Frames /sing


Tag Archives: Remarks on the Foundations of Mathematics III

Spinoza’s Ethics, A Polished Lens

Polishing Lenses and Propositions

I want to set out some basic thoughts on a guiding intuition of my research on Spinoza’s optical experiences and products. This is the notion that perhaps Spinoza conceived of his Ethics, and the entire network of cross-referenced, mutually inferring propositions, demonstrations and scholia, to be something like a lens, polished to the improvement of our mind; and by virtue of his metaphysical parallelism, to the improvement of our body, giving those who use it, greater capacity to act. The analogy that is at work here is a hopefully satisfying and sophisticated elaboration of “he polishes lenses, he polishes propositions”, a thought given birth in Borges’ poem on the philosopher.

If we are to embrace this analogy in a literal sense so as to gain access to the ways Spinoza’s lens-grinding may have affected his approach to his metaphysics, drawing a conceptual connection between the attentive, precise, manual craftsmanship he engaged in during the day, and that studious argumentation he produced at night: the idea of the “eyes of the mind” is one that we should be take careful note of. 

I shall not treat the more philosophically suggestive of his uses from the second part of the Ethics here, where he warns against what he seemed to find as a Cartesian temptation, to “fall into pictures”:

We must investigate, I say, whether there is any other affirmation or negation in the Mind except that which the idea involves, insofar as it is an idea…so that our thought does not fall into pictures. For by ideas I understand, not the images that are formed at the back of the eye (and if you like, at the middle of the brain), but concepts of Thought [or the objective Being of a thing, insofar as it exists only in Thought]

Ethics, 2p48s.

This is a passage that is important, and deserves a separate treatment, though I have approached it elsewhere, (not sufficiently) :A Diversity of Sight: Descartes vs. Spinoza , Spinoza: The Body of Ideas as Lens . Here though I want to instead look at Spinoza’s use of the phrase in the Fifth Part, where he addresses the problematic claim that through the mind we know that we are eternal. I do not want to focus at all the subject of the eternity of mind, but rather his use of the phrase, and his way of illuminating what he means by it. I quote the passage below, with two of its most successful translations, along with my own:

At nihilominus sentimus experimurque, nos aeternos esse. Nam mens non minus res illas sentit, quas intelligendo concipit, quam quas in memoria habet. Mentis enim oculi, quibus res videt observatque, sunt ipsae demonstrationes…

Ethics V P23s

Still, we sense and experience ourselves to be eternal. For the mind no less senses those things that through thinking it grasps, than those it has through memory. For the mind’s eyes, by which it sees and observes things, are demonstrations themselves…(Mine)

…still, we feel and know by experience we are eternal. For the Mind feels those things that it conceives in understanding no less than those it has in memory. For the eyes of the mind, which sees and observes things, are the demonstrations themselves…(Curley)

Nevertheless, we feel and experience that we are eternal. For the mind senses those things that it conceives by its understanding just as much as those which it has in its memory. Logical proofs are the eyes of the mind, whereby it sees and observes things…(Shirley)

We can see what appears to be an analogy, the mind’s eyes are demonstrations, or as some translate, logical proofs. I think it is important to understand that because of Spinoza’s parallelism (again, the principle that anything that occurs mentally, in the exact same order and connection occurs in extension), we have to consider anything, including thoughts and arguments, along with their material counterparts. Understanding that the demonstrations and proofs of the Ethics are not just ideas, but also, as text are also material expressions of Substance, our relationship to them is not just that of a mind to an idea, but also our body to the body, a material assemblage. If we are to think consistently along with Spinoza, the mind’s eyes literally become the demonstrations of the Ethics, such that our minds and body come into material and ideational combination with their reality. In this understanding, we literally “see through” the text of the Ethics. It is not just prosthetic, but cybernetic to our capacity to act, giving us greater freedom, as a body.

Spinoza via Wittgenstein?

This passage from Spinoza was highlighted by Wim Klever in his essay “Anti-Falsificationism: Spinoza’s Theory of Experience and Experiments” found in Spinoza: Issues and Directions : the Proceedings of the Chicago Spinoza Conference(1986). There he puts it into relation to two Wittgenstein citations, which help make clear the way in which we can “see through” proofs or demonstrations:

“Because of the proof our view will be changed… Our view will be remodeled… The proof guides our experiences, so to speak, in distinct canals [ in bestimmte Kanäle ].” – Remarks on the Foundations of Mathematics III (30-31).

“In another mind-space – one might say – the Thing [ das Ding ] appears differently.” Remarks on the Philosophy of Psychology (98).

There is an experiential sensing with the mind, an actual perception, in the process of thinking, and argumental proofs not only are means by which the mind senses, their material existence are the organs of the mind, as we combine with them. And if we follow Wittgenstein’s lead, through our thinking [Spinoza’s  intelligendo ] we sense res, things and situations. The proofs and propositions of the Ethics can be considered as material combinations which enhance our powers of action, through their conditioning of our experiences.

As I have pointed out elsewhere, Deciphering Spinoza’s Optical Letters , Descartes, in his Dioptrics, conceived of the telescope as a literal extension of the physical extension of the eye. His hyperbolic model of the ideal lens was meant to accomplish the same refractions that normally occur at the surface of the eye, just further out, so that “…there will be no more refraction at the entrance of that eye” (120) (as he says of his prototype, water-filled model of a telescope). And, as I have pointed out in the same article, because Spinoza wants to understand seeing as a “mind’s eye” event, Spinoza’s ideal lens was a more panoptical design, one that focused rays equally, comprehensively, coming from all directions: based on the powers of the sphere.

I suggest that Spinoza’s Ethics, in its symmetrically of internal reference, was thought by Spinoza to be something of a physical-mental extension of the mind, a rationally polished refraction of all the kinds of causal relations a human being could undergo, meant to bring those events into rough focus so that in that clarity, we may have a greater power to act. Just as Descartes’ imagined his hyperbolic telescope to be attuned to the narrow focus of a frontally discerning Will, extending the eye out into space, so Spinoza, more grandly, pictured the Ethics literally to be the eyes of the mind, propositions and demonstrations being panoptical perfections, to the degree that humanly we, or he, could make them. These “eyes” were vectors of power.

Spinozas letter 39 diagram, with Descartes hyperbola projected upon it, to show the contrast in ideal visions

Spinoza's letter 39 diagram, with Descartes' hyperbola projected upon it, to show the contrast in ideal visions

This has been a rough outline of the general idea I am putting forth, founded on the essential Spinozist assurance that whatever occurs mentally, occurs physically, and Spinoza’s pan-directional ambitions in his thinking of optics.