Spinoza's Parallelism & The PSR

Here I discuss Spinoza’s so-called “parallelism” doctrine, as well as its relation to his overall project of articulating the conditions of the intelligibility of reality.

The central passage of the Ethics for understanding Spinoza’s conception of the relation between extension and thought is E2p7, which states:

P7: The order and connection of ideas is the same as the order and connection of things. [Ordo, et connexio idearum idem est, ac ordo, et connexio rerum].

Dem.: This is clear from IA4. For the idea of each thing caused depends on the knowledge of the cause of which it is the effect.

Cor.: From this it follows that God’s [NS: actual] power of thinking is equal to his actual power of acting. That is, whatever follows formally from God’s infinite nature follows objectively in God from his idea in the same order and with the same connection.

Schol.: Before we proceed further, we must recall here what we showed [NS: in the First Part], namely, that whatever can be perceived by an infinite intellect as constituting an essence of substance pertains to one substance only, and consequently that the thinking substance and the extended substance are one and the same substance, which is now comprehended under this attribute, now under that. So also a mode of extension and the idea of that mode are one and the same thing, but expressed in two ways. Some of the Hebrews seem to have seen this, as if through a cloud, when they maintained that God, God’s intellect, and the things understood by him are one and the same.

For example, a circle existing in Nature and the idea of the existing circle, which is also in God, are one and the same thing, which is explained through different attributes. Therefore, whether we conceive Nature under the attribute of extension, or under the attribute of thought, or under any other attribute, we shall find one and the same order, or one and the same connection of causes, that is, that the same things follow one another.

When I said [NS: before] that God is the cause of the idea, say of a circle, only insofar as he is a thinking thing, and [the cause] of the circle, only insofar as he is an extended thing, this was for no other reason than because the formal being of the idea of the circle can be perceived only through another mode of thinking, as its proximate cause, and that mode again through another, and so on, to infinity. Hence, so long as things are considered as modes of thinking, we must explain the order of the whole of Nature, or the connection of causes, through the attribute of thought alone. And insofar as they are considered as modes of extension, the order of the whole of Nature must be explained through the attribute of extension alone. I understand the same concerning the other attributes.

So of things as they are in themselves, God is really the cause insofar as he consists of infinite attributes. For the present, I cannot explain these matters more clearly. (II/89-91; (Spinoza 1994, 119–20)

1 The Proposition

Let’s take the central claims in turn. First, the proposition itself.

E2p7: The order and connection of ideas is the same as the order and connection of things. [Ordo, et connexio idearum idem est, ac ordo, et connexio rerum].

Note that the contrast here is between ideas and things. “Thing” (res) here should not be equated with “body”, though of bodies (or modes of extension) are things. But ideas are things as well. Perhaps then, what Spinoza means to indicate is that the order and connection of ideas is the same as the order and connection of other things (including bodies). This seems to fit with the end of the Scholium, where Spinoza states that,

so long as things are considered as modes of thinking, we must explain the order of the whole of Nature, or the connection of causes, through the attribute of thought alone. And insofar as they are considered as modes of extension, the order of the whole of Nature must be explained through the attribute of extension alone. I understand the same concerning the other attributes.

So we can consider “things” as modes of thinking, and as modes of extension, and as modes of whatever other attributes there are.

2 The Demonstration

In the “demonstration”, Spinoza contends that p7 follows from E1a4:

E2p7d: This is clear from [E1a4]. For the idea of each thing caused depends on the knowledge of the cause of which it is the effect.

And E1a4 states that,

E1a4: The knowledge of an effect depends on, and involves, the knowledge of its cause [Effectus cognitio à cognitione causae dependet et eandem involvit].

It is not immediately clear why E1a4 supports E2p7. Spinoza must be thinking that the form of “dependence” of one cognition (or bit of “knowlege”) on the other is similar to the form of dependence between an effect and its cause.¹

The proposition and what follows raises a variety of questions. The statement of p7 is often considered to the be that of “parallelism”, in one sense or another (note that Spinoza himself never uses this term). The basic idea being that there is a “mirroring”, or “isomorphism”, or “mapping” of modes of thought to modes of “things”, including modes of extension.

3 The Scholium & Corollary

While the metaphors of “mirroring”, etc., are fine as far as they go, Spinoza also articulates a seemingly related claim concerning ideas (or modes of thought) and “things” (including modes of extension).

E2p7s: Before we proceed further, we must recall here what we showed [in E1], namely, that whatever can be perceived by an infinite intellect as constituting an essence of substance pertains to one substance only, and consequently that the thinking substance and the extended substance are one and the same substance, which is now comprehended under this attribute, now under that. So also a mode of extension and the idea of that mode are one and the same thing, but expressed in two ways. Some of the Hebrews seem to have seen this, as if through a cloud, when they maintained that God, God’s intellect, and the things understood by him are one and the same.

The claim in the scholium is not obviously the same as that in the proposition, for it references not a parallelism between ideas and things, but a parallelism between modes of one attribute and modes of another. These are not equivalent.² The postulate is seemingly compatible with there being a lack of parallel between the relations of modes other than ideas to modes of other (infinitely many) attributes. The scholium, on the other hand, is seemingly compatible with a lack of parallel within the attribute of thought (e.g. of lower-order ideas and higher-order ideas) even though there is a parallel between the order of modes in one attribute and that of another.

