Spinoza's Ethics: I.20: Existence Equals Essence

In this demonstration, Spinoza uses the verbs exprimit and explicant which I have translated as "express" and "unfold" respectively. Most translators use the word "express"for exprimit and employ "explain" for explicant. In my view, these translations seem to overly utilize verbal activity. Perhaps this is rooted in John's uses of logos. My reading of Spinoza is that anthropomorphizing is misleading. Here, Spinoza is using express and unfold in the sense of cause immanens like that of a seed expressing its nature and unfolding that nature through time.

Dei existentia ejusque essentia unum et idem sunt.

Translated as,

God's existence and its essence are one and the same.

Demonstratio: Deus (per antecedentem propositionem) ejusque omnia attributa sunt aeterna hoc est (per definitionem 8) unumquodque ejus attributorum existentiam exprimit. Eadem ergo Dei attributa quae (per definitionem 4) Dei aeternam essentiam explicant, ejus simul aeternam existentiam explicant hoc est illud ipsum quod essentiam Deo constituit, constituit simul ipsius existentiam adeoque haec et ipsius essentia unum et idem sunt. Q.E.D.

Translated as,

God (by P19) and all of its attributes are eternal, that is (by D8), each and every one of its attributes expresses existence. Therefore, the same attributes of God which (by D4) unfold God's eternal essence at the same time unfold its eternal existence, that is, that itself which constitutes God's essence at the same time constitutes its existence. To this extent are its existence and essence one and the same.

Corollarium I: Hinc sequitur I Dei existentiam sicut ejus essentiam aeternam esse veritatem.

Translated as,

From this it follows, first, that God's existence, just as its eternal essence, is truth.

Corollarium II: Sequitur, II, Deum sive omnia Dei attributa esse immutabilia. Nam si ratione existentiae mutarentur, deberent etiam (per propositionem praecedentem) ratione essentiae mutari, hoc est (ut per se notum) ex veris falsa fieri quod est absurdum. 

It follows, second, that God, or all of God's attributes, are immutable. For if they were changed by the reason for their existence, they would also (by P20) change as to reason for their essence, that is (as is known through itself), from being true things to becoming false things, which is absurd.

Spinoza's Ethics: I.P19: Eternal God

After a long hiatus from aeternitas or "eternity," (I.D8) Spinoza returns to this topic. From that definition, "eternity" is a form of existence independent of duration, even permanent duration. I conceptualize it in the following way. The essence of a triangle is three-sidedness. There may be an infinite number of particular triangles, but the essence remains consistent. Furthermore, this essence is eternal, that is, it is true regardless of duration. Similarly God is eternal, that is, the existence of God is not explained by duration or time. The concept of God as "the nature of nature" is helpful to me here. as "nature of nature" is conceptually very separate from time and duration, as opposed to "nature" which is clearly affected.

Here is the quote from Descartes's Principles, Part I, Proposition 19:"God is eternal. Demonstration: God is a perfect being (Def.8), and therefore necessarily exists. If we attribute only a limited existence to Him these limits must be known, if not by us, by God Himself (per Prop.9), who is omniscient. But then God who is omniscient (per Def.8), would know no existence beyond these limits, which is absurd (per Prop.5). Therefore God does not have a limited but an infinite existence, which we call eternity. (Vid. Chap.I, Part II, of our Appendix). God therefore is eternal. Q.E.D."

Rather than "nature of nature," there is a more complex, yet more nuanced way to think about this eternity and existence discussion. God as causa immanens is virtual, not actual. Actual is historical - it is a thing's duration as a process of creation and destruction, emergence and disappearance. All things actual come and go. The virtual, on the other hand, is immanent to the actual as contemporaneous with the present, but forms its a priori condition and the future potential. Virtual is a realm of pure potential that can be thought of in terms of Einstein's matter-energy equivalence - that all matter is merely an actualization of energy, an energy that remains immanent to matter, that is enveloped within matter; it is the condition of matter's origin and presence while simultaneously an enveloped potential. The actual present reveals the past and is pregnant with the future. But the usage of time-words in reference to the virtual is misleading as the virtual only appears temporal. In Spinoza, the virtual (a term he does not use but is useful to apply to this area) considered apart from the actual - as an infinite realm of pure potential - is eternal. But even this separation is misleading, for the actual is the sole destination of the virtual. The virtual is destined to eternal creation of the actual, but this immanence is eternally immanent to itself as substance. This eternal virtual immanence does not unfold within the actual spatial-temporal, but unfolds the actual spatial-temporal.

Deus sive omnia Dei attributa sunt aeterna. 

Translated as,

God or all attributes of God are eternal.

Demonstratio: Deus enim (per defintionem 6) est substania quae (per propositionem 11) necessario existit hoc est (per propositionem 7) ad cujus naturam pertinet existere sive (quod idem est) ex cujus defintione sequitur ipsum existit adeoque (per definitionem 8) est aeternus. Deinde per Dei attributa intelligendum est id quod (per defintionem 4) divinae substantiae essentiam exprimit hoc est id quod ad substantiam pertinet : id ipsum inquam ipsa attributa involvere debent. Atqui ad naturam substantiae (ut jam ex propositionem 7 demonstravi) pertinet aeternitas. Ergo unumquodque attributorum aetenitatem involvere debet adeoque omnia sunt aeterna. Q.E.D. 

Translated as,

For God (by D6) is substance, which (by P11) necessarily exists, that is (by P7) to whose nature it pertains to exist, or (what is the same) from whose definition it follows that it exists and to such an extent (by D8), he is eternal. Next, by God's attributes it must be understood that which (by D4) expresses the essence of divine substance, that is, what pertains to substance. The attributes themselves, I say, must involve it itself. Still, eternity pertains to the nature of substance (as I have already demonstrated from P7). Therefore each and every one of the attributes must involve eternity and to this extent they are all eternal.

