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I'm having a rather difficult time understanding this proof. While the rest of the propositions are relatively easy to follow, I am completely lost as to how it is absurd to think that the essence doesn't involve existence. Would someone mind walking me through the proof? Nothing online seems to help...

PROP. XI. God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists.

Proof: If this be denied, conceive, if possible, that God does not exist: then his essence does not involve existence. But this (Prop. vii.) is absurd. Therefore God necessarily exists.

  • Here's a comment from @André Souza Lemos from here See definition II, part II: "I consider as belonging to the essence of a thing that, which being given, the thing is necessarily given also, and, which being removed, the thing is necessarily removed also; in other words, that without which the thing, and which itself without the thing, can neither be nor be conceived". It is a reciprocal definition. Existence is involved in the essence of substance, and the being of other things is within substance. – Cicero Mar 18 '16 at 4:16
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The argument of Spinoza's Ethics is:

Prop.XI. God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists.

Proof. If this be denied, conceive, if possible, that God does not exist: then his essence does not involve existence. But this (Prop.VII) is absurd. Therefore God necessarily exists.

The "essence implies existence" relies on:

Prop.VII. Existence belongs to the nature of substances.

Proof. Substance cannot be produced by anything external (Corollary, Prop.VI), it must, therefore, be its own cause—that is, its essence necessarily involves existence, or existence belongs to its nature.

and this, in turn, with the definition of God:

Def.VI. By God, I mean a being absolutely infinite — that is, a substance consisting in infinite attributes, of which each expresses eternal and infinite essentiality.

licenses the conclusion.


Comment

Seemingly, in the "proof" of Prop.IX we need also:

Ax.VII. If a thing can be conceived as non-existing, its essence does not involve existence.

Thus: "conceive, if possible, that God does not exist [...] But this is absurd. Therefore God necessarily exists."


In conclusion, we can state at least two "debatable" points:

  • is it really "absurd" to conceive "that God does not exist" ?

  • is it really necessary that for substance "essence involves existence" ?

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