Spinoza's Ethics: II.P37

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

That which is common to all things (concerning these, see IIL2) each equal in 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.

If you deny this, conceive if it is possible, that the essence of some singular thing constitutes the certain essence B. Therefore (by IID2) that without B it is neither able to be nor be conceived; and yet this is contrary to the hypothesis: thus that does not pertain to the essence B and does not constitute the essence of another singular thing.

Spinoza's Ethics: II.P36

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

In adequate and confused ideas follow by the same necessity as adequate or clear and distinct ideas.

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.

All ideas are in God (by IP15) and insofar as they refer to God, they are true (by IIP32) and (by IIP7C) are adequate to such a degree not inadequate and not confused unless insofar as they refer to the singular mind of something (about which see IIP24 and IIP28) to such a degree that all are just as adequate as inadequate following by the same necessity (by IIP6C).

Spinoza's Ethics: II.P35

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

Falsity consists of the privation of understanding 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.

Nothing positive in ideas is given which constitutes the form of falsity (by IIP33); but falsity cannot consist in absolute privation (for minds, not bodies are said to wander and not be deceived) and not even in absolute ignorance; for to be ignorant and to be mistaken are different; thus it consists in the privation of understanding which inadequate understanding of things or inadequate and confused ideas involve.

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. 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.

In IIP17S, I have explained by what reason error consists in the privation of understanding but for a more fruitful explanation of this matter I give, of course, that men are deceived which think themselves to be free, which opinion consists in this alone which they are conscious of their actions and ignore of the causes by which they are determined. Therefore this is the idea of their liberty which they understand no cause of their actions. For they say that human actions follow from will, they are words of which they have no idea. For whatever will might be in which way it might move the body, all are ignorant; those who boast something else and imagine the seat and dwelling of the soul, they are accustomed to cause laughter or disgust. Thus, when we look at the sun, we imagine it about two hundred feet from us, which error does not consist in the imagination alone but in that which as long as we imagine thus, we are ignorant of the true distance and the cause of this imagination. For although we understand later that the same is more than 600 diameters of the earth away from us, nevertheless we imagine it to be near by; for we do not imagine the sun near to such a degree because we are ignorant of the true distance of it, but for the reason the affection of our body involves the essence of the sun insofar as the body itself is affected by the sun.

Spinoza's Ethics: II.P34: Adequate Idea is True

Every idea which is absolute or adequate and perfect in us is true.

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

When we say that an idea is adequate and perfect in us, we say nothing other (by IIP11C) than that which is in God insofar as it constitutes the essence of our mind, let it be given that the idea is adequate and perfect and consequently (by IIP32) we say nothing other than that such idea 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.

Spinoza's Ethics: IIP.33: Positive and False are Exclusive

Here Spinoza ties together the notions of positivity as a structural form of truth in the attribute of thought that forms a relationship to existence in the attribute of extension. Just as existence precludes non-existence within God, so too positivity precludes falsehood within God.

Nihil in ideis positivum est propter quod falsæ dicuntur.

Nothing is positive in ideas on account of which they are deemed 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.

If you deny this, conceive if it is possible, a positive mode of understanding which constitutes the form of error or falsity. This mode of understanding is not possible in God (by IIP32); moreover, beyond God it is even unable to be or be conceived (IP15). And so nothing is able to be positive in ideas on account of which they are deemed false.

Spinoza's Ethics: IIP.32: God's Ideas are True

At this point, Spinoza shifts from a rigorous focus on the generally inadequate ideas by which we operate to a recognition that infinite ideas are adequate. Here he brings us back to the perfection of Part I while holding the mind of Part II as of the fabric of perfection. In this way, Spinoza does not join the chorus of skeptics who argue for a nature which is unruly and not subject to reason. Instead, he agrees with skeptics concerning the limitations of our capacity for understanding while affirming the inherent reason structure of the world around us.

Omnes ideæ quatenus ad Deum referuntur, veræ sunt.

All ideas insofar as they refer 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.

For all ideas which are in God since they correspond completely with their objects (by IIP7C) to such an extent (by IA6) they are all true.

Spinoza's Ethics: II.P31: Duration of Singular Things

Here Spinoza extends the reasoning that denies our knowledge of the extent of our lives to other things. Despite our best efforts of understanding, we are simply limited by our inability to have full knowledge of all of the causal chains operating.

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

We are able to have nothing except a completely inadequate understanding of the duration of singular things which are outside us.

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.

For whatsoever singular thing so as the human body ought to be determined from another singular thing to exist and operate by a certain and determined reason and this again from another and thus into infinity (by IP28). Moreover since we have demonstrated from this common property of singular things in the preceding proposition that we do not have anything concerning the duration of our body except a completely inadequate understanding, therefore this same ought to be concluded concerning the duration of singular things because just as this we are not able to have anything except an inadequate understanding.

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.

From this it follows that all particular things are contingent and corruptible. For we are able to have no adequate understanding of the duration of these (by IIP30) and that is we ought to know that by the contingency and possibility of corruption of things (see IP33S1). For (by IP29), except this nothing is contingent.

Spinoza's Ethics: II.P30: Idea of the Duration of the Body

Here Spinoza addresses a fundamental concern for every person: knowing the extent of our lives. He does not diminish the quest here, but simply establishes that it is, so to speak, a closed book. The knowledge of an effect is dependent on its cause. Since the duration of our lives does not depend on our essence or on God, but only on an infinite chain of causality, knowledge of all things would be the requirement for an adequate understanding of the extent of our lives.

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

We are able to have nothing except a completely inadequate understanding about the duration of our body.

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. Q.E.D. 

The duration of our body is not dependent on its essence (by IIA1) and not even on the absolute nature of God (by IP21). But (by IP28) it is determined to exist and operate from such causes which are determined by others to exist and to operate by a clear and determined reason and these again from others and thus into infinity. Therefore, the duration of our body depends on the common order of nature and the constitution of things. Moreover, by which reason things are constituted, an adequate understanding of its thing is given in God insofar as ideas of all things and not insofar as it has such idea of the human body (by IIP9C); for what reason, the understanding of the duration of our body is in God is completely inadequate insofar as it is considered to constitute such nature of the human mind, that is (by IIP11C) this understanding is completely inadequate in our mind.