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Spinoza’s Optical Letters: Redux

As some know, primarily last summer I spent my time researching and theorizing on Spinoza’s lensgrinding and optical concepts, a largely underdeveloped field in Spinoza studies. The greater portions of my findings are listed here on this site under the sub-heading Spinoza’s Foci. A spearpoint of this research was uncovering the substantive arguments and conceptions that lay behind Spinoza’s rejection of Descartes’ optics, as found in his two letters 39 and 40, letters that have be nearly completely ignored by commentators on Spinoza, or if address, addressed in what seems a delinquent, or dismissive fashion. Spinoza is mostly thought to not know what he is talking about. On the other hand, Spinoza’s objections if carefully examined reveal both technically an alternate position on the problem of “spherical aberration,” but more deeply, a radically distinct conception of what vision is, in particular how it works as an insufficient analogy for consciousness. While Descartes wanted to emphasize the power of the central clarity powers of hyperbolic vision (both in the human eye, and in his proposed lenses), Spinoza understood vision and conciousness both as holistic events, ones best approached with the pragamatic appreciation of our limitations. I provide very little philosophical extrapolation here, though the implications are vast, perhaps running through down to the root of Idealism and Phenomenology. This epistolary commentary also does not touch on such other important factors such as the kind of lathe Spinoza likely used, nor much on his likely technique, and kinds of instruments he made and calculated for, which form a significant secondary branch of my research. Yet as these letters remain nearly the only first hand statement Spinoza made on optical matters, they are the anchorage point for anything else that is likely to be asserted.

For the convience of interested readers I here post a Word document version of my line-by-line explication of these rarely read and rather under-interpreted letters. I realized that the previous weblog versions were very difficult to read and browse through, hopefully something this version will correct. The two entries that can be found in this document are: Deciphering Spinoza’s Optical Letters and  Spinoza: Letter 40 and Letter 39. These are both the English translation of the two letters by Spinoza, and then my explication. This version is not footnoted (though there are citations), and it retains some of the idiocyncratic paragraphing and color coding. It is a 14,000 word document (48 pages), though Spinoza’s letters are only 900 words or so.

[click download]: Deciphering Spinoza’s Optical Letters Line by Line

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The “Picture” behind Intention: What Lies at the Center of Perception

Some Considerations of Objecf-Object Oriented Philosophy

Recent engagement with Graham Harman’s “Object-Oriented Philosophy” as it stems from Brentano and Husserl, stirs in me a terrible disagreement (I use “terrible” in the Greek sense). It comes from the “picture” that for me lies behind phenomenological preoccupations with the object, and I think also is core to Heidegger’s, at least rhetorical, notion of hiddenness (dear Sophocles, your Aias  meditation on Time!)…this is the intensely visual metaphor for how the mind works, and thus how we are to orient ourselves philosophically towards the imagined “object”, philosophically equated with Being. The entire heritage in my view suffers from this essentialized orientation to the object, the thing that reveals itself only in part.

In a soon to be published text Graham Harman quotes to some effect Husserl’s object orientation in Logical Investigations:

“every intention is either an objectifying act or has its basis in such an act.” 

“whether I look at this book from above or below, from inside or outside, I always see this book. It is always one and the same thing, and that not merely in some purely physical sense [which plays no role in Husserl’s philosophy- g.h.], but in the view of our percepts themselves. If individual properties dominate variably at each step, the thing itself, as a perceived unity, is not in essence set up by some over-reaching act, founded upon these separate percepts.”

As I have argued elsewhere (linked far below), and found in my research into Spinoza’s optical theories and practices, this modern conception of a picture of consciousness as somehow oriented towards the object, in a sense, being composed by its object, is something that has its modern origin in optical metaphors drawn from the rise of dioptics, the science of the lensed refaction of rays. The transition from the Perspectivist tradition which matched linear rays from points on an object to points in the back of the eye, to the philosophical meditation on what it takes to have “clear and distinct” ideas (Descartes), led us to understand consciousness itself as oriented towards a central clarity, a clarity which, however obscure the borders, as the object of the mind composes a kind of “truth”. Under such a view it is the very nature of consciousness to be somehow defined by this centrality, this clear picture, and the obscure boundary spaces do nothing more than “serve” this center (Kepler, Descartes).

The “Clear and Distinct” Center

As just suggested, Descartes is responsible for bringing to the fore this notion of consciousness through a pursuit of the “clear and distinct” idea. It is important to note that this phrasing comes directly from dioptrics where it carried a specific meaning. In an age wherein refraction was barely understood (the law had just been identified), the quality of glass incredibly fogged and bubble-ridden, and methods of glass grinding unsettled and under continual invention, an image in a lens that was “clear” (clare) was one which was bright, and one that was “distinct” was one which, if bright enough and the properties of the glass and curve optimal, all the parts could be made out. A bright idea was one that struck one with obviousness, a distinct one one that struck with detail, that is, as being sufficiently differentiated. When looking through a microscope a “clear and distinct” image was a good image. In keeping with his preoccupations with the future science of the dioptrics of microscopes and telescopes, Descartes felt that mentally the “clear and distinct” idea was the focus of mental perception, just as the clear and distinct image is the focus of visual perception. Emotions and sensations were indistinct quite often. A pain might be very “bright” (obvious) but indistinct as to its cause or nature.  

 

In my studies I find, following Graham Burnett’s inspiration, that Descartes’ hyperbolic lens, designed as it was to bring a central object into view as clearly and distinctly as possible, was related to his hyperbolic doubt, which was meant to help focus the mind on the most bright and disguishable ideas. In both Descartes hyperbolic lens and imagination, it is the visual center of consciousness which stabilizes truth. It is the object of one’s eye and mind. I argue that Spinoza’s objection to the efficacy of Descartes’ optical hyperbolic lens contains also an objection to the notion of a central clarity, a clarity that works to anchor the mind to truth.

The Dissonance Hole

Now back to the inheritors of a concept of consciousness which finds at is center an (object) clarity. These are the phenomenological sons of Descartes’s preoccupations with the optical metaphor. To this inheritance I would like to raise a deeper question than simply exposing a central metaphor (and its possible contingent relationship of the validity of arguments that depend on it: chose another metaphor, like for instance how Plotinus uses sound, and possibly end up with different conclusions). I want to suggest that if one attends to consciousness itself, and looks to the very center of consciousness, one doesn’t find a stability there at all. In fact, there is hole at the center of vision.

Richard Sennett’s recent, and thought-provoking The Craftsman  includes the importance of this “hole”:

The capacity to localize names the power to specify where something important is happening…Localizing can result from sensory stimulation, when in a dissection a scalpel unexpected hard matter; at this moment the anatomist’s hand movements become slower and smaller. Localization can also occur when the sensory stimulation is of something missing, absent or ambiguous. An abscess in the body, sending the physical signal of a loss of tension, will localize the hand movement…

In cognitive studies, localizing is sometimes called “focal attention.” Gregory Bateson and Leon Festinger suppose that human beings focus on the difficulties and contradictions they call “cognitive dissonances.” Wittgenstein’s obsession with the precise height of a celing in one room of his house [citing that the philosopher had a ceiling lowered 3 centimeters in a house he had designed just the construction was being completed] derives from what he perceivedj as a cognitive dissonance in his rules of proportion. Localization can also occur when something works successfully. Once Frank Gehry could make titanium quilting work [citing the design of a material of specific relfective and textural capacities], he became more focused on the possibilities of the material. These complicated experiences of cognitive dissonance trace directly, as Festinger has argued, from animal behavior; the behavior consists in an animal’s capacity to attend to “here” or “this.” Parallel processing in the brain activates different neural circuits to establish the attention. In human beings, particularly in people practicing a craft, this animal thinking locates specifically where a material, a practice, or a problem matters.

