Friday, July 17, 2020

Spinoza's Ethics: I.P13: One Substance Indivisible

This proposition follows in a clear form from those the precede it. However, I do find it particularly interesting to note that he finds it relevant to note note a substantiam corpoream or "corporeal substance." If the essence of substance is existence, then isn't "corporeal substance" redundant? If it's not, then what is the manifestation of existence as substance? 

Substantia absolute infinita est indivisibilis.

Translated as,

An absolutely infinite substance is indivisible.

Demonstratio: Si enim divisibilis esset, partes in quas divideretur vel naturam substantiae absolute infinitae retinebunt vel non. Si primum, dabuntur ergo plures substantiae ejusdem naturae, quod (per propositionem 5) est absurdum. Si secundum ponatur, ergo (ut supra) poterit substantia absolute infinita desinere esse, quod (per propositionem 11) est etiam absurdum.

Proof: For if it were divisible, the parts into which it would be divided will either retain the nature of an absolutely infinite substance or they will not. If the first, then there will given more substances of the same nature, which (by P5) is absurd. But if the second is put forth, thus (as above in P12), an absolutely infinite substance would be able to cease existing, which (by P11) is also absurd.

Corollarium: Ex his sequitur nullam substantiam et consequenter nullam substantiam corpoream, quatenus substantia est, esse divisibilem.

Translated as,

From these propositions, it follows that no substance, and thus no corporeal substance, insofar as it is a substance, is divisible.

Scholium: Quod substantia sit indivisibilis, simplicius ex hoc intelligitur quod natura substantiae non potest concipi nisi infinita et quod per partem substantiae nihil aliud intelligi potest nisi quam substantia finita, quod (per propositionem 8) manifestam contradictionem implicat.

Translated as,

With respect to that substance is indivisible, is understood more simply from this, that the nature of substance cannot be conceived unless as infinite, and that by a part of substance nothing else can be understood except a finite substance, which (by P8) implies a clear contradiction.

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Spinoza's Ethics: III.P47

Lætitia quæ ex eo oritur quod scilicet rem quam odimus destrui aut alio malo affici imaginamur, non oritur absque ulla animi tristitia. Joy ...