Demonstration in Spinoza

Kant and Hegel both objected to Spinoza’s unusual presentation of his Ethics in something resembling the style of Euclid’s geometry. I think of philosophy mainly as interpretation rather than simple declaration, so I am broadly sympathetic to this point. On the other hand, I think Pierre Macherey is profoundly right when he emphasizes the non-foundationalist character of Spinoza’s thought.

The unique meaning Spinoza gives to “Substance” (not to be confused with its Aristotelian, Scholastic, Cartesian, or general early modern senses) is that of a complex relational whole that encompasses everything, rather than a separate starting point for deduction of the details of the world. Because of this, the apparent linearity of his development is just that — a mere appearance.

Hegel does not seem to recognize that Spinoza’s Substance resembles the relational whole of Force that Hegel himself developed in the Phenomenology. This is inseparable from an implicit notion of process in which relations of force are exhibited.

Macherey says Spinoza sees the world in terms of an infinite process, i.e., one without beginning or end or teleological structure (Hegel or Spinoza, p. 75).

(I would argue that neither Aristotle nor Hegel actually endows the world with teleological structure, though they each give ends a significance that Spinoza would deny. For Aristotle, it is particular beings in themselves that have ends. For Hegel, teleological development is a retrospectively meaningful interpretation, not an explanatory theory that could yield truth in advance. But for Spinoza, ends are either merely subjective, or involve an external providence that he explicitly rejects.)

It seems to me that the “point of view of eternity” that Spinoza associates with truth is actually intended to be appropriate to this infinite process. Spinoza points out that eternity does not properly mean a persistence in time that lasts forever, but rather a manner of subsistence that is entirely outside of — or independent of — the linear progression and falling away that characterizes time.

(Kant’s famous assertion of the “ideality of space and time”, which means that space and time are only necessary features of our empirical experience, is not inconsistent with Spinoza’s commendation of the point of view of eternity. Though it has other features Spinoza would be unlikely to accept, Kant’s “transcendental” as distinct from the empirical is thus to be viewed from a perspective not unlike Spinoza’s “point of view of eternity”.)

Spinoza wants to maintain that the order of causes and the order of reasons are the same. Whereas Aristotle deconstructs “cause” into a rich variety of kinds of “reasons why” (none of which resembles the early modern model of an impulse between billiard balls), Spinoza narrows the scope of “cause” to “efficient causes” in a sense that seems close to that of Suárez with inflections from Galilean physics, and suggests that true reasons are causes in this narrower sense. It seems to me that Spinoza’s “order of causes” resembles the infinite field of purely relational “force” that Hegel discusses in the Force and Understanding chapter.

Spinoza wants us to focus on efficient causes of things, but to do so mainly from the “point of view of eternity”. This takes us away from the event-oriented perspective of linear time, toward a consideration of general patterns of the interrelation of different kinds of means by which things end up as they concretely tend to do. In speaking of means rather than forces, I am tacitly substituting what I think is a properly Aristotelian notion of “efficient” cause for the meaning it historically seems to have had for Spinoza.

In pursuit of this, he takes up a stance toward demonstration that is actually like the one I see in Aristotle, in that it is more about improvement of our understanding through its practical exercise in inference than about proof of some truth assumed to be already understood (see also Demonstrative “Science”?). As Macherey puts it, for Spinoza “knowledge is not simply the unfolding of some established truth but the effective genesis of an understanding that nowhere precedes its realization” (p. 50). (Unlike Macherey, though, I think this is true for Aristotle and Hegel as well.)

Demonstration in both Aristotle’s and Spinoza’s sense is intended to improve our normative understanding of concepts by “showing” their inferential uses and points of application. It is only through their inferential use in the demonstrations that Spinoza’s nominal definitions and axioms acquire a meaning Spinoza would call “adequate”.

Cause of Itself

Spinoza famously begins his Ethics with a definition of “cause of itself” (causa sui). This will become the hallmark of his “Substance”, of which he says there can be only one, and which he identifies with his own heterodox conception of God. Cause of itself would be that the essence of which involves existence.

In Hegel or Spinoza (French ed. 1979), Pierre Macherey writes that “First of all we can show, as Guéroult does, that the concept of causa sui does not really have an initial foundational value for Spinoza: it does not represent a kind of first truth, a principle in the Cartesian sense, from which the entire system can be developed, as if from the starting point of a germ of truth” (p. 16).

“Here we can begin to be astonished: does Hegel ignore that this aporia of beginning — which sets his Logic in motion, this impossibility of grounding the infinite process of knowledge in a first truth which in itself as principle or foundation — is also an essential lesson of Spinozism, the principal objection that he himself opposes to the philosophy of Descartes? In such a sense that it is only… ‘so to speak’, the geometric exposition of the Ethics ‘begins’ with definitions, which for that matter do not have an effective sense, except at the moment when they function in demonstrations or they really produce the effects of truth: Spinozist thinking precisely does not have this rigidity of a construction relying on a base and pushing its analytic to an end point, which would find itself thus limited between a beginning and an end” (p. 17).

For Hegel according to Macherey, “The causa sui is based on a substantial principle that ‘lacks the principle of the personality’. It thus constitutes a substance that cannot become subject, which fails in this active reflection of self, which would permit it to undertake its own liberation in its own process…. This is an arrested and dead spirit” (p. 18).

This is supposed to be the individuality and freedom denying “Oriental” attitude that Hegel with broad brush unfortunately really does attribute to Judaism, Islam, Hinduism, Buddhism, the Roman Empire, Catholicism, the pre-Socratic philosopher Parmenides, and Spinoza, among others. This unfortunate over-the-top anti-anti-subjectivity theme of Hegel’s kept me from really appreciating his work for a long time.

On the other hand, the details of his argument about freedom and subjectivity as affirmative values actually make sense, even to the point of winning over an old sympathizer of French anti-Hegelianism like myself.