Spinoza's Ethics: I.D3: Substance

This definition of "substance" is like the definition of “self-caused” (or I.D1) since it follows that substance might also be described as "cannot be conceived except as existing" due to the challenges of conceiving something which is "in itself" and "conceived through itself" which does actually not exist. Further, Spinoza implies substance as not limited (thus infinite) as defined in I.D2, since it cannot be limited in its own kind if "it is in itself and is conceived through itself." 

If these implications are true of substance, as self-caused from I.D1 and not finite from I.D2, then it may follow that nothing exists except substance - and even logically implies only one substance. 

Again, the verb is all-important. Spinoza uses “conceive” or concipit as a verb of thinking with the particular sense of having “a view from nowhere” structured by general logic (mathematically delimiting, but non-numerical). He is not using a verb of thinking that is set in a particular time or place. Instead, he is using a verb to describe something which is true for all time. 

Another way to understand “a view from nowhere” is the implication here that substance is Knowing. Knowing has a sense of seeing as a whole, while Thinking is a term that we use for more of a process. So it may mean (and I believe it does) that Knowing is intrinsic to substance. The duality from the first two definitions is carried through here as well. The “mind-body” duality identified in the first two definitions unfolds into substance duality as “conceived through itself” or Knowing and “is in itself” or Being. 

Per substantiam, intellego id quod in se est et per se concipitur hoc est id cujus conceptus non indiget conceptu alterius rei a quo formari debeat.

Translated as:

By substance, I understand what is in itself and is conceived through itself, that is, that whose concept does not lack the concept of another thing by which it needs to be formed.

Spinoza's Ethics: I.D2: Finitude

In I.D2, Spinoza carefully defines something as finite "in its own kind." For anything to have limits, these limits are created jointly, not unilaterally. There needs to be something or somethings at all limiting points. For this something (or collection of somethings) to jointly create a limit outside of the primary thing itself, the outsidedness must be greater than that insidedness.

Ea res dicitur in suo genere finita quae alia ejusdem naturae terminari potest. Exempli gratia corpus dicitur finitum quia aliud semper majus concipimus. Sic cogitatio alia cogitatione terminatur. At corpus non terminatur cogitatione nec cogitatio corpore.

Translated as:

That thing is said to be finite in its own kind that can be limited by another of the same nature. For example, a body is called finite because we always conceive another that is greater. Thus a thought is limited by another thought. But a body is not limited by a thought nor a thought by a body.