Scholium: Haec propositio quam clarissime etiam patet ex modo quo (propositione 11) Dei existentiam demonstravi; ex ea inquam demonstratione constat Dei existentiam sicut ejus essentiam aeternam esse veritatem. Deinde (propositione 19 Principiorum Cartesii) alio etiam modo Dei aeternitatem demonstravi nec opus est eum hic repetere.

Translated as,

Also, this proposition is as clear as possible from the way I have demonstrated the existence of God (P11). For from that demonstration, I say, it is established that the existence of God, like its essence, is an eternal truth. Next (Decartes' Principles IP19) I have also demonstrated the eternity of God in another way and there is no need to repeat it here.

Spinoza's Ethics: I.P18: Immanence

His proof follows logically from prior propositions. In fact, the concept of a single substance forces this notion of causality (I.P14C1). Further, in the definitions, I.D1 on self-caused and I.D7 on freedom both convey notions that are grounded in immanence.

The notion of a causa transiens seems to be one of those in which we are inclined to anthropomorphize God - as we struggle with our environment, we impute the same transitive causality to God, but simply on a more powerful basis. I think of my learning in physics with notions of things banging around as causa transiens. Here is the billiard ball's causality of Newtonian physics - that there exists an absolute space and linear time within which all interactions occur. Particle A travels distance X in time Y and hits particle B. Within the realm of identity, there is unity of subject A and object B, moving and interacting in absolute (Cartesian) space.

But Spinoza has drawn his framework from God, not our human framework. The resulting insights do allow us to reanalyze our experiences as a sense of acting within a reality of an unfolding bumping up against a contiguous unfolding around us. The notion seems biological. When I think of plants, there is a sense of unfolding. The concept of a seed seems to embody causa immanens. A seed contains DNA which is composed of differential relations and singular points (both as potentia or "intensive power") which create the plant, expressing itself (as Potestas or "actualized power") in a process of morphogenesis or progressive differentiation.

Deus est omnium rerum causa immanens, non vero transiens. 

Translated as,

God is the immanent cause of all things, specifically not the transitive cause.

The distinction between immanens or "immanent" and transiens or "transitive" is critical and has profound ramifications. Causally, God's infinity does not allow for a non-God space in which the effect is not also God. Cause and effect are both God. Viewed correctly, this distinction removes many false perceptions of God's engagement. 

Demonstratio: Omnia quae sunt, in Deo sunt, et per Deum concipi debent (per propositionem 15) adeoque (per corollarium I propositionis 16 hujus) Deus rerum quae in ipso sunt, est causa, quod est primum. Deinde extra Deum nulla potest dari substantia (per propositionem 14) hoc est (per definitionem 3) res quae extra Deum in se sit, quod erat secundum. Deus ergo est omnium rerum causa immanens, non vero transiens. Q.E.D.

Translated as,

Everything which is, is in God, and must be conceived through God (by P15) and to such an extent (by P16C1) God is the cause of things which are in itself. That is the first thing. Next, outside God no substance (by P14) can be given, that is (by D3) a thing which in itself outside God. That was the second. God, therefore, is the immanent cause of all things, specifically not the transitive cause.

Spinoza's Ethics: I.P17: God as Free Cause

Spinoza's definition of free in I.D7 reads "a thing is called free which exists from the necessity of its nature alone, and is determined to act by itself alone." God acts from its divine nature and, since there is no power greater than God, is essentially free.

The issue of causa libera or "free cause" is profound. It ties together I.D1 and I.D7 while focusing on the various types of causes. I have not seen a "free cause" approached by prior thinkers. As covered in I.P16 on the Aristotle's four causes, a "cause" is best translated as an explanatory factor. So, it appears that Spinoza is saying that free is the explanatory factor as much as "four legs and a top" is an explanatory factor of a table - that is, it is essential. 

Spinoza opens the nature of God as fully free, but in a sense that we would typically characterize as deterministic. Our personal notions of freedom rest on cognitive experiences of choice. For example, I can choose 2+2=4 or 2+2=5. But God is perfection is 2+2=4 and unable to be 2+2=5. God's perfection is free from constraints and choices. Freedom here is truly expressive. 

To paraphrase my high school teacher, absolute power expresses absolutely. In this difference is a key to his thought. Spinoza views the universe as an unfolding of power that optimizes a fullness and saturation of expression. There are no gaps or limitations that facilitate choice.  

The scale of power implied here is magnificent and logical. Earlier he has argued that if power is limited, it must be limited by something. What is that something? If there is no answer, then unlimited power exists. Unlimited power is freedom to express itself as is with the same unfolding as the nature of a triangle whose three angles sum to two right angles. An absolutely powerful triangle cannot express itself without three angles and cannot express itself without those three angles summing to two right angles. Spinoza is articulating that absolute power does not include the power to deny its essence. For this reason, modes do not deny substance but express the capacity of substance. This is unlike attributes which express the essence of substance. 

Although there are parts of Spinoza's Latin that use masculine gender for God, on a go-forward basis I am using the neuter gender. Spinoza is consistently opposed to our tendency to anthropomorphize God. In this section, he highlights the problem again. Here we see that our cognitive experiences are a reflection of our limited power and yet we attribute that to God. We tend to affirm that God understands all things and yet only creates a subset of these things. But Spinoza is arguing that God's knowing is God's being and vice versa. The implication is that whatever does not exist does not exist due to imperfections of the definition (as in a triangle with only two angles). Those who argue with Spinoza raise a valid point - if God's knowing is doing, then if God knows all, hasn't all been done? Spinoza's position seems to be based in the reasoning of a line and points raised earlier - between any two points on a line lie infinite points. The line is analogous to the invariability of eternity while the capacity of the variability of the points on the line is analogous to a time-based and logical variability of God's expressive knowing and doing. 

