Ordine Geometrico Demonstrata

In the next few posts I’d like to develop a few arguments concerning Spinoza’s method, hence the title of this post, then move on to Spinoza’s notion of substance as a radical aberrant monism, and finally touch upon the third kind of knowledge as the solution to the problems with which Spinoza began his Treatise on the Emendation of the Intellect. These will be sketches of arguments, or trial runs so to speak, and I will not address the voluminous secondary literature to the extent a published argument would need to do so. This blog is for me a working blog, in the same vein as Shaviro, and not a depository for finished work, so feel free to point out the dead ends I’m venturing into, or point out secondary sources, etc., that should not be ignored, or that have already said what I’m saying here.

As I pointed out in Philosophy at the Edge of Chaos, Spinoza begins his Treatise on the Emendation of the Intellect (hereafter TIE) and the latter half of part 5 of the Ethics with the same concern: namely, to show how we can overcome suffering and misery and live a good life. The first paragraph of the TIE reads as follows:

After experience had taught me the hollowness and futility of everything that is ordinarily encountered in daily life, and I realized that all things which were the source and object of my anxiety held nothing of good or evil in themselves in so far as the mind was influenced by them, I resolved at length to enquire whether there existed a true good, one which was capable of communicating itself and could alone effect the mind to the exclusion of all else, whether, in fact, there was something whose discovery and acquisition would afford me a continuous and supreme joy to all eternity.

As Spinoza moves into the latter half of part 5 of the Ethics, at 5P20S, a similar concern is expressed:

‘…it should be noted that sickness of mind and misfortunes take their origin especially from too much love toward a thing which is liable to many variations and which we can never fully possess.’

There are two points to make right off the bat. First, in both cases what concerns Spinoza is how the mind is influenced by things, its attachment to things, especially things which are ‘liable to many variations and which we can never fully possess.’ Secondly, Spinoza begins the TIE with a classical ethical concern – how to live a good life – which then becomes the very title of his masterpiece. This fact should not be overlooked and as a result as we come to an understanding of Spinoza’s metaphysics we should remember to situate it into Spinoza’s broader ethical concerns. The ethical claims at the end of the Ethics are not to be understood as an addendum to Spinoza’s metaphysical project, and an addendum Spinoza would have been better to have left out of the work entirely (as Jonathan Bennett has argued); to the contrary, if the Ethics is to be interpreted as an effort to realize the efforts with which Spinoza began the TIE, then the ethical claims ought instead to be placed at the center of Spinoza’s project in the Ethics.

But is Spinoza continuing in the Ethics with an effort to realize the task he set for himself in beginning the TIE? I have argued that this is indeed what Spinoza is doing in the Ethics. The subsequent question then is why Spinoza abandoned the TIE and started over with the Ethics, developing the arguments this time by way of an axiomatic, geometric method (Ordine Geometrico Demonstrata)? To begin to answer this question involves understanding how the mind itself is related to things, and in particular to the eternal truths that will eventually emerge as the way to move beyond the ‘sickness of mind’ that results when we become overly attached to that ‘which we can never fully possess.’ In the TIE Spinoza’s effort was to demonstrate how a finite, discrete mind could come to fully know and possess an eternal, timeless truth. When Spinoza comes to an understanding of truth itself he claims that it ‘is nothing but the objective essence itself, i.e., the mode by which we are aware of the formal essence is certainty itself. And from this, again, it is clear that, for the certainty of the truth, no other sign is needed than having a true idea’ (§35, II/15). In other words, and to avoid the skeptical argument of criterion, Spinoza argues that the truth of an idea does not depend upon some independent criterion or method which will verify and justify this truth, which would lead to the skeptical argument of what justifies this independent criterion, and so on; instead, the very mode in which a true idea is grasped is the truth and certainty of this idea. But how are we to know whether the ‘very mode in which a true idea is grasped is the truth and certainty of this idea’? Key here for Spinoza is to begin with true definitions. As Spinoza puts it, ‘that Method will be good which shows how the mind is to be directed according to the standard of a given true idea’ (§38, II/15), and these are to be the ‘true and legitimate definitions.’ Thus, late in the TIE Spinoza returns to the knowledge of eternal things and claims that

When the mind attends to a thought—to weigh it, and deduce from it, in good order, the things legitimately to be deduced from it – if it is false, the mind will uncover the falsity; but if it is true, the mind will continue successfully, without any interruption, to deduce true things from it. (§104, II/37-8).

