In this proposition, Spinoza states and proves the existence of one and only one substance. This is critical to the rest of his work. Yet the second Scholium provides the first mention and usage of the Latin word affectus in this work. I have chosen here to translate the Latin word affectus with the English word "emotion". Affectus will become a critical word later and many translators use the word "feelings" to describe it. For many, "emotion" and "feelings" are interchangeable. But I choose to use the word "emotion" for translation because its Latin roots ex- "out" and movere "to move" are more related to Spinoza's use of affectus. Affectus is a variational mode of thinking, not a physical mode of extending, which accompanies a representational mode of thinking. For example, in the sentence "John loves Mary," John has a variational mode of thinking called "love" which is an emotion or change or, more specifically, a movement to a greater perfection which is accompanied by a representational mode of thinking called "Mary". Much of this usage is detailed later, but Spinoza makes it clear in this Scholium that people are ignorant of the way affectus in mente producuntur "emotions (or changes) are produced in the mind." Spinoza is establishing the nature of affectus as a mode of thinking in this first mention in the Ethics and the only mention in Part I. This is logical, since God is perfect and does not move to a greater or lesser perfection, there is no possibility for emotion or change or variational mode of thinking in God. For Spinoza, the sentence "God loves humans" is nonsense, not because God doesn't exist and not because God doesn't have ideas, but because God doesn't have variational modes of thinking.
Omnis substantia est necessario infinita.
Translated as,
Every substance is necessarily infinite.
Demonstratio: Substantia unius attributi non nisi unica existit (per propositionem 5) et ad ipsius naturam existere pertinet (per propositionem 7). Erit ergo de ipsius natura vel finita vel infinita existere. At non finita. Nam (per definitionem 2) deberet terminari ab alio ejusdem naturae quae etiam necessario deberet existere (per propositionem 7) adeoque darentur duae substantiae ejusdem attributi, quod est absurdum (per propositionem 5). Existit ergo infinita. Q.E.D.
Translated as,
A substance of one attribute does not exist unless it is unique (through P5) and existence belongs to its nature (through P7). So its nature is to exist either as finite or infinite. But it is not finite because (through D2) it would have to be limited by something of its own nature which also exists necessarily (through P7). This is absurd (through P5) because it would mean that two substances of the same attribute would exist. So substance exists as infinite.
Scholium I: Cum finitum esse revera sit ex parte negatio et infinitum absoluta affirmatio existentiae alicujus naturae, sequitur ergo ex sola propositione 7 omnem substantiam debere esse infinitam.
Translated as,
Since being finite is truly a negation in part and being infinite is an absolute affirmation of the existence of some nature, it follows from P7 alone that every substance has to be infinite.
This proposition follows logically from those preceding it. Spinoza did not include the phrase "of its own kind" with infinite in contrast to D6 where God was described as "absolutely infinite." It seems that he does not find it necessary to delineate substance with "of its own kind" as substance's exclusive nature (in terms of attribute) is demonstrated in P5.
On to an extremely long, but significant note:
Scholium II: Non dubito quin omnibus qui de rebus confuse judicant nec res per primas suas causas noscere consueverunt, difficile sit demonstrationem 7 propostionis concipere; nimirum quia distinguunt inter modificationes substantiarum et ipsas substantias neque sciun quomodo res producuntur. Unde fit ut principium quod res naturales habere vident substantiis affingant; qui enim veras rerum causas ignorant, omnia confundunt et sine ulla mentis repugnantia tam arbores quam homines loquentes fingunt et homines tam ex lapidibus quam ex semine formari et quascunque formas in alias quascunque mutari imaginantur. Sic etiam qui naturam divinam cum humana confundunt, facile Deo affectus humanos tribuunt praesertim quamdiu etiam ignorant quomodo affectus in mente producuntur. Si autem homines ad naturam substantiae attenderent, minime de veritate 7 propositionis dubitarent; imo haec propositio omnibus axioma esset et inter notiones communes numerarentur. Nam per substantiam intellegerent id quod in se est et per se concipitur hoc est id cujus cognitio non indiget cognitione alterius rei. Per modificationes autem id quod in alio est et quarum conceptus a conceptu rei in qua sunt, formatur: quocirca modificationum non existentium veras ideas possumus habere quandoquidem quamvis non existant actu extra intellectum, earum tamen essentia ita in alio comprehenditur ut per idem concipi possint. Verum substantiarum veritas extra intellectum non est nisi in se ipsis quia per se concipiuntur. Si quis ergo diceret se claram et distinctam hoc est veram ideam substantiae habere et nihilominus dubitare num talis substantia existat, idem hercle esset ac si diceret se veram habere ideam et nihilominus dubitare num falsa sit (ut satis attendenti sit manifestum); vel si quis statuat substantiam creari, simul statuit ideam falsam factam esse veram, quo sane nihil absurdis concipi potest adeoque fatendum necessario est substantiae existentiam sicut ejus essentiam aeternam esse veritatem. Atque hinc alio modo concludere possumus non dari nisi unicam ejusdam naturae, quod hinc ostendere operae pretium esse duxi. Ut autem hoc ordine faciam notandum est I veram uniuscujusque rei definitionem nihil involvere neque exprimere praeter rei definitae naturam. Ex quo sequitur hoc II nempe nullam definitionem certum aliquem numerum individorum involvere neque exprimere quandoquidem nihil aliud exprimit quam naturam rei definitae. Exempli gratia definitio trianguli nihil aliud exprimit quam simplicem naturam trianguli; at non certum aliquem triangulorum numerum. III notandum dari necessario uniuscujusque rei existentis certam aliquam causam propter quam existit. IV denique notandum hanc causam propter quam aliqua existit, vel debere contineri in ipsa natura et definitione rei existentis (nimirum quod ad ipsius naturam pertinet existere) vel debere extra ipsam dari. His positis sequitur quod si in natura certus aliquis numerus individuorum existat, debeat necessario dari causa cur illa individua et cur non plura nec pauciora existunt. Si exempli gratia in rerum natura 