His arguments and examples are clear, but do raise a challenge embedded in the word effluxisse or "flowed out." There is a sense of motion and expression in Spinoza's system. The argument here about the connection between God's knowing and being raises the issue if God's knowing is a "flowing out" in the same way as God's being. Since that appears to be the case, it may appear to deny God's perfection in the sense of some incompleteness. However, absolute infinity may be the critical connection here - only in a complete set, i.e. finite, would a concept of completeness and doneness be applicable.

 The focus here is on aeternam Dei essentiam or "the eternal essence of God." The example of the constellation in the form of a dog compared to the actual barking dog is useful in terms of its highly limited commonality. But the following example of a man causing the existence of another man raises as many issues as it solves. Spinoza's key point is that man cannot create the essence of another man because essences are eternal truths. The eternal essence of God is the only causal factor and it is free cause in the sense that Spinoza has defined.

Deus ex solis suae naturae legibus et a nemine coactus agit.

Translated as,

God acts from only the laws of its own nature and is compelled by no one.

Demonstratio: Ex sola divinæ naturæ necessitate vel (quod idem est) ex solis ejusdem naturæ legibus infinita absolute sequi modo propositione 16 ostendimus et propositione 15 demonstravimus nihil sine Deo esse nec concipi posse sed omnia in Deo esse; quare nihil extra ipsum esse potest a quo ad agendum determinetur vel cogatur atque adeo Deus ex solis suæ naturæ legibus et a nemine coactus agit. Q.E.D. 

Translated as,

Solely from the necessity of its own divine nature or (what is the same) from only the laws of the same [divine] nature, we have shown just now that infinite things follow absolutely in proposition 16 and we have demonstrated in proposition 15 that nothing exists nor is able to be conceived outside God but everything is in God. This is why nothing is able to exist outside of God itself by which God might be determined or compelled to act. And to this degree, God acts from only the laws of its own nature and is compelled by no one.

Corollarium I: Hinc sequitur I nullam dari causam quæ Deum extrinsece vel intrinsece præter ipsius naturæ perfectionem incitet ad agendum. 

Translated as,

From this it follows, first, that no cause is to be given which may arouse God to action, either extrinsically or intrinsically except for the perfection of its own nature.

Corollarium II: Sequitur II solum Deum esse causam liberam. Deus enim solus ex sola suæ naturæ necessitate existit (per propositionem 11 et corollarium I propositionis 14) et ex sola suæ naturæ necessitate agit (per propositionem præcedentem). Adeoque (per definitionem 7) solus est causa libera. Q.E.D. 

Translated as,

It follows, second, that God alone is free cause. For God alone exists from only the necessity of its own nature (by P11 and P14C1) and acts from only the necessity of its own nature (by P16). To this extent (by I.D7) God alone is free cause.

Scholium: Alii putant Deum esse causam liberam propterea quod potest ut putant efficere ut ea quae ex ejus natura sequi diximus hoc est quae in ejus potestate sunt, non fiant sive ut ab ipso non producantur. Sed hoc idem est ac si dicerent quod Deus potest efficere ut ex natura trianguli non sequatur ejus tres angulos aequales esse duobus rectis sive ut ex data causa non sequatur effectus, quod est absurdum. 

Translated as,

Some think that God is free cause for the following reason. They think that God is able to effect things which do not happen or are not produced by God - things which we have said follow from its nature, that is which are in its power. But this is the same as if they were to say because God is able to make it so that it does not follow from the nature of a triangle that three angles are equal to two right angles or that from a given cause an effect does not follow, which is absurd.

Porro infra absque ope huius propositionis ostendam ad Dei naturam neque intellectum neque voluntatem pertinere. Scio equidem plures esse qui putant se posse demonstrare ad Dei naturam summum intellectum et liberam voluntatem pertinere; nihil enim perfectius cognoscere sese aiunt quod Deo tribuere possunt quam id quod in nobis summa est perfectio. Porro tametsi Deum actu summe intelligentem concipiant, non tamen credunt eum posse omnia quae actu intelligit, efficere existant nam se eo modo Dei potentiam destruere putant. Si omnia inquiunt quae in ejus intellectu sunt, creavisset, nihil tum amplius creare potuisset, quod credunt Dei omnipotentiae repugnare ideoque maluerunt Deum ad omnia indifferentem statuere nec aliud creantem praeter id quod absoluta quadam voluntate decrevit creare. 

Translated as,

Further on below, I will show without the need of this proposition that neither intellect nor will pertain to the nature of God. Certainly, I know that there are many more who think that they can demonstrate that the height of intellect and free will pertain to the nature of God. Indeed, they say that they reason that nothing more perfect could be attributed to God than what is the height of perfection in ourselves. Again, although they may conceive God's understanding to be at the highest level, nevertheless they do not believe that it can do everything at the level of its own understanding. For they think to prove that all this is so means that in such a way they would demolish the power of God. If, they argue, everything which exists in its [God's] intellect, it [God] had already created, then it [God] could have created nothing more. This they believe the omnipotence of God to be incompatible with and for that reason they have preferred to hold that God is indifferent to everything and creates nothing except that which it decides to create by a certain absolute will.

