nec aliquid commune nisi quod ejusdem hominis corpus ab his duobus affectum sæpe fuit hoc est quod ipse homo sæpe vocem pomum audivit dum ipsum fructum videret et sic unusquisque ex una in aliam cogitationem incidet prout rerum imagines uniuscujusque consuetudo in corpore ordinavit.

For truly (by proposition 16 of this) the ideas are of the affections of the human body which involve both the nature of this body and of external bodies. Secondly I say that this concatenation is made according to the order and concatenation of the affections of the human body, so that I may distinguish it from the concatenation of ideas which is made according to the order of the intellect by which the mind perceives things through their primary causes and which is the same in all men. And from this furthermore we clearly understand why the mind, from the thought of one thing, immediately falls into the thought of another thing which has no resemblance to the former; for, for example, from the thought of the voice of a pomum a Roman man immediately falls into the thought of the fruit, which has no similarity with that articulated sound nor anything in common except that the same man’s body was often affected by these two — that is, that the man himself often heard the voice “pomum” while he saw the fruit — and thus each person falls from one thought into another according as the bodily habit has ordered the images of things.

Nam miles exempli gratia visis in arena equi vestigiis statim ex cogitatione equi in cogitationem equitis et inde in cogitationem belli etc. incidet. At rusticus ex cogitatione equi in cogitationem aratri, agri etc.

For a soldier, for example, having seen in the sand the hoof‑prints of a horse, he will immediately fall from the thought of a horse into the thought of a horseman and thence into the thought of war, etc. But a peasant, from the thought of a horse into the thought of a plough, of the field, etc.

incidet et sic unusquisque prout rerum imagines consuevit hoc vel alio modo jungere et concatenare, ex una in hanc vel aliam incidet cogitationem.

he falls, and thus each one, as the imagines of things has accustomed him to join and concatenate this way or another, falls from one cogitation into this or that cogitation.

PROPOSITIO XIX: Mens humana ipsum humanum corpus non cognoscit nec ipsum existere scit nisi per ideas affectionum quibus corpus afficitur.

PROPOSITIO 19: The human mind does not know the human body itself nor knows it to exist except through ideas of the affections by which the body is affected.

DEMONSTRATIO: Mens enim humana est ipsa idea sive cognitio corporis humani (per propositionem 13 hujus) quæ (per propositionem 9 hujus) in Deo quidem est quatenus alia rei singularis idea affectus consideratur vel quia (per postulatum 4) corpus humanum plurimis corporibus indiget a quibus continuo quasi regeneratur et ordo et connexio idearum idem est (per propositionem 7 hujus) ac ordo et connexio causarum, erit hæc idea in Deo quatenus plurimarum rerum singularium ideis affectus consideratur. Deus itaque ideam corporis humani habet sive corpus humanum cognoscit quatenus plurimis aliis ideis affectus est et non quatenus naturam humanæ mentis constituit hoc est (per corollarium propositionis 11 hujus) mens humana corpus humanum non cognoscit. At ideæ affectionum corporis in Deo sunt quatenus humanæ mentis naturam constituit sive mens humana easdem affectiones percipit (per propositionem 12 hujus) et consequenter (per propositionem 16 hujus) ipsum corpus humanum idque (per propositionem 17 hujus) ut actu existens; percipit ergo eatenus tantum mens humana ipsum humanum corpus.

DEMONSTRATIO: For the human mind is itself the idea or cognition of the human body (by proposition 13 of this), which (by proposition 9 of this) is in God indeed insofar as the affect of another singular thing’s idea is considered, or because (by postulate 4) the human body depends on many bodies from which it is continuously, as it were, regenerated, and the order and connexion of ideas is the same (by proposition 7 of this) as the order and connexion of causes; this idea will therefore be in God insofar as it is the affect of the ideas of very many singular things. God therefore has the idea of the human body or knows the human body insofar as he is affected by very many other ideas and not insofar as he constitutes the nature of the human mind; that is (by the corollary of proposition 11 of this) the human mind does not know the human body. But the ideas of the body’s affections are in God insofar as they constitute the nature of the human mind, or the human mind perceives those same affections (by proposition 12 of this) and consequently (by proposition 16 of this) perceives the human body itself — and this (by proposition 17 of this) as actually existing; therefore the human mind perceives the human body only to that extent.

Q.E.D.

Which was to be demonstrated.

PROPOSITIO XX: Mentis humanæ datur etiam in Deo idea sive cognitio quæ in Deo eodem modo sequitur et ad Deum eodem modo refertur ac idea sive cognitio corporis humani.

PROPOSITION 20: The idea or cognition of the human mind is likewise given in God, which in God follows in the same manner and is referred to God in the same manner as the idea or cognition of the human body.

DEMONSTRATIO: Cogitatio attributum Dei est (per propositionem 1 hujus) adeoque (per propositionem 3 hujus) tam ejus quam omnium ejus affectionum et consequenter (per propositionem 11 hujus) mentis etiam humanæ debet necessario in Deo dari idea. Deinde hæc mentis idea sive cognitio non sequitur in Deo dari quatenus infinitus sed quatenus alia rei singularis idea affectus est (per propositionem 9 hujus). Sed ordo et connexio idearum idem est ac ordo et connexio causarum (per propositionem 7 hujus); sequitur ergo hæc mentis idea sive cognitio in Deo et ad Deum eodem modo refertur ac idea sive cognitio corporis. Q.E.D.

DEMONSTRATIO: Thought is an attribute of God (by proposition 1 of this) and therefore (by proposition 3 of this) both his and of all his affections, and consequently (by proposition 11 of this) an idea must necessarily be given in God of the human mind also. Then this idea or cognition of the mind does not follow to be given in God insofar as he is infinite but insofar as it is the idea of the affection of some singular thing (by proposition 9 of this). But the order and connection of ideas is the same as the order and connection of causes (by proposition 7 of this); it follows therefore that this idea or cognition of the mind is given in God and refers to God in the same manner as the idea or cognition of the body. Q.E.D.

PROPOSITIO XXI: Hæc mentis idea eodem modo unita est menti ac ipsa mens unita est corpori.

PROPOSITIO 21: This idea of the mind is united to the mind in the same manner as the mind itself is united to the body.

DEMONSTRATIO: Mentem unitam esse corpori ex eo ostendimus quod scilicet corpus mentis sit objectum (vide propositiones 12 et 13 hujus) adeoque per eandem illam rationem idea mentis cum suo objecto hoc est cum ipsa mente eodem modo unita esse debet ac ipsa mens unita est corpori. Q.E.D.

DEMONSTRATIO: We demonstrate that the mind is united to the body from the fact that the body is the object of the mind (see propositions 12 and 13 of this); and therefore by that same reasoning the idea of the mind with its object — that is, with the mind itself — must be united in the same way as the mind itself is united to the body. Q.E.D.

SCHOLIUM: Hæc propositio longe clarius intelligitur ex dictis in scholio propositionis 7 hujus; ibi enim ostendimus corporis ideam et corpus hoc est (per propositionem 13 hujus) mentem et corpus unum et idem esse individuum quod jam sub cogitationis jam sub extensionis attributo concipitur; quare mentis idea et ipsa mens una eademque est res quæ sub uno eodemque attributo nempe cogitationis concipitur. Mentis inquam idea et ipsa mens in Deo eadem necessitate ex eadem cogitandi potentia sequuntur dari. Nam revera idea mentis hoc est idea ideæ nihil aliud est quam forma ideæ quatenus hæc ut modus cogitandi absque relatione ad objectum consideratur; simulac enim quis aliquid scit, eo ipso scit se id scire et simul scit se scire quod scit et sic in infinitum.

SCHOLIUM: This proposition is far more clearly understood from the things said in the scholium of proposition 7 of this work; for there we showed that the idea of the body and the body, that is (by proposition 13 of this work) the mind and the body, are one and the same individual which is conceived now under the attribute of thought now under the attribute of extension; therefore the idea of the mind and the mind itself are one and the same thing which is conceived under one and the same attribute, namely thought. The idea of the mind, I say, and the mind itself follow from the same necessity in God from the same power of thinking to be given. For in truth the idea of the mind, that is the idea of the idea, is nothing else than the form of the idea insofar as this is considered as a mode of thinking without relation to an object; for as soon as someone knows something, by that very fact he knows that he knows it, and at the same time knows that he knows that which he knows, and so to infinity.

Sed de his postea.

But of these things, later.

PROPOSITIO XXII: Mens humana non tantum corporis affectiones sed etiam harum affectionum ideas percipit.

PROPOSITION 22: The human mind perceives not only the affections of the body but also the ideas of these affections.

DEMONSTRATIO: Affectionum idearum ideæ in Deo eodem modo sequuntur et ad Deum eodem modo referuntur ac ipsæ affectionum ideæ; quod eodem modo demonstratur ac propositio 20 hujus. At ideæ affectionum corporis in mente humana sunt (per propositionem 12 hujus) hoc est (per corollarium propositionis 11 hujus) in Deo quatenus humanæ mentis essentiam constituit; ergo harum idearum ideæ in Deo erunt quatenus humanæ mentis cognitionem sive ideam habet hoc est (per propositionem 21 hujus) in ipsa mente humana quæ propterea non tantum corporis affectiones sed earum etiam ideas percipit. Q.E.D.

DEMONSTRATION: The ideas of the ideas of affections in God follow and are referred to God in the same way as the very ideas of the affections; which is demonstrated in the same way as proposition 20 of this work. But the ideas of bodily affections are in the human mind (by proposition 12 of this work), that is (by the corollary of proposition 11 of this work) in God insofar as He constitutes the essence of the human mind; therefore the ideas of these ideas will be in God insofar as the human mind has the cognition or idea of them, that is (by proposition 21 of this work) in the very human mind which therefore perceives not only the bodily affections but also the ideas of those affections. Q.E.D.

PROPOSITIO XXIII: Mens se ipsam non cognoscit nisi quatenus corporis affectionum ideas percipit.

PROPOSITION 23: The mind does not know itself except insofar as it perceives the ideas of the body's affections.

DEMONSTRATIO: Mentis idea sive cognitio (per propositionem 20 hujus) in Deo eodem modo sequitur et ad Deum eodem modo refertur ac corporis idea sive cognitio. At quoniam (per propositionem 19 hujus) mens humana ipsum humanum corpus non cognoscit hoc est (per corollarium propositionis 11 hujus) quoniam cognitio corporis humani ad Deum non refertur quatenus humanæ mentis naturam constituit; ergo nec cognitio mentis ad Deum refertur quatenus essentiam mentis humanæ constituit atque adeo (per idem corollarium propositionis 11 hujus) mens humana eatenus se ipsam non cognoscit. Deinde affectionum quibus corpus afficitur ideæ naturam ipsius corporis humani involvunt (per propositionem 16 hujus) hoc est (per propositionem 13 hujus) cum natura mentis conveniunt; quare harum idearum cognitio cognitionem mentis necessario involvet; at (per propositionem præcedentem) harum idearum cognitio in ipsa humana mente est; ergo mens humana eatenus tantum se ipsam novit.

DEMONSTRATIO: The idea or cognition of the mind (by proposition 20 of this work) in God follows in the same manner and is referred to God in the same manner as the idea or cognition of the body. But since (by proposition 19 of this work) the human mind does not know the human body itself, that is (by the corollary of proposition 11 of this work) because the cognition of the human body is not referred to God insofar as it constitutes the nature of the human mind; therefore neither is the cognition of the mind referred to God insofar as it constitutes the essence of the human mind, and thus (by the same corollary of proposition 11 of this work) the human mind so far does not know itself. Furthermore, the ideas of the affections by which the body is affected involve the nature of that very human body (by proposition 16 of this work), that is (by proposition 13 of this work) they agree with the nature of the mind; wherefore the cognition of these ideas will necessarily involve the cognition of the mind; but (by the preceding proposition) the cognition of these ideas is in the human mind itself; therefore the human mind knows itself only to that extent.

Q.E.D.

Which was to be demonstrated.

PROPOSITIO XXIV: Mens humana partium corpus humanum componentium adæquatam cognitionem non involvit.

PROPOSITION 24: The human mind does not involve an adequate cognition of the parts composing the human body.

