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Tag Archives: Lenses

The Optica Promota and Spinoza’s concept of focus

Spinoza: Against Hyperbolic Vision

Optica Promota, figures 1 and 2

Optica Promota, figures 1 and 2, refraction in the densest medium

There are several points of correspondence between Spinoza’s objections to Descartes’ treatment of the magnification of images in the L’Dioptrique in his letters 39 and 40, and the analyses found in James Gregory’s Optica Promota, but perhaps the most significant touching point occurs in Gregory’s conclusion, where he brings up the lone failings of parabolic mirrors and hyperbolic lenses, which Spinoza is sensitive to. Here you have a presentation of the weakness of the hyperbola as an ideal of lenses, and yet the appeal to the human eye as somehow exemplary and natural, which I have pointed out in regards to Kepler’s Paralipomena, [thought about here: A Diversity of Sight: Descartes vs. Spinoza and more broadly here Some Observations on Spinoza’s Sight ]. The entirety of Spinoza’s referential borrowings from Gregory must be fleshed out, (they seem proliferate through these two letters) but for the moment I present this conclusion alone, which marks out the limitations of hyperbolic lenses, apart from their difficulty of manufacture:

But against hyperbolic lenses, it is only objected that nothing will be able to be most clearly seen, except a visible point arising on the axis of the instrument. But this weakness [ infirmitas ] (if it would be worthwhile to call it that) is sufficiently manifested in the eye itself, though not to be impuning Nature, for whom nothing is in vain, but how much all things most appropriately she carries out [ peragit ]. Nevertheless, with conical lenses and mirrors not granted, it shall be rather with spherical portions used in place of spheriods and paraboloids in catoptrics; as with hyperboloids in dioptrics, in which portions of spheres are less appropriate.

With these we go to the stars – His itur ad astra

One can see how Spinoza would have sympathy to the notion that Nature does not err, but the subtle question of the “infirmitas” of human, hyperbolic vision is one that he would pause at. Insofar as human vision is used as a model for mental vision, any weakness “natural” to human beings is not redeemed by that natural state. All states a human being finds herself in are “natural”, but there is a degree of perfection which works as a fulcrum point for change and improvement in Spinoza’s thinking. The question remains whether Spinoza’s appraisal of spherical lenses as ideal is a pragmatic solution to the problem of finding the best lenses possible in the real world, or is a mistaken extension in analogy from his concept of ideal mental vision back down to the question of lens shapes, over-valuing the capacity of spherical lenses to handle otherwise would be paraxial rays.  

Spinoza’s Picture of the Omni-axial Spherical Lens

As Spinoza writes in his letters 39 and 40, following Gregory’s warning about hyperbolics:

Letter 39 – …Perhaps he was silent so as not to give any preference to the circle above other figures which he introduced; for there is not doubt that in this matter the circle surpasses all other figures that can be discovered. If, for example, circle ABCD should have the property that all rays coming from direction A and parallel to axis AB are refracted at its surface in such a way that they thereafter all meet at point B; and also all rays coming from point C and parallel to axis CD are refracted at its surface so that they all meet together at point D, this is something that could be affirmed of no other figure, although the hyperbola and the ellipse have infinite diameters. 

diagram letter 39

And then..

Letter 40 – …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. Now since a definite segment of a circle can bring it about that all the rays coming from one point are (using the language of Mechanics) brought together at another point on its diameter, it will also bring together all the other rays which come from other points of the object, at so many other points. For from any point on an object a line can be drawn passing through the center of a circle…What I here say of the circle cannot be said of the ellipse or the hyperbola, and far less of other more complex figures, since from one single of the object only one line can be drawn passing through both the foci. This what I intended to say in my first letter regarding this matter.

As said, much more than this needs to be assessed regarding these two optical letters, but in this vein we identify a prominent theme of naturalized, hyperbolic vision and its critique, stretching from Kepler, to Descartes, and alternately Gregory to Spinoza.

The Optica Promota, by James Gregory (1663)

A valuable Spinoza resource: we have an on-line photocopy edition of the 1663 work Optica Promota by James Gregory, an edition found in Spinoza’s library of books. One can see the imprint that Spinoza likely looked at. This copy is found here.

Not only this, Ian Bruce has supplied us with a marvelous English translation and Latin transcript, with explanatory notes, found here in PDF parts.

This is a signficant text, as I believe that Spinoza is arguing with Gregory’s propositions and diagrams in mind in his March 1667 letters 39 and 40 to Jelles, as he makes his objections to Descartes, and perhaps also in his June 1666 letter 36 to Hudde, showing that he had studied this volume at least by this point in time.