Verum ego me satis clare ostendisse puto (vide propositionem 16) a summa Dei potentia sive infinita natura infinita infinitis modis hoc est omnia necessario effluxisse vel semper eadem necessitate sequi eodem modo ac ex natura trianguli ab aeterno et in aeternum sequitur ejus tres angulos aequari duobus rectis. Quare Dei omnipotentia actu ab aeterno fuit et in aeternum in eadem actualitate manebit. Et hoc modo Dei omnipotentia longe meo quidem judicio perfectior statuitur. Imo adversarii Dei omnipotentiam (liceat aperte loqui) negare videntur. Coguntur enim fateri Deum infinita creabilia intelligere quae tamen nunquam creare poterit. Nam alias si scilicet omnia quae intelligit crearet, suam juxta ipsos exhauriret omnipotentiam et se imperfectum redderet. Ut igitur Deum perfectum statuant, eo rediguntur ut simul statuere debeant ipsum non posse omnia efficere ad quae ejus potentia se extendit, quo absurdius aut Dei omnipotentiae magis repugnans non video quid fingi possit.

Translated as,

Indeed I think that I have shown clearly enough (see P16) that everything necessarily has flowed from or, by the same necessity, follows from the height of God's power, whether as infinite nature or infinite things by infinite modes in the same way as from eternity and to eternity it follows from the nature of a triangle that its three angles are equal to two right angles. For this reason, the omnipotence of God has been at this level from eternity and will remain at the same actuality for eternity. And in this way the omnipotence of God, in my opinion at any rate, is established far more perfectly. To the contrary, my adversaries seem to deny the omnipotence of God (allow [me] to speak openly) because they are forced to admit that God understands infinite creations which, nevertheless, God will never be able to create. For otherwise if [God] created everything which it understands, according to them, [God] would exhaust its omnipotence and render itself imperfect. So, as they establish that God is perfect, by this they are reduced so that at the same time they must establish that [God] is not able to effect all things to which [God's] power extends. I do not see what could be formed to be more absurd or contrary to the omnipotence of God.

Porro ut de intellectu et voluntate quos Deo communiter tribuimus, hic etiam aliquid dicam, si ad aeternam Dei essentiam intellectus scilicet voluntas pertinent, aliud sane per utrumque hoc attributum intelligendum est quam quod vulgo solent homines. Nam intellectus et voluntas qui Dei essentiam constituerent, a nosto intellectu et voluntate toto caelo differre deberent nec in ulla re praeterquam in nomine convenire possent; non aliter scilicet quam inter se conveniunt canis, signum caeleste et canis, animal latrans. Quod sic demonstrabo. Si intellectus ad divinam naturam pertinet, non poterit uti noster intellectus posterior (ut plerisque placet) vel simul natura esse cum rebus intellectis quandoquidem Deus omnibus rebus prior est causalitate (per corollarium I propositionis 16) sed contra veritas et formalis rerum essentia ideo talis est quia talis in Dei intellectu existit objective. Quare Dei intellectus quatenus Dei essentiam constituere concipitur, est revera causa rerum tam earum essentiae quam earum existentiae, quod ab iis videtur etiam fuisse animadversum qui Dei intellectum, voluntatem et potentiam unum et idem esse asseruerunt. Cum itaque Dei intellectus sit unica rerum causa videlicet (ut ostendimus) tam earum essentiae quam earum existentiae, debet ipse necessario ab iisdem differre tam ratione essentiae quam ratione existentiae. Nam causatum differt a sua causa praecise in eo quod a causa habet. Exempli gratia homo est cause existentiae, non vero essentiae alterius hominis; est enim haec aeterna veritas et ideo secundum essentiam prorsus convenire possunt; in existendo autem differre debent et propterea si unius existentia pereat; non ideo alterius peribit sed si unius essentia destrui posset et fieri falsa, destrueretur etiam alterius essentia. Quapropter res quae et essentiae et existentiae alicujus effectus est causa, a tali effectu differre debet tam ratione essentiae quam ratione existentiae. Atqui Dei intellectus est et essentiae et existentiae nostri intellectus causa; ergo Dei intellectus quatenus divinam naturam essentiam constituere concipitur, a nostro intellectu tam ratione essentiae quam ratione existentiae differt nec in ulla re praeterquam in nomine cum eo convenire potest, ut volebamus. Circa voluntatem eodem modo proceditur, ut facile unusquisque videre potest.

Translated as,

Next we have commonly attributed things to God concerning the intellect and the will. Here I will even say something - if the intellect, namely the will, pertain to the eternal essence of God, something more sensible must be understood about each attribute than which men are generally accustomed. For the intellect and the will which constitute the essence of God, must be diametrically different than our intellect and will and cannot have anything in common except for the name. In same way does a dog as a heavenly constellation and a dog as a barking animal have anything in common. This I will demonstrate. If intellect pertains to divine nature, then it cannot function with things understood, as our intellect [does], posterior to (as pleases the majority) and at the same time in nature when indeed God is prior to all things by causality (by P16C1) but instead, truth, and thus the formal essence of things, is of such kind because such exists objectively within the intellect of God. For this reason, the intellect of God, insofar as it is conceived to constitute the essence of God, is in reality the cause of things as of their essence and of their existence. This seems to have been observed by those who have asserted that the intellect, will and power of God are one and the same. Since in this way the intellect of God is the one and only cause of all things (as we have shown) namely as of the essence of things and of their existence, it itself necessarily differs from those same things as the reason for its essence and as the reason for its existience. For what is caused differs from its own cause in that which it [effect] has from from a cause. For example, a man is the cause of the existence of, but not in truth the essence of another man. For this essence is an eternal truth and for that reason they can entirely agree following their essence. In existence, however, they must be different and for this reason, if the existence of one perishes, then the other will not perish. But if the essence of one is able to be destroyed and become false, it would also destroy the essence of the other. So a thing which is the cause of some effect of both the essence and the existence must be different from such effect both as the reason for the essence as well as the reason for existence. Further the intellect of God is the cause of the essence and the existence of our intellect. So the intellect of God, insofar as it is conceived to constitute the essence of divine nature, differs from our intellect both by reason of essence and by reason of existence and in no thing can it be in common with it except in name, as we intended. Concerning the will, it would be deduced in the same way, as everyone is easily able to see.

