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 what Aristotle would call “efficient causes” or means by which things end up as they do, and suggests that true reasons are causes in this narrower sense. Again, 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 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”.