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.
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