Spinoza's Ethics: I.P16: Infinite Things By Necessity

Here Spinoza uses the force of ex necessitate or "necessity" to describe the operation of divine nature. In this usage, Spinoza denies teleology, that is, he specifically denies that God or the universe has a direction in mind. Yet, at the same time, Spinoza makes clear that God or the universe is not operating mindlessly as he specifically identifies intellectum infinitum or "infinite intellect" of God. This distinction highlights a key way in which Spinoza's God is different than those of traditional religions. The "infinite intellect" does not solve problems, but simply expresses solutions. 

His demonstration does not bear the geometric simplicity of others. Instead, his comment si modo ad hoc attendat or "if someone would attend to this" reflects the language of his scholia or commentaries. His definitional emphasis of the first half of the demonstration reflects a continuation of the tightness of cause and effect - the effect is only known if the cause is known. Spinoza's system (as I discussed in I.P15S) is grounded in an intuition of the infallibility of clear reason. Here he is providing an example of the components of clear reason - definitions are more real insofar as they are more property laden. This is unlike our conventional scientific thought in which specifics are stripped away to discover essences. Spinoza is the thinker of the specifics, rather than generics. Within the specificity of each individual mode, there are infinite individual things. Rather than counting infinite angels on an imaginary pin, Spinoza articulates infinite properties discoverable on each "real" thing defined. He takes this framework to develop the second half of the demonstration as an analogy to the "infinitely infinite" already presented in I.P6. 

Aristotle worked under a framework of four causes: efficient, material, formal and final. In this proposition, Spinoza is clearly denying that God operates with a final cause. In the corollary, Spinoza focuses on God's role. First, God is the efficient cause. Nothing else is truly causal. Second, God is the immediate, not accidental or derivative cause. God does not operate through some non-God intermediaries. Third, God is the first cause and does not share any aspect of that causal pattern with anything else.

Ex necessitate divinæ naturæ infinita infinitis modis (hoc est omnia quæ sub intellectum infinitum cadere possunt) sequi debent.

Translated as,

From the necessity of divine nature, infinite things must follow from infinite modes (that is, everything which is able to fall within infinite intellect.)

Demonstratio: Hæc propositio unicuique manifesta esse debet si modo ad hoc attendat quod ex data cujuscunque rei definitione plures proprietates intellectus concludit, quæ revera ex eadem (hoc est ipsa rei essentia) necessario sequuntur et eo plures quo plus realitatis rei definitio exprimit hoc est quo plus realitatis rei definitæ essentia involvit. Cum autem natura divina infinita absolute attributa habeat (per definitionem 6) quorum etiam unumquodque infinitam essentiam in suo genere exprimit, ex ejusdem ergo necessitate infinita infinitis modis (hoc est omnia quæ sub intellectum infinitum cadere possunt) necessario sequi debent. Q.E.D. 

Translated as,

This proposition ought to be clear to every single person if only he (or she) would attend to this - that the intellect deduces more properties from the definition given of a specified thing, which (increase in the number of properties) really follows necessarily from the definition (that is, the essence itself of the thing) and the definition of the thing expresses more properties where there is more reality - that is, where the essence of the thing defined involves more reality. Moreover, since divine nature has absolutely infinite attributes (by P6) each of which still express infinite essence in their own kind, from the same necessity, infinite things must follow from infinite modes (that is, everything which is able to fall within the infinite intellect.)

Corollarium I: Hinc sequitur Deum omnium rerum quæ sub intellectum infinitum cadere possunt, esse causam efficientem. 

Translated as,

From this, it follows that God is the efficient cause of everything which is able to fall within the infinite intellect. 

Corollarium II: Sequitur II Deum causam esse per se, non vero per accidens. 

Translated as,

It follows, second, that God is the cause through itself, truly not through an accidental cause.

Corollarium III: Sequitur III Deum esse absolute causam primam. 

Translated as,

It follows, third, that God is absolutely the first cause.

Spinoza's Ethics: I.P15: Nothing But God

As they might say in Texas, "them's fighting words." Here Spinoza is explicitly stating the basics for what became known as pantheism (a term coined by a mathematician describing Spinoza's system posthumously). Prior to Spinoza, many pantheistic ideas had been expressed poetically, but here for the first time, these ideas are presented in a methodical proof. The implications of this explicit proof had significant impact on subsequent philosophical, religious, scientific and political thought. Given its radical implications, Spinoza follows his proof with a lengthy note presented here. 

Spinoza's note addresses those who believe that God exists outside rather than within creation. He begins humorously saying that he dismisses those who see God in terms of imagery. He follows the arguments of those who view God as transcendent and separate from creation. His argument is that corporeal substance must be made of substance and since substance can't produce substance, then corporeal substance must be God. But given the significance of this proposition, he proceeds through more reasonings. 

Spinoza's final note is highly useful. The exploration of the example of the line made up of points is a useful way of thinking about substance and modifications. If we take a line between two points, we understand that the line is made up of an infinity of points. In an imperfect analogy, substance is like the line with modifications like the points. The line is unchanging despite the varieties and singularities of the individual points. Further the line remains unbroken. But as an analogue to Spinoza's substance, the line would be infinitely infinite. This analogy illustrates immanence beautifully as well. Further, I believe that his comment claram rationem infallibelem or "clear reason is infallible" references the underlying metaphysical intuition of his framework; in my mind it is how the framework is bolted to reality and the non-tautological basis of its appeal and comfort.