DEMONSTRATIO: Partes corpus humanum componentes ad essentiam ipsius corporis non pertinent nisi quatenus motus suos certa quadam ratione invicem communicant (vide definitionem post corollarium lemmatis 3) et non quatenus ut individua absque relatione ad humanum corpus considerari possunt. Sunt enim partes humani corporis (per postulatum 1) valde composita individua quorum partes (per lemma 4) a corpore humano, servata omnino ejusdem natura et forma, segregari possunt motusque suos (vide axioma 1 post lemma 3) aliis corporibus alia ratione communicare adeoque (per propositionem 3 hujus) cujuscunque partis idea sive cognitio in Deo erit et quidem (per propositionem 9 hujus) quatenus affectus consideratur alia idea rei singularis, quæ res singularis ipsa parte ordine naturæ prior est (per propositionem 7 hujus). Quod idem præterea etiam de quacunque parte ipsius individui corpus humanum componentis est dicendum adeoque cujuscunque partis corpus humanum componentis cognitio in Deo est quatenus plurimis rerum ideis affectus est et non quatenus corporis humani tantum habet ideam hoc est (per propositionem 13 hujus) ideam quæ humanæ mentis naturam constituit atque adeo (per corollarium propositionis 11 hujus) humana mens partium corpus humanum componentium adæquatam cognitionem non involvit. Q.E.D.

DEMONSTRATION: The parts composing the human body do not pertain to the essence of that very body except insofar as they communicate their motions to one another in a certain determinate manner (see the definition after corollary of lemma 3) and not insofar as they can be considered as individuals apart from relation to the human body. For the parts of the human body (by postulate 1) are highly composite individuals whose parts (by lemma 4) can be segregated from the human body, the same nature and form being wholly preserved, and can communicate their motions to other bodies in another manner (see axiom 1 after lemma 3) and therefore (by proposition 3 of this work) the idea or cognition of any part in God will be, and indeed (by proposition 9 of this work) insofar as an affect is considered, another idea of a singular thing, which singular thing itself is prior in the order of nature to the part (by proposition 7 of this work). The same must moreover be said of any part of that individual composing the human body and therefore the cognition in God of any part composing the human body is insofar as it is affected by many ideas of things and not insofar as it has the idea of the human body alone — that is (by proposition 13 of this work) the idea which constitutes the nature of the human mind and therefore (by the corollary of proposition 11 of this work) the human mind does not involve an adequate cognition of the parts composing the human body. Q.E.D.

PROPOSITIO XXV: Idea cujuscunque affectionis corporis humani adæquatam corporis externi cognitionem non involvit.

PROPOSITIO 25: The idea of any affection of the human body does not involve an adequate cognition of the external body.

DEMONSTRATIO: Ideam affectionis corporis humani eatenus corporis externi naturam involvere ostendimus (vide propositionem 16 hujus) quatenus externum ipsum humanum corpus certo quodam modo determinat. At quatenus externum corpus individuum est quod ad corpus humanum non refertur, ejus idea sive cognitio in Deo est (per propositionem 9 hujus) quatenus Deus affectus consideratur alterius rei idea quæ (per propositionem 7 hujus) ipso corpore externo prior est natura. Quare corporis externi adæquata cognitio in Deo non est quatenus ideam affectionis humani corporis habet sive idea affectionis corporis humani adæquatam corporis externi cognitionem non involvit.

DEMONSTRATIO: We have shown that the idea of the affection of the human body involves the nature of an external body insofar as the external itself determines the human body in a certain way (see proposition 16 of this). But insofar as the external body is an individual which is not referred to the human body, its idea or cognition is in God (by proposition 9 of this) insofar as God is considered the affect of the idea of another thing which (by proposition 7 of this) is prior in nature to that external body. Therefore the adequate cognition of the external body is not in God insofar as it has the idea of the affection of the human body; that is, the idea of the affection of the human body does not involve an adequate cognition of the external body.

Q.E.D.

Which was to be demonstrated.

PROPOSITIO XXVI: Mens humana nullum corpus externum ut actu existens percipit nisi per ideas affectionum sui corporis.

PROPOSITION 26: The human mind perceives no external body as actually existing except through the ideas of the affections of its own body.

DEMONSTRATIO: Si a corpore aliquo externo corpus humanum nullo modo affectum est, ergo (per propositionem 7 hujus) nec idea corporis humani hoc est (per propositionem 13 hujus) nec mens humana idea existentiæ illius corporis ullo etiam modo affecta est sive existentiam illius corporis externi ullo modo percipit. At quatenus corpus humanum a corpore aliquo externo aliquo modo afficitur eatenus (per propositionem 16 hujus cum corollario I ejusdem) corpus externum percipit. Q.E.D.

DEMONSTRATION: If the human body is in no way affected by any external body, then (per proposition 7 of this) neither the idea of the human body — that is (per proposition 13 of this) — nor the human mind is in any way affected by the idea of the existence of that body, nor does it in any way perceive the existence of that external body. But insofar as the human body is in any way affected by some external body, to that extent (per proposition 16 of this with Corollary 1 of the same) it perceives the external body. Q.E.D.

COROLLARIUM: Quatenus mens humana corpus externum imaginatur eatenus adæquatam ejus cognitionem non habet.

COROLLARIUM: Insofar as the human mind imagines an external body, to that extent it does not have an adequate knowledge of it.

DEMONSTRATIO: Cum mens humana per ideas affectionum sui corporis corpora externa contemplatur, eandem tum imaginari dicimus (vide scholium propositionis 17 hujus) nec mens alia ratione (per propositionem præcedentem) corpora externa ut actu existentia imaginari potest. Atque adeo (per propositionem 25 hujus) quatenus mens corpora externa imaginatur, eorum adæquatam cognitionem non habet. Q.E.D.

DEMONSTRATIO: Since the human mind contemplates external bodies by means of the ideas of the affections of its own body, we then say that it imagines the same (see the scholium to proposition 17 of this), nor can the mind in any other way (by the preceding proposition) imagine external bodies as actually existing. And therefore (by proposition 25 of this) insofar as the mind imagines external bodies, it does not have an adequate cognition of them. Q.E.D.

PROPOSITIO XXVII: Idea cujuscunque affectionis corporis humani adæquatam ipsius humani corporis cognitionem non involvit.

PROPOSITION 27: The idea of any affection of the human body does not involve an adequate knowledge of that human body itself.

DEMONSTRATIO: Quælibet idea cujuscunque affectionis humani corporis eatenus naturam corporis humani involvit quatenus ipsum humanum corpus certo quodam modo affici consideratur (vide propositionem 16 hujus). At quatenus corpus humanum individuum est quod multis aliis modis affici potest, ejus idea etc. Vide demonstrationem propositionis 25 hujus.

DEMONSTRATION: Any idea of whatever affection of the human body involves the nature of the human body insofar as the human body itself is considered to be affected in a certain definite way (see proposition 16 of this). But insofar as the human body is an individual which can be affected in many other ways, its idea etc. See the demonstration of proposition 25 of this.

PROPOSITIO XXVIII: Ideæ affectionum corporis humani quatenus ad humanam mentem tantum referuntur, non sunt claræ et distinctæ sed confusæ.

PROPOSITIO 28: The ideas of the affections of the human body, insofar as they are referred only to the human mind, are not clear and distinct but confused.

DEMONSTRATIO: Ideæ enim affectionum corporis humani tam corporum externorum quam ipsius humani corporis naturam involvunt (per propositionem 16 hujus) nec tantum corporis humani sed ejus etiam partium naturam involvere debent; affectiones namque modi sunt (per postulatum 3) quibus partes corporis humani et consequenter totum corpus afficitur. At (per propositiones 24 et 25 hujus) corporum externorum adæquata cognitio ut et partium corpus humanum componentium in Deo non est quatenus humana mente sed quatenus aliis ideis affectus consideratur. Sunt ergo hæ affectionum ideæ quatenus ad solam humanam mentem referuntur, veluti consequentiæ absque præmissis hoc est (ut per se notum) ideæ confusæ. Q.E.D.

DEMONSTRATIO: For the ideas of the affections of the human body involve the nature both of external bodies and of the human body itself (by proposition 16 of this), and they must involve not only the human body but also the nature of its parts; for affections are modes (by postulate 3) whereby the parts of the human body and consequently the whole body are affected. But (by propositions 24 and 25 of this) an adequate cognition of external bodies, as well as of the parts composing the human body, in God is not considered as referred to the human mind but as referred to other ideas of affections. Therefore these ideas of affections, insofar as they are referred to the human mind alone, are confused — namely consequents without premisses, that is (as self-evident) confused ideas. Q.E.D.

SCHOLIUM: Idea quæ naturam mentis humanæ constituit, demonstratur eodem modo non esse, in se sola considerata, clara et distincta, ut etiam idea mentis humanæ et ideæ idearum affectionum corporis humani quatenus ad solam mentem referuntur, quod unusquisque facile videre potest.

SCHOLIUM: The idea which constitutes the nature of the human mind is demonstrated in the same way not to be, when considered by itself alone, clear and distinct, as too the idea of the human mind and the idea of the ideas of the affections of the human body insofar as they are referred to the human mind alone, which anyone can easily see.

PROPOSITIO XXIX: Idea ideæ cujuscunque affectionis corporis humani adæquatam humanæ mentis cognitionem non involvit.

PROPOSITION 29: The idea of the idea of any affection of the human body does not involve an adequate cognition of the human mind.

DEMONSTRATIO: Idea enim affectionis corporis humani (per propositionem 27 hujus) adæquatam ipsius corporis cognitionem non involvit sive ejus naturam adæquate non exprimit hoc est (per propositionem 13 hujus) cum natura mentis non convenit adæquate adeoque (per axioma 6 partis I) hujus ideæ idea adæquate humanæ mentis naturam non exprimit sive adæquatam ejus cognitionem non involvit. Q.E.D.

DEMONSTRATION: For the idea of an affection of the human body (by proposition 27 of this) does not involve an adequate knowledge of that body nor adequately express its nature — that is (by proposition 13 of this) it does not agree adequately with the nature of the mind — and therefore (by axiom 6 of Part 1) the idea of this idea does not adequately express the nature of the human mind, or does not involve an adequate cognition of it. Q.E.D.

COROLLARIUM: Hinc sequitur mentem humanam quoties ex communi naturæ ordine res percipit, nec sui ipsius nec sui corporis nec corporum externorum adæquatam sed confusam tantum et mutilatam habere cognitionem. Nam mens se ipsam non cognoscit nisi quatenus ideas affectionum corporis percipit (per propositionem 23 hujus). Corpus autem suum (per propositionem 19 hujus) non percipit nisi per ipsas affectionum ideas per quas etiam tantum (per propositionem 26 hujus) corpora externa percipit atque adeo quatenus eas habet, nec sui ipsius (per propositionem 29 hujus) nec sui corporis (per propositionem 27 hujus) nec corporum externorum (per propositionem 25 hujus) habet adæquatam cognitionem sed tantum (per propositionem 28 hujus cum ejus scholio) mutilatam et confusam. Q.E.D.

COROLLARIUM: Hence it follows that the human mind, whenever it perceives things according to the common order of nature, has not an adequate cognition of itself nor of its body nor of external bodies, but only a confused and mutilated one. For the mind does not know itself except insofar as it perceives the ideas of the affections of the body (by proposition 23 of this work). And its body (by proposition 19 of this work) is perceived only through those same ideas of the affections by which likewise (by proposition 26 of this work) external bodies are perceived, and therefore insofar as it has those ideas it has neither an adequate cognition of itself (by proposition 29 of this work) nor of its body (by proposition 27 of this work) nor of external bodies (by proposition 25 of this work), but only a mutilated and confused one (by proposition 28 of this work with its scholium). Q.E.D.

SCHOLIUM: Dico expresse quod mens nec sui ipsius nec sui corporis nec corporum externorum adæquatam sed confusam tantum et mutilatam cognitionem habeat quoties ex communi naturæ ordine res percipit hoc est quoties externe, ex rerum nempe fortuito occursu, determinatur ad hoc vel illud contemplandum et non quoties interne, ex eo scilicet quod res plures simul contemplatur, determinatur ad earundem convenientias, differentias et oppugnantias intelligendum; quoties enim hoc vel alio modo interne disponitur, tum res clare et distincte contemplatur, ut infra ostendam.