20 homines existant (quos majoris perspicuitatis causa suppono simul existere nec alios antea in natura exstitisse) non satis erit (ut scilicet rationem reddamus cur 20 homines existant) causam naturae humanae in genere ostendere sed insuper necesse erit causam ostendere cur non plures nec pauciores quam 20 existant quandoquidem (per III notam) uniuscujusque debet necessario dari causa cur existat. At haec causa (per notam II et III) non potest in ipsa natura humana contineri quandoquidem vera hominis definitio numerum vicenarium non involvit adeoque (per notam IV) causa cur hi viginti homines existunt et consequenter cur unusquisque existit, debet necessario extra unumquemque dari et propterea absolute concludendum omne id cujus naturae plura individua existere possunt, debere necessario ut existant causam externam habere. Jam quoniam ad naturam substantiae (per jam ostensa in hoc scholio) pertinet existere, debet ejus definitio necessariam existentiam involvere et consequenter ex sola ejus definitione debet ipsius existentia concludi. At ex ipsius definitione (ut jam ex nota II et III ostendimus) non potest sequi plurium substantiarum existentia; sequitur ergo ex ea necessario unicam tantum ejusdem naturae existere, ut proponebatur.
Translated as,
Even more, I do not doubt that it is difficult to conceive the demonstration of P7 for all who assess things confusedly and are not accustomed to identifying things through their true causes. It is not surprising since they do not distinguish between measured modifications of substance and substances themselves nor do they understand how things are produced. From this, it follows that they embellish substances with a beginning point that they see natural things possess. For those who are ignorant of the true causes of things confuse everything. And without any cognitive dissonance they invent trees speaking just as men do and they imagine that men are formed from stones in the same way as from sperm and any form whatsoever can be changed into any other form. In this way there are those who confuse divine nature with human nature, easily attributing human emotions to God especially since they are ignorant of the way in which emotions are produced in the mind.
Moreover, if people would pay close attention to the nature of substance, then they would have the least doubt about the truth of P7. No, indeed this proposition would even be an axiom for everyone and be counted among common ideas. For they would comprehend that substance means that which is in itself and conceived through itself, that is, the cognition of which does not require the cognition of anything else. Further, (they would comprehend) that what is formed through (measured) modifications is in another and the concepts of it are from the concept of another thing in which it exists. For this reason, we are able to have true ideas of (measured) modifications that do not exist, seeing that although they do not actually exist outside the intellect, nevertheless the essence of these (ideas) is grasped in another thing so that the ideas are able to be conceived through that same thing. However, the true conception of substances does not exist outside the intellect unless that conception exists within the intellect by means of the substances themselves because substances are conceived through themselves. So, if anyone might claim to have a clear and distinct idea of substance, that is a true one, and nevertheless doubts whether such substance exists would be the same as if, (seriously!) he claimed to have a true idea and nevertheless doubts whether it is false (as enough consideration should make clear). Or if anyone might claim that substance is created, he is at the same time determining that a falsified idea is true. In a sane way of thinking, nothing more absurd can be conceived. To this degree it must necessarily be acknowledged that the existence of a substance, just as its eternal essence, is a true conception.
So next we may deduce in another way that substance cannot exist unless it is unique in terms of having the same nature as another - which I outline here to show the value of the effort. Further, so that I might do so in an orderly fashion, it should be noted that:
1) the true definition of each and every thing involves and expresses nothing except the nature of the thing defined,
2) from this, it follows that certainly no definition involves or expresses some certain number of individuals, (since the definition expresses nothing other than the nature of the thing defined. For example, the definition of a triangle expresses nothing other than the simple nature of the triangle, but not a certain number of triangles.)
3) it should be noted that there is necessarily some certain cause for the existence of each and every thing by which it exists,
4) finally, it should be noted that this cause (on account of which some thing exists) must be contained in the nature and definition of the existing thing itself (that is, which pertains to its nature to exist) or must be outside it.
Due to these propositions, it follows that if a certain number of individuals exists in nature, then it is necessary to provide the reason why those specific individuals exist and neither more nor less. If, for example, in the course of nature 20 men were to exist, (who, for the sake of clarity, I suppose all to exist at the same time and no others to have existed before them) it will not be enough (so with certainty that we can give the reason why 20 men exist) to show the cause of human nature in general, but it will be necessary to further show why not more or less than 20 men exist since (under point 3) the reason why each and every one of them exist must be provided. But this cause (under points 2 and 3) is not held in human nature itself since the true definition of human does not involve the number twenty. As a result, (under point 4) the reason why these twenty men exist and, consequently, why each and everyone of them exists is necessarily outside each and everyone of them. So one may absolutely conclude that everything whose nature allows multiple individuals of it to exist necessarily has an external cause for their existence. Now, since it is the nature of a substance to exist (as we have already shown in this note), the definition of substance must include necesssary existence and from this definition alone existence itself should be acknowledged. Further, from the definition of substance itself, the existence of multiple substances does not follow (as we just showed in points 2 and 3). So it follows that only one substance of the same nature exists, as was proposed.
