Spinoza took all possible things that could be [infinity] and called it God - Then proved that things cannot exist without existing within God.

There is no with'out' God, so there is no 'nothing' - God (infinity, Substance) is 'all'things, 'every'thing.

Spinoza's infinity [God] is an abstraction that accounts for everything that could possibly ever exist [he gives it the essence of existence] and thus, says that all that appears are manifestations of this infinite existence [modes].

He argues that all ideas are within God too [God is infite after all!].

By his own argument - The idea of nothingness must be within God [Note, not the object of nothingness, the 'idea'] and thus, must exist, even as an abstraction 'potential', or 'idea'.

Hmm... Paradox?

Nothingness is by necessity [according to Spinoza] a representation of an aspect of God [Substance] - Because otherwise, we could not think about it.

This to me suggests something:

Spinoza had an idea of infinity [absolute, not limited by its kind] that must account for all existence.
Substance then, not willingly, [God has no free will for Spinoza] had in it, the idea of nothingness, and this nothingness is modulated as 'nothingness'.

I count this 'nothing' as an absence, not as a thing-itself.

This idea of nothingness, this plagues even Spinoza's Substance - Because the idea exists, then, it must also exist within Substance [God].

To me, the idea that all that exists, exists within God is not hard to understand - Spinoza simply means that whatever exists, does in-fact exist, and whatever doesn't exist, doesn't exist [These 'not-existing' things cannot exist].
However, 'nothingness' as an idea implies an absence, something that is not possible within Spinoza's Substance, as that would imply a finite essence [but Substance is infinite].
So, how can Substance have a module that apparently expresses no-thing?

I can think of one answer right now:

- No-thing exists [It exists as much as anything that we can express must exist in God, even though we cannot understand it] [Spinoza made a point of stating that Nature [God] was not made for men, we simply attempt to understand].

This would mean that, existence [as per the essence of Substance] must include the idea of all absence of existence [note, this is not the negation of existence itself] because the idea of an absence of existence is expressable [Note again, this is not the negation of existence, simply the idea of the absence of the existence of something]

I cannot see how Spinoza's Substance is not a dichotomy, I see it as the logical limit of Ontology.
- That what is, is by its very existence [is, that is]

It also allows for the negation of existence of things [the idea of the absence of a thing - The fact that things are all seperate, by virtue of our module of existence].

Mono, did spinoza translate god into set theory?
in that case, my poor right brain cannot even make it to entrance examination .....

As far as I understand his work (the Ethics) Spinoza utilised ideas that may have become parts of 'set theory', though I am no expert on set-theory! Given that he used the concepts of an 'infinite set' as a logical axiom (Substance), and then many sub-sets (modulation) that are expressed within that infinite Substance...

If you are holding out on information, then please fill me in!

I suppose, the paradox I have highlightes seems to be something akin to the 'set of all sets' paradox, a set made of elements that cannot be contained in the set without contradiction -
Russell's barber (male) that only shaves all the men that do not shave themselves, and so, would have to shave himself if he does not shave himself...

This is much like the idea of the nothingness idea as a part of the set that cannot contain the antithesis of itself -
Spinoza's Substance contains within it, everything, including the idea of the absence of everything within it...

Have you read Being & Nothingness by Jean-Paul Sartre?