SCHOLIUM: I say expressly that the mind has not an adequate but only a confused and mutilated cognition of itself, of its body, nor of external bodies whenever it perceives things from the common order of nature — that is, whenever externally, by the fortuitous occurrence of things, it is determined to contemplate this or that, and not whenever internally, namely because it is determined to understand the concordances, differences and oppositions of several things contemplated together; for whenever it is disposed internally in this or some other way, then the things are contemplated clearly and distinctly, as I shall show below.

PROPOSITIO XXX: Nos de duratione nostri corporis nullam nisi admodum inadæquatam cognitionem habere possumus.

PROPOSITIO 30: We can have no cognition of the duration of our body except a very inadequate one.

DEMONSTRATIO: Nostri corporis duratio ab ejus essentia non dependet (per axioma 1 hujus) nec etiam ab absoluta Dei natura (per propositionem 21 partis I). Sed (per propositionem 28 partis I) ad existendum et operandum determinatur a talibus causis quæ etiam ab aliis determinatæ sunt ad existendum et operandum certa ac determinata ratione et hæ iterum ab aliis et sic in infinitum. Nostri igitur corporis duratio a communi naturæ ordine et rerum constitutione pendet. Qua autem ratione constitutæ sint, ejus rei adæquata cognitio datur in Deo quatenus earum omnium ideas et non quatenus tantum humani corporis ideam habet (per corollarium propositionis 9 hujus); quare cognitio durationis nostri corporis est in Deo admodum inadæquata quatenus tantum naturam mentis humanæ constituere consideratur hoc est (per corollarium propositionis 11 hujus) hæc cognitio est in nostra mente admodum inadæquata.

DEMONSTRATION: The duration of our body does not depend on its essence (by axiom 1 of this) nor yet on the absolute nature of God (by proposition 21 of Part I). But (by proposition 28 of Part I) to exist and to act it is determined by such causes as are themselves determined by others to exist and to act in a certain and determinate way, and these again by others, and so into infinity. Therefore the duration of our body depends on the common order of nature and the constitution of things. In what manner these are constituted, an adequate cognition of that thing is given in God insofar as He has the ideas of all of them and not insofar as He has only the idea of the human body (by the corollary of proposition 9 of this); wherefore the cognition of the duration of our body is in God very inadequate insofar as it is considered only to constitute the nature of the human mind — that is (by the corollary of proposition 11 of this) this cognition is in our mind very inadequate.

Q.E.D.

Which was to be demonstrated.

PROPOSITIO XXXI: Nos de duratione rerum singularium quæ extra nos sunt, nullam nisi admodum inadæquatam cognitionem habere possumus.

PROPOSITIO 31: We can have no cognition of the duration of singular things which are outside us, except a very inadequate one.

DEMONSTRATIO: Unaquæque enim res singularis sicuti humanum corpus ab alia re singulari determinari debet ad existendum et operandum certa ac determinata ratione et hæc iterum ab alia et sic in infinitum (per propositionem 28 partis I). Cum autem ex hac communi rerum singularium proprietate in præcedenti propositione demonstraverimus nos de duratione nostri corporis non nisi admodum inadæquatam cognitionem habere, ergo hoc idem de rerum singularium duratione erit concludendum quod scilicet ejus non nisi admodum inadæquatam cognitionem habere possumus. Q.E.D.

DEMONSTRATION: For each singular thing, just as a human body, must be determined by another singular thing to exist and to act in a certain and determinate manner, and this again by another, and thus to infinity (by proposition 28 of part 1). And since from this common property of singular things we demonstrated in the preceding proposition that we have of the duration of our body no more than a very inadequate knowledge, therefore the same is to be concluded about the duration of singular things, namely that we can have of it no more than a very inadequate knowledge. Q.E.D.

COROLLARIUM: Hinc sequitur omnes res particulares contingentes et corruptibiles esse. Nam de earum duratione nullam adæquatam cognitionem habere possumus (per propositionem præcedentem) et hoc est id quod per rerum contingentiam et corruptionis possibilitatem nobis est intelligendum (vide scholium I propositionis 33 partis I). Nam (per propositionem 29 partis I) præter hoc nullum datur contingens.

COROLLARIUM: Hence it follows that all particular things are contingent and corruptible. For concerning their duration we can have no adequate cognition (by the preceding proposition), and this is what is to be understood by the contingency of things and the possibility of corruption (see scholium I of proposition 33 of part I). For (by proposition 29 of part I) no other contingent is given beyond this.

PROPOSITIO XXXII: Omnes ideæ quatenus ad Deum referuntur, veræ sunt.

PROPOSITION 32: All ideas, insofar as they are referred to God, are true.

DEMONSTRATIO: Omnes enim ideæ quæ in Deo sunt, cum suis ideatis omnino conveniunt (per corollarium propositionis 7 hujus) adeoque (per axioma 6 partis I) omnes veræ sunt. Q.E.D.

DEMONSTRATIO: For all ideas which are in God altogether coincide with their ideates (by the corollary of Proposition 7 of this), and therefore (by Axiom 6 of Part I) all are true. Q.E.D.

PROPOSITIO XXXIII: Nihil in ideis positivum est propter quod falsæ dicuntur.

PROPOSITIO 33: Nothing positive is in the ideas on account of which they are called false.

DEMONSTRATIO: Si negas, concipe si fieri potest, modum positivum cogitandi qui formam erroris sive falsitatis constituat. Hic cogitandi modus non potest esse in Deo (per propositionem præcedentem); extra Deum autem etiam nec esse nec concipi potest (per propositionem 15 partis I). Atque adeo nihil potest dari positivum in ideis propter quod falsæ dicuntur. Q.E.D.

DEMONSTRATIO: If you deny it, conceive, if it be possible, a positive mode of thinking that would constitute a form of error or falsity. This mode of thinking cannot be in God (by the preceding proposition); and outside God it likewise can neither be nor be conceived (by proposition 15 of part 1). And therefore nothing positive can be given in the ideas on account of which they are called false. Q.E.D.

PROPOSITIO XXXIV: Omnis idea quæ in nobis est absoluta sive adæquata et perfecta, vera est.

PROPOSITION 34: Every idea that is in us, absolute or adequate and perfect, is true.

DEMONSTRATIO: Cum dicimus dari in nobis ideam adæquatam et perfectam, nihil aliud dicimus (per corollarium propositionis 11 hujus) quam quod in Deo quatenus nostræ mentis essentiam constituit, detur idea adæquata et perfecta et consequenter (per propositionem 32 hujus) nihil aliud dicimus quam quod talis idea sit vera. Q.E.D.

DEMONSTRATIO: When we say that an adequate and perfect idea is given in us, we mean nothing else (by the corollary of proposition 11 of this) than that in God, insofar as he constitutes the essence of our mind, an adequate and perfect idea is given; and consequently (by proposition 32 of this) we mean nothing else than that such an idea is true. Q.E.D.

PROPOSITIO XXXV: Falsitas consistit in cognitionis privatione quam ideæ inadæquatæ sive mutilatæ et confusæ involvunt.

PROPOSITIO 35: Falsity consists in the privation of cognition which inadequate, or mutilated and confused, ideas involve.

DEMONSTRATIO: Nihil in ideis positivum datur quod falsitatis formam constituat (per propositionem 33 hujus); at falsitas in absoluta privatione consistere nequit (mentes enim, non corpora errare nec falli dicuntur) neque etiam in absoluta ignorantia; diversa enim sunt ignorare et errare; quare in cognitionis privatione quam rerum inadæquata cognitio sive ideæ inadæquatæ et confusæ involvunt, consistit. Q.E.D.

DEMONSTRATIO: Nothing positive is given in ideas that would constitute the form of falsity (by proposition 33 of this); but falsity cannot consist in absolute privation (for minds, not bodies, are said neither to err nor to be deceived) nor even in absolute ignorance; for to be ignorant and to err are distinct; therefore it consists in the privation of cognition which inadequate cognition of things, or inadequate and confused ideas, involve. Q.E.D.

SCHOLIUM: In scholio propositionis 17 hujus partis explicui qua ratione error in cognitionis privatione consistit sed ad uberiorem hujus rei explicationem exemplum dabo nempe falluntur homines quod se liberos esse putant, quæ opinio in hoc solo consistit quod suarum actionum sint conscii et ignari causarum a quibus determinantur. Hæc ergo est eorum libertatis idea quod suarum actionum nullam cognoscant causam. Nam quod aiunt humanas actiones a voluntate pendere, verba sunt quorum nullam habent ideam.

SCHOLIUM: In the scholium of proposition 17 of this part I have explained by what reasoning error consists in a privation of cognition, but for a more ample explication of this matter I will give an example, namely that men are deceived in thinking themselves free, an opinion which consists in this alone, that they are conscious of their own actions and ignorant of the causes by which those actions are determined. Thus the idea of their freedom is that they know no cause of their actions. For the words that human actions depend on the will are mere words which have no idea.

Quid enim voluntas sit et quomodo moveat corpus, ignorant omnes; qui aliud jactant et animæ sedes et habitacula fingunt, vel risum vel nauseam movere solent. Sic cum solem intuemur, eum ducentos circiter pedes a nobis distare imaginamur, qui error in hac sola imaginatione non consistit sed in eo quod dum ipsum sic imaginamur, veram ejus distantiam et hujus imaginationis causam ignoramus. Nam tametsi postea cognoscamus eundem ultra 600 terræ diametros a nobis distare, ipsum nihilominus prope adesse imaginabimur; non enim solem adeo propinquum imaginamur propterea quod veram ejus distantiam ignoramus sed propterea quod affectio nostri corporis essentiam solis involvit quatenus ipsum corpus ab eodem afficitur.

For all are ignorant what the will is and how it moves the body; those who fancy some other seat and habitations of the soul, or imagine that it moves laughter or nausea, are wont to err. Thus when we behold the sun, we imagine it to be about 200 feet distant from us; that error does not consist in this imagination alone but in that, while we so imagine it, we are ignorant of its true distance and of the cause of this imagination. For although afterwards we learn that it is more than 600 earth-diameters away from us, yet we shall nevertheless imagine it to be near; for we do not imagine the sun so near because we are ignorant of its true distance, but because an affection of our body involves the essence of the sun insofar as that body is affected by it.

PROPOSITIO XXXVI: Ideæ inadæquatæ et confusæ eadem necessitate consequuntur ac adæquatæ sive claræ ac distinctæ ideæ.

PROPOSITIO 36: Inadequate and confused ideæ follow with the same necessity as adequate, or clear and distinct, ideæ.

DEMONSTRATIO: Ideæ omnes in Deo sunt (per propositionem 15 partis I) et quatenus ad Deum referuntur, sunt veræ (per propositionem 32 hujus) et (per corollarium propositionis 7 hujus) adæquatæ adeoque nullæ inadæquatæ nec confusæ sunt nisi quatenus ad singularem alicujus mentem referuntur (qua de re vide propositiones 24 et 28 hujus) adeoque omnes tam adæquatæ quam inadæquatæ eadem necessitate (per corollarium propositionis 6 hujus) consequuntur. Q.E.D.

DEMONSTRATION: All ideas are in God (by proposition 15 of part 1) and insofar as they are referred to God they are true (by proposition 32 of this) and, by the corollary of proposition 7 of this, adequate; and therefore none are inadequate nor confused except insofar as they are referred to the singular mind of any person (concerning which see propositions 24 and 28 of this); and therefore all, both adequate and inadequate, follow with the same necessity (by the corollary of proposition 6 of this). Q.E.D.

PROPOSITIO XXXVII: Id quod omnibus commune (de his vide supra lemma 2) quodque æque in parte ac in toto est, nullius rei singularis essentiam constituit.

PROPOSITIO 37: That which is common to all (of these see above lemma 2) and which is equally in the part and in the whole, does not constitute the essence of any singular thing.

DEMONSTRATIO: Si negas, concipe si fieri potest, id essentiam alicujus rei singularis constituere nempe essentiam B. Ergo (per definitionem 2 hujus) id sine B non poterit esse neque concipi; atqui hoc est contra hypothesin : ergo id ad essentiam B non pertinet nec alterius rei singularis essentiam constituit. Q.E.D.

DEMONSTRATIO: If you deny, conceive, if it is possible, that this constitutes the essence of some singular thing, namely the essence B. Therefore (by definition 2 of this) this cannot be nor be conceived without B; yet this is contrary to the hypothesis: therefore this does not pertain to the essence B nor does it constitute the essence of any other singular thing. Q.E.D.

