First off, the way you phrase Spinoza's conception of "divine nature for the existence of anything" is more complicating than it should be.
In a broad overview of Spinoza The Ethics
, it is divided into 5 distinct sections.
Section 1 is on the nature of God.
Section 2 is on the nature and origins of the mind.
Section 3 is on the nature and origins of emotion.
Section 4 is on the power of emotions (i.e. human bondage)
Section 5 is on the human freedom (i.e. power of intellect)
Section 1 deals with the metaphysical aspects of Spinoza's philosophy. His ontology of the universe is essential to everything in both Ethics I
and Ethics II
. But this brings up a very important point that should always be taken into account before reading Spinoza. Put in the context of Spinoza's predecessor Descartes, Spinoza follows a "Synthetic" approach to his philosophy. Descartes, most importantly in Meditations
and Discourse on Method
, follows an "analytic" type of philosophy. It should also be noted that these terms (i.e. analytic and synthetic) are official terms recognized in the academic community. Anyway, Descartes follows an analytic philosophy. In the works that I just mentioned written by him, he follows a system not unlike modern scientific method. He breaks everything down (med 1), analyzes down to the simplest components, reconstructs what he knows clearly and distinctly, and renumerates. So Descartes is building from the ground up so to speak. Now Spinoza comes along and does things differently.
Spinoza in Ethics follows an interesting pattern. Look at how he sets up Ethics
. The very first section concerns god of course, but look at the format. He starts off with definitions, axioms, and then leads into propositions for the rest of the book. Spinoza, unlike Descartes is building his methodology the other way round
by assuming the existence of god first instead of building from the ground up as Descartes had.
Spinoza departs from the form of Descartes' methodology and bases his system on quite the opposite of Descartes, a system based on an initial set of axioms, propositions, and definitions as put down in beginning of The Ethics.
These established "provisions" at it were, form the basis for Spinoza's assumptions and deductions in the latter parts of his text. So Spinoza in the first part of The Ethics
concerns himself with the properties and nature of God. Spinoza maintains that God is a being who is absolute, is the only substance and also that all other things are modes of God, etc. But throughout all of these derived attributes of God, Spinoza depends on the pre-established sets of axioms and definitions in order to prove his position, namely that of God.
Now coming to your post, I don't follow your syllogism. In Ethicssubstance