Note: From now on, I will use my own translations and dispense with using those of others. The quarantine has allowed time for me to significantly improve my Latin translating ability.
The proposition follows logically from those preceding. Spinoza establishes that two different substances cannot share the same attribute (I.P5). If there were two different substances with two different attributes, then they would have nothing in common with one another (I.P2). If these substances have nothing in common, then one cannot produce the other because causality requires commonality (I.P3).
The demonstration is fairly close to my own comments on the proposition. The demonstration does have a couple of interesting aspects. The first to note is that Spinoza has yet to prove exactly how many or how few substances exist. The second is his usage of the Latin conjunction sive. Sive is different than aut. Aut is translated as "or" as a mutually exclusive term. Sive comes Latin words meaning "if you prefer" - the second term renders an equivalent to the first term and the reader gets to choose the preferred term.
The corollary takes a slight different logical tactic by relying primarily on the axioms and definitions rather than the propositions. In this approach, Spinoza takes a "view from nowhere" and does not include a discussion of attributes or a discussion of intellect or perception. This seems appropriate as the discussion is of substances only.
The alternative explanation takes a novel approach to eliminating the
notion that substance can produce substance. However, this approach does
not assist in limiting the number of substances to one. Rather, each
substance would only be understood through itself only.
Una substantia non potest produci ab alia substantia.
Translated as,
One substance cannot be produced by another substance.
Demonstratio: In rerum natura non possunt dari duae substantia ejusdem attributi (per propositionem praecedentem) hoc est (per propositionem 2) quae aliquid inter se commune habent. Adeoque (per propositionem 3) una alterius causa esse nequit sive ab alia non potest produci. Q.E.D.
Translated as,
In the nature of things, two substances of the same attribute are unable to exist (through the preceding proposition), that is, (through proposition 2) two substances which have something in common. And to such an extent (through proposition 3) one substance is unable to be the cause of another or, said differently, one substance is unable to be produced by another.
Corollarium: Hinc sequitur substantiam ab alio produci non posse. Nam in rerum natura nihil datur praeter substantias earumque affectiones ut patet ex axiomate 1 definitionibus 3 et 5. Atqui a substantia produci non potest (per praecedentem propositionem). Ergo substantia absolute ab alio produci non potest. Q.E.D.
Translated as,
From here it follows that substance is unable to be produced by anything else. For nothing exists in the nature of things except substances and their modifications as explained in axiom 1 and definitions 3 and 5. Further, a substance cannot be produced by a substance (through the preceding proposition). Thus, a substance is absolutely unable to be produced by anything else.
Aliter: Demonstratur hoc etiam facilius ex absurdo contradictorio. Nam si substantia ab alio posset produci, ejus cognitio e cognitione suae causae deberet pendere (per axioma 4) adeoque (per definitionem 3) non esset substantia.
This is shown even more easily by an absurd contradiction. For if a substance is able to be produced by anything else, then the knowledge of a substance would be gained by the knowledge of its cause (through axiom 4) and to such an extent (through definition 3), it would not be a substance.
No comments:
Post a Comment