Jan Hendriksz Glazemaker…the Glazier

Jan Hendriksz Glazemaker was born in 1619 or 20, married in 1651, and buried Dec 5 1682.

Assumed to be the translator of Spinoza’s works into Dutch, on the strength of the evidence from Duijkerius’ Philopater novel, Glazemaker is seen to be a thorough participant in the Van den Enden and Jan Rieuwertsz circle of Cartesian-Collegiant politicists. Nadler counts him, taking him as part of the Mennonite Amsterdam community, a likely friend of Jelles from youth. It should be noted as a very shallow but perhaps significant resource that, as per his adopted name, he worked as a glazier before becoming a professional translator. As a glazier, and part of a glazier family (after his step father Wijbrandt Reijndersz), he was familiar with techniques of glass making (if peripherally), sources for very good glass, and possibly spectacle makers.

(There is a history that connects the glass used for lens-grinding to the glass used for windows and mirrors. Rolf Willach in his “Development of Lens Grinding and Polishing…” reports that at least in the early part of the century, the glass used was window glass cut into circles, and deduces that three telescopes from the first decades of the 1600s used Venetian mirrors to grind into their plano-convex shape.)

Though a negligable lead in the quest for Spinoza’s early lens-grinding knowledge, because Hudde’s technique of microscope lenses was a glass-beading technique, and by one report Van Leeuwenhoek was inspired to learn lens-crafting from watching a fair glass-blower, it is something to mark.


A list of some of Glazemaker’s translations and their dates [Spinoza leaves Amsterdam mid 1661]

De deugdelijke vrou (1643)
Joh. Barclai, D’Argenis (1643)
Toonneel der werreltsche veranderingen (1645)
Romainsche Historien van Titus Luvius, sedert de bouwing van Romen tot aan d’ondergang van ‘t Macadonische Rijk. (1646)
Nikolous Coeffeteau, Romanische historien (1649)
D. Erasmus, Onderwijs tot de ware godgeleertheit (1651)
Homerus, De Iliaden (1654)
Descartes, Redenering om ‘t beleed, om zijn reden wel te beleiden ende waarheit in de wetenschappen te zoeken (1656)
Descartes, Meditationes de prima philosophia: of bedenkingen van d’eerste wijsbegeerte (1656-1657)
Descartes, Principia philosophiae: of beginselen der wijsbegeerte (1657)
Descartes, Proeven der wijsbegeerte (1659)
J. Lily, De vermaakelijke Historie, Zee- en Land-Reyze van Euphues (1668 )

Two more looks at the Rijnsburg Draaibank

[note: the nature of the Rijnsburg Lathe has been resolved: The Rijnsburg Lathe: Like the Sun, not 200 Feet Away]

Adding to the post below, here are two more looks at the Rijnsburg lathe, passed on to me by Mr. Verdult who runs the excellent Spinoza resource site

A detail from a photo from Theun de Vries’ book on Spinoza (1972) (page 101)

A photo found at

A Closer Look at the Rijnsburg Lathe

[note: the nature of the Rijnsburg Lathe has been resolved: The Rijnsburg Lathe: Like the Sun, not 200 Feet Away]

I am still attempting to assess the documentation and authority of the lens lathe at the Rijnsburg Spinozahuis. If anyone has notions of either the historical accuracy of this device, or even the working designs of its construction, your thoughts are appreciated. Posted are two perspectives, one taken from a Spinozahuis photograph, the second is of an illustration of something of the same as found in Rebecca Goldstein’s Betraying Spinoza (2006).

A detail of Goldstein’s illustration

How Much were Spinoza’s Lenses and Microscopes?

In the interest of making Spinoza’s lens-grinding, polishing, and telescope and microscope building more vivid to those considering his metaphysics, this evidence is posted as to the kinds of prices for those services one would expect.

Lueken and Lueken (1694)

E. G. Ruestow writes:

At a date I read to be late 1670′s: “…Johan van Musschenbroek in Leiden [sold micro-beaded lenses] forty for a gilder – roughly a day’s wages for skilled manual labor in the Netherlands. Musschenbroek otherwise advertised his cheapest simple microscope for 7½ gilders and his most elaborate, with nine seperate and interchangeable lenses, for nearly ten times as much” (The Microscope and the Dutch Republic, 28).

And the footnote reads: “Johan van Musschenbroek advertised six beads – “Glaze dropjes, en bolletjes” – for three stuivers, which, there being twenty stuivers to the guilder, was the price equivalent to forty for a guilder…Earlier in the century, Constanijn Huygens, Sr., had paid forty guilders for one of Drebbel’s microscopes.”