PROPOSITIO XXXVIII: Illa quæ omnibus communia quæque æque in parte ac in toto sunt, non possunt concipi nisi adæquate.

PROPOSITIO 38: Those things which are common to all and which are equally in part and in whole cannot be conceived except adequately.

DEMONSTRATIO: Sit A aliquid quod omnibus corporibus commune quodque æque in parte cujuscunque corporis ac in toto est. Dico A non posse concipi nisi adæquate. Nam ejus idea (per corollarium propositionis 7 hujus) erit necessario in Deo adæquata tam quatenus ideam corporis humani quam quatenus ideas habet ejusdem affectionum quæ (per propositiones 16, 25 et 27 hujus) tam corporis humani quam corporum externorum naturam ex parte involvunt hoc est (per propositiones 12 et 13 hujus) hæc idea erit necessario in Deo adæquata quatenus mentem humanam constituit sive quatenus ideas habet quæ in mente humana sunt; mens igitur (per corollarium propositionis 11 hujus) A necessario adæquate percipit idque tam quatenus se quam quatenus suum vel quodcunque externum corpus percipit nec A alio modo potest concipi.

DEMONSTRATIO: Let A be something common to all bodies and equally present in a part of any body and in the whole. I say that A cannot be conceived except adequately. For its idea (by the corollary of proposition 7 of this work) will necessarily be in God adequately, both insofar as he has the idea of the human body and insofar as he has the ideas of the same affections which (by propositions 16, 25 and 27 of this work) in part involve the nature of both the human body and external bodies — that is (by propositions 12 and 13 of this work) this idea will necessarily be in God adequate insofar as he constitutes the human mind or insofar as he has the ideas which are in the human mind; the mind therefore (by the corollary of proposition 11 of this work) necessarily perceives A adequately, and perceives it both insofar as itself and insofar as its own or any external body perceives; nor can A be conceived otherwise.

Q.E.D.

Which was to be demonstrated.

COROLLARIUM: Hinc sequitur dari quasdam ideas sive notiones omnibus hominibus communes. Nam (per lemma 2) omnia corpora in quibusdam conveniunt, quæ (per propositionem præcedentem) ab omnibus debent adæquate sive clare et distincte percipi.

COROLLARIUM: Hence it follows that certain ideas or notions are given common to all men. For (per lemma 2) all bodies agree in certain respects, which (per the preceding proposition) ought to be perceived by all adequately, that is, clearly and distinctly.

PROPOSITIO XXXIX: Id quod corpori humano et quibusdam corporibus externis a quibus corpus humanum affici solet, commune est et proprium quodque in cujuscunque horum parte æque ac in toto est, ejus etiam idea erit in mente adæquata.

PROPOSITIO 39: That which to the human body and to certain external bodies by which the human body is wont to be affected is common, both what is common and what is proper in any part of each of these, equally as in the whole, its idea will also be in the adequate mind.

DEMONSTRATIO: Sit A id quod corpori humano et quibusdam corporibus externis commune est et proprium quodque æque in humano corpore ac in iisdem corporibus externis et quod denique æque in cujuscunque corporis externi parte ac in toto est. Ipsius A dabitur in Deo idea adæquata (per corollarium propositionis 7 hujus) tam quatenus ideam corporis humani quam quatenus positorum corporum externorum ideas habet. Ponatur jam humanum corpus a corpore externo affici per id quod cum eo habet commune hoc est ab A; hujus affectionis idea proprietatem A involvet (per propositionem 16 hujus) atque adeo (per idem corollarium propositionis 7 hujus) idea hujus affectionis quatenus proprietatem A involvit, erit in Deo adæquata quatenus idea corporis humani affectus est hoc est (per propositionem 13 hujus) quatenus mentis humanæ naturam constituit adeoque (per corollarium propositionis 11 hujus) hæc idea est etiam in mente humana adæquata.

DEMONSTRATIO: Let A be that which is common to and proper of the human body and of certain external bodies, equally in the human body and in those same external bodies, and which finally is equally in any part of an external body as in the whole. The idea of A itself will be given in God adequately (by the corollary of proposition 7 of this) both insofar as he has the idea of the human body and insofar as he has the ideas of the posited external bodies. Now suppose the human body is affected by an external body through that which it has in common with it, that is, by A; the idea of this affection will involve the property A (by proposition 16 of this) and therefore (by the same corollary of proposition 7 of this) the idea of this affection insofar as it involves the property A will be in God adequate insofar as the idea of the affection of the human body is—that is (by proposition 13 of this) insofar as it constitutes the nature of the human mind—and consequently (by the corollary of proposition 11 of this) this idea is also in the human mind adequate.

Q.E.D.

Which was to be demonstrated.

COROLLARIUM: Hinc sequitur quod mens eo aptior est ad plura adæquate percipiendum quo ejus corpus plura habet cum aliis corporibus communia.

COROLLARIUM: Hence it follows that the mind is the more apt to perceive many things adequately, the more its body has in common with other bodies.

PROPOSITIO XL: Quæcunque ideæ in mente sequuntur ex ideis quæ in ipsa sunt adæquatæ, sunt etiam adæquatæ.

PROPOSITIO 40: Whatever ideas in the mind follow from ideas which in it are adequate, 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.

DEMONSTRATIO: It is clear. For when we say that an idea in the human mind follows from ideas which are adequate in it, we say nothing else (by the corollary of proposition 11 of this) than that in the divine intellect itself there is given an idea of which God is the cause, not insofar as He is infinite nor insofar as He is affected by ideas of very many singular things, but insofar as He alone 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.

SCHOLIUM I: By these I have explained the cause of the notions which are called common and which are the foundations of our reasoning. But other causes of certain axioms or notions are given which it would be fitting to explain by this our method; from these, for it would be plain which notions are more useful than the rest, and which indeed would scarcely be of any use. Then which commons, and which are clear and distinct only to those who are not burdened with prejudices, and which finally are ill‑founded.

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.

Moreover it would be evident whence those notions which they call secondary, and consequently the axioms founded on them, derived their origin, and other matters about these which I have sometimes contemplated. But since I have devoted these to another tract and also, lest through excessive prolixity of this matter I create weariness, I have resolved to omit this here. Nevertheless, lest I leave out anything of these that is necessary to know, I will briefly add the causes from which the so-called transcendental terms have taken their origin, as 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.

These terms arise from this: namely, that the human body, since it is limited, is only capable of forming within itself a certain number of distinct images at once (what an image is I explained in the scholium to proposition 17 of this), which, if exceeded, these images will begin to be confused; and if the number of images which the body is capable of forming simultaneously be far exceeded, they will all plainly become confounded with one another. Since this is so, it is clear from the corollary of proposition 17 and from proposition 18 of this work that the human mind will be able to imagine distinctly as many bodies at once as images can be formed simultaneously in its body. But where images in the body are plainly confused, the mind will also imagine all bodies confusedly without any distinction, and will as it were comprehend them under one attribute, namely under the attribute of being, of thing, 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.

This can also be deduced from the fact that images do not always equally prevail, and from other analogous causes which it is not necessary to explain here; for to our aim it suffices to consider only one. For all things return to this: that these terms — ideas — signify things confused to the highest degree. From similar causes, moreover, arose those notions which they call universals, such as 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.

namely because in the human body so many images, for example of men, are formed simultaneously that the power of imagining, not entirely but yet so far remains, cannot imagine the small differences of each (namely each one’s colour, size, etc.) and their determinate number, and can only imagine that in which all, insofar as the body is affected by them, agree, distinctly—for the body was especially affected by that one singular and on that account signifies “man,” and predicates this of the innumerable singulars. For, as we have said, it cannot imagine a determinate number of singulars. But it should be noted that these notions are not formed in all in the same way, but vary in each person according to the thing by which the body has been more often affected, and which the mind more readily imagines or recalls.

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.

For example, those who have oftentimes contemplated with admiration the stature of men, under the name "man" will understand an animal of erect stature; but those who are accustomed to contemplate other things will form another common image of men, namely that man is a risible animal, a bipedal animal without feathers, a rational animal; and thus each one, according to the disposition of his body, will form the universal images of things. Therefore it is not wonderful that among philosophers who wished to explain natural things by mere images there should have arisen so many controversies.

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.

SCHOLIUM II: From all the foregoing it clearly appears that we form many perceptions and universal notions 1° from singulars presented to the intellect by the senses, mutilated, confused, and without order (see corollary of proposition 29 of this), and therefore I have been wont to call such perceptions a cognition derived from vague experience. 2° from signs, for example from the fact that by hearing or reading certain words we recall things and form certain ideas similar to those by which we imagine the things (see scholium of proposition 18 of this). I will call each of these two modes of contemplating things a cognition of the first kind, an opinion or imagination afterward. 3° finally from the fact that we have common notions and adequate ideas of the properties of things (see corollary of proposition 38 and proposition 39 with its corollary and proposition 40 of this), and I will call this reason and a cognition of the second kind.

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.

Besides these two genera of cognition there is given, as I shall show in what follows, a third other which we shall call intuitive science. And this kind of knowing proceeds from an adequate idea of the formal essence of certain attributes of God to an adequate cognition of the essences of things. I will explain all these by the example of one thing.

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.

Given, for example, three numbers to obtain a fourth which shall be to the third as the second to the first. Merchants do not hesitate to carry the second into the third and divide the product by the first, because, namely, those things which they heard from the master without any demonstration have not yet been surrendered to oblivion, or because they have often experienced it in the simplest numbers, or by the force of the demonstration of Proposition 19 of Book 7 of Euclid, namely from the common property of proportionals. But in the simplest numbers none of these is necessary.

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.

For example, with the numbers 1, 2, 3 given, everyone sees that the fourth proportional number is 6, and this all the more clearly because from the very ratio which the first has to the second we see with a single intuition, we infer that very fourth.

PROPOSITIO XLI: Cognitio primi generis unica est falsitatis causa, secundi autem et tertii est necessario vera.

PROPOSITION 41: Knowledge of the first kind alone is a cause of falsity, whereas that of the second and third is necessarily true.

DEMONSTRATIO: Ad primi generis cognitionem illas omnes ideas diximus in præcedenti scholio pertinere quæ sunt inadæquatæ et confusæ atque adeo (per propositionem 35 hujus) hæc cognitio unica est falsitatis causa. Deinde ad cognitionem secundi et tertii illas pertinere diximus quæ sunt adæquatæ adeoque (per propositionem 34 hujus) est necessario vera. Q.E.D.

DEMONSTRATIO: To the cognition of the first kind we said that all those ideas mentioned in the preceding scholium pertain which are inadequate and confused, and therefore (by proposition 35 of this) this cognition alone is the cause of falsity. Then to the cognition of the second and third we said those pertain which are adequate and therefore (by proposition 34 of this) are necessarily true. Q.E.D.

PROPOSITIO XLII: Secundi et tertii et non primi generis cognitio docet nos verum a falso distinguere.

PROPOSITIO 42: The cognition of the second and third, and not of the first, kind teaches us to distinguish the true from the false.

DEMONSTRATIO: Hæc propositio per se patet. Qui enim inter verum et falsum scit distinguere, debet adæquatam veri et falsi habere ideam hoc est (per II scholium propositionis 40 hujus) verum et falsum secundo aut tertio cognitionis genere cognoscere.

DEMONSTRATION: This proposition is evident in itself. For he who knows how to distinguish between the true and the false ought to have an adequate idea of truth and falsity, that is (per 2 scholium of this proposition 40) to know the true and the false by the second or third kind of cognition.

PROPOSITIO XLIII: Qui veram habet ideam, simul scit se veram habere ideam nec de rei veritate potest dubitare.

PROPOSITIO 43: He who has a true idea simultaneously knows that he has a true idea, nor can he doubt concerning the truth of the thing.

