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This is the english translation I am reading from for Spinoza's Ethics Geometrically. In proposition IX of this work, spinoza states:

PROP. IX. The more reality or being a thing has, the greater the number of its attributes (Def. iv.)

Here, no proof is given (most of Spinoza's propositions are proven, but for simple ones at the beginning Spinoza merely cites the appropriate definitions and axioms). Hence, it appears that this proposition should follow from definition iv.

Now, definition iv states

By attribute, I mean that which the intellect perceives as constituting the essence of substance.

What I don't understand is how this definition informs us about the magnitude of the reality of a being thing. How does Spinoza's definition of an attribute render proposition ix a trivial consequence (as the mere citation as opposed to explicit proof seems to indicate)?

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The substance (of which Spinoza will later state that there is only one, and that it is God) is truly known by the intellect, in its essence, from itself, and by itself, through its attributes.

That there are a multitude of attributes is not contradictory to the fact that the substance they express is one:

It is, then, far from an absurdity to ascribe several attributes to one substance: for nothing in nature is more clear than that each and every entity must be conceived under some attribute, and that its reality or being is in proportion to the number of its attributes expressing necessity or eternity and infinity. (PROP. X - Note)

As "each and every entity must be conceived under some attribute", the conception of any entity whatsoever implies an expression of the substance. An interpretation could be that substance expresses itself, in entities, in different degrees, according to the abundance of attributes. More substance, more attributes. "Signs" of existence are not actually signs; they are what existence is. That's why def. iv comes to the rescue here.

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    Is this reasoning correct -- Attributes express the essence of a substance. So the more attributes, the more essence. And because something's essence is its reality or being, the more essence something has, the more reality or being it has. – Cicero Jul 1 '15 at 1:44
  • The point of confusion for me was the notion that something's essence is its reality or being. Is this idea correct? – Cicero Jul 1 '15 at 1:45
  • There is no "a" substance. Only substance - singular. According to Spinoza, humans can only know two attributes: thought and extension, because we are made of spirit and body. We know that there is an infinity of attributes, because God has an absolutely infinite potency of existing, that is not limited by thought or extension. – André Souza Lemos Jul 1 '15 at 2:26
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    Regarding essence, take a look at the definition II at 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. – André Souza Lemos Jul 1 '15 at 2:43
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    I understand there is only one substance, but that is established by a later proposition. Hence, I am trying to understand the preceding reasoning by presupposing there is not necessarily one substance. By understanding the logic and building my way up, I can then understand how Spinoza establishes that there is only one substance. Besides that, your second comment is very insightful, which is why I have upvoted it. Thank you very much. – Cicero Jul 1 '15 at 4:23

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