Quicquid est, in Deo est, et nihil sine Deo esse neque concipi potest.

Translated as,

Whatever is, is in God, and without God, nothing can exist or be conceived.

Demonstratio: Praeter Deum nulla datur neque concipi potest substantia (per 14 propositionem) hoc est (per definitionem 3) res quae in se est et per se concipitur. Modi autem (per definitionem 5) sine substantia nec esse nec concipi possunt; quare hi in sola divina natura esse et per ipsam solam concipi possunt. Atqui praeter substantias et modos nil datur (per axioma 1). Ergo nihil sine Deo esse neque concipi potest. Q.E.D.

Translated as,

Except for God, no substance is provided nor able to be conceived (by P14), that is (by D3), a thing which is in itself and is conceived through itself. Moreover, modes (by D5) are neither able to be nor be conceived without substance. Thus only in divine nature are they (modes) able to be and be conceived. But outside of substances and modes, nothing exists (by A1). Thus, without God, nothing can exist or be conceived.

Scholium: Sunt qui Deum instar hominis corpore et mente constantem atque passionibus obnoxium fingunt sed quam longe hi a vera Dei cognitione aberrent, satis ex jam demonstratis constat. Sed hos mitto : nam omnes qui naturam divinam aliquo modo contemplati sunt, Deum esse corporeum negant. Quod etiam optime probant ex eo quod per corpus intelligimus quamcunque quantitatem longam, latam et profundam, certa aliqua figura terminatam, quo nihil absurdius de Deo, ente scilicet absolute infinito, dici potest. Attamen interim aliis rationibus quibus hoc idem demonstrare conantur, clare ostendunt se substantiam ipsam corpoream sive extensam a natura divina omnino removere atque ipsam a Deo creatam statuunt. Ex qua autem divina potentia creari potuerit, prorsus ignorant; quod clare ostendit illos id quod ipsimet dicunt, non intelligere. Ego saltem satis clare meo quidem judicio demonstravi (vide corollarium propositionis 6 et scholium II propositionis 8) nullam substantiam ab alio produci vel creari. Porro propositione 14 ostendimus præter Deum nullam dari neque concipi posse substantiam atque hinc conclusimus substantiam extensam unum ex infinitis Dei attributis esse.

Translated as,

There are those who shape God as an image composed of the body and mind of a man and liable to passions. But how far these stray from the true recognition of God, enough demonstration is already evident. These I dismiss. For everyone who has in some way reflected on divine nature does deny that God is endowed with a body. It can be said what they best prove by this - that by body we understand whatsoever quantity of length, breadth, and depth that is limited by some kind of figure than which nothing is more absurd concerning God, namely, of a being absolutely infinite. But yet in the meantime, by other reasons by which they try to prove this same thing they clearly show that they altogether remove substance itself, whether corporeal or extended, from divine nature and they maintain that substance itself has been created by God. However from what divine power it could have been created they absolutely are ignorant of - which clearly shows that they do not understand what they themselves say. At any rate, I have demonstrated clearly enough, certainly in my judgment, that no substance can be produced or created by another thing (see P6C and P8S2). Later, by P14 we show that except for God, no substance can either exist or be conceived, and from this we have concluded that extended substance is one of God's infinite attributes.

Verum ad pleniorem explicationem adversariorum argumenta refutabo quæ omnia huc redeunt primo quod substantia corporea quatenus substantia constat ut putant partibus et ideo eandem infinitam posse esse et consequenter ad Deum pertinere posse negant. Atque hoc multis exemplis explicant ex quibus unum aut alterum afferam. Si substantia corporea aiunt est infinita, concipiatur in duas partes dividi; erit unaquæque pars vel finita vel infinita. Si illud, componitur ergo infinitum ex duabus partibus finitis, quod est absurdum. Si hoc, datur ergo infinitum duplo majus alio infinito, quod etiam est absurdum. Porro si quantitas infinita mensuratur partibus pedes æquantibus, infinitis talibus partibus constare debebit ut et si partibus mensuretur digitos æquantibus ac propterea unus numerus infinitus erit duodecies major alio infinito. Denique si ex uno puncto infinitæ cujusdam quantitatis concipiatur duas lineas ut AB, AC, certa ac determinata in initio distantia in infinitum protendi, certum est distantiam inter B et C continuo augeri et tandem ex determinata indeterminabilem fore. Cum igitur hæc absurda sequantur ut putant ex eo quod quantitas infinita supponitur, inde concludunt substantiam corpoream debere esse finitam et consequenter ad Dei essentiam non pertinere.

Translated as,

Indeed, for a fuller explanation I will refute my adversaries' arguments - which all come back to this point: first because (as they think) corporeal substance, insofar as it is substance, is composed of parts. For this reason they deny that the same substance is able to be infinite and consequently that it can pertain to God. And they even explain this with many examples from which I will bring forth one or two. If they say corporeal substance is infinite, let it be conceived to be divided into two parts. Each one of the parts will either be finite or infinite. If the former, an infinite thing is from placing together two finite parts - which is absurd. If the latter, an infinite thing doubly large is created by adding another infinite thing - which is also absurd. If an infinite quantity is measured by splitting into parts equal to feet, it will be composed of infinite such parts. And if it is measured by splitting into parts equal to inches, it will be an infinite number twelve times greater than the other infinity. Finally if it is conceived that two lines of some infinite quantity as AB and AC are lengthened from one point that is certain and determined at the beginning into infinity at a distance, it is certain that the distance between B and C continues to increase so that finally it becomes indeterminate from determinate. Therefore, since these absurdities follow (as they think) from this because an infinite quantity is supposed, from this they conclude that corporeal substance must be finite and consequently not pertain to the essence of God.