DEMONSTRATIO: Idea vera in nobis est illa quæ in Deo quatenus per naturam mentis humanæ explicatur, est adæquata (per corollarium propositionis 11 hujus). Ponamus itaque dari in Deo quatenus per naturam mentis humanæ explicatur, ideam adæquatam A. Hujus ideæ debet necessario dari etiam in Deo idea quæ ad Deum eodem modo refertur ac idea A (per propositionem 20 hujus cujus demonstratio universalis est). At idea A ad Deum referri supponitur quatenus per naturam mentis humanæ explicatur; ergo etiam idea ideæ A ad Deum eodem modo debet referri hoc est (per idem corollarium propositionis 11 hujus) hæc adæquata idea ideæ A erit in ipsa mente quæ ideam adæquatam A habet adeoque qui adæquatam habet ideam sive (per propositionem 34 hujus) qui vere rem cognoscit, debet simul suæ cognitionis adæquatam habere ideam sive veram cognitionem hoc est (ut per se manifestum) debet simul esse certus. Q.E.D.

DEMONSTRATIO: The true idea in us is that which, insofar as it is explained in God through the nature of the human mind, is adequate (by the corollary of proposition 11 of this work). Let us therefore suppose given in God, insofar as it is explained through the nature of the human mind, an adequate idea A. Of this idea there must necessarily be given in God also an idea which refers to God in the same way as idea A (by proposition 20 of this work, whose demonstration is universal). But idea A is supposed to be referred to God insofar as it is explained through the nature of the human mind; therefore the idea of idea A must also be referred to God in the same way, that is (by the same corollary of proposition 11 of this work) this adequate idea of the idea A will be in the very mind which has the adequate idea A; and therefore he who has an adequate idea, or (by proposition 34 of this work) who truly knows the thing, must at the same time have an idea adequate to his cognition, or a true cognition, that is (as self-evident) he must at the same time be certain. Q.E.D.

SCHOLIUM: In scholio propositionis 21 hujus partis explicui quid sit idea ideæ sed notandum præcedentem propositionem per se satis esse manifestam. Nam nemo qui veram habet ideam, ignorat veram ideam summam certitudinem involvere; veram namque habere ideam nihil aliud significat quam perfecte sive optime rem cognoscere nec sane aliquis de hac re dubitare potest nisi putet ideam quid mutum instar picturæ in tabula et non modum cogitandi esse nempe ipsum intelligere et quæso quis scire potest se rem aliquam intelligere nisi prius rem intelligat? hoc est quis potest scire se de aliqua re certum esse nisi prius de ea re certus sit?

SCHOLIUM: In the scholium of proposition 21 of this part I have explained what the idea of an idea is, but it must be noted that the preceding proposition is by itself sufficiently manifest. For no one who has a true idea is unaware that a true idea involves the highest certainty; for to have a true idea signifies nothing other than to know the thing perfectly or best, and certainly no one can doubt this unless he thinks the idea to be something mute, like a picture on a panel, and not a mode of thinking, namely the very act of understanding; and I ask, who can know that he understands some thing unless first he understands the thing? That is, who can know that he is certain about any thing unless first he is certain about that thing?

Deinde quid idea vera clarius et certius dari potest quod norma sit veritatis? Sane sicut lux seipsam et tenebras manifestat, sic veritas norma sui et falsi est. Atque his me ad has quæstiones respondisse puto nempe si idea vera quatenus tantum dicitur cum suo ideato convenire, a falsa distinguitur, nihil ergo realitatis aut perfectionis idea vera habet præ falsa (quandoquidem per solam denominationem extrinsecam distinguuntur) et consequenter neque etiam homo qui veras præ illo qui falsas tantum ideas habet?

Moreover, how can it be given more clearly and more certainly that the true idea is the norm of truth? Indeed, just as light discloses itself and darkness, so truth is the norma of itself and of the false. And by these things I think I have replied to these questions, namely: if a true idea is said only insofar as it agrees with its ideatum, and thereby is distinguished from a false one, then the true idea has no greater reality or perfection than the false (since they are distinguished by mere extrinsic denomination), and consequently neither is the man who has true ideas superior to him who has only false ideas?

Deinde unde fit ut homines falsas habeant ideas? Et denique unde aliquis certo scire potest se ideas habere quæ cum suis ideatis conveniant? Ad has inquam quæstiones me jam respondisse puto.

Then whence comes it that men have false ideas? And finally, how can anyone know for certain that he has ideas which agree with their ideata? To these questions, I say, I think I have already replied.

Nam quod ad differentiam inter ideam veram et falsam attinet, constat ex propositione 35 hujus illam ad hanc sese habere ut ens ad non-ens. Falsitatis autem causas a propositione 19 usque ad 35 cum ejus scholio clarissime ostendi. Ex quibus etiam apparet quid homo qui veras habet ideas, homini qui non nisi falsas habet, intersit.

For as to the difference between a true idea and a false one, it is established from proposition 35 of this work that the former stands to the latter as being to non-being. The causes of falsity, however, from proposition 19 through 35, together with its scholium, have been shown most clearly. From these things it also appears what difference there is between a man who has true ideas and a man who has only false ones.

Quod denique ultimum attinet nempe undenam homo scire potest se habere ideam quæ cum suo ideato conveniat, id modo satis superque ostendi ex hoc solo oriri quod ideam habet quæ cum suo ideato convenit sive quod veritas sui sit norma. His adde quod mens nostra quatenus res vere percipit, pars est infiniti Dei intellectus (per corollarium propositionis 11 hujus) adeoque tam necesse est ut mentis claræ et distinctæ ideæ veræ sint ac Dei ideæ.

Finally, as to the last point, namely whence a man can know that he has an idea which agrees with its ideatum, this has been shown now sufficiently and more than sufficiently to arise from this alone: that he has an idea which agrees with its ideatum, or that the truth of himself is the norm. Add to these that our mind, insofar as it truly perceives things, is a part of the infinite intellect of God (by the corollary of proposition 11 of this), and therefore it is as necessary that the mind’s clear and distinct ideas be true as that God’s ideas are.

PROPOSITIO XLIV: De natura rationis non est res ut contingentes sed ut necessarias contemplari.

PROPOSITION 44: Concerning the nature of reason, it is not to be contemplated as a thing of contingents but as one of necessities.

DEMONSTRATIO: De natura rationis est res vere percipere (per propositionem 41 hujus) nempe (per axioma 6 partis I) ut in se sunt hoc est (per propositionem 29 partis I) non ut contingentes sed ut necessarias. Q.E.D.

DEMONSTRATION: To the nature of reason belongs to perceive a thing truly (by proposition 41 of this), namely (by axiom 6 of Part I) that they are in themselves — that is (by proposition 29 of Part I) not as contingent but as necessary. Q.E.D.

COROLLARIUM I: Hinc sequitur a sola imaginatione pendere quod res tam respectu præteriti quam futuri ut contingentes contemplemur.

COROLLARY 1: Hence it follows that from imagination alone depends that we contemplate things as contingent both with respect to the past and with respect to the future.

SCHOLIUM: Qua autem ratione hoc fiat paucis explicabo. Ostendimus supra (propositione 17 hujus cum ejus corollario) mentem, quamvis res non existant, eas tamen semper ut sibi præsentes imaginari nisi causæ occurrant quæ earum præsentem existentiam secludant. Deinde (propositione 18 hujus) ostendimus quod si corpus humanum semel a duobus corporibus externis simul affectum fuit, ubi mens postea eorum alterutrum imaginabitur, statim et alterius recordabitur hoc est ambo ut sibi præsentia contemplabitur nisi causæ occurrant quæ eorum præsentem existentiam secludant.

SCHOLIUM: By what manner this is done I will explain in few words. We showed above (proposition 17 of this with its corollary) that the mind, although the things do not exist, nevertheless always imagines them as present to itself unless causes occur which exclude their present existence. Then (proposition 18 of this) we showed that if the human body once was affected simultaneously by two external bodies, when the mind afterwards will imagine either one of them, immediately it will remember the other — that is, both will be contemplated as present to it unless causes occur which exclude their present existence.

Præterea nemo dubitat quin etiam tempus imaginemur nempe ex eo quod corpora alia aliis tardius vel celerius vel æque celeriter moveri imaginemur. Ponamus itaque puerum qui heri prima vice hora matutina viderit Petrum, meridiana autem Paulum et vespertina Simeonem atque hodie iterum matutina hora Petrum. Ex propositione 18 hujus patet quod simulac matutinam lucem videt, illico solem eandem cæli quam die præcedenti viderit partem percurrentem sive diem integrum et simul cum tempore matutino Petrum, cum meridiano autem Paulum et cum vespertino Simeonem imaginabitur hoc est Pauli et Simeonis existentiam cum relatione ad futurum tempus imaginabitur et contra si hora vespertina Simeonem videat, Paulum et Petrum ad tempus præteritum referet, eosdem scilicet simul cum tempore præterito imaginando atque hæc eo constantius quo sæpius eos eodem hoc ordine viderit.

Moreover no one doubts that we also imagine time, namely from the fact that we imagine other bodies to move more slowly or more quickly or equally quickly relative to other bodies. Let us suppose, then, a boy who yesterday at the first morning hour saw Peter, at the midday hour Paul, and at the evening hour Simeon, and who today again at the morning hour sees Peter. From proposition 18 of this work it is clear that as soon as he sees the morning light, immediately he will imagine the same sun of the sky which he saw on the preceding day passing through its part, or the whole day, and together with the morning time he will imagine Peter, with the midday time Paul, and with the evening time Simeon — that is, he will imagine the existences of Paul and Simeon with relation to future time — and conversely, if he sees Simeon at the evening hour, he will refer Paul and Peter to past time, imagining them together with past time; and this will be the more constant the more often he has seen them in that same order.

Quod si aliquando contingat ut alia quadam vespera loco Simeonis Jacobum videat, tum sequenti mane cum tempore vespertino jam Simeonem jam Jacobum, non vero ambos simul imaginabitur. Nam alterutrum tantum, non autem ambos simul tempore vespertino vidisse supponitur. Fluctuabitur itaque ejus imaginatio et cum futuro tempore vespertino jam hunc jam illum imaginabitur hoc est neutrum certo sed utrumque contingenter futurum contemplabitur.

If it should ever happen that on some evening, in the place of Simeon, he sees Jacob, then the following morning, with the evening-time, he will imagine now Simeon, now Jacob, not however both at once. For it is supposed that he saw only one or the other, not both together at the evening hour. Thus his imagination will waver, and with the future evening-time he will imagine now this one, now that one — that is, neither certainly but each contingently future will be contemplated.

Atque hæc imaginationis fluctuatio eadem erit si imaginatio rerum sit quas eodem modo cum relatione ad tempus præteritum vel præsens contemplamur et consequenter res tam ad tempus præsens quam ad præteritum vel futurum relatas ut contingentes imaginabimur.

And this fluctuation of imagination will be the same if the imagination is of things which we contemplate in the same way with relation to past or present time, and consequently we shall imagine the things as related both to present time and to the past or to the future, as contingent.

COROLLARIUM II: De natura rationis est res sub quadam æternitatis specie percipere.

COROLLARIUM 2: It is of the nature of reason to perceive a thing under a certain species of eternity.

DEMONSTRATIO: De natura enim rationis est res ut necessarias et non ut contingentes contemplari (per propositionem præcedentem). Hanc autem rerum necessitatem (per propositionem 41 hujus) vere hoc est (per axioma 6 partis I) ut in se est, percipit. Sed (per propositionem 16 partis I) hæc rerum necessitas est ipsa Dei æternæ naturæ necessitas; ergo de natura rationis est res sub hac æternitatis specie contemplari. Adde quod fundamenta rationis notiones sint (per propositionem 38 hujus) quæ illa explicant quæ omnibus communia sunt quæque (per propositionem 37 hujus) nullius rei singularis essentiam explicant quæque propterea absque ulla temporis relatione sed sub quadam æternitatis specie debent concipi.

DEMONSTRATIO: For it is of the nature of reason to contemplate things as necessary and not as contingent (by the preceding proposition). Now this necessity of things (by proposition 41 of this) is truly, that is (by axiom 6 of Part 1), perceived as in itself. But (by proposition 16 of Part 1) this necessity of things is the very necessity of God’s eternal nature; therefore it is of the nature of reason to contemplate a thing under this species of eternity. Add that the foundations of reason are notions (by proposition 38 of this) which explain those things common to all, and which (by proposition 37 of this) explain the essence of no singular thing, and which therefore must be conceived without any relation to time but under a certain species of eternity.

Q.E.D.

WHICH WAS TO BE DEMONSTRATED.