Pay attention to the dissonance that lies at the center of one’s attention. As the eye plays over the surface of an object, the gaze is not upon the “object” but at the living line which erupts out of the sense of it.  If we take up Husserl’s book, we don’t even have to look at its inside, outside and bottom. We merely need to look at its cover. The eye flits across it, an electric line that traces out the variations of its color, its choice of title typeface, its wear on a corner, its color that reminds us of a dress we saw. Yes, we are “seeing” the book, but it is an eruptive book. These are not accidents to the essence of the book, but rather are produts of our engagment with it. But more than this, the “book” is not a center of our consciousness, it is is not the “object” of our consciousness, or even intentionality. In fact there is no object at all which is the focus of our altering gaze. But it goes further than even this, for if the living line does erupt from the book, we understand that the book itself is present to us as a ground of sense for which this line depends. It is not that the book is somehow constructed out of these in some “over-reaching act” but rather that the book already serves as a ground, an under-reaching ground. The dissonance of our awareness depends upon an awareness of consonance. And this consonance is not though made up of the object of the book either, for the book is perceived as a book against (or in coherence with)  a vast array of other boundary perceptions and beliefs (I see that it is a book because that is a table, and I am in a room, and “I believe that writing exists, that there are authors” etc.). Not only is the “object” not at the center of our gaze, but neither is it the whole of the sense from which we do derive our center. Our awareness is a breadth. We say that we are “looking at the book” or “thinking of the book” as a kind of short hand for mutitudnal effects which are only understood as layers or degrees. And we also “picture” (retroactively) a stability of what we are looking at, paying less attention to what it is that we are attending to (a living line of dissonance, and a counter-boundary of outer sense) .

Intentional and Other Objects

When “object-orientation” concepts of Being flow from this notion of central apparition (and also for Heideggerians necessary hiddenness), the full sense of what the mind does, what consciousness is, I think gets lost. I have not read Graham Harman extensively (only an unpublished essay, a lecture listened to, and some informative comments), but I cannot help but have the sense that there is something of a central clarity conception of consciousness that he has taken from the sons of Descartes. What is interesting to me though is that tool orientation, a craft understanding of consciousness, actually is what calls our attention to the very hole at the center of vision. A craftsman is the one that focuses on the eruptive amid an organized sense, plan or workability.

So when we consider what Graham Harman takes to be the “object” of philosophy…

1. Intentional objects (such as phenomenal trees) exist in uneasy alliance with their accidents

2. Real objects (such as real trees) exist in uneasy alliance with their qualities

3. Real objects are deeper than the phenomenal qualities that emanate from them in relations

4. Intentional objects are unreal but are made up of real moments

This fourfold of accidents, relations, qualities, and moments can be restated in cosmologically more interesting fashion:

1. The tension between an intentional object and its accidents is precisely what we mean by TIME

2. The withdrawal of a real object from any relation is what we call SPACE

3. The duality between a real thing and its own real qualities can be called ESSENCE

4. A merely intentional thing’s possession of genuine qualities can be called, in a Husserlian sense, EIDOS

I feel that we need to ask how much of this falls back upon the essentialized notion of central clarity, the idea that our minds should be directed (philosophically) towards the focus upon “intentional objects” or “real objects” (or the interplay between them); how much does this direction rely upon a mistaken over-simplified “picture” of consciousness, and the historical inheritance of conceptions derived from Descartes fascination with refraction and the correction/enhancement of vision? It seems that when we realize that it is rather the “accidents” of an object that actually compose our intentionality, the eruptive semiotics of a dissonance that flows out from a ground of sense-making, the game of recapturing the buried “essence” of an object, the “real” object, apart from its intentionality loses its footing. It is the accidents themselves that connect us to the object, the flash of light across a surface that redirects our orientation to the object and causes us to care about it in a new way, to encamp it with a cathexis of our informing affects, and understand the world differently through these connective effects. When the intentionality of consciousness is understood not directed towards a clarity, an object (however present or hidden), but rather towards the breakdown of that object, not through an attention to the regain of an eidos behind it, but through a bodily reconfiguration of ourselves in orientation to the world itself wherein there is no accident for each accident signifies, then we understand the mind much more as an activity rather than a representation device (an important step I feel). It is in this constant re-vectorialization of the self through reporting others and a world that gives knowledge its uumph, its power and freedom. I am unsure how far Graham Harman’s Object-Oriented Philosophy deviates from my thoughts on this, for we share a distinct interest in the post-human, a sense that flat ontologies should be in some ways deepened, and would work toward a cybernetic understanding. I look forward to a continual and edifying communication with Graham Harman’s writings, in particular the coming book on Latour, Prince of Neworks. These thoughts come out of what for me was a strong sense that he yearns for a solidity behind (or in front of) the orientation of philosophy, a solidity which he reads as “depth”, yet an anchor point which by my brief reading takes its cue from a tradition that pursues a central clarity in what for me are misleading metaphors of vision, a tradition which works to stablize and centralize the human self (soul) which he looks to de-centralize.

In addition to this, as a last remark, there is in modern philosophy a tendency to think in irreducible dyads, that is: How do we get from here (let us say, that intentional object) to there (the real object); or how do we get from here (a true proposition) to there (a state of the world); or how do we get from here (thoughts in my mind) to there (thoughts in your mind); or most generally, how do we get from here (the self) to there (the world). This binary thinking which haunts much of representational analysis is a continuation of the primary problem of much of theology, how to get the soul back to God. All kinds of mediating paths are offered to what is imagined to be a fundamentally binary relationship (we expect the mediations to vanish). Many of these philosophical conundrums disappear when the dyad turns into a triad (and not a Hegelian triangle), that is, when the A/B line becomes a triangle of orientations. This is part of Latour’s philosophy of the “same”, but also central to Donald Davidson’s triangulation. It is not self/world, but self/self/world. I think part of the problem of thinking in terms of mind/object-essence dyads is that the triangle does not become properly emphasized. What happens when we find a fissure at the center of consciousness is that the third term (be it another informing person/object, or a causal state of the world) comes into view to help consolidate the fissure, bringing it into a clarity which then erupts. The fullness of a philosophy should be directed towards the necessity of the third term in any binary preoccupation, the way in which the third completes the sense. Not Object-Oriented Philosophy, but Oriented Object Philosophy, perhaps.

As Plotinus tells us:

If they are two, the knower will be one thing, and the known the other, and contemplation (theõria) has not yet made this pair akin to each other (õieiõsen) (Enn. 3.8.8). 

For thoughts related to these:

1. A Diversity of Sight: Descartes vs. Spinoza

2. The Hole at the “Center of Vision”

3. Deciphering Spinoza’s Optical Letters

Spinoza as Craftsman: A Closer Look

The Craftsman

An initial synthesis of some of the aspects of my research and a more refined notion of craftsmanship: writing to think through.

This is not the place to write a review of Richard Sennett’s provocative, subtly powerful book The Craftsman. I can only say in that vein, it is a book I highly recommend for those who enjoy looking at recurrent themes in culture and technology, wih an eye to informed thinking about the challenges and opportunities that face us today. The book is chock-full of illuminating analogies and narratives of human progress in problem solving [what he does with chicken recipes is astounding]. Aside from this general appreciation I believe Mr. Sennett’s observations on the significance of the wisdom of the craftsman has great consonance with the same point I am have been attempting to establish: Spinoza’s view of seeing technology as a continuous interface between bodies in assemblage. To put it one way the Craftsman represents the bodily knowledge shore between ideas held and our capacity to act, something I believe is embraced by Spinoza’s parallel grasp of both Mind and Body, thought and extension.

