E1P21D
Demonstration — Part I
Latin
Concipe si fieri potest (siquidem neges) aliquid in aliquo Dei attributo ex ipsius absoluta natura sequi quod finitum sit et determinatam habeat existentiam sive durationem exempli gratia ideam Dei in cogitatione. At cogitatio quandoquidem Dei attributum supponitur, est necessario (per propositionem 11) sua natura infinita. Verum quatenus ipsa ideam Dei habet, finita supponitur. At (per definitionem 2) finita concipi non potest nisi per ipsam cogitationem determinetur. Sed non per ipsam cogitationem quatenus ideam Dei constituit; eatenus enim finita supponitur esse : ergo per cogitationem quatenus ideam Dei non constituit, quæ tamen (per propositionem 11) necessario existere debet. Datur igitur cogitatio non constituens ideam Dei ac propterea ex ejus natura quatenus est absoluta cogitatio, non sequitur necessario idea Dei (concipitur enim ideam Dei constituens et non constituens). Quod est contra hypothesin. Quare si idea Dei in cogitatione aut aliquid (perinde est quicquid sumatur quandoquidem demonstratio universalis est) in aliquo Dei attributo ex necessitate absolutæ naturæ ipsius attributi sequatur, id debet necessario esse infinitum; quod erat primum. Deinde id quod ex necessitate naturæ alicujus attributi ita sequitur, non potest determinatam habere existentiam sive durationem. Nam si neges, supponatur res quæ ex necessitate naturæ alicujus attributi sequitur, dari in aliquo Dei attributo exempli gratia idea Dei in cogitatione eaque supponatur aliquando non exstitisse vel non exstitura. Cum autem cogitatio Dei attributum supponatur, debet et necessario et immutabilis existere (per propositionem 11 et corollarium II propositionis 20). Quare ultra limites durationis ideæ Dei (supponitur enim aliquando non exstitisse aut non exstitura) cogitatio sine idea Dei existere debebit; atqui hoc est contra hypothesin; supponitur enim ex data cogitatione necessario sequi ideam Dei. Ergo idea Dei in cogitatione aut aliquid quod necessario ex absoluta natura alicujus attributi Dei sequitur, non potest determinatam habere durationem sed per idem attributum æternum est, quod erat secundum. Nota hoc idem esse affirmandum de quacunque re quæ in aliquo Dei attributo ex Dei absoluta natura necessario sequitur.
English (Elwes 1883)
Conceive, if it be possible (supposing the proposition to be denied), that something in some attribute of God can follow from the absolute nature of the said attribute, and that at the same time it is finite, and has a conditioned existence or duration; for instance, the idea of God expressed in the attribute thought. Now thought, in so far as it is supposed to be an attribute of God, is necessarily (by Prop. xi.) in its nature infinite. But, in so far as it possesses the idea of God, it is supposed finite. It cannot, however, be conceived as finite, unless it be limited by thought (by Def. ii.); but it is not limited by thought itself, in so far as it has constituted the idea of God (for so far it is supposed to be finite); therefore, it is limited by thought, in so far as it has not constituted the idea of God, which nevertheless (by Prop. xi.) must necessarily exist.
We have now granted, therefore, thought not constituting the idea of God, and, accordingly, the idea of God does not naturally follow from its nature in so far as it is absolute thought (for it is conceived as constituting, and also as not constituting, the idea of God), which is against our hypothesis. Wherefore, if the idea of God expressed in the attribute thought, or, indeed, anything else in any attribute of God (for we may take any example, as the proof is of universal application) follows from the necessity of the absolute nature of the said attribute, the said thing must necessarily be infinite, which was our first point.
Furthermore, a thing which thus follows from the necessity of the nature of any attribute cannot have a limited duration. For if it can, suppose a thing, which follows from the necessity of the nature of some attribute, to exist in some attribute of God, for instance, the idea of God expressed in the attribute thought, and let it be supposed at some time not to have existed, or to be about not to exist.
Now thought being an attribute of God, must necessarily exist unchanged (by Prop. xi., and Prop. xx., Coroll. ii.); and beyond the limits of the duration of the idea of God (supposing the latter at some time not to have existed, or not to be going to exist) thought would perforce have existed without the idea of God, which is contrary to our hypothesis, for we supposed that, thought being given, the idea of God necessarily flowed therefrom. Therefore the idea of God expressed in thought, or anything which necessarily follows from the absolute nature of some attribute of God, cannot have a limited duration, but through the said attribute is eternal, which is our second point. Bear in mind that the same proposition may be affirmed of anything, which in any attribute necessarily follows from God's absolute nature.
Modern English
Suppose, for the sake of argument, that something in some attribute of God can follow from its absolute nature and yet be finite and have a determinate existence or duration — for example, the idea of God in thought. But thought, since it is supposed to be an attribute of God, is by its nature necessarily infinite (E1P11). Yet insofar as it has the idea of God, it is supposed finite. Now by (E1D2), a finite thing cannot be conceived unless it is bounded by thought itself. But not by thought insofar as it constitutes the idea of God (for in that respect it is supposed to be finite); so it must be bounded by thought insofar as it does not constitute the idea of God — thought which nevertheless (E1P11) must necessarily exist. There is, then, a thought that does not constitute the idea of God; and so from its nature, insofar as it is absolute thought, the idea of God does not necessarily follow. For it is conceived both as constituting and as not constituting the idea of God. Which is against our hypothesis. So if the idea of God in thought, or anything (it makes no difference what is taken, since the demonstration is universal) in any attribute of God, follows from the necessity of the absolute nature of that attribute, it must necessarily be infinite. Which was the first point.
Next: what follows from the necessity of the nature of some attribute cannot have a determinate existence or duration. For suppose otherwise — suppose a thing that follows from the necessity of the nature of some attribute is given in some attribute of God (for example, the idea of God in thought), and suppose it at some time did not exist, or is not going to exist. But since thought is supposed to be an attribute of God, it must exist both necessarily and unchangeably (E1P11) and (E1P20C2). So beyond the limits of the duration of the idea of God (for the idea is supposed not to have existed at some time, or not to be going to exist), thought would have to exist without the idea of God. But this is against our hypothesis: it was supposed that from given thought the idea of God necessarily follows. Therefore the idea of God in thought, or anything that follows necessarily from the absolute nature of some attribute of God, cannot have a determinate duration; through that same attribute it is eternal. Which was the second point. Note that the same is to be affirmed of any thing whatever that follows necessarily in some attribute of God from God's absolute nature.