PROPOSITIO XLV: Unaquæque cujuscunque corporis vel rei singularis actu existentis idea Dei æternam et infinitam essentiam necessario involvit.

PROPOSITION 45: Each and every idea of any body or singular thing actually existing necessarily involves the eternal and infinite essence of God.

DEMONSTRATIO: Idea rei singularis actu existentis ipsius rei tam essentiam quam existentiam necessario involvit (per corollarium propositionis 8 hujus). At res singulares (per propositionem 15 partis I) non possunt sine Deo concipi sed quia (per propositionem 6 hujus) Deum pro causa habent quatenus sub attributo consideratur cujus res ipsæ modi sunt, debent necessario earum ideæ (per axioma 4 partis I) ipsarum attributi conceptum hoc est (per definitionem 6 partis I) Dei æternam et infinitam essentiam involvere. Q.E.D.

DEMONSTRATIO: The idea of a singular thing actually existing involves necessarily both the essence and the existence of that thing itself (by the corollary of proposition 8 of this). But singular things (by proposition 15 of part 1) cannot be conceived without God; and because (by proposition 6 of this) they have God as a cause insofar as He is considered under the attribute of which those things are modes, their ideas must necessarily (by axiom 4 of part 1) involve the concept of that very attribute, that is (by definition 6 of part 1) God's eternal and infinite essence. Q.E.D.

SCHOLIUM: Hic per existentiam non intelligo durationem hoc est existentiam quatenus abstracte concipitur et tanquam quædam quantitatis species. Nam loquor de ipsa natura existentiæ quæ rebus singularibus tribuitur propterea quod ex æterna necessitate Dei naturæ infinita infinitis modis sequuntur (vide propositionem 16 partis I). Loquor inquam de ipsa existentia rerum singularium quatenus in Deo sunt. Nam etsi unaquæque ab alia re singulari determinetur ad certo modo existendum, vis tamen qua unaquæque in existendo perseverat, ex æterna necessitate naturæ Dei sequitur.

SCHOLIUM: By existence here I do not mean duration, that is, existence insofar as it is abstractly conceived and as a kind of quantity. For I speak of the very nature of existence that is attributed to singular things because from the eternal necessity of God’s infinite nature they follow in infinite modes (see proposition 16 of Part I). I say, then, that I speak of the very existence of singular things insofar as they are in God. For even though each thing is determined by another singular thing to exist in a certain way, the power by which each perseveres in existing follows from the eternal necessity of God’s nature.

Qua de re vide corollarium propositionis 24 partis I.

On this matter see the corollary of Proposition 24 of Part I.

PROPOSITIO XLVI: Cognitio æternæ et infinitæ essentiæ Dei quam unaquæque idea involvit, est adæquata et perfecta.

PROPOSITION 46: The knowledge of the eternal and infinite essence of God which each idea involves is adequate and perfect.

DEMONSTRATIO: Demonstratio præcedentis propositionis universalis est et sive res ut pars sive ut totum consideretur, ejus idea sive totius sit sive partis (per propositionem præcedentem) Dei æternam et infinitam essentiam involvet. Quare id quod cognitionem æternæ et infinitæ essentiæ Dei dat, omnibus commune et æque in parte ac in toto est adeoque (per propositionem 38 hujus) erit hæc cognitio adæquata. Q.E.D.

DEMONSTRATION: The demonstration of the preceding proposition is universal, and whether a thing is considered as part or as whole, its idea, whether of the whole or of the part (by the preceding proposition), will involve God's eternal and infinite essence. Therefore that which gives the cognition of God's eternal and infinite essence is common to all and equally in part and in whole, and consequently (by proposition 38 of this) this cognition will be adequate. Q.E.D.

PROPOSITIO XLVII : Mens humana adæquatam habet cognitionem æternæ et infinitæ essentiæ Dei.

PROPOSITION 47 : The human mind has an adequate cognition of the eternal and infinite essence of God.

DEMONSTRATIO: Mens humana ideas habet (per propositionem 22 hujus) ex quibus (per propositionem 23 hujus) se suumque corpus (per propositionem 19 hujus) et (per corollarium I propositionis 16 et per propositionem 17 hujus) corpora externa ut actu existentia percipit adeoque (per propositiones 45 et 46 hujus) cognitionem æternæ et infinitæ essentiæ Dei habet adæquatam. Q.E.D.

DEMONSTRATIO: The human mind has ideas (by proposition 22 of this), from which (by proposition 23 of this) it perceives itself and its body (by proposition 19 of this) and (by corollary 1 of proposition 16 and by proposition 17 of this) external bodies as existing in act, and therefore (by propositions 45 and 46 of this) has an adequate cognition of the eternal and infinite essence of God. Q.E.D.

SCHOLIUM: Hinc videmus Dei infinitam essentiam ejusque æternitatem omnibus esse notam. Cum autem omnia in Deo sint et per Deum concipiantur, sequitur nos ex cognitione hac plurima posse deducere quæ adæquate cognoscamus atque adeo tertium illud cognitionis genus formare de quo diximus in scholio II propositionis 40 hujus partis et de cujus præstantia et utilitate in quinta parte erit nobis dicendi locus. Quod autem homines non æque claram Dei ac notionum communium habeant cognitionem, inde fit quod Deum imaginari nequeant ut corpora et quod nomen "Deus" junxerunt imaginibus rerum quas videre solent; quod homines vix vitare possunt quia continuo a corporibus externis afficiuntur.

SCHOLIUM: From this we see that God's infinite essence and his eternity are known to all. And since all things are in God and are conceived through God, it follows that from this knowledge we can deduce very many things which we adequately know and thus form that third kind of knowledge of which we spoke in scholium II of proposition 40 of this part, and concerning whose excellence and usefulness we shall have occasion to speak in the fifth part. But that men do not have an equally clear knowledge of God as of common notions comes from the fact that they cannot imagine God as a body and that the name "Deus" they have joined to images of things which they are accustomed to see; which men can hardly avoid because they are continually affected by external bodies.

Et profecto plerique errores in hoc solo consistunt quod scilicet nomina rebus non recte applicamus. Cum enim aliquis ait lineas quæ ex centro circuli ad ejusdem circumferentiam ducuntur esse inæquales, ille sane aliud tum saltem per circulum intelligit quam mathematici. Sic cum homines in calculo errant, alios numeros in mente, alios in charta habent.

And indeed most errors consist in this alone, namely that we do not correctly apply names to things. For when someone says that the lines which are drawn from the center of a circle to its circumference are unequal, he certainly then at least understands by "circle" something different from what mathematicians do. Thus when men err in calculation, they have one set of numbers in the mind and another upon the paper.

Quare si ipsorum mentem spectes, non errant sane; videntur tamen errare quia ipsos in mente putamus habere numeros qui in charta sunt. Si hoc non esset, nihil eosdem errare crederemus; ut non credidi quendam errare quem nuper audivi clamantem suum atrium volasse in gallinam vicini quia scilicet ipsius mens satis perspecta mihi videbatur. Atque hinc pleræque oriuntur controversiæ nempe quia homines mentem suam non recte explicant vel quia alterius mentem male interpretantur.

Therefore, if you regard their very mind, they certainly do not err; yet they appear to err because we suppose them to have in mind the numbers that are on the paper. If this were not so, we would deem them to err in nothing; as I did not think that a certain man erred whom I lately heard crying that his neighbor’s hen had flown into his atrium, since his mind seemed to me sufficiently clear. And from this most controversies spring up, namely because men do not properly explain their mind or because they badly interpret another’s mind.

Nam revera dum sibi maxime contradicunt, vel eadem vel diversa cogitant ita ut quos in alio errores et absurda esse putant, non sint.

For in truth, while they most contradict themselves, they think either the same things or different things, so that those things which they deem errors and absurdities in another are not.

PROPOSITIO XLVIII: In mente nulla est absoluta sive libera voluntas sed mens ad hoc vel illud volendum determinatur a causa quæ etiam ab alia determinata est et hæc iterum ab alia et sic in infinitum.

PROPOSITION 48: In the mind there is no absolute or free will, but the mind is determined to will this or that by a cause which is likewise determined by another, and this again by another, and so on to infinity.

DEMONSTRATIO: Mens certus et determinatus modus cogitandi est (per propositionem 11 hujus) adeoque (per corollarium II propositionis 17 partis I) suarum actionum non potest esse causa libera sive absolutam facultatem volendi et nolendi habere non potest sed ad hoc vel illud volendum (per propositionem 28 partis I) determinari debet a causa quæ etiam ab alia determinata est et hæc iterum ab alia etc. Q.E.D.

DEMONSTRATIO: The mind is a certain and determined mode of thinking (by proposition 11 of this) and therefore (by corollary 2 of proposition 17 of Part 1) cannot be the cause of its actions; it cannot have a free or absolute faculty of willing and not willing, but to will this or that (by proposition 28 of Part 1) it must be determined by a cause which is itself determined by another, and this again by another, etc. Q.E.D.

SCHOLIUM: Eodem hoc modo demonstratur in mente nullam dari facultatem absolutam intelligendi, cupiendi, amandi etc. Unde sequitur has et similes facultates vel prorsus fictitias vel nihil esse præter entia metaphysica vel universalia quæ ex particularibus formare solemus. Adeo ut intellectus et voluntas ad hanc et illam ideam vel ad hanc et illam volitionem eodem modo sese habeant ac lapideitas ad hunc et illum lapidem vel ut homo ad Petrum et Paulum.

SCHOLIUM: In the same way it is demonstrated that in the mind no absolute faculty of understanding, desiring, loving, etc., is given. Whence it follows that these and similar faculties are either altogether fictitious or are nothing besides metaphysical beings or universals which we are wont to form out of particulars. So that intellect and will stand toward this or that idea, or toward this or that volition, in the same manner as lapidity stands toward this or that stone, or as a man toward Peter and Paul.

Causam autem cur homines se liberos esse putent explicuimus in appendice partis primæ. Verum antequam ulterius pergam, venit hic notandum me per voluntatem affirmandi et negandi facultatem, non autem cupiditatem intelligere; facultatem inquam intelligo qua mens quid verum quidve falsum sit, affirmat vel negat et non cupiditatem qua mens res appetit vel aversatur. At postquam demonstravimus has facultates notiones esse universales quæ a singularibus ex quibus easdem formamus, non distinguuntur, inquirendum jam est an ipsæ volitiones aliquid sint præter ipsas rerum ideas. Inquirendum inquam est an in mente alia affirmatio et negatio detur præter illam quam idea quatenus idea est, involvit, qua de re vide sequentem propositionem ut et demonstrationem 3 hujus ne cogitatio in picturas incidat.

We have explained in the appendix of part 1 the reason why men think themselves to be free. But before I proceed further, it must be noted here that by voluntas I mean the faculty of affirming and denying, not cupiditas; by faculty I mean that whereby the mind affirms or denies what is true or false, and not the desire whereby the mind appetites or shuns things. Now after we have shown that these faculties are universal notions, which are not distinguished from the singulars out of which we form the same, it remains to be inquired whether the volitions themselves are anything beyond the very ideas of things. I say it must be inquired whether there is in the mind any affirmation and negation besides that which the idea, insofar as it is an idea, involves — on which matter see the following proposition and demonstration 3 of this, lest thought fall into pictures.

Non enim per ideas imagines quales in fundo oculi et si placet, in medio cerebro formantur sed cogitationis conceptus intelligo.

For I do not mean ideas as images, such as are formed on the back of the eye and, if you please, in the middle of the brain, but I mean the concepts of cogitation (conceptus of thought).

PROPOSITIO XLIX: In mente nulla datur volitio sive affirmatio et negatio præter illam quam idea quatenus idea est, involvit.

PROPOSITIO 49: In the mind no volition, whether affirmation or negation, is given except that which an idea, insofar as an idea, involves.

DEMONSTRATIO: In mente (per propositionem præcedentem) nulla datur absoluta facultas volendi et nolendi sed tantum singulares volitiones nempe hæc et illa affirmatio et hæc et illa negatio. Concipiamus itaque singularem aliquam volitionem nempe modum cogitandi quo mens affirmat tres angulos trianguli æquales esse duobus rectis. Hæc affirmatio conceptum sive ideam trianguli involvit hoc est sine idea trianguli non potest concipi.