But from this book I would like to concentrate on a few distinctions of analysis Sennett makes to study they way that tools are used, and to assess their epistemic value as a means of intuition and inference. I cite from his chapter “Arousing Tools”.

Mr. Sennett starts with a general appraisal of the place of tools in our process of learning and acting:

Getting better at using tools comes to us, in part, when the tools challenge us, and this challenge often occurs just because the tools are not fit-for-purpose. They may not be good enough or it’s hard to figure out how to use them. The challenge becomes greater when we are obliguedto use these tools to repair or undo mistakes. In bothcreationand repair, the challenge can be met by adapting the form of a tool, or improvising with it as it is, using it in ways it was not meant for. However we come to use it, the very incompleteness of the tool has taught us something (194).

He goes onto make a distinction between a fit-for-purpose tool and an all-purpose tool. The example he uses for each is a screwdriver. A philips-head screwdriver is fit for one purpose, yet a flat-blade driver has a flexibility to it, “it can gouge, lift, and line as well as screw”. It is tempting to apply Spinoza’s definition of power to this distinction, the flat-blade tool actually has a greater number of ways it can “affect or be affected”. This does not make it a better tool at any given instance, for it its capacities must be assessed in assemblage to situations and to among other things, screws, but there does seem to be a fundamental difference to be noted.

The all-purpose tool has something of an openness to it:

…in its sheer variety this all-purpose tool admits all manner of unfathomed possibilities: it, too, can expand our skills if only our imagination rises to the occasion. Without hesitation, the flat-edged screwdriver can be described as sublime – the word sublime standing, as it does in philsophy and the arts, for the potentially strange. In craftwork, that sentiment focuses especially on objects very simple in form that seemingly can do anything.

I’d like to stop here for a moment, for I am attempting to look through Richard Sennett’s lens at the discoveries I have come upon in regard to Spinoza’s technical-optical practices. There is no doubt that Spinoza, at least in life, if not in philosophical theory, embodies the core values of the craftsman. He lived a thrift life upon the intentionally thin thread of the earnings of his lens-grinding and instrument making. He came from the artisan class of Amsterdam Sephardic Jewry, and devoted himself to the perfection of things for their own sake, a mark of craftsmanship. And his hands-on experiences with materials and the lathe gave him a distinctly craftsman approach to problems of light and glass. If we ask, For Spinoza, what tools would strike him as “sublime” in the sense that Sennett defines it? It would seem safe to say that the lathe in its simplicity and multiplicity of uses would be sublime. Nearly every required lens could be ground on his bench provided the right glass, abrasives and forms were available. This spinning concentric action must have been “potentially strange” and a source of many, perhaps unconscious, inferences.

I think though that in my close reading of Spinoza’s two Optical Letters, it would seem that Spinoza also regarded the spherical lens as sublime. In his argument for its superiority its essential multiplicity, as long as one accepted its one inherent drawback of slight spherical aberration, gave it a certain panopticalquality, the way that it addressed rays coming from all points of a field of view. One can say that this understanding came from a failure to properly understand the optics involved, but I suspect that it is rather overestimated how correct the understanding of contemporary optics was. A theorist could hold what we take to be a “true” optical belief, but only due to fact that he also held a great number of beliefs we would regard as false. In a sense, to assess the truth or falsity of a scientific belief, one should perhaps take a more tool-oriented view toward these beliefs, asking how they worked to solve which problems.

Keeping this in mind, I think it safe to say that Descartes’ also found his discovered (imagined) hyperbolic lens “sublime”. For Descartes the simplicity of its form (a hyperbola could be made with two sticks and string in the garden he tells us), the elegance of its line bespoke a remarkable potential for applicability. But there is something to the foundational thinking of Descartes’ hyperbola (shown in Kepler), which also seemed to make it something like a fit-for-purpose tool, a philips-head. The way that Descartes saw it, it matched the human eye, acting like a hand and glove prosthetic extension of the organ out into space. It fit its purpose. Additionally to this, it not only fit the shape and powers of the eye, but it also snugly secured itself within Descartes larger conception of perception and the exercise of the Will. The hyperbola’s narrow aim of focus matched Descartes’ idea of the “clear and distinct” object of perception, crispened in a field of obscured images. This field was a background for the exercise of valuations and free choice. It was this fit-for-purpose aspect of the lens that I believe Spinoza instinctively had some objection to. It could be argued that Spinoza’s embrace of spherical lenses also had a fit-for-purpose quality to it, as indeed it did. The sphere was evocative of the completeness of mental-vision that in the pre-requisite acceptance of inadequate and imaginary ideas, strived for a total awareness of the causal matrices that brought things together. What needs to be pointed out is that Spinoza is not the only holder of such conceptual relations. Rather, they are likely endemic to all descriptive, problem-solving thought. At the time the understanding of refraction and spherical aberration was still quite confused, even in the minds of those that would make the most progress in these areas.

In a certain way, Mr. Sennett wants us to know that the very ambiguity of a tool, the fuzziness of its ability to work, is that which stimulates us to imagine what must be the case that would make the tool work (or require a new tool). He tells a wonderful story about the problems that arose with the invention the surgical scalpel (15th century), born of the introduction of silica into the iron, giving a new and remarkable sharpness. It enabled precise anatomical dissections and discovery, as well as advances in living operations. Remarkably this new knife produced the difficulty of now to cut, what techniques of muscle movements could handle this suddenly fine instrument (less shoulder and a co-operations of figures Sennett tells us). It seems it took a century or more to be able to master these new powers. The tool imposes itself upon the imagination in the context of the resistances of the world.

It is easy to think that Descartes had in mind that his hyperbolic lens would act something like the new scalpel, like his hyperbolic doubt, it would cut through the murky imperfections of the field and clearly select out what is essential. It would carry the eye to distant things, by extending the eye itself. Generally it is assumed that Descartes valuably got it right with the hyperbola, as he identified a solution to spherical aberration (already pointed out by Kepler). And if we are to imagine that he got it wrong, there are likely two ways he was wrong. The first was the widely assumed connection between what turned out to be chromatic aberration (the obscuringcolored ring in telescope observations), and spherical aberration. But, as Graham Burnett has pointed out, he also got wrong his assumption that he could just take a mathematical formula, engineer on paper a machine that could would carry it out, and with a little advice and sweat from a hired craftsman, his paradisaical lens could easily be produced. Again and again he expressed frustration with hired artisans that either they or the materials were failing him.

Four Stages

Sennett gives us a guide to stages of technological development that might help us see Descartes difficulty more clearly, and perhaps gain the value of Spinoza’s craft-sensitive, if metaphysical objections. First he says that there is reformatting. Reformatting is simply the “willingness to see if a tool or practice can be changed in use”. The example offered is the way that Christopher Wren used chiaroscuro techniques of shading in his illustrations of specimens shown in Robert Hooke’s microscope, so to produce plates more vivid than what could actually have been seen in the poor quality glass and light, while still being perceivedas quite accurate. Descartes indeed employed reformatting in both his development of mathematical tools (a forwarding of the Law of Refraction), and his inventive design of an automatic lens-lathe, but lacked any capacity to reformat techniques of placing materials in relation to each other in real machines, assuming that this was the least difficult portion of the process, just getting the matter to do what the mind wished it to.

Secondly, there is adjacency. “Two unlike domains are brought close together; the closer they are, the more stimulating their twined presence”. This seems precisely what Descartes did in terms of his imagination of the eye and his hyperbolic lens. By placing the two hyperbolic forms, organic and glass, together in an assemblage, his inferences to the clarity of thought and vision took wide gallop.

