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.

5 thoughts on “Ordine Geometrico Demonstrata

  1. Jeffrey,

    I don’t have any properly formed thoughts on this topic, but perhaps the below might be suggestive to you. To begin with, I think there is a lot to be said for focusing on the quintet of Spinoza/Hume/Deleuze/Lewis/Meillassoux. Probably one of the key themes here is the one you allude to by comparing Spinoza’s desire to escape the mind’s attachment to things which are “liable to many variations and which we can never fully possess” with Lewis’ aim of using modal logic and semantics to escape correlationism. (I’m not sure I agree with your characterisation of Lewis’ aim, but I’d like it to be true.) There seems to be an analogue of this theme in each of these five philosophers, and interesting connections between them.

    It is salient to note that, whilst in your post you (rightly) emphasise the equal importance for Spinoza of escaping the mind’s attachment to things both “intellectually” AND “ethically”, that in Lewis’ case the focus seems to be more on the former. Perhaps there is no justification for (and thus little point in inquiring into) Lewis’ preference here: after all, I don’t think that Lewis was the most epistemologically self-aware of philosophers. Nevertheless, I doubt he would (if you proposed it to him) find any solution to the correlationist dilemma which appeals, in the spirit of Fichte et al, to the primacy of practical reason or morality/ethics, as dubious and intellectually unsatisfying. (Though there are complacent appeals to common sense scattered throughout Lewis’ writings – which indicate that he never confronted the underlying issue head-on.)

    Regarding Spinoza, I think you put your finger right on it by asking about the status or nature of the common notions. Describing the common notions in terms of a “zone of objective indetermination” or “problematic” indicates a Deleuzean perspective, of which I am a fan. Having said this, I cannot decide whether this approach is ultimately a dead-end or not. The reason it might be a dead-end is that I cannot detect in Deleuze’s work any consistent or satisfying response to the correlationist problem. In other words, assuming there is a problem in Spinoza, I do not (presently) see how Deleuze might help us address it. Is there a way by which invoking the primacy of the problematic can be made equal to this task? I take it that this is part of what you intend to sketch an answer to in your next post. In this regard, I wonder if you have considered the debate between Alquie and Gueroult, concerning the status of intuition in Spinoza’s method, as being relevant here? I remember reading an interesting paper by Knox Peden about this – and it is surely an an important part of the context for grasping what Deleuze is up to in his reading of Spinoza. Also, Simon Duffy’s book laboriously develops the Deleuzean reading of Spinoza, though I remember being dissatisfied with his attempts to explain those aspects of this reading (such as the criticism Deleuze levels against Spinoza in Difference and Repetition) which remain most mysterious to me.

    In any case, Deleuze does not, it seems, ultimately settle on an answer to the question of what the epistemological status of the “problematic” actually is. That this is true is evidenced by the shift in the status accorded to “presuppositions” in his epistemology, between Difference and Repetition (where we catch a fleeting glimpse of the “thought without image”), and What is Philosophy (where a plurality of images and planes of immanence predominate). In this regard, I think there is something to be said for construing After Finitude as a continuation of the former, ostensibly more radical, thread of Deleuze’s project, centred around a reconfiguration of Spinoza’s substance in terms of the notion of “Hyper-Chaos”.



  2. JTH,
    Thanks for your suggestions. A few of your points get right to the heart of issues that I feel need to be worked through not only in contemporary Deleuze scholarship, but contemporary philosophy more generally. First, I agree Lewis would not likely accept my characterization of his project as an effort to escape correlationism, although I think a case can be made that a fully fleshed out explication would nonetheless be within the spirit of his project. In particular, by arguing that there is more to reality than what is actual, to what is given to conscious beings in this world – namely, the reality of possible worlds, including worlds without givenness – Lewis sets the stage for making similar arguments in contexts other than semantic analysis (even though he does not carry out such analyses and may not even think it is possible [it may be too speculative for his tastes]). And this gets to the key question or concern you had – what is the epistemological status of the ‘problematic’? How does it relate to semantic, modal, and normative modes of discourse? This is an important question for many reasons and I do think it can be addressed and a robust epistemology can be built around the notion of the problematic that will address them. Doing so would in turn address concerns of those who come from both the critical and analytic traditions while remaining true to the radical immanence of Deleuzian metaphysics. Thanks as well for reminding me of the debate between Alquie and Gueroult. Deleuze’s reading of Spinoza was greatly influenced by both and so it is important to see how, if at all, Deleuze reconciles their differences.

  3. Pingback: Questions of Substance | Aberrant Monism

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