Secundum argumentum petitur etiam a summa Dei perfectione. Deus enim inquiunt cum sit ens summe perfectum, pati non potest : atqui substantia corporea quandoquidem divisibilis est, pati potest; sequitur ergo ipsam ad Dei essentiam non pertinere. Hæc sunt quæ apud scriptores invenio argumenta quibus ostendere conantur substantiam corpoream divina natura indignam esse nec ad eandem posse pertinere. Verumenimvero si quis recte attendat, me ad hæc jam respondisse comperiet quandoquidem hæc argumenta in eo tantum fundantur quod substantiam corpoream ex partibus componi supponunt, quod jam (per propositionem 12 cum corollario propositionis 13) absurdum esse ostendi. Deinde si quis rem recte perpendere velit, videbit omnia illa absurda (siquidem omnia absurda sunt, de quo non jam disputo) ex quibus concludere volunt substantiam extensam finitam esse, minime ex eo sequi quod quantitas infinita supponatur sed quod quantitatem infinitam mensurabilem et ex partibus finitis conflari supponunt; quare ex absurdis quæ inde sequuntur, nihil aliud concludere possunt quam quod quantitas infinita non sit mensurabilis et quod ex partibus finitis conflari non possit. Atque hoc idem est quod nos supra (propositione 12 etc.) jam demonstravimus.

Translated as,

The second argument is also sought from the height of God's perfection. God, they say, since he is a being of the height of perfection is unable to be acted on. But since corporeal substance is divisible, it is able to be acted on. So, it follows that (corporeal substance) itself does not pertain to the essence of God. These are the arguments which I find among writers by which they try to show that corporeal substance is unworthy of divine nature and is unable to pertain to the same (divine) nature. But, in fact, if anyone is paying close attention, he will find that I have already responded to these arguments since they are based only on this - that they suppose that corporeal substance is composed of parts which has already been shown to be absurd (P12 and P13S). So anyone who wants to weight the matter correctly will see that all those absurdities (if indeed they are all absurd, about which I do not now dispute), from which they wish to conclude that extended substance is finite, do not follow in the least because an infinite quantity is supposed, but because they suppose an infinite quantity to be measurable and forged from finite parts. So from the absurdities which follow from they can conclude only that infinite quantity is not measurable and that it is not forged from finite parts. This is the same thing we have already demonstrated above (P12, etc).

Quare telum quod in nos intendunt, in se ipsos revera conjiciunt. Si igitur ipsi ex suo hoc absurdo concludere tamen volunt substantiam extensam debere esse finitam, nihil aliud hercle faciunt quam si quis ex eo quod finxit circulum quadrati proprietates habere, concludit circulum non habere centrum ex quo omnes ad circumferentiam ductæ lineæ sunt æquales. Nam substantiam corpoream quæ non nisi infinita, non nisi unica et non nisi indivisibilis potest concipi (vide propositiones 8, 5 et 12) eam ipsi ad concludendum eandem esse finitam, ex partibus finitis conflari et multiplicem esse et divisibilem concipiunt. Sic etiam alii postquam fingunt lineam ex punctis componi, multa sciunt invenire argumenta quibus ostendant lineam non posse in infinitum dividi. Et profecto non minus absurdum est ponere quod substantia corporea ex corporibus sive partibus componatur quam quod corpus ex superficiebus, superficies ex lineis, lineæ denique ex punctis componantur. Atque hoc omnes qui claram rationem infallibilem esse sciunt, fateri debent et imprimis ii qui negant dari vacuum. Nam si substantia corporea ita posset dividi ut ejus partes realiter distinctæ essent, cur ergo una pars non posset annihilari manentibus reliquis ut ante inter se connexis? et cur omnes ita aptari debent ne detur vacuum? Sane rerum quæ realiter ab invicem distinctæ sunt, una sine alia esse et in suo statu manere potest. Cum igitur vacuum in natura non detur (de quo alias) sed omnes partes ita concurrere debent ne detur vacuum, sequitur hinc etiam easdem non posse realiter distingui hoc est substantiam corpoream quatenus substantia est, non posse dividi.

Translated as,

So the weapon they intend for us, they actually throw back on themselves. If, therefore, they want to conclude from this absurdity of theirs that extended substance must be finite, they are in reality doing nothing more than if someone created a circle has the properties of a square, and concluded that the circle has no center from which all lines drawn to the circumference are equal. For corporeal substance, which cannot be conceived except as infinite, one and only, and indivisible (see P8, 5, and 12), in order to conclude that it is finite, they conceive as forged from finite parts, to be numerous and divisible. So also others, after they create that a line is composed of points, know how to invent many arguments, by which they show that a line cannot be divided into infinity. And really it is no less absurd to assert that corporeal substance is composed of bodies or parts than that a body is composed of surfaces, the surfaces of lines, and the lines, finally, of points. All those who know that clear reason is infallible must admit this - above all those who deny that there is a vacuum. For if corporeal substance were able to be divided so that its parts were really distinct, then why could one part not be annihilated with the rest remaining conncected with one another as before? And why must they all be so fitted together that there is no vacuum? Reasonably, with things which are really distinct from one another, each one (of them) can be and remain in its condition without the other. Since, therefore, there is no vacuum in nature (about which elsewhere), but all its parts must so meet together that there is no vacuum, it also follows from this that the same (parts) cannot be really distinguished, that is that corporeal substance, insofar as it is a substance, cannot be divided.