Thirdly, is intuitive leap or surprise. “Although you were preparing for it you didn’t know in advance precisely what you would make of the close comparison. In this third stage you begin to dredging up a tacit knowledge into consciousness to to the comparing – and you are surprised. Surprise is a way of telling yourself that something you know can be other than you assumed” (211). This no doubt lead to the writing of the Dioptrics, and his more than decade-long pursuit of a grinding machine capable of making his very precise lens.

Fourth is Gravity. “The final stage is recognition that a leap does not defy gravity; unresolved problems remain unresolved in the transfer of skills and practices…The recognition that an intuitive leap cannot defy gravity matters more largely because it corrects a frequently held fantasy about technology transfer. This is that importing a procedure will clarify a murky problem; more often, the technical import, like any immigrant, will bring with it its own problems” It is in gravity that Descartes seems to have failed, and is there no better evidence of this than Descartes (feigned?) glee that his craftsman de Beaune had severely cut his hand trying to make the desired lens, proving to Descartes the superiority of his rational vision! Descartes lacked the connection to material practices to adequately transfer his familiar terrain of mathematics and geometry to lathes and glass. His lens was impossible to make.

These four stages help us enframe something of Descartes’ failings and also help suggest to us something of Spinoza’s resistance to the lens and its attendant conceptions. There is one more tidbit that Richard Sennett offers us in this chapter that I want to bring to the issue. He says that in his distinction between a fit-for-purpose tool and an all-purpose tool, as they are designed specifically to either repair something broken or seek to improve it upon repair,

The tool that simply restores is likely to be put mentally in the toolbox of fit-for-purpose-only, whereas the all purpose tool allow us to explore deeper the act of making a repair. The difference matters because it signal two sorts of emotional responses we make to an object that doesn’t work. We can want simply to relieve its frustration and will employ a fit-for-purpose tool to do so. Or we can tolerate the frustration because we are now also curious; the possibilities of making a dynamic repair will stimulate, and the multi-purpose tool will serve as a curiosity’s instrument (200).

It is fair to say that both Spinoza and Descartes, in their philosophies, imagined the possibility of radical improvements in the minds and lives of their readers. Descartes’ radical doubt, and Spinoza’s “clear and distinct” excellerated leap to the Totality of Causes: God, are figured as sublime simplicities. And each thinker has characterized the process as that of the making of tools that could make other tools, like a blacksmith (Spinoza borrowing the image from Descartes). What I would want to ask would be, what is the role of the simplicity of craftsman understanding of the lathe and the lens in Spinoza’s vision of what is clear? For Spinoza I think it likely that he thought of the spherical lens as something like the flat-edged screwdriver, capable of a workman-like enhancement of human bodily powers. This all-purpose property allowed him to remain with this curiosity focused upon a more systematic and comprehensive vision of what made vision clear: the Ideas that we hold. I suspect that it was his hands-on practice of grinding glass to required mathematically describe shapes, and his physical understanding of the fancifulness of Descartes’ hyperbola, that lead him to disparage the enthusiasm for the shape. This did not prevent him from investigating it, but it did keep him in deep suspicion of metaphysical and scientific foundations of its importance.

I think also that this resistance to the hyperbola, and the fundamental acceptance of spherical aberration as a slight and perhaps necessary impairment, draws our attention to Spinoza’s understanding that real change occurs in the world of human imagination and affects, within the realities of our weaknesses. Despite his great concentration upon rationality and abstract reasoning, the model of Euclid’s Geometry, it is within human sociability that the hands touch the matter at hand. The realities of the properties of present conditions are the actual vectors of the power we may have. Any active use of reason does not transcend its earth. As he understood that any change in power and freedom requires a change in the body, and that any ideational move was a physical move, so must he to some degree have gleaned this understanding from the resistances of the cloudy glass and the spinning of the lathe, in the cybernetic feedback of his body’s own actions and experiences. The polishing of a lens was prosthetic, but not prosthetic to the eye, prosthetic and expressive of the body and mind.

I think that that in the gap between the two Substances of Descartes lies Spinoza at his lathe.

A related post writen some time before: The Lathe Mind: What Spinoza Meant by “Individual”

A Diversity of Sight: Descartes vs. Spinoza

Different Foci of “Clear and Distinct”

This may be premature in my process, but I would like to set down some simple correspondences that have arisen in my reading of Kepler’s Paralipomena to Witelo (1604), correspondences that elicit strong tidal differences between Descartes’ approach to vision – with its attendant metaphysical counterpart, the clear and distinct Idea – and Spinoza’s. That this is found in some of the historically least interesting of Spinoza texts, what has been taken by many to be Spinoza’s blundering into optical theory [ letters 39 and 40 to Jelles, full text ], is suggestive of Spinoza’s critical brilliance. For within Spinoza’s conception of optics and his close-cut rejection of Descartes reasoning seem to be important radical divergences, insofar as vision and light are understood to be more than analogous of metaphysical truths. In these letters Spinoza questions the very vision-philosophy that privileges a central-line of axis, one that fundamentally connects a viewer within to an external and opposing point: a hidden, underpinning assumption of Descartes’ mathematization of the experiential self, Will and the world. Though there is much in Descartes’ philosophy that substantially departs from the Perspectiva epistemology tradition, his enthused embrace of the powers of the hyperbola embody a grounding of the eye, (and therefore the mind), in a centralized perception and knowledge upon which Spinoza places his criticism.  

I have not encountered any analysis which shows that Descartes’ enthusiasm for the hyperbola derives directly from Kepler’s Paralipomena, yet as I am not fully familiar with the literature perhaps this is a commonplace understanding. Gaukroger, for instance, gives evidence that Descartes read this text around 1620, and allows three possible points of influence, but does not speak to the potential influence of Kepler’s offer of the hyperbola as a natural normative of vision. Yet in the process of reconstructing Spinoza’s conceptions in these two letters of objection to Cartesian optics this connection with Kepler owes be fleshed out. One will see that in the Paralipomena Kepler not only sets out the virtues of the hyperbola’s anaclastic line in terms of its resolution of spherical aberration from focus – the primary and crowning demostration of Descartes’s 8th discourse of La Dioptrique – but he also naturalizes the hyperbola, claiming that the hyperbolic shape of the posterior of the crystalline humor is the very thing that helps establish the soul’s satisfaction with centered-object viewing. In fact, the wide sweep of Descartes’ metaphysics and optics in brief seems signaled by Kepler in his treatment of the hyperbola. And, because I suspect that Spinoza has Kepler’s descriptions in mind when responding to Jelles, making an argument for the importance of a radii of axes of perception, and emphasizing the importance of the angle of incidence in the measure of magnification (see letters linked above), his alternate response to Kepler provides a valuable clue to the stake Spinoza is making against Descartes, both in philosophy and science. In short, Descartes makes a virtue out of the Kepler’s description of the hyperbola and the eye, and Spinoza makes it something of a flaw or limitation. 

Setting Forth Kepler’s Hyperbola

Kepler's illustration exploring the properties of refraction, page 106

First, perhaps it is best to set out what Kepler has to say about the hyperbola so that a comparison can be made. Initially, he embraces the figure in an attempt to assess a law of refraction, which he hopes to find through the virtue of its special properties. He will not attain the law of refraction, but what he does make clear is that the hyperbola alone possesses the capacity to focus parallel rays to a single mathematical point, or vice versa. Thus, he writes of the figure above:

What is required is to say what sort of surface it is upon which these radiations in this position coming forth from α, so that they strike just as do here the lines βλ, μγ, and so on, so that these lines are either tangents to that surface, or lines equidistant to the tangents…These, moreover, are found only in the hyperbola, not in the parabola, which tends toward a straight line parallel to the axis, not one meeting the axis, as X A here. (107-108).

