Spinoza's demonstration is thorough and slightly different than what
might be anticipated. Spinoza's first argument relates to the division
of substance as a problematic creation of a substance. However, his
second demonstration relates to a parts and whole reasoning process,
where the division would destroy a substance. Both of them make sense
and reveal Spinoza's pattern of finding more than one way to demonstrate
and confirm his propositions. It is also interesting that in this
proposition he pairs the term attribute with conceived instead of
perceived. It is likely that the reason for this is that the nature of
this proposition is more a "view from nowhere" rather than a "view from
somewhere."
Nullum substantiae attributum potest vere concipi ex quo sequatur substantiam posse dividi.
Also translated as,
No attribute of a substance can be truly conceived from which it could follow that a substance can be divided.
Demonstratio: Partes enim in quas substantia sic concepta divideretur, vel naturam substantiae retinebunt vel non. Si primum, tum (per propositionem 8) unaquaeque pars debebit esse infinita et (per propositionem 6) causa sui et (per propositionem 5) constare debebit ex diverso attributo adeoque ex una substantia plures constitui poterunt, quod (per propositionem 6) est absurdum. Adde quod partes (per propositionem 2) nihil commune cum suo toto haberent et totum (per definitionem 4 et per propositionem 10) absque suis partibus et esse et concipi posset, quod absurdum esse nemo dubitare poterit. Si autem secundum ponatur quod scilicet partes naturam substantiae non retinebunt, ergo cum tota substantia in aequales partes esset divisa, naturam substantiae amitteret et esse desineret, quod (per propositionem 7) est absurdum.
Translated as,
For the parts into which substance is conceptually divided either retain the nature of a substance or not. If the first, then (by P8) each and every part will have to be infinite, and (by P6) its own cause and (by P5) each part will have to be structured from different attribute so that many (substances) can be formed from one substance, which is absurd (by P6). Add that the parts would have nothing in common with their whole (by P2), and the whole (by D4 and P10) could be and be conceived without its parts which no one will be able to doubt is absurd. Moreover, if the latter were supposed, namely that the parts do not retain the nature of substance, then when dividing the whole substance into equal parts, it would lose the nature of substance and cease to exist which (by P7) is absurd.
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