DEMONSTRATIO: In the mind (by the preceding proposition) no absolute faculty of willing and not-willing is given, but only singular volitions, namely this and that affirmation and this and that negation. Let us therefore conceive some singular volition, namely a mode of thinking whereby the mind affirms that the three angles of a triangle are equal to two right angles. This affirmation involves the concept or idea of triangle — that is, without the idea of triangle it cannot be conceived.

Idem enim est si dicam quod A conceptum B debeat involvere ac quod A sine B non possit concipi. Deinde hæc affirmatio (per axioma 3 hujus) non potest etiam sine idea trianguli esse. Hæc ergo affirmatio sine idea trianguli nec esse nec concipi potest.

For it is the same if I say that concept A must involve B and that A cannot be conceived without B. Moreover this affirmation (by axiom 3 of this work) likewise cannot be without the idea of triangle. Therefore this affirmation without the idea of triangle can neither be nor be conceived.

Porro hæc trianguli idea hanc eandem affirmationem involvere debet nempe quod tres ejus anguli æquentur duobus rectis. Quare et vice versa hæc trianguli idea sine hac affirmatione nec esse nec concipi potest adeoque (per definitionem 2 hujus) hæc affirmatio ad essentiam ideæ trianguli pertinet nec aliud præter ipsam est. Et quod de hac volitione diximus (quandoquidem eam ad libitum sumpsimus) dicendum etiam est de quacunque volitione nempe quod præter ideam nihil sit.

Furthermore this idea of the triangle must involve this same affirmation, namely that its three angles equal two right angles. Wherefore, and conversely, this idea of the triangle without this affirmation can neither be nor be conceived; and therefore (by definition 2 of this) this affirmation pertains to the essence of the idea of the triangle and is nothing else beside it. And what we said of this volition (since we have taken it at will) must also be said of any volition, namely that nothing exists besides the idea.

Q.E.D.

Which was to be demonstrated.

COROLLARIUM: Voluntas et intellectus unum et idem sunt.

COROLLARIUM: The will and the intellect are one and the same.

DEMONSTRATIO: Voluntas et intellectus nihil præter ipsas singulares volitiones et ideas sunt (per propositionem 48 hujus et ejusdem scholium). At singularis volitio et idea (per propositionem præcedentem) unum et idem sunt, ergo voluntas et intellectus unum et idem sunt. Q.E.D.

DEMONSTRATIO: The will and the intellect are nothing except the very singular volitions and ideas themselves (by proposition 48 of this work and its scholium). But a singular volition and idea (by the preceding proposition) are one and the same, therefore will and intellect are one and the same. Q.E.D.

SCHOLIUM: His causam quæ communiter erroris esse statuitur, sustulimus. Supra autem ostendimus falsitatem in sola privatione quam ideæ mutilatæ et confusæ involvunt, consistere. Quare idea falsa quatenus falsa est, certitudinem non involvit.

SCHOLIUM: From these we have removed the cause which is commonly asserted to be error. Above we showed that falsity consists in the mere privation which mutilated and confused ideas involve. Therefore a false idea, insofar as it is false, does not involve certainty.

Cum itaque dicimus hominem in falsis acquiescere nec de iis dubitare, non ideo ipsum certum esse sed tantum non dubitare dicimus vel quod in falsis acquiescit quia nullæ causæ dantur quæ efficiant ut ipsius imaginatio fluctuetur. Qua de re vide scholium propositionis 44 hujus partis. Quantumvis igitur homo falsis adhærere supponatur, nunquam tamen ipsum certum esse dicemus.

Therefore when we say that a man acquiesces in false things and does not doubt about them, we do not thereby say that he is certain but only that he does not doubt — either because he acquiesces in falsehoods or because no causes are given that would make his imagination waver. Wherefore see the scholium of proposition 44 of this part. However much, then, a man is supposed to adhere to false things, we nevertheless never call him certain.

Nam per certitudinem quid positivum intelligimus (vide propositionem 43 hujus cum ejusdem scholio) non vero dubitationis privationem. At per certitudinis privationem falsitatem intelligimus. Sed ad uberiorem explicationem præcedentis propositionis quædam monenda supersunt.

For by certitude we understand something positive (see proposition 43 of this work with its scholium), not the privation of doubt. But by the privation of certitude we understand falsity. Yet for a more abundant explanation of the preceding proposition, certain warnings remain to be given.

Superest deinde ut ad objectiones quæ in nostram hanc doctrinam objici possunt, respondeam et denique ut omnem amoveam scrupulum, operæ pretium esse duxi hujus doctrinæ quasdam utilitates indicare. Quasdam inquam nam præcipuæ ex iis quæ in quinta parte dicemus, melius intelligentur.

It remains, then, that I reply to the objections which can be made against our doctrine, and finally that I remove every scruple; I judged it worth the pains to point out certain advantages of this doctrine. Certain, I say, indeed the chief among those which we shall set forth in the fifth part will be better understood.

Incipio igitur a primo lectoresque moneo ut accurate distinguant inter ideam sive mentis conceptum et inter imagines rerum quas imaginamur. Deinde necesse est ut distinguant inter ideas et verba quibus res significamus. Nam quia hæc tria, imagines scilicet verba et ideæ, a multis vel plane confunduntur vel non satis accurate vel denique non satis caute distinguuntur, ideo hanc de voluntate doctrinam scitu prorsus necessariam tam ad speculationem quam ad vitam sapienter instituendam plane ignorarunt.

I therefore begin at the first, and I warn readers to distinguish accurately between an idea or the mind’s concept and the images of things which we imagine. Next it is necessary that they distinguish between ideas and the words by which we signify things. For because these three — images, words, and ideas — are by many either altogether confounded, or not distinguished accurately enough, or finally not distinguished cautiously enough, therefore they have wholly ignored this doctrine concerning the will, a doctrine utterly necessary to knowledge, both for speculation and for ordering life wisely.

Quippe qui putant ideas consistere in imaginibus quæ in nobis ex corporum occursu formantur, sibi persuadent ideas illas rerum quarum similem nullam imaginem formare possumus, non esse ideas sed tantum figmenta quæ ex libero voluntatis arbitrio fingimus; ideas igitur veluti picturas in tabula mutas aspiciunt et hoc præjudicio præoccupati non vident ideam quatenus idea est, affirmationem aut negationem involvere. Deinde qui verba confundunt cum idea vel cum ipsa affirmatione quam idea involvit, putant se posse contra id quod sentiunt velle quando aliquid solis verbis contra id quod sentiunt affirmant aut negant. Hæc autem præjudicia exuere facile is poterit qui ad naturam cogitationis attendit, quæ extensionis conceptum minime involvit atque adeo clare intelliget ideam (quandoquidem modus cogitandi est) neque in rei alicujus imagine neque in verbis consistere.

For those who think that ideas consist in the images which are formed in us from the encounter of bodies persuade themselves that those ideas of things for which we can form no similar image are not ideas but only figments which we fashion from the free arbitrium of will; therefore they regard ideas as mute pictures on a tablet, and preoccupied with this prejudice they do not see that an idea, insofar as it is an idea, involves affirmation or negation. Then those who confuse words with the idea or with the very affirmation which an idea involves, suppose that they can will against what they feel when they assert or deny by mere words something contrary to what they feel. These prejudices, however, he who attends to the nature of thinking can easily cast off, which in no wise involves the concept of extension and therefore will clearly understand that the idea (inasmuch as it is a mode of thinking) consists neither in the image of any thing nor in words.

Verborum namque et imaginum essentia a solis motibus corporeis constituitur, qui cogitationis conceptum minime involvunt. Atque hæc pauca de his monuisse sufficiat, quare ad prædictas objectiones transeo.

For the essence of words and of images is composed from mere bodily motions, which in no wise involve the concept of thought. And let these few admonitions about these matters suffice; therefore I pass on to the afore‑said objections.

Harum prima est quod constare putant voluntatem latius se extendere quam intellectum atque adeo ab eodem diversam esse. Ratio autem cur putant voluntatem latius se extendere quam intellectum est quia se experiri aiunt se non majore assentiendi sive affirmandi et negandi facultate indigere ad infinitis aliis rebus quas non percipimus, assentiendum quam jam habemus, at quidem majore facultate intelligendi. Distinguitur ergo voluntas ab intellectu quod finitus hic sit, illa autem infinita.

The first of these is that they hold the will to extend more widely than the intellect and therefore to be different from it. The reason they think the will extends more widely than the intellect is because they say they experience themselves as not needing a greater faculty of assenting — that is, of affirming and denying — to assent to infinitely many other things which we do not perceive than the assent we already have, whereas they do require a greater faculty of understanding. Therefore the will is distinguished from the intellect in that the latter is finite, the former infinite.

Secundo nobis objici potest quod experientia nihil clarius videatur docere quam quod nostrum judicium possumus suspendere ne rebus quas percipimus, assentiamur; quod hinc etiam confirmatur quod nemo dicitur decipi quatenus aliquid percipit sed tantum quatenus assentitur aut dissentitur. Exempli gratia qui equum alatum fingit, non ideo concedit dari equum alatum hoc est non ideo decipitur nisi simul concedat dari equum alatum; nihil igitur clarius videtur docere experientia quam quod voluntas sive facultas assentiendi libera sit et a facultate intelligendi diversa.

Secondly it can be objected to us that experience seems to teach nothing more clearly than that our judgment we can suspend so as not to assent to the things which we perceive; which is also confirmed by this, that no one is said to be deceived insofar as he perceives anything but only insofar as he assents or dissents. For example, he who imagines a winged horse does not thereby concede that a winged horse is given — that is, he is not thereby deceived — unless at the same time he concedes that a winged horse is given; therefore nothing seems clearer from experience than that the will, or the faculty of assenting, is free and distinct from the faculty of understanding.

Tertio objici potest quod una affirmatio non plus realitatis videtur continere quam alia hoc est non majore potentia indigere videmur ad affirmandum verum esse id quod verum est, quam ad aliquid quod falsum est, verum esse affirmandum; at unam ideam plus realitatis sive perfectionis quam aliam habere percipimus; quantum enim objecta alia aliis præstantiora tantum etiam eorum ideæ aliæ aliis perfectiores sunt; ex quibus etiam constare videtur differentia inter voluntatem et intellectum.

Thirdly it may be objected that one affirmation does not seem to contain more reality than another; that is, we appear not to need a greater power to affirm as true that which is true than to affirm as true something which is false; yet we perceive that one idea has more reality or perfection than another; for insofar as some objects excel others, so likewise are the ideas of those things more perfect than the ideas of others; from which things the difference between will and intellect also seems to be established.

Quarto objici potest si homo non operatur ex libertate voluntatis, quid ergo fiet si in æquilibrio sit ut Buridani asina? Famene et siti peribit? Quod si concedam, viderer asinam vel hominis statuam, non hominem concipere; si autem negem, ergo seipsum determinabit et consequenter eundi facultatem et faciendi quicquid velit, habet.

Fourth, it may be objected: if a man does not act from the liberty of the will, what then will happen if he is poised in equilibrium like Buridan’s ass? Will he perish of hunger and of thirst? If I grant that, I would seem to conceive an ass or a statue of a man, not a man; but if I deny it, then he will determine himself and consequently has the faculty of going and of doing whatever he wishes.

Præter hæc alia forsan possunt objici sed quia inculcare non teneor quid unusquisque somniare potest, ad has objectiones tantum respondere curabo idque quam potero breviter.

Besides these, perhaps other objections may be raised; but since I am not bound to inculcate what any one may dream, I will take care to answer only these objections, and that as briefly as I can.

Et quidem ad primam dico me concedere voluntatem latius se extendere quam intellectum si per intellectum claras tantummodo et distinctas ideas intelligant sed nego voluntatem latius se extendere quam perceptiones sive concipiendi facultatem nec sane video cur facultas volendi potius dicenda est infinita quam sentiendi facultas; sicut enim infinita (unum tamen post aliud nam infinita simul affirmare non possumus) eadem volendi facultate possumus affirmare, sic etiam infinita corpora (unum nempe post aliud) eadem sentiendi facultate possumus sentire sive percipere. Quod si dicant infinita dari quæ percipere non possumus? regero nos ea ipsa nulla cogitatione et consequenter nulla volendi facultate posse assequi.