Not to get lost, were are simply establishing that Kepler points out the solitary characteristic of the hyperbola which will make a lens of this shape central to Descartes’ ambitions for providing aberration-free vision through hyperbolic lenses.

The next apparence of the hyperbola in Kepler’s text occurs in chapter 5, where the geometry and anatomy of the human eye is discussed. Here Kepler presents a small, simple drawing of the “crystalline humor” which behind the cornea in the eye is the primary means of focusing light. I enlarge it here for clarity:

Keplers drawing of the crystalline humor

Kepler's drawing of the crystalline humor, page 167

Kepler writes of the shape of the humor:

 On the posterior side…[the] figure is a hyperbolic cononoid, a hyperbola rotated on its axis. For [Johannes] Jessenius thus relates, that it is not spherical as [Felix] Platter said but that it protrudes markedly, and is made oblong stretching up almost into a cone; and that on its anterior face it is of a flattened roundness…(167).

Kepler has emphasized a correction. The humor is not spherical as Platter claimed, but hyperbolic, and made nearly like a cone. It is this particularity of the eye, coupled with his earlier hyperbolic observations that will create a certain naturalization of hyperbolic vision, something that speaks to the very nature of the human soul. The aspherical effect of the crystalline humor on vision is made clear a few pages later where Kepler discusses how the various cones of light coming from each of the points of an object to be seen, interact with and refract upon the cornea and the crystalline humor. What will be shown is that the humor is biased towards the production of clarity oriented towards its central axis, and that light cones that come obliquely to this angle, will appear less clear to the human eye, as they are focused to the borders of the image:

All the lines of the direct cone [whose axis is the same as the axis of the cornea and crystalline] are approximately perpendicular to the crystalline, none of those of the oblique cones are. The direct cone is cut equally by the anterior surface of the crystalline; the oblique cones are cut very unequally, because where the anterior surface of the crystalline is more inclined, it cuts the oblique cone more deeply. The direct cone cuts the hyberbolic surface of the crystalline, or the boss, circularly and equally; the oblique cone cuts its unequally. All the rays of the direct cone are gathered together at one point in the retina, which is the chief thing in the process; the lines of the oblique cones cannot quite be gathered together, because of the causes previously mentioned here, as a result, the picture is more confused.The direct cone aims the middle ray at center of the retina; the oblique cones aim the rays to the side…(174)

Kepler then takes these facts of refraction and uses them to explain the experience we have of satisfactory vision. What is most notable is that Kepler wants us to understand how the oblique “more confused” images at the borders of an image actually complete and serve the focus of vision around the central axis:

…so the sides of the retina use their measure of sense not for its own sake, but whatever they can do they carry over to the perfection of the direct vision. That is we see an object perfectly when at last we perceive it with all the surroundings of the hemisphere. On this account, oblique vision is least satisfying to the soul, but only invites one to turn the eyes thither so that they may be seen directly (174). 

The “surroundings of the hemisphere” invite our eye from to this or that. Oblique vision proves satisfying to the soul only to the degree that it inspires the eye to turn its hyperbolically-aided central axis across its field. The concept is that the deprivation of clarity somehow drives the soul to complete its picture. This is an important point when considering the influence of vision as a primary analogy for Cartesian metaphysics.

Kepler Completes the Synthesis of Eye and Lens

Lastly, Kepler will place the facts and inclinations of vision within the context of the powers of hyperbolic focus, and he does this in such a way that it would seem sure that when Descartes looks to solve the problem of spherical aberration he would see in the hyperbola a natural bias towards centralized focus.

Keplers illustration of the spherical aberration of rays

Kepler's illustration of the spherical aberration of rays, page 194

After a protracted investigation of the behavior of light rays in refraction through a crystal globe filled with water, and an explanation of our visual experiences of the images and confusions that result, Kepler will conclude that the hyperbola alone resolves the need for gathering a cone of rays into a single point:

Proposition 24 – Rays converging towards some single point within a denser medium are gathered by the hyperbolic conoidalsurfacebounding the medium to one single point, closer than the former point…These two things [two requirements], however, are accomplished, not by one or another circle but by conic sections…Further, of the conic sections, only the hyperbola or some line very close to it, is the measure of refractions, as was shown in Sect. 5 of chapter 4. Indeed, this very thing was demonstrated there: that the surface making all the rays outside the denser medium parallel is a conoid that does not differ from hyperbolic (198).

Given this remarkable property, Kepler then concludes that “nature’s plan” has endorsed the priorty of the hyperbola. And it seems that there can be little doubt that Descartes worked to synthesize this priorty which his own metaphysical priorty for “clear and distinct” ideas:

Hence it is evident nature’s plan concerning the posterior surface of the crystalline humor in the eye. That is, she wished to gather all the radiation of any visible object entering the opening of the uvea [pupil] into a single point of the retina in order both that the point of the picture might be all the more evident, and that the rest of of the points of the picture might not be confused by extraneous rays whether stray or gathered together. – Chapter 5, proposition 24, corollary (199).

Spinoza: “the eye is not so exactly constructed..” (letter 40)

To pull back for a moment. If this analysis is correct, that a decisive rift in Cartesian philosophy could be seen in Spinoza’s letter to a friend discussing what at most appears to be a trivial oversight on Descartes’ part is striking. Many scholars seem to have struggled over the meaning of Spinoza’s words in these letters (39 and 40) sensing that there is an elementary blunder in Spinoza’s thinking, but, as seen in their lack of a careful examination of it, there is an inability to locate just what this blunder would be. Instead, because Spinoza has been read as solely a metaphysician, his foray into optical matters in these two letters was largely dismissed as Spinoza simply wading in too deep a water. With very few exceptions, most only assumed that Spinoza was unfamiliar with the issues at stake, and his in-concordant use of terms appeared to prove this; yet a change in scholarship is occurring. Perhaps our examination of these two letters can add to this shift of perspective.

What does Spinoza mean in his letter 40 talk about the inexactness of the human eye?:

Moreover, it is certain that, in order to see an entire object, we need not only rays coming from a single point but also all the other rays that come from all the other points. And therefore it is also necessary that, on passing through the glass, they should come together in as many other foci. And although the eye is not so exactly constructed that all the rays coming from different points of an object come together in just so many foci at the back of the eye, yet it is certain that the figures that can bring this about are to be preferred above all others (letter 40, full text)

We have seen from Kepler that the likely reference is to the distortions of “more confused images” at the borders of vision, in part due to the aspherical, single axis nature of the eye’s lenses. This stands in contrast to Spinoza’s diagram, which he takes to be an ideal spherical refraction: 

Spinozas diagram of the virtue of spherical refraction, Letter 39

Spinoza's diagram of the virtue of spherical refraction, Letter 39

Spinoza is extolling the comprehensive capacities of spherical refraction, and his embrace of this concept marks out a distinct divergence from Descartes’ naturalized emdorsement of a center-focused vision.  Descartes will develop a theory of clear and distinct thinking which narrows the field of mental vision. This vision is imagined to be in concert with what Nature had planned in having given the eye its own hyperobolic lens; conversely, Spinoza will take from Descartes the notion of “clear and distinct”, but the concept of vision in which it is to be deployed is dramatically different. Spinoza emphasises the clarity of a connective, hemispherical scope; Descartes is aimed at the close focus on the surest of things.