Si quis tamen jam quærat cur nos ex natura ita propensi simus ad dividendam quantitatem? ei respondeo quod quantitas duobus modis a nobis concipitur, abstracte scilicet sive superficialiter prout nempe ipsam imaginamur vel ut substantia, quod a solo intellectu fit. Si itaque ad quantitatem attendimus prout in imaginatione est, quod sæpe et facilius a nobis fit, reperietur finita, divisibilis et partibus conflata; si autem ad ipsam prout in intellectu est, attendimus et eam quatenus substantia est, concipimus, quod difficillime fit, tum ut jam satis demonstravimus, infinita, unica et indivisibilis reperietur. Quod omnibus qui inter imaginationem et intellectum distinguere sciverint, satis manifestum erit, præcipue si ad hoc etiam attendatur quod materia ubique eadem est nec partes in eadem distinguuntur nisi quatenus materiam diversimode affectam esse concipimus, unde ejus partes modaliter tantum distinguuntur, non autem realiter. Exempli gratia aquam quatenus aqua est, dividi concipimus ejusque partes ab invicem separari; at non quatenus substantia est corporea; eatenus enim neque separatur neque dividitur. Porro aqua quatenus aqua generatur et corrumpitur; at quatenus substantia nec generatur nec corrumpitur. Atque his me ad secundum argumentum etiam respondisse puto quandoquidem id in eo etiam fundatur quod materia quatenus substantia divisibilis sit et partibus confletur. Et quamvis hoc non esset, nescio cur divina natura indigna esset quandoquidem (per propositionem 14) extra Deum nulla substantia dari potest a qua ipsa pateretur. Omnia inquam in Deo sunt et omnia quæ fiunt per solas leges infinitæ Dei naturæ fiunt et ex necessitate ejus essentiæ (ut mox ostendam) sequuntur; quare nulla ratione dici potest Deum ab alio pati aut substantiam extensam divina natura indignam esse tametsi divisibilis supponatur dummodo æterna et infinita concedatur. Sed de his impræsentiarum satis.

Translated as,

Nevertheless, if someone asks now why we, by nature, may be inclined to divide quantity, I shall respond to him that quantity is conceived by us in two ways: abstractly or, that is to say, superficially as of course we  imagine it or as substance, which is done by the intellect alone. So if we attend to quantity as it is in the imagination, which is done by us often and more easily, it will be found to be finite, divisible, and composed of parts; however if we attend to it just as it is in the intellect, and conceive it insofar as it is a substance, which happens with the most difficulty, then (as we have already demonstrated enought) it will be found to be infinite, one and only, and indivisible. This will be clear enough to all who know how to distinguish between the intellect and the imagination, particularly if it is also attended to that matter is everywhere the same and that parts are not distinguished unless insofar as we conceive matter to be affected in different ways, from whose parts are distinguished only modally, but not really. For example, we conceive that water is divided and its parts separated from one another insofar as it is water, but not insofar as it is corporeal substance. For as long as it is substance, it is neither separated nor divided. Further, water, insofar as it is water, is generated and corrupted, but insofar as it is substance, it is neither generated nor corrupted. But still with these I think I have even replied to the second argument too, since it is founded on this - that matter, insofar as it is substance, may be divisible and composed of parts. Even if this (argument) were not (adequate), I do not know why (matter) would be unworthy of divine nature. Since (by P14) outside of God there can be no substance by which it might be acted on. Everything, I say, is in God, and all things that happen, happen only through the laws of God's infinite nature and follow (as I shall show) from the necessity of his essence. So by no reason can it be said that God is acted on by another, or that extended substance is unworthy of the divine nature, even if it is supposed to be divisible, so long as it is granted to be eternal and infinite. But enough of this for the present.

Spinoza's Ethics: I.P14: Nothing But God

Here Spinoza raises the word affectiones which has been translated as "modifications" here, but is variously translated "accidents," "affections" and "states" by other translators. As I commented earlier, modifications seems most applicable. The concepts rem extensam, "extended thing" and rem cogitatem, "thinking thing" make their first appearance here. It is interesting that such profound distinctions are introduced in a Corollary 2 note.

Praeter Deum, nulla dari neque concipi potest substantia.

Translated as,

Except God, no substance can be nor be conceived.

Demonstratio: Cum Deus sit ens absolute infinitum de quo nullum attributum quod essentiam substantiae exprimit, negari potest (per definitionem 6) isque necessario existat (per propostionem 11) si aliqua substantia praeter Deum daretur, ea explicari deberet per aliquod attributum Dei sicque duae substantiae ejusdem attributi existerent, quod (per propositionem 5) est absurdum adeoque nulla substantia extra Deum dari potest et consequenter non etiam concipi. Nam si posset concipi, deberet necessario concipi ut existens; atqui hoc (per primam parem huius demonstrationis) est absurdum. Ergo extra Deum dari neque concipi potest substantia. Q.E.D.

Translated as,

Since God is an absolutely infinite being, about which no attribute that expresses the essence of substance can be denied existence (by D6). And God exists necessarily (by P11). If any substance except God were to exist, it would have to be explained through some attribute of God, and so two substances of the same attribute might exist, which (by P5) is absurd. And to such an extent, no substance beyond God can exist and consequently even be conceived. For if it could be conceived, it must necessarily be conceived as existing. But this conception (by the first part of this demonstration) is absurd. So, beyond God, substance can neither be nor be conceived.

Corollarium I: Hinc clarissime sequitur I Deum esse unicum hoc est (per definitionem 6) in rerum natura non nisi unam substantiam dari eamque absolute infinitam esse, ut in scolio propositionis 10 iam innuimus.

Translated as,

From this it follows most clearly, first, that God is one and only, that is (by D6), that in the nature of things there is only one substance and it is absolutely infinite, as we intimated in P10S.

Corollarium: Sequitur II rem extensam et rem cogitatem vel Dei attributa esse vel (per axioma 1) affectiones attributorum Dei.

Translated as,

It follows, second, that an extended thing and a thinking thing are either attributes of God, or (by A1) modifications of God's attributes.