If indeed Spinoza made simple bead lenses, provided a buyer was available – which for these type lenses would be likely be infrequently – he could make a laborer’s day’s wages in about an hour (Ruestow points out that Swammerdam said he could make them at this rapid rate, 40 and hour). The prices of any primary grinding of lenses to specific focal lengths or uses for other salesmen or instrument makers of course are not reflected here. But perhaps a week’s wages could be made for his simplest microscopes.

Lenses not Rare

One can see from the depiction of a spectacle makers’ storefront, strewn with glimmering lenses and spy glasses, that by the late 17th century such devices are quite common. In fact, when Descartes writes his Dioptrics in 1637, when Spinoza is five years old, he mentions how common “flea glasses” have become. It is good to remember both the commonality of Spinoza’s trade, its brute, craftsman standing, but also the elite circulation of ideas which came about in applying these somewhat widespread devices, both in terms of theories about the nature of what was seen, but also changing techniques and optical conceptions on how to see it. Spinoza stood in both worlds.

Van Leeuwenhoek’s View of Technology and Spinoza

Part of this process of looking into the lensed conception of Spinoza’s metaphysics is understanding how at the cusp of a change in the technological interface - that is, with Descartes, an increased mathematization of nature and its corresponding instrumentization of devices - there also existed alternate conceptions of what viewing, observing and measuring entailed. The idea that a device could be of a fixed nature, a neutral embodiment of mathematics, and thus could be pointed in any direction, and at any number of objects, revealingly, is an imaginary simplification. Such a conception of device implies a certain invisibility of the mechanism in that the phenomena is simply shown for what it “is”, denuded. It is my sense that Spinoza, in his metaphysical grasp of the consubstantiality of the material and the ideationalas informed by his experiences as a maker of representational devices, and therefore instruments of both the micro- to macrological sort, conceived of instrumentation in a different kind of way. It was a way which may help inform us of our own potentiated relationship to technology. Rather than experiencing the object as simply being “revealed” it perhaps is better understood as staged, framed, part of an assemblage of observation and use. This is what alternate conceptions of technology may help us see.

In the personof van Leeuwenhoek, praised by history for his explorational conception of the micrological, a man who shared with Spinoza a merchant class origin, shunning for the greater part the fame of Scientific standing, we have a clue to something of the inveterate possibilities of instrumental use. I suggest below the example of the intimacy involved in van Leeuwenhoek’s experience of both his devices and his specimens. The “microscope” for him, was not understood, nor felt to be, a mechanism without context.

Pictured here is a composite drawing of van Leeuwenhoek’s “microscope” bringing together the significant features from the few surviving devices examined by Clifford Dobell. It shows boththe rod upon which a specimen needle is mounted, and the parallel plates between which a very fine lens would be inserted. The height of the specimen needle, and its proximity of it to the lens-plates, could be exactly and stably secured by the turn of screws. These devices are incredibly small, actually smaller than is pictured. What is significant about this device, other than its simplicity and size, is that the lens was so very small, its focal length could be less than 1/30th of an inch. The eye must be placed so as to be nearly touching the lens.

Van Leeuwenhoek made nearly five hundred of these palm-sized instruments, and famously was able to achieve magnification so as to vividly see bacteria and protozoa, the first of humankind to do so. Many of the plates were made of silver, and three of them are known to be made of gold, but none of them are in their material finely crafted in detail. They were tiny work-tools by van Leeuwenhoek’s conception. But there is something more about his concept that is important to dwell upon. After his fame had spread, some of the most important personages of Europe came to his merchant’s house in Delft to see these wonders. What is compelling is that he would let people view specimens on devices of only moderate magnification, and not sell a one. The most profound of his glasses, those upon which he made his most spectacular discoveries, he would not even allow a glimpse. People would ask him, bewildered, why would he make so many devices and never sell any. Various theories have arisen to explain this relation between van Leeuwenhoek and the number of his microscopes. Was he saving them up for sale by his daughter when he had passed? Was he secreting away the most precious facts of his observation capacities, making something of a mystery of it?

I think a clue to the number of devices is provided in the 26 samples he had sent to the Royal Society by his devoted daughter upon his death. None of the 26 are actually capable of the serious magnification that he must have attained in other devices, but each arrived, notably with their specimen already attached (the same is true for most of those auctioned off after his passing). The embryo of a Cochineal, or a thread of sheep’s wool, or the spinning organ of a spider’s abdomen was glued upon its requisite needle, perfectly positioned before its lens. One need only hold it up to light. I believe that far from conceiving of his microscopes as neutral devices which could be made machinically in relationship to laws of nature, and therefore could be turned ubiquitously upon any number of phenomena, each device was handmade for what was to be observed. He made so many devices because he had so many things to look at.