Looking With the “Mind’s Eye”

This difference perhaps can be made more distinct by considering the use of the phrase “the Mind’s eye” by both thinkers. For instance, in his Regulae, after his very influential Rule 8 [the full text of which I post and briefly engage here ], Descartes tells us in Rule 9 how we must compare improvements in thinking by attending to how we naturally see things. Human vision provides the exemplar of how of mental vision is, and the issue is one of central focus:

Rule 9: We must concentrate our mind’s eye totally upon the most insignificant and easiest matters, and dwell upon them for long enough to acquire the habit of intuiting the truth distinctly and clearly.

…We can best learn how mental intuition is to be employed by comparing it with ordinary vision. If one tries to look at many objects at one glance, one sees none of them distinctly. Likewise, if one is inclined to attend to many things at the same time in a single act of thought, one does so with a confused mind. Yet craftsmen who engage in delicate operations, and are used to fixing their eyes on a single point, acquire through practice the ability to make perfect distinctions between things, however minute and delicate. The same is true of those who never let their thinking be distracted by many different objects at the same time, but always devote their whole attention to the simplest and easiest of matters: they become perspicacious.

– Descartes, The Regulae, Rule 9

It is not without significance that Descartes in his metaphor of close focus appeals to artisans and craftsmen to praise the powers of concentrated vision. These are not a class of persons that he would embrace in society- his attitude toward de Beaune and Ferrier is well known – but their analogous use in a hierarchy of powers is in keeping with his concept of knowledge being like an ascent of mechanized complexity, from primitive mental tools to those most intricate (Rule 8, Regulae). The same artisan trope is found again in his La Dioptrique, where the limits of the eye are by craftsmen strained and improved by the exercise of ocular muscles. I quote at length below because it is an important passage. For one, it is found at the end of the 7th Discourse which is the text that Spinoza and Jelles are commenting on in their letters, and is at the cusp of his presentation of the 8th Discourse praise of the hyperbola. Secondly, here the virtue of a dispersive vision (which Kepler describes as limited by the hyperbolic shape of the lens) is denied: seeing more is not seeing better, as is testified by experience; and thirdly, Descartes treats the possible alteration of the limits of crystalline humor and pupil’s capacities as being achievable, not in the direction that Spinoza would like (tpward a more-than-human breadth of clear vision), but in terms of an exceedingly close narrowing, achieved by trained specialists:

There is only one other condition which is desirable on the part of the exterior organs, which is that they cause us to perceive as many objects as possible at the same time. And it is to be noted that this condition is not in any way requisite for the improvement for seeing better, but only for the convenience of seeing more; and it should be noted that it is impossible to see more than one object distinctly at the same time, so that this convenience, of seeing many others confusedly, at the same time, is principally useful only in order to ascertain toward what direction we must subsequently turn our eyes in order to look at the one among them which we will wish to consider better. And for this, Nature has so provided that it is impossible for art to add anything to it.

I have still to warn you that the faults of the eye, which consist in our inability to change sufficiently the shape of the crystalline humor or size of the pupil, can bit by bit diminish or be corrected through practice: for since this crystalline humor and the membrane which contains this pupil are true muscles, their functions become easier and greater as we exercise them, just like those of other muscles of our body. And it is in this way that hunters and sailors train themselves to look at very distant objects, and engravers or other artisans who do very subtle work to look at very close ones. 

– Descartes, Seventh Discourse

In the highlighted passage Descartes repeats Kepler’s summation of the benefits of a hemisphere of vision, that it simply leads to a field of vision which helps serve our central axis: Kepler: “On this account, oblique vision is least satisfying to the soul, but only invites one to turn the eyes thither so that they may be seen directly “. Yet Descartes has changed the emphasis some and placed the notion of “willing” at this central axis (a literal conflation). The widening of a view only provides the occasion for free choice, which will express itself in the turning of the single axis of the eye. (It is thus clear that Descartes and Spinoza mean different things by “the faults of the eye” and “the eye is not so exactly constructed”.)

Spinoza: “so that we must not fall into pictures”

What is compellingly consistent is that Spinoza’s own use of Descartes’ “Mind’s eye” phrasing will directly address the Cartesian issue of the freedom of the will, not to mention the pictorial conception of clarity and distinctness. The phrase is most pointedly found in his Ethics, just where the distinction between willing and understanding is by Spinoza denied (E2p48 and 49):

E2p48 – In the mind there is no absolute, or free, will, but the Mind is determined to will this or that by a cause which is also determined by another, and this again by another, as so to infinity.

Scholium – 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 – on this see the following Proposition [49] and also D3 – 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, in the middle of the brain), but concepts of Thought [NS: or the objective Being of a thing insofar as it consists only in Thought]; – trans. Curley

Descartes’ notion of looking with the “Mind’s Eye” requires learning what distinctness is in terms of our experience of human vision, a lesson that requires that we focus closer and closer upon obvious things, training our eye to become more and more exact, a lesson which in turn gives us to understand the centrality of the focus of a single axis, and the use of a breadthof vision as merely the field for a freedom of choices; yet in Spinoza the human eye itself is seen as “inexact” in its singular axis of focus. And looking with the Mind’s eye is for Spinoza not so much a process of learning to see clearer and clearer pictures, (or even holding one clear idea or another in mental vision), but rather learning to look in a way quite unlike the way of the human eye, within a matrix of conceptual understandings; and this matrix is one which decenters the central axis of vision (and one could say the “self”), strives to achieve something akin to an infinity of axes of vision, (nothing more than a breadth understanding of the order of Adequate Ideas and thus the causes of the phenomena we witness, and that we affectively experience). While Descartes would say, following closely our analogous experiences of human vision, that seeing more is not seeing better, Spinoza would say that one is only seeing better if one is seeing more: hence his thought moves very, very quickly to the intuition of the Adequate Idea of God.

A Difference in Method

One grasps this if one compares Descartes’ notion of method with Spinoza’s own early Emendation notion of method, which is in response to it. The below passage is important because it follows several points which bear 8th Rule influence (a focus upon human powers, viewing knowledge building like blacksmithing, for instance). While Descartes is interested in focusing the mind on simple truths which may serve ultimately to connect one to a transcendent God, Spinoza’s method is not one of focus upon this or that truth, but upon the standard of truth itself as it immediately directs one’s attention to a maximalizationof thought: a most perfect Being. It is the distinction between one kind of perception and all others, which throws the vision wide:

That is, the most perfect method will be one which shows how the mind should be directed according to the standard of a given idea of the most perfect Being…From this one can readily understand how the mind, as it understands more things, at the same time acquires other tools which facilitate its further understanding. For, as my gathered from what has been said, there must first of all exist in us a true idea as an innate tool, and together with the understanding of this idea there would likewise be an understanding of the difference between this perception and all other perceptions. Herein consists on part of our method. And since it is self-evident that the more the mind understands Nature, the better it understands itself, it clearly follows that this part of our method will become that much more perfect as the mind understands more things, and will become then most perfect when the mind attends to, or reflects upon, the knowledge of the most perfect Being. (trans. Shirley 39)

The web of truths that “Mind’s eye” vision focuses on is a breadth of vision, governed by a comprehension of determined causes. And in a sense, this begins with God, God as a totalizing reality of Being from which we are not separate. A field of vision, which for Descartes provides an array of choices which an axis-eye then willfully judges and picks its way through, for Spinoza is an incandescent weave of causes and effects, any adequate understanding of which leads to all others. It is a spherical conception of a refraction along an infinity of axes, in which the Will plays no part.

