Generations and generations come and go, but the Earth remains forever.
- Ecclesiastes 1:4
[In this translation, when 'or' is in italics it translates to the Latin sive or seu, which normally indicates an equivalence rather than an alternative. In my notes parantheses are simply another method of providing emphasis.]
D1: By [cause of itself] I understand that whose essence involves existence, or that whose nature cannot be conceived except as existing.
D2: 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 an other 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.
D3: By [substance] I understand what is in itself and is conceived through itself, that is, that (whose concept does not require the concept of another thing,) from which it must be formed.
D4: By [attribute] I understand what the intellect perceives of a substance, as constituting its essence.
D5: By [mode] I understand the affections of a substance, or that which is in another through which it is also conceived.
D6: By God I understand a being absolutely infinite, that is, a substance consisting of an infinity of attributes, of which each one expresses an eternal and infinite essence.
Exp: ... but if something is absolutely infinite, whatever expresses essence and involves no negation pertains to its essence.
D7: That thing is called [free] which exists from the necessity of its nature alone, and is determined to act by itself alone. But a thing is called [necessary,] or rather compelled, which is determined by the nature of another to exist and to produce an effect in a certain and determinate manner.
D8: By [eternity] I understand existence itself, insofar as it is conceived to follow necessarily from the definition alone of the eternal thing.
Exp: For such existence, like the essence of a thing, is conceived as an eternal truth, and on that account cannot be explained by duration or time, (even if the duration is conceived to be without beginning or end.)
A1: Whatever is, is either in itself or in another.
A5: Things that have nothing in common with one another also cannot be understood through one another, or the concept of the one does not involve the concept of the other.
P1: A substance is prior in nature to its affections.
P2: Two substances having different attributes have nothing in common with one another.
P4: Two or more distinct things are distinguished from another, either by a difference in the attributes of the substances or by a difference in their affections.
Dem: ... outside the intellect there is nothing except substances and their affections.
P5: In Nature there cannot be two or more substances of the same nature or attribute.
Dem: ...considered truly, one cannot be conceived to be distinguished from another, that is (by P4), there cannot be many, only one [of the same nature and attribute].
P6: One substance cannot be produced by another substance.
[P7: It pertains to the nature of a substance to exist.]
Dem: A substance cannot be produced by anything else (by P6C); therefore it will be the cause of itself...
P8: Every substance is necessarily infinite.
Schol. 1: Since being finite is really, in part, a negation, and being infinite is an absolute affirmation of the existence of some nature, it follows from P7 alone that every substance must be infinite.
Schol. 2: ...So also, those who confuse the divine nature with the human easily ascribe human affects to God, particularly so long as they are also ignorant of how those affects are produced in the mind.
But if men would attend to the nature of substance, they would have no doubt at all of the truth of P7. Indeed, this proposition would be an axiom for everyone. ... So it must be confessed that the existence of a substance, like its essence, is an eternal truth.
...Finally, it is to be noted,
IV. that this cause, on account of which a thing exists, either must be contained in the very nature and definition of the existing thing (viz. that it pertains to its nature to exist) or must be outside it.
P10: Each attribute of a substance must be conceived through itself.
Dem: For an attribute is what the intellect perceives of a substance, as constituting its essence (by D4); so (by D3) it must be conceived through itself.
Schol: ...For it is of the nature of a substance that each of its attributes is conceived through itself, since all the attributes it has have always been in it together, and one could not be produced by another, but each expresses the reality, or being of substance.
...And consequently there is also nothing clearer than that a being absolutely infinite must be defined (as we taught in D6) as a being that consists of infinite attributes, each of which expresses a certain eternal and infinite essence.
But if someone now asks by what sign we shall be able to distinguish the diversity of substances, let him read the following propositions, which show that in Nature there exists only one substance, and that it is absolutely infinite. So that sign would be sought in vain.