Why Did van Leeuwenhoek Refuse to Let Others Look?

Key to this device/object dyad is understanding that the viewing itself must have been a personal, intimate event. The staging of the specimen, the vice-like recursivity with which it was positioned to its glass, a minuscule glass sometimes ground just for that specimen, was an experiential revelation. As mentioned, the eye must be pressed so close as to practically touch the lens. In his most minute observations his microscopes and their specimens formed a circularity of object, means and eye that was physically closed.

There might be very good explanations why van Leeuwenhoek did not allow others – with the possible exception of his daughter, hired draughtsmen, and perhaps even anatomist Ruysch - to look into his strongest microscopic glasses, the obvious being his stated desire for secrecy; but beneath secrecy, most concerting was the likely intensive intimacy involved in these witnessings. And constitutive of this intimacy were two points. First was that Van Leeuwenhoek’s conception of minute observation was dioramic: frame and object met such that the frame was part of the view. It was an engagement. Secondly, because the device was small and could be held in the hand, and the eye was pressed so near, the consciousness of the viewer was a participation with the frame (metal plate and lens) as much as with the object viewed, so much so that there was no anonymity of vision. In a sense, perhaps van Leeuwenhoek came to feel that viewer could no more easily be exchanged with a particular device, than could its specimen. Individual glasses and individual objects matched, as did the eye, and as the magnification became more intense, so did the investment. This, I suggest, is what van Leeuwenhoek was protecting. One could say, just as one could not share dental braces, nor would not share contact lenses, van Leeuwenhoek refused to share the smallest of scopes. They fit his eye and his vision, prosthetically, and in terms of experience, privately. The math was thus affect-rich and context dependent.

(Could it be that there is closely related reason why van Leeuwenhook may have denied the privledge of looking into his strongest lenses? He was, admittedly, very sensitive to criticism. The game of assertion and denial was quiet unpleasant, and it was in part because of this sensitivity that he did not relish the thought of publishing his findings with the Royal Society at first opportunity. It could have been that this sensitivity extended itself to personal experiences as well. Van Leeuwenhoek was gifted. He had not only diligent powers of observation, but also incredibly acute eyesight, far better than even above average. It may have been likely that he had shown others, early on, his strongest glasses, and others simply could not see in them what he could see. His observations were, in a way, personalized to a more specific degree than even already mentioned, not just by context, but by capacity; he could not afford being told that what he saw simply was not there. They were is own assemblage.)

“…you then hold the microscope toward the sky…as though you had a telescope and were trying to look at the stars in the sky through it,”

he wrote of the process of illuminating a specimen. In such a view the conceptions of the linked Macrocosm and the Microcosm collapse into a single relational whole, (for one knew that optically a telescope could be turned into a microscope through a rearrangement of the lenses). But holding a specimen glass up to the light was more than this, it was a person’s investment in observation and device, and the one-to-one context between the specimen and its process of viewing that is exhibited by van Leeuwenhoek and his microscopes. This reflexivity of concept is shown everywhere in his staging choices, but perhaps none so evident as when he had carefully ground a grain of sand in order to see a smaller grain of sand, seeing sand with sand: 

The two grains, one a lens, the other fixed in ratio, were viced into exact proportion. This speaks strongly to a closed and event-specific notion of technology, one which involves the viewer as well. The sand-sand-eye-sky’s light looping form an intimacy which opens up an alternate understanding of what observation is, one where what is being looked at cannot be cut off from its mechanism of viewing, nor from who is viewing. Instead it is a putting of objects, including one’s eye, into relation.