Descartes’s Hyperbolic Doubt and Hyperbolic Lens

In considering Kepler’s introduction of hyperbolic lenses and his Nature’s single-axis plan for the eye, and then Descartes synthesis of the two, there is the happy result of support found for a contested interpretation of Descartes offered by Graham Burnett, in his book Descartes and the Hyperbolic Quest . Professor Burnett offers that Descartes’ obsessive, mechanized pursuit of the grinding of a hyperbolic lens, and his project of legitimatizing his Natural Philosophy through “hyperbolic doubt” are something more than a mere conflation of uses of the word “hyperbolic”. Burnett tells us, citing Gaukroger’sbiography, that the two may correspond to a single conception of mind, (quoting at length):

What configuration of mind of mind allows natural light to coalesce into a clear and distinct idea? The answer…is hyperbolic doubt. If once we saw, as in a glass darkly, and if at some (beatific) point we will see face to face, for the time being the best we can seem to do is to see through the right kind of glass that one that does not distort or obscure: and this just might be, at least least initially, the focusing glass of hyperbolic doubt. To play out the suggestion then: Descartes greatest scientific success lay from his perspective, in his systematic investigation of optics and the perfection of human vision those investigations promised; his optics presented an instanteous light that could be focused into clear and distinct images by means of the imposition of ahyperbolic form. Descartes’ greatest philosophical success lay, from his perspective, in a systematic investigation of the human mind and the perfection of cognitive operations those investigations promised; that the human mind received, via natural light of reason, an instanteous, clear and distinct illumination, but only by means of the interposition of another hyperbolic focusing device – the hyperbolic doubt.

I do not wish to overemphasize the signification of the parallelism, tantalizing as it is. Following Gaukroger’s reconstruction of Descartes’ psychology [Descartes, an intellectual biography ], a quite elaborate extension of the hyperbolic (lens)/hyperbolic (doubt) analogy would be possible. In Gaukroger’s reading, the imagination mediates between the pure intellect and the realm of the senses, and the experience of cognition inheres in this intermediate faculty, which represents the content of the intellect and the content of the senses both as “imagination.” Where these two map onto each other the experience is that of “perceptual cognition.” As the project of hyperbolic doubt is abundantly imaginative, and as Descartes has insisted that the natural light of reason does not stream down from God but is within our intellects, it would be possible to argue that the imagination plays the role of the focusing of the hyperbolic lens, and receives the light emanating from the intellect, which normally enters the imagination confusedly, quickly distorted by the “blinding” profusion of imagery from the senses (126-127).

Indeed, if we follow professor Burnett’s conclusion, and allow it to have a substance greater than mere lexical coincidence, we find that when armed witha knowledge of Kepler’s antecedent approach to the hyperbola such a reading begins to cohere. Descartes’ embrace of Kepler’s hyperbola of the human eye shows that “extreme doubt” and the focus of the Will that it accomplishes is for Descartes truly both a mechanism for focusing the mind upon simple truths and a naturalized legitimization of a will-centered, single axis organized perception. What professor Burnett intuited through his study of Descartes’ life-long pursuit of an automated, hyperbolic lens-grinding machine, is given traction when the genealogy of Descartes’ conception of the importance of the hyperbola is traced back to Kepler, its orgin. And this is exposed in two almost-ignored letters written by Spinoza on a subject he long had been considered deficient in, as the force of Spinoza’s attack upon both Descartes’ metaphysics andhis optics is to be considered as being of one cloth. Spinoza has Kepler in mind because Descartes had Kepler in mind. This is suggestive of the power of Spinoza’s critique, and the level at which he carried it forth. It touched not only the abstraction of Descartes’ metaphysics, but also the optical-theory origins of Descartes preoccupation, that human vision was somehow naturally hyperbolic and therefore offering a guide toward the perfection of the mind. Because our inheritance of the optical trope of human vision is so rooted in our conceptions of the world, and our acceptance of Descartes’ approach to thought and mechanism is so pervasive, Spinoza’s optical critque proves promising of a radical importance at the very least.

Lasting Questions

None of this goes any distance toward proving whether Spinoza’s critique of Descartes in letters 39 and 40 was correct in the terms he meant it by, speaking of how light and lenses behave. Clearly Spinoza was well informed about the nature of Descartes’ claim as to the importance of the hyperbola. He had read and followed Johannes Hudde’s Specilla circularia, which dismissed the importance of spherical aberration in a mathematically exact way, minimizing Descartes’ impractical solution; and he was likely familiar with ChristiaanHuygens’ own complaints about Descartes’ failures in treating telescope magnification accurately. Additionally, it seems quite likely that Spinoza was familiar with the Ur-source of Descartes’ own embrace of the hyperbola, Kepler’s Paralipomena to Witelo, since he addresses specific terms of its explanation, and the argument he presents in brief cuts to the quick of the virtues of the hyperbola presented there: the idea that the human eye’s hyperbola somehow expresses Nature’s plan which in Cartesian hands would naturalize a priorty of a single-axis, will-driven priority of focus and choice. By arguing for the “inexactness” of the eye, Spinoza is undermining a primary vision/knowledge metaphor which helps form part (but most certainly not all !) of Descartes’ metaphysics of clarity.

There are therefore a few questions that remain. For one, Kepler does not merely serve as a source for a negative critique of Descartes, insofar as he has followed Kepler. For instance Kepler’s conception of light in many ways diverges from Descartes’, and could be said to have concepts which presage Christiaan Huygens’ own wave theory, which would eclipse Descartes’ optics. It remains to be seen if Spinoza’s optical understanding stems directly from Kepler in a positive sense, that is, if Spinoza’s holds optical concepts which were superior to Descartes’ theories due to Kepler’s influence. Spinoza has used Kepler to undercut Descartes’ metaphysics, but where does Spinoza stand in terms of contemporary optics? For this to be answered, Spinoza’s praise of the versatility of an infinity of axes has to be set up against the contemporary science of telescope construction. For though Descartes’ hyperbolic lenses were nearly impossible to make at that time, in theory at least they would have offered an advantage. Spinoza’s objection is that Descartes is incomplete in his analysis of magnification, and that the capacity of a lens to handle a variety of axes is important in compound telescope magnification. Such a possible importance remains unaddressed, though all existing telescopes obviously achieved their magnification without hyperbolic lenses (and notably, Christiaan Huygens had privately solved the issue of spherical aberration using only spherical lenses in the summer of 1665, when Spinoza and he were closest).

The other question that remains is to determine the large scale consequences of Spinoza’s rejection of a naturalized, single-axis concept of hyperbolic vision, upon his own preoccupation with lens-grinding and instrument making. The grinding of a lens, after all, is exactly the kind of “craftsman” or “artisan” practice that Descartes lauded in his 9th Rule, one that lead to an acuity of vision. The purpose of a lens is most often to achieve a magnification which concentrates the vision at a local point. And this is the mode of narrow focus to which Spinoza seems to making his objection. But if we allow the analogy between craftwork and mental tools found in the works of both Descartes and Spinoza, the careful refinement of a proposition, such as those found in Spinoza’s Ethics, would be read as a kind of development of perspicuity. Permitting the Ethics to stand as our model for complex, intricate knowledge, by analogy any grinding of glass into a polished shape must be seen as part of an interlocking of all other actions, ideas and material states; for just as there is extensive cross-reference in Spinoza’s Ethics, Spinoza’s own daily preoccupation with lens-grinding and instrument building must be seen as cross-referenced to an infinity of other causes and actions, all leading to an theorized increase in freedom. As Spinoza clarified a piece of glass and made it capable of magnfication, was it that he was concerned not just withthe the lens, but how this magnification fit with other lenses, in devices, with phenomena to be discerned, and the Ideas we hold as we use them? It would seem at that this is so, but this question has to be answered more fully.