And indeed, to the first I say that I concede the will to extend more broadly than the intellect if by intellect they mean only clear and distinct ideas; but I deny that the will extends more broadly than perceptions or the faculty of conceiving, nor do I see why the faculty of willing should be called infinite rather than the faculty of sensing; for just as we can affirm infinite things by the same faculty of willing (one indeed after another, for we cannot affirm infinite things simultaneously), so likewise we can feel or perceive infinite bodies by the same faculty of sensing or perceiving (one, namely, after another). But if they say that infinite things are given which we cannot perceive, I reply that those very things we cannot reach by any thought and, consequently, by any faculty of willing.

At dicunt si Deus vellet efficere ut ea etiam perciperemus, majorem quidem facultatem percipiendi deberet nobis dare sed non majorem quam dedit volendi facultatem; quod idem est ac si dicerent quod si Deus velit efficere ut infinita alia entia intelligeremus, necesse quidem esset ut nobis daret majorem intellectum sed non universaliorem entis ideam quam dedit ad eadem infinita entia amplectendum. Ostendimus enim voluntatem ens esse universale sive ideam qua omnes singulares volitiones hoc est id quod iis omnibus commune est, explicamus. Cum itaque hanc omnium volitionum communem sive universalem ideam facultatem esse credant, minime mirum si hanc facultatem ultra limites intellectus in infinitum se extendere dicant.

But they say: if God wished to effect that we should perceive those things too, certainly he would have to give us a greater faculty of perceiving, but not a greater faculty of willing than he gave us; which is the same as if they said that if God wished to effect that we should understand infinite other entities, it would indeed be necessary that he give us a greater intellect, but not a more universal idea of being (ens) than he gave for embracing those same infinite entities. For we have shown that the will is a universale, or the idea by which all singular volitions — that is, that which is common to them all — are explicated. And so, since they believe this common or universal idea of all volitions to be a faculty, it is not at all surprising that they say this faculty extends itself beyond the limits of the intellect into infinity.

Universale enim æque de uno ac de pluribus ac de infinitis individuis dicitur.

For the universal is spoken equally of the one, of the many, and of infinite individuals.

Ad secundam objectionem respondeo negando nos liberam habere potestatem judicium suspendendi. Nam cum dicimus aliquem judicium suspendere, nihil aliud dicimus quam quod videt se rem non adæquate percipere. Est igitur judicii suspensio revera perceptio et non libera voluntas.

To the second objection I answer by denying that we have a free power to suspend judgment. For when we say that someone suspends judgment, we say nothing else than that he sees that he does not adequately perceive the thing. Therefore the suspension of judgment is truly a perception and not a free will.

Quod ut clare intelligatur, concipiamus puerum equum alatum imaginantem nec aliud quicquam percipientem. Quandoquidem hæc imaginatio equi existentiam involvit (per corollarium propositionis 17 hujus) nec puer quicquam percipit quod equi existentiam tollat, ille necessario equum ut præsentem contemplabitur nec de ejus existentia poterit dubitare quamvis de eadem non sit certus. Atque hoc quotidie in somnis experimur nec credo aliquem esse qui putet se, dum somniat, liberam habere potestatem suspendendi de iis quæ somniat, judicium efficiendique ut ea quæ se videre somniat, non somniet et nihilominus contingit ut etiam in somnis judicium suspendamus nempe cum somniamus nos somniare.

So that this may be clearly understood, let us conceive a boy imagining a winged horse and perceiving nothing else. Since this imagination involves the horse’s existence (by the corollary of proposition 17 of this) and the boy perceives nothing that would negate the horse’s existence, he will necessarily contemplate the horse as present and will not be able to doubt its existence, although he is not certain about it. And we experience this daily in dreams; nor do I think there is anyone who supposes that, while he dreams, he has a free power to suspend judgment about the things he dreams, and yet it happens that even in dreams we suspend judgment — namely when we dream that we are dreaming.

Porro concedo neminem decipi quatenus percipit hoc est mentis imaginationes in se consideratas nihil erroris involvere concedo (vide scholium propositionis 17 hujus) sed nego hominem nihil affirmare quatenus percipit. Nam quid aliud est equum alatum percipere quam alas de equo affirmare? Si enim mens præter equum alatum nihil aliud perciperet, eundem sibi præsentem contemplaretur nec causam haberet ullam dubitandi de ejusdem existentia nec ullam dissentiendi facultatem nisi imaginatio equi alati juncta sit ideæ quæ existentiam ejusdem equi tollit vel quod percipit ideam equi alati quam habet esse inadæquatam atque tum vel ejusdem equi existentiam necessario negabit vel de eadem necessario dubitabit.

Moreover I concede that no one is deceived insofar as he perceives — that is, I concede that the imaginations of the mind, considered in themselves, involve no error (see the scholium to proposition 17 of this) — but I deny that a man affirms nothing insofar as he perceives. For what else is to perceive a winged horse than to affirm wings of a horse? For if the mind perceived nothing besides a winged horse, it would contemplate it as present to itself and would have no cause whatever to doubt of that same one’s existence nor any faculty of dissent, unless the imagination of a winged horse be joined to an idea which removes the existence of that same horse, or unless the idea of a winged horse which it perceives it judges to be inadequate, and then either it will necessarily deny the existence of that same horse or will necessarily doubt concerning it.

Atque his puto me ad tertiam etiam objectionem respondisse nempe quod voluntas universale quid sit quod de omnibus ideis prædicatur quodque id tantum significat quod omnibus ideis commune est nempe affirmationem. Cujus propterea adæquata essentia quatenus sic abstracte concipitur, debet esse in unaquaque idea et hac ratione tantum in omnibus eadem sed non quatenus consideratur essentiam ideæ constituere nam eatenus singulares affirmationes æque inter se differunt ac ipsæ ideæ. Exempli gratia affirmatio quam idea circuli ab illa quam idea trianguli involvit æque differt ac idea circuli ab idea trianguli. Deinde absolute nego nos æquali cogitandi potentia indigere ad affirmandum verum esse id quod verum est quam ad affirmandum verum esse id quod falsum est.

And with these things I think I have answered the third objection as well, namely that the will is a universal — what is predicated of all ideas — and that it signifies only that which is common to all ideas, namely affirmation. Whose therefore adequate essence, insofar as it is thus abstractly conceived, must be in each particular idea, and in this respect only the same in all, but not insofar as it is considered to constitute the essence of an idea; for insofar as that goes, singular affirmations differ from one another just as much among themselves as the ideas themselves do. For example, the affirmation which the idea of a circle involves differs just as much from that which the idea of a triangle involves as the idea of a circle differs from the idea of a triangle. Moreover I absolutely deny that we need an equal power of thinking to affirm that what is true is true as to affirm that what is false is true.

Nam hæ duæ affirmationes, si mentem spectes, se habent ad invicem ut ens ad non-ens; nihil enim in ideis positivum est quod falsitatis formam constituit (vide propositionem 35 hujus cum ejus scholio et scholium propositionis 47 hujus). Quare hic apprime venit notandum quam facile decipimur quando universalia cum singularibus, et entia rationis et abstracta cum realibus confundimus.

For these two affirmations, if you consider the mind, stand to one another as being to non-being; for nothing in ideas is positive that constitutes the form of falsity (see proposition 35 of this with its scholium and the scholium of proposition 47 of this). Wherefore it is especially to be noted here how easily we are deceived when we confuse universals with singulars, and intelligible and abstract entities with real ones.

Quod denique ad quartam objectionem attinet, dico me omnino concedere quod homo in tali æquilibrio positus (nempe qui nihil aliud percipit quam sitim et famem, talem cibum et talem potum qui æque ab eo distant) fame et siti peribit. Si me rogant an talis homo non potius asinus quam homo sit æstimandus? dico me nescire ut etiam nescio quanti æstimandus sit ille qui se pensilem facit et quanti æstimandi sint pueri, stulti, vesani, etc.

Lastly, as to the fourth objection, I say that I completely concede that a man placed in such an equipoise (namely one who perceives nothing else but thirst and hunger, such food and such drink as are equally distant from him) will perish of hunger and thirst. If they ask me whether such a man ought rather to be reckoned an ass than a man, I say I do not know—just as I do not know how much he who makes himself a pendulum is to be esteemed, nor how much children, fools, madmen, etc., are to be esteemed.

Superest tandem indicare quantum hujus doctrinæ cognitio ad usum vitæ conferat, quod facile ex his animadvertemus. Nempe

It remains at last to indicate how much the knowledge of this doctrine contributes to the conduct of life, which we shall easily perceive from these things. Namely

I° quatenus docet nos ex solo Dei nutu agere divinæque naturæ esse participes et eo magis quo perfectiores actiones agimus et quo magis magisque Deum intelligimus. Hæc ergo doctrina præterquam quod animum omnimode quietum reddit, hoc etiam habet quod nos docet in quo nostra summa felicitas sive beatitudo consistit nempe in sola Dei cognitione ex qua ad ea tantum agenda inducimur quæ amor et pietas suadent. Unde clare intelligimus quantum illi a vera virtutis æstimatione aberrant qui pro virtute et optimis actionibus tanquam pro summa servitute, summis præmiis a Deo decorari exspectant quasi ipsa virtus Deique servitus non esset ipsa felicitas et summa libertas.

1° insofar as it teaches us to act from the sole will of God and to be sharers (participes) of the divine nature, and all the more in proportion as we perform more perfect actions and know God more and more. This doctrine, therefore, besides rendering the soul altogether tranquil, has also this: it teaches us wherein our highest felicity or beatitude consists, namely in the sole cognition of God, from which we are led to do only those things which love and piety counsel. Hence we clearly perceive how far they err from a true estimation of virtue who, for virtue and the best actions, as if for the greatest servitude, expect to be adorned by God with the highest rewards, as if virtue itself and service of God were not themselves happiness and supreme liberty.

II° Quatenus docet quomodo circa res fortunæ sive quæ in nostra potestate non sunt hoc est circa res quæ ex nostra natura non sequuntur, nos gerere debeamus nempe utramque fortunæ faciem æquo animo exspectare et ferre : nimirum quia omnia ab æterno Dei decreto eadem necessitate sequuntur ac ex essentia trianguli sequitur quod tres ejus anguli sunt æquales duobus rectis.

2° Insofar as it teaches how, concerning matters of fortune or those that are not in our power—that is, concerning things which do not follow from our nature—we ought to behave, namely to await and to bear with an even mind each aspect of fortune; for certainly all things follow from the eternal decree of God with the same necessity as, from the essence of a triangle, it follows that its three angles equal two right angles.

III° Confert hæc doctrina ad vitam socialem quatenus docet neminem odio habere, contemnere, irridere, nemini irasci, invidere. Præterea quatenus docet ut unusquisque suis sit contentus et proximo auxilio, non ex muliebri misericordia, partialitate neque superstitione sed ex solo rationis ductu prout scilicet tempus et res postulat ut in quarta parte ostendam.

3° This doctrine contributes to social life insofar as it teaches that one should bear hatred toward no one, contemn, mock, be angry with, or envy no one. Moreover, insofar as it teaches that each person should be content with his own and a help to his neighbor, not from muliebral mercy, partiality, nor superstition, but from the sole guidance of reason, as, namely, time and circumstances demand, as I will show in the fourth part.

IV° Denique confert etiam hæc doctrina non parum ad communem societatem quatenus docet qua ratione cives gubernandi sint et ducendi nempe non ut serviant sed ut libere ea quæ optima sunt, agant. Atque his quæ in hoc scholio agere constitueram, absolvi et eo finem huic nostræ secundæ parti impono in qua puto me naturam mentis humanæ ejusque proprietates satis prolixe et quantum rei difficultas fert, clare explicuisse atque talia tradidisse ex quibus multa præclara, maxime utilia et cognitu necessaria concludi possunt, ut partim ex sequentibus constabit.

IV° Finally, moreover, this doctrine contributes not a little to the common society insofar as it teaches in what manner citizens are to be governed and led, namely not that they should serve but that they should freely do those things which are best. And with the matters which I had resolved to treat in this scholium having been completed, I close and impose this end on our second part, in which I think I have, sufficiently at length and as much as the difficulty of the subject permits, clearly explained the nature of the human mind and its properties, and have delivered such things from which many excellent, very useful, and knowledge‑necessary conclusions can be drawn, as will partly be shown by what follows.

Finis secundæ partis

End of the second part