We can make better sense of the two forms of parallelism by noticing something about both the discussion in the scholium and in the preceding corollary, namely that in both cases Spinoza is concerned with a distinction between “formal” reality and “objective” reality. To understand this distinction properly we need to look to Descartes. Emotions, judgments, ideas, and acts of will are all modes of the mind. But ideas are distinguished from these other mental modes in virtue of being “as it were the images of things” (7:36-7). Descartes does not think that all our ideas are sensory images of things. We can have purely intellectual ideas of objects, as Descartes argues we do in the case of substantial beings, or complex mathematical objects, such as a chilliagon. But our sensory and intellectual ideas share a common feature, which makes them both ideas, namely they present an object to the mind, either by resembling them (as is perhaps the case with sensory ideas), or by some other means. As he says in reply to both Hobbes and Gassendi, an idea is what is immediately present to or perceived by the mind (7:366, 393).

Descartes then introduces two ways of considering an idea. The first is the idea merely as a mode of the mind. In this sense the ’formal reality’ of the idea is that of a mental mode. But an idea may also be considered in virtue of what it makes present to the mind—what it, as it were, is an image of – this is to consider the ’objective reality’ of the idea (7:40-1)

Reality, according to Descartes, comes in degrees or levels. We’ve seen this already in our discussion of substance, attribute, and mode above. The highest or most “perefect” level of reality is that of an infinite substance. The only such substance is God. So the highest level of reality is ascribed to God. The next highest level of reality is that of finite or created substance as defined by its principle attribute (i.e. mental or material) . Finally, at the lowest level of reality, we have modes or characteristics of substances other than (or derived from) their principle attribute. Each degree of reality is dependent on the prior. So modes depend on the attributes of substances, and finite substance depends on the creative activity of infinite substance. This is true not only of the formal reality of things but also the objective reality of our ideas of things.

Spinoza’s view is very similar to Descartes. Where he differs concerns the extent to which the formal reality of all modes is captured by the objective reality of ideas.³ For Descartes, there are various ideas whose objective reality corresponds to nothing in nature. Reciprocally, there are many beings whose formal reality has no objective correlate, at least in finite beings. But Spinoza holds that all things having formal reality also have objective reality in some idea as a mode of God’s attribute of thought (this also includes ideas themselves, which have higher-order ideas of those ideas, etc.).

So for anything at all, any being, there is an idea “of” that being – i.e. a being whose formal reality is that of a mode of thought and whose objective reality is that of (or perhaps simply identical with) the being of which the idea is an idea. This is what Spinoza means in saying in the corollary that,

whatever follows formally from God’s infinite nature follows objectively in God from his idea in the same order and with the same connection.

God is nature, but God also has an idea of itself as such (and this idea has an idea, etc). We can thus see Spinoza’s position as a manner of articulating a view (whether Spinoza recognized this or not) held by Aristotle. As expressed in Metaphysics Λ,

it is itself which the intellect [nous] thinks, by sharing in the object of thought; for <intellect> comes to be an object of thought in touching and thinking <it>, so that the intellect and the object of thought are the same. For that which is receptive of the object of thought, i.e. of the substance, is intellect, and it is active when it possesses <the object of thought> (1072b19-25; (Aristotle 2019, 32))

Spinoza’s God is that of thought thinking itself (and every other mode of the infinitely many attributes). In this sense Spinoza remains thoroughly in the Aristotelian tradition.

4 The Intelligibility of Everything

Spinoza is often characterized as committed to the intelligibility of everything, and this is often how scholars characterize the principle of sufficient reason with respect to Spinoza’s work.⁴ We might then ask, how the parallelism doctrine connects with this commitment, and with the PSR. One way to think about this question is to ask whether parallelism is a consequence of Spinoza’s position regarding intelligibility or is a premise in arguing for that commitment.

It’s hard to see how it could be the latter, for Spinoza is already committed to the in principle conceivability of everything in E1a2-4. Those axioms require that everything must be conceived – either through itself or another (1a2); that conception must be through causes (1a4); and that causes always necessitate (1a3). From these it follows that everything that is (and that could be) is the result of a necessitating cause, and since causal relations are rational relations, everything conceivable is rationally grounded. At best then, parallelism allows Spinoza to spell out, in greater detail, commitments already initially articulated in E1. But really this is as it should be, since all things are supposed to follow from God’s essence and so all the conseuqences of the subsequent books of the Ethics should already be in a sense contained in the content of the first book.

However, this does leave the axioms of E1 in a vulnerable position, for there does not seem to be any argument that Spinoza can provide for them (they are axioms). The best that perhaps can be said is that they are the more plausible given the overall plausibility of the consequences drawn from them. This also indicates a broader question: is there anything that can actually be pointed to in the way of an argument for explanatory rationalism of the sort articulated by Spinoza? What would such an argument look like, without out presupposing a version of the PSR itself?

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