 

 

Slightly, Re-evaluating Descartes

The Flexed Lens of Hyperbolic Doubt, as it Imaginatively Focuses the MInd

 

Instead of seeing Descartes as the harbinger of the tremendous severing of the Body and the Mind, as philosophy can be thought to have suffered over the centuries that followed, there are more subtle readings that grasp the cohesive project that Descartes attempting, one in which the imagination is seen to play a role in rational understanding. Such a take remains critical, but at a level which is more nuanced in the historical contexts of his ideas, while understanding the breadth of Descartes’ vision of how things cohere.

An important if prospective conclusion in concert with Descartes’ re-evaluation is reached by Graham Burnett, as he places Descartes’ pursuit of hyperbolic lenses in tentative relation to the use of hyperbolic doubt (I find this connection to be brilliant):

Descartes’ greatest philosophical success lay, from his perspective, in a systematic investigation of the human mind and the perfection of cognitive operations those investigations promised; that human mind received, via natural light of reason, an instantaneous, clear, and distinct illumination, but only by means of interposition of another hyperbolic focusing device – hyperbolic doubt…

…In Gaukroger’s reconstruction of Descartes’ psychology [Descartes, an intellectual biography ], a quite elaborate extension of the hyperbolic (lens)/hyperbolic (doubt) analogy would be possible. In Gaukroger’s reading, the imagination mediates between the pure intellect and the realm of the senses, and the experience of cognition inheres in this intermediate faculty, which represents the content of the intellect and the content of the senses both as “imagination.” Where these two map onto each other the experience is that of “perceptual cognition.” As the project of hyperbolic doubt is abundantly imaginative, and as Descartes has insisted that the natural light of reason does not stream down from God but is within our intellects, it would be possible to argue that the imagination plays the role of the focusing of the hyperbolic lens, and receives the light emanating from the intellect, which normally enters the imagination confusedly, quickly distorted by the “blinding” profusion of imagery from the senses.

Descartes and the Hyperbolic Quest

Compare this conclusion to Augustine’s own Neo-Platonic conception of our own self-knowledge, Augustine whose “Si fallor sum” preceded Descartes “Cogito ergo sum”, and we can see the legs of this approach in relation to an pervasive conception of the divine:

For we exist and we know that we exist, and we take delight in our existence and our knowledge of it. Moreover, in respect of these three things of which I speak [a trinity of being, knowing and loving], no falsehood which only resembles the truth troubles us. For we do not make contact with these things by means of our bodily senses, as we do in the case of things extrinsic to ourselves…[in] these cases it is the images resembling the sensible objects, but not the corporeal objects themselves, which we perceive in the mind and retain in the memory, and which excite us to desire the objects…

City of God against the Pagans, Book XI, Chapter 24

The much defamed “doubt” of Descartes really is not so much a doubt for skeptical doubt’s sake, or even a doubt played as a pretense for the foundation of an augment; it rather acts as a kind of imaginary corrective to sense images and experience itself, a use of the imagination upon the imagination, something that focuses the mind on just what is most sure, under a conception that reason is something that both resides and connects. When seen in this way, the division of mind and the body becomes not only ludicrously joined by the pituitary gland, but also by the imagination itself.

Descartes Sans Homunculus!?

One might productively add to this John Yolton’s reconfiguration of Descartes’ project to be one of an immediate Realism, and Natural Philosophy. Here, the scholastic division of the sign’s two parts, that of its signfication, and that of its representation, promises to free up the cliched reading of Descartes as harboring the perverse theoretical imp of an infinity of homunculi buried inside the head. As David Behan points out, scholastic formal signs (ideas) can be read by minds entirely without awareness. Representation, per se, no longer becomes the standard for Descartes’ notion of knowledge. A Few Selections…

The being of an object of the mind is epistemic; it is (in a phrase that I picked up from Norman Wells) the being of being known. The epistemic rendering of “being in the mind” is an important shift from an attempted ontic transfer of an objects reality to a cognitive transfer. The explication of “existence in the mind” does not only occur in Descartes. Behan calls attention to a passage from William of Auvernue which employs the same language, “What it does mean is that it is in the soul according the mode of the being of the soul, which is cognitive”…

David Behan interprets Descartes’ brain motions as formal signs. In support of this interpretation, he refers to the scholastic tradition just behind Descartes, a tradition to which Descartes must have been exposed. As Behan explains, formal signs in that tradition are not themselves known, they signify without without or being aware of them. If we read Descartes’ suggestion of brain motions as signs in this way, the supposed need, which commentators are fond of insisting upon, for a code-reader or, as Wolf-Devine repeatedly says, a homunculus, does not arise…

As a mode of mind, an idea does not…make ‘something other than itself come into the mind’. If an idea represents or if,…the act of cognizing by means of ideas does the representing (the combination of act and idea), in that function, ideas are not ideas as such. That is, in that representing function, they are not modes of mind. I do not suppose that there are any ideas on Descartes’ account that are only modes of mind in the narrow sense I am suggesting. I simply want to distinguish their nature as modes of mind from their nature of function as objectively real. It is this objective reality that is in some cases (e.g. the idea of God, some physical objects) caused by something other than the mind. Ideas as objectively real (or the combination of act and idea) do not play a sign role: they simply are the objects, that which is known.

There is an interesting similarity in Descartes’ account of brain motions and ideas: both play two roles or have two function. Brain motions are both physical events and signs carrying meaning. The motions become something other than motion. Ideas are ideas and objects, modes of mind and the object known. In this secondary role, ideas are something other than ideas. Brain motions become signs to a mind. Signs must refer beyond themselves. Ideas as objects do not really refer beyond themselves on Descartes’ account: they are the objects known. Thus the relation or function of representation is not a signifying relation, signifying differs from representing. Both are necessary for knowledge and perceptual awareness. To represent is to be that which is represented. The combination of signifying and representing ‘gets the object into the mind’, that is, makes the object known.

John Yolton, “Response to Fellow Symposiasts” found in, Descartes’ Natural Philosophy

I think sometimes we moderns, (even we post-moderns), are in the habit of setting up our grand narratives. And in our story about the errors of our historic ways Descartes has come to play the conveniently villanous role that makes any good story worth telling. He plays this role in a curious way though, in particular in the form of the rather easily used and ubiquitous adjective “Cartesian”. We should watch just how satisfying this word is, how simplifying. It is tossed about in Philosophy of Mind and in so many other fields with remarkable reassurance. In regards to it, there is supposed to be a neat and tidy error – some want to call it a irrefutable sounding “categorical error” – which is consistently present in Descartes’ program, and ferreting out this error (or even defending it obstinately) wherever we may find it makes up a very good portion of our philosophical endeavors.

In such a perspective Spinoza can be of very good use for he represents a turning point just before Idealism took up and swallowed the Cartesian poisoned pill. Descartes severed the Mind from the Body, but Spinoza just would not let him. I do think that there is much to be said for such a broad brushing of philosophical history on the West, and even for the very useful distinctions which underpin it. But I also suspect that Descartes’ thought holds within itself much more subtlety and tension that is otherwise granted. Representation simply does not hold such a privledged, and pristine place in Descartes’ thinking about knowing. And in this way, Spinoza’s thought, in relation to Descartes, is perhaps more complex and sympathetic than we otherwise might suspect.

This does not make Spinoza’s thinking “Cartesian” – that adjective again ! how it works something like the words “Communist” or “Racist” – for I am not even sure how frequently we can be assured that Descartes is entirely “Cartesian”; but it does make the connections between the two thinkers more imbricated than a simple comparison of a position of Attributes affords. I suspect that in the grey penumbra of Descartes, somewhere in Descartes’ conception of the blind man’s cane, for instance, in the folds of his treatment of the Imagination, and in the signifying, homunculus-defying aspects of Idea, there are sweet-spots of affinity between the two that may be good to trace.