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WARNING: extremely nerdy thread incoming.
There's something odd about the rhetoric of Spinoza's demonstrations in the Ethics.
Ordinarily, the structure you'd expect is:
Proposition: _______
Demonstration:_______
.
.
.
QED
right? (1/n)
There's something odd about the rhetoric of Spinoza's demonstrations in the Ethics.
Ordinarily, the structure you'd expect is:
Proposition: _______
Demonstration:_______
.
.
.
QED
right? (1/n)
And this is usually the structure he uses. But not always. In particular, he sometimes omits the QED. So I decided that I'd try and find out whether there's some commonality to the proofs in which he omits the QED. The results were... mixed. (2/n)
The tally of demonstrations w/o QEDs is:
EI: 11
EII: 8
EIII:1
EIV: 3
EV: 2
(This is omitting propositions whose proofs say "this is proved in the same manner as some antecedent proposition"; those, I figured, don't affect this analysis.) (3/n)
EI: 11
EII: 8
EIII:1
EIV: 3
EV: 2
(This is omitting propositions whose proofs say "this is proved in the same manner as some antecedent proposition"; those, I figured, don't affect this analysis.) (3/n)
Initially I thought that he might omit the QED in cases where the proposition was self-evident, or evident through definitions alone. And this fits most of them, but not all. (4/n)
For example, EIp12 ("No attribute of substance can be truly conceived from which it would follow that substance can be divided") omits QED, but usesEIp2, p5, p6, p8,p10, and d4. The others from EI area
mixture of stuff like that and following immediately from the defs. (5/n)
mixture of stuff like that and following immediately from the defs. (5/n)
Further, the demonstration of EIp10 uses only definitions, but has QED! So that hypothesis doesn't fit the data perfectly. (6/n)
But it does fit some of the rhetoric in the proofs. 19/25 of the propositions which don't use QED say that the prop is either self-evident or from something else. So it's looking to fit my initial guess of "he doesn't use them when it's self-evident", but not perfectly. (7/n)
Of the remaining 6 propositions 4 (possibly 5) are proved by reductio. One could argue that this bequeaths to the propositions a certain amount of self-evidence (i.e., that is self-evident whose contrary is contradictory). (8/n)
So that leaves us with the stubbornest proposition of all, EVp35, which says that God loves himself with infinite intellectual love. Not sure what to do with it, but I must admit that the rest fits the hypothesis fairly well. So not sure where to go from here. (9/9)
(this thread brought to you by two-coffees-and-an-energy-drink-after-workout bourbaki)
