Spinoza's Ethics: II.P5: Formal Essence of Ideas

This proposition is difficult. Aristotle outlined four causes: material, efficient, formal and final. Part of Spinoza's genius is to clearly identify final cause as a human-based mental tool that is useful but illusion-generating. Final cause is not a true cause.

The other three causes remain components of Spinoza's heavily cause-effect understanding. As it relates to ideas, the material cause is the specific content of an idea, the efficient cause is God as substance and the formal cause of ideas, or formal essence of ideas here, is God expressing that efficient causality within the attribute of thinking. The formal essence of ideas is only within the attribute of thinking. 

The distinction is subtle but important. Ideas sometimes represent objects and sometimes ideas do not represent objects. This is addressed in II.A3. Thus, the ideas are materially different. However, all of them are formally ideas. The shared sense in which an idea is an idea is the formal essence or formal cause of the idea and this itself is also considered a mode of thinking (a small third category of ideas - the "idea of an idea").

The difficulty here is that the formal cause within Aristotle is typically tied to what we consider the idea of the object. While Spinoza has a one-to-one connection between an idea and its modal cause, the one-to-one connection is not about the object. As a result, the formal cause or essence of an idea is different than that found in Aristotle.

Language note: Most translators render God as subject of consideratur or "is considered." As mentioned in the Language note in II.A1, the subject of is considered is the nominative singular res cogitans or "thinking aspect."  The correct rendering allows a natural translation of explicatur or "be explained" to have esse formale or "formal essence" as the subject.

Esse formale idearum Deum quatenus tantum ut res cogitans consideratur, pro causa agnoscit et non quatenus alio attributo explicatur. Hoc est tam Dei attributorum quam rerum singularium ideæ non ipsa ideata sive res perceptas pro causa efficiente agnoscunt sed ipsum Deum quatenus est res cogitans.

Translated as,

The formal essence of ideas acknowledges God as cause insofar as only the thinking aspect [of God] is considered, and not insofar as it [the formal essence] is explained by some other attribute. That is, ideas just as much of the attributes of God as of singular things acknowledge as their efficient cause not the ideations themselves or things perceived but God itself insofar as it is the thinking aspect [of God].

Demonstratio: Patet quidem ex propositione 3 hujus. Ibi enim concludebamus Deum ideam suæ essentiæ et omnium quæ ex ea necessario sequuntur, formare posse ex hoc solo nempe quod Deus est res cogitans et non ex eo quod sit suæ ideæ objectum. Quare esse formale idearum Deum quatenus est res cogitans, pro causa agnoscit. Sed aliter hoc modo demonstratur. Esse formale idearum modus est cogitandi (ut per se notum) hoc est (per corollarium propositionis 25 partis I) modus qui Dei naturam quatenus est res cogitans, certo modo exprimit adeoque (per propositionem 10 partis I) nullius alterius attributi Dei conceptum involvit et consequenter (per axioma 4 partis I) nullius alterius attributi nisi cogitationis est effectus adeoque esse formale idearum Deum quatenus tantum ut res cogitans consideratur etc. Q.E.D. 

Translated as,

Indeed it is clear from IIP3. For there we concluded that God is able to form the idea of its essence and all things which necessarily follow from [the idea of its essence] from this alone, namely, because God is a thinking thing and not from that which might be the object of its [God's] idea. Therefore the formal essence of ideas acknowledges God as cause insofar as it [God] is a thinking thing. But otherwise in this way it is demonstrated. The formal essence of ideas is a mode of thinking (as noted through itself) that is (by IP25C) a mode which expresses in a certain way the nature of God insofar as it is the thinking aspect, to such an extent (by IP10) that it [the mode of thinking] involves the concept of no other attribute of God and consequently (by IP4) is the effect of no other attribute unless of thinking to the degree that the formal essence of ideas [acknowledges] God [as cause] insofar as only the thinking aspect is considered, etc.