Spinoza's Ethics' Axiom Seven

Question

There seems to be a problem with Axiom VII from Spinoza's Ethics:

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

1. How can this be axiomatic? God can be conceived as non-existing, so by this Axiom, His essence should not involve existence. Yet, the author is striving to prove God's existence as the one and only substance. Moreover, we can hardly conceive a tesseract as existing, but that does not mean that it cannot exist in a metaphysical ontological space. In other words, how can we prove the non-existence of things that we cannot conceive?

2. On the other hand,

   • By Definition VI, God has unlimited attributes: 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.

   • By Prop. XIV, only God exists. PROP. XIV. Besides God no substance can be granted or conceived.
     

   Therefore, if only God has unlimited attributes, only He has unlimited power of understanding, in other words, only He could conceive anything as existing, and thus give existence to anything. On the other hand, He can also conceive anything as non-existing, and thus anything may not exist.

So, can this axiom be reconciled in any way?

Answer 1

How can this be axiomatic?

Spinoza is using an axiomatic method to think through a certain emanationist theory.

Axioms by their nature are to be taken as granted; and it is the reasoning that follows that is usually subject to considerations of soundness.

To put this into context, consider the first few definitions in Euclidean geometry as Euclid theorised and conceived it.

1.1A point is that which has no part

1.2 A line is a breadthless width

1.3 The extremities of lines are points

Now if one began to do geometry by disputing all of these (and they can be disputed - there are objects with no points, there are points which always have parts, or have extension) then one is hardly learning geometry; and the disputation is of no (mathematical) consequence, because as a sustained critique it came after, and not before; thus to display this knowledge, charitably can be excused as enthusiasm; less charitably as flattering themselves with a little purloined knowledge.

The point I'm making is that if one is not interested in geometry then one ought not to be taking a class in geometry.

Similarly, if one isn't interested in neo-Platonism and how it has intersected the Abrahamic traditions it seems quixotic to dispute it, before one has begun to understand it.

A secondary but still important point is that Euclid, far from inventing geometry placed it on coherent foundations; and this is part of the nature of axiomatic systems - if one looks into the history of axiomatics one generally notices a pattern of accumulating propositions until they are placed in a coherent manner - to give a recent example structuralism in Algebra before being put into a coherent axiomatic form through the notion of Category and Functor (by MaClane and Eilenberg).

God can be concieved as not existing

This is incoherent, and like saying 'I can concieve that Green is not Green', which might make for an interesting poetics, but logically inconsistent.

If one accepts the axiom that God exists, and this in the sense described by the three monotheisms; then one can't immediately deny it.

What one can do is simply deny the first axiom: that there is a God; and many people do make this move - and not as a move on a game but as a reality.