Spinoza's Ethics: I.P1: Priority

Here we have reached the end of definitions (what things are) in book one as well as the axioms (how things relate). This is the first of the propositions - a series of statements made in the form of a geometric proof that logically extrapolates the definitions and axioms. 

Another rendering to proposition 1 might be "A substance is prior in nature to its states." Basically, I understand Spinoza to describe a universe of immanent causality rather than transitive or transcendent causality. This distinction is that immanent causality is the way in which a circle causes roundness. The roundness is caused by the definition of or nature of the circle. Such causality is different than the watchmaker who makes a watch. The watchmaker has a transitive or transcendent causality. The watchmaker makes the watch and is separate from the watch itself. The circle is prior to roundness and can only be different if the definition of circle changes. Thus, the importance of definitions 3 and 5. He refers us to the definitions of substantia or "substance" (I.D3) and substantiae affectiones or "modifications of substance" (I.D5). The clear contrast between these two definitions is that "substance is in itself" and "is conceived through itself," while "modifications of substance are in another through which they are also conceived." From this distinction, substance is independent, while modifications of substance (or affections or states or modes) are dependent. In the same sense (although on a fundamentally different level and just for clarity's sake), "roundness" might be understood as a dependent modification while a "circle" might be understood (not Spinozistically, of course) as an independent concept. In this way substance has priority over its modification in the same way as a circle has priority over roundness. (Of course the example here fails in terms of an essence that involves existence. A circle could simply not exist - unlike substance.) 

Substantia prior est natura suis affectionibus.

Translated as,

Substance is by Nature prior to its modifications.

Also translated as,

A substance is prior in nature to its affections.

Demonstratio: Patet ex definitione 3 et 5.

Dem: This is evident from I.D3 and I.D5.

Spinoza's Ethics: I.A7: Non-existence

It is interesting to me that Spinoza chose to make this an axiom when a similar issue of the relationship of essence and existence is present in I.D1's definition of "self-caused." The difference seems to be the description of that essence and existence relationship as self-cause. So, it would appear that the axioms are more fundamental and might more appropriately precede the section of definitions.

In reviewing the difference between the definitions, the axioms and the propositions, it appears that Spinoza uses the axioms for the basic fabric of his thought. These axioms describe the relationships between things and things, between ideas and ideas and between things and ideas.

Quicquid ut non existens potest concipi, ejus essentia non involvit existentiam.

Translated as,

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

Spinoza's Ethics: I.A6: Correspondence

Here it seems that Spinoza is describing how knowing and being operate: they correspond completely. It's axiomatic. Left unclear is whether this is Knowing and Being or whether this is a function of the relationship of the attributes of thought and extension. However, it's not necessary to take a decision, as this axiom may operate fundamentally for both areas. (As for whether the iterations of an idea of an idea is a thing, it may be so in the same sense of a thing of a thing ad infinitum.)

Idea vera debet cum suo ideato convenire.

Translated as,

A true idea must agree with its object.

Spinoza's Ethics: I.A5: Interactivity

invicem means "in turn, alternately, mutually, reciprocally". It seems to come from vicis which means "change, interchange or alternation" and may the basis for the English words vicissitude and vice versa. Many translations do not capture this dynamic. Even though this is an axiom, Spinoza seems to describe a dynamic process, highlighting the word invicem twice. 

Up to this point, the axioms seem somewhat static. Here, Spinoza begins to introduce the dynamic of change and process. This touches on his use of the word exprimit or "express" that he first employs in I.D6.

Quae nihil commune cum se invicem habent, etiam per se invicem intelligi non possunt sive conceptus unius alterius conceptum non involvit.

Translated as,

Things which have nothing in common with one another interactively, also cannot be understood through themselves interactively where the concept of the one does not involve the concept of the other.

Spinoza's Ethics: I.A4: Knowledge of Effect

I see I.A4 as relating to either Knowing or the attribute of thought (two significantly different interpretations) as the emphasis is on cognitio or "knowledge" in the same way as I.A3 deal with either Being or the attribute of extension (again significantly different interpretations) where cause and effect are related. He is careful to stress in this axiom the kind of connection of cause and effect. Again, a level of inherence that requires not only "depends" but also "involves." The absence of any so-called wiggle room seems to imply a level of determinism that works at large scale, but seems diminished at smaller scales. It will be interesting to see how this is addressed. 

Effectus cognitio a cognitione causae dependet et eandem involvit.

Translated as,

The knowledge of an effect depends on and involves the knowledge of its cause.

Spinoza's Ethics: I.A3: Effect

This tying together of cause and effect seems incredibly tight and seems to be on the order of inherence. By that I mean that the effect seems almost present to the definite cause, as in the effect of roundness is in the definite cause of a circle. It seems that this cause-effect connection moves to level of immanence as opposed to transcendence; almost definitional rather than relational. The unfolding of cause and effect appears to inhere in the true nature of the cause.

Ex data causa determinata necessario sequitur effectus et contra si nulla detur determinata causa, impossibile est ut effectus sequatur.

Translated as,

From a given determinate cause the effect follows necessarily; and conversely, if there is no determinate cause, it is impossible for an effect to follow.

Spinoza's Ethics: I.A2: Knowing

This axiom seems like a companion to 1.A1 in the way of Spinoza's parallelism of the mind and the body. One key question is whether this parallelism is employing "a view from nowhere" or "a view from somewhere." The verb used here is "conceive" or concipi which typically signifies a "view from nowhere." It may be that this is irrelevant as an axiom because Spinoza is simply outlining the operation of logic rather than content as in the definitions. If so, it would make sense to use the "view from nowhere" verbs, but not be pointing to substance versus attributes.

Id quod per aliud not potest concipi, per se concipi debet.

Translated as,

That which cannot be conceived through another, must be conceived through itself.