It is therefore the activity of the mind itself, whether unimpeded or impeded from true, legitimate definitions, that is the only foundation for Spinoza upon which the truth of our thoughts is to be determined. But this is precisely where problems begin. If the axiomatic method is to succeed on the basis of true and legitimate definitions, it will be because of the power of the mind to proceed, ‘without any interruption, to deduce true things’ from these definitions; and yet Spinoza admits to lacking a clear understanding of the powers of the mind, and hence the proper place for the mind to begin upon its axiomatic path:

But so far we have had no rules for discovering definitions. And because we cannot give them unless the nature, or definition, of the intellect, and its power are known, it follows that either the definition of the intellect must be clear through itself, or else we can understand nothing. It is not, however, absolutely clear through itself… (§107, II/38).

In the final paragraphs of the TIE Spinoza attempts to work through this problem, to provide a way for understanding the powers of the mind. He begins first with an effort to understand the mind by way of the properties of the mind. Early in the TIE, however, Spinoza ruled out this approach. When Spinoza contrasts knowing something through itself or through its proximate cause such as its properties, Spinoza favors the former and criticizes Descartes for understanding the mind in terms of its proximate, transcendent cause (i.e., God), and thus one can see he would resist reverting to that solution himself. As Spinoza would claim later in the Short Treatise, properties, or ‘Propria’, do ‘indeed belong to a thing, but never explain what it is.’ (ST 1.vi.6). What Spinoza needs, therefore, and what was lacking for him in the TIE, is a way of understanding how the knowledge of the eternal and infinite could be founded upon the essence of a our singular, finite mind rather than upon something that transcends this mind (Propria, for example). Because of the dissatisfaction with the alternatives he had before himself in the TIE he would abandon this work and then, in the Ethics, approach them from a different perspective.

Of the few commentators to attempt to nail down precisely why Spinoza abandoned the TIE and moved on to the Ethics, Deleuze, in his Spinoza: Practical Philosophy, offers a simple explanation: ‘when he discovers and invents the common notions, Spinoza realizes that the positions of the Treatise on the Intellect are inadequate in several respects, and that the whole work would have to be revised and rewritten.’ (pp. 120-1). We can understand the implications of this discovery, and the resultant axiomatic method that emerges in the Ethics, if we recall the previous post on Deleuzian supervenience (a now slightly modified and corrected post). In his effort to understand the powers of the mind and its ability to move through an axiomatic process from true and legitimate definitions to further truths, and hence to escape the mind’s attachment to things which are ‘liable to many variations and which we can never fully possess,’ Spinoza encountered a similar problem to Lewis as Lewis sought to use the tools of modal logic and semantics to move beyond the correlationist trap (though of course Lewis would not have used this terminology). In short, the common notions are neither to be understood as the clearly defined truths and definitions with which the axiomatic method begins, nor are they the truths one arrives at after successfully moving through the processes of deduction. They are, instead, to use again the terminology of the previous post, a ‘zone of objective indetermination’ (the problematic) upon which the axiomatic method supervenes and which it is nonetheless irreducible to. This accounts for another aspect of Spinoza’s method that Deleuze also stresses; namely, the role the scholia play in the midst of the axiomatic deductions. For Deleuze ‘the use of the geometric method involves no problems at all’ (DR 323, n.21) and it is for this reason that Spinoza, on Deleuze’s reading, interspersed the scholia into the axiomatic deductions of the Ethics in order to fuel the necessity and inventiveness of the geometric method by supervening upon problems of the scholia. And it is for this reason as well that Spinoza begins his Ethics not with a stated ethical concern as he did in the TIE, but with six definitions that lead to the definition of God as substance: ‘By God I mean an absolutely infinite being; that is, substance consisting of infinite attributes, each of which expresses eternal and infinite essence.’ (D6). Substance, in other words, is to be understood not as an axiomatic given from which the remaining deductions follow, but rather as the problematic upon which the axiomatic deductions supervene. And it is with this approach in hand that Spinoza will attempt to address the ethical concerns with which he began the TIE. The next post will begin to sketch how this works.