Van Leeuwenhoek, Technology and Spinoza

Van Leeuwenhoek lived but 4 miles from Spinoza in the summer of 1665, and it is not at all certain that he had even invented his viewing glasses at that point in time (the earliest record of his observations come during a trip to England in 1668; and some [Ford for instance] propose that he was originally inspired by Hooke’s Micrographia which would have barely reached Delft in 1665). Yet one imagines that it is quite likely that the history of van Leeuwenhoek’s experiments with glassblowing and lens-craft go back further than our first record of them in regard to his English, chalk-gazing holiday [Ruestow suggests that A.v.L. intimates a date as early as 1659]. It is conceivable that the two lens-grinders were both making lenses contemporaneously, a few miles apart. But the point really is not to establish a personal contact point between van Leeuwenhoek and Spinoza, though they do share a matrix of possible relations, it is rather to suggest a conceptual contact point. They are physically proximate and they are both of merchant families (not a small cultural fact). Each pursued knowledge in a hermited, semi-private way. Mostly, though, they likely embody a conception of technology and lens which was not part of the dominate instrumental conception of device; theirs was one where what is personally made (even if it is an instrument) is not divorced from the circumstances of its use, either by its object, or its witness. What van Leeuwenhoek’s technological conception potentially reveals for the Spinozist, is the thought that despite the prevailing mathematicization of Nature, brought forth by Descartes’ lead, the combinatory experience of observer, device and object remains a determining factor in the meaning of what was discovered. This is something that Spinoza brings out when he speaks of our experience of the Sun being only 200 hundred feet away despite our knowledge that it is much farther and larger (Ethics 2p35s): our essence and the sun’s essence interact to produce the affect of a meaningful, imaginary experience, a kind of phenomenal knowledge, a knowledge which, though inadequate and confused, makes up a greater portion of our world. Simply the crystalizing of the phenomenal image into clarity, making it large and sharp, was not enough for “knowledge” in Spinoza’s view. This was not the “clear and adequate” idea. 

Spinoza’s notion of technology - in that he can be said to have one that we can conclude from his philosophy and assumed to be given through his experiences of lens and instrument making – calls our attention to the continual circumstance of our use, including our affective investments, and to the notion that object, device and eye are part of an assemblage of perception organized by our ideas. More than an ever more crispening of the image is the relation of that precision to our own exactness, and therefore for Spinoza, our own power. The conception is really Cybernetic.


Spherical Aberration: Descartes’ Solution

Philosophical Context: Optics

For those unclear about what spherical aberration is, and attempting to follow Spinoza’s comments about Descartes below, it is the tendency of rays at the edge of a spherical lens to refract at a focal length shorter than those near the axis:

This tendency is corrected by a hyperbolic lens, as theorized by Rene Descartes, which in its progressive sloping, sends the rays to one mathematical point.

It was Spinoza’s thought, probably working from the theories of mathematician Johannes Hudde, that light rays gathered at what he called a “mechanical point” and not a mathematical point. So spherical aberration was considered inconsequential, a fact of working with lenses and light. (A practical mid-century address of spherical aberration in telescopes was the use of much larger, flatter lenses, with longer focal lengths, making telescopes sometimes reach lengths over 30 ft.)

Unfortunately, for the greater part of the 17th century this spherical aberration effect was confused with, and assumed to be the cause of, chromatic aberration which produced a bluish halo at the edges of images, and which is, in most cases, more disruptive than spherical blurring. Not until Newton discovered the spectrum components of light from 1670 – 72 was it theoretically realized that the one was not the other. Even Christiaan Huygens, as he worked to resolve spherical aberration solely with spherical lenses, probably thought that he was resolving what was latter understood to be chromatic, as he was somewhat deflated by Newton’s discovery:

Spinoza and Hooke’s Micrographia: The minascule made Large

Look at Robert Hooke’s incredible, and conception-changing Micrographia (1664). And see it as if you are looking at the very book with excellent viewing software, at Turning the Pages Online (click “Turn The Pages”). This book must have struck one as if from another planet. See the overleafs open up into the most extraordinary illustrations of the smallest of things. It was the 3D, Surround Sound, epic film of its time.


As wiki writes of it:

Hooke most famously describes a fly’s eye and a plant cell (where he coined that term because plant cells, which are walled, reminded him of a monk’s quarters). Known for its spectacular copperplate engravings of the miniature world, particularly its fold-out plates of insects, the text itself reinforces the tremendous power of the new microscope. The plates of insects fold out to be larger than the large folio itself, the engraving of the louse in particular folding out to four times the size of the book. Although the book is most known for foregrounding the power of the microscope, Micrographia also describes distant planetary bodies, the wave theory of light, the organic origin of fossils, and various other philosophical and scientific interests of its author

Published under the aegis of The Royal Society, the popularity of the book helped further the society’s image and mission of being “the” scientifically progressive organization of London. Micrographia also focused attention on the miniature world, capturing the public’s imagination in a radically new way. This impact is illustrated by Samuel Pepys’ reaction upon completing the tome: “the most ingenious book that I ever read in my life.

This is the book that Oldenburg speaks of when he writes Spinoza about his hope that English booksellers will soon be able to send copies of various important books (the Second Anglo-Dutch War had interrupted commerse):

There has appeared a notable treatise on sixty microscopic observations, where there are many bold but philosophical assertions, that is, in accordance with mechanical principles (April 28th, 1665)

Spinoza answers in May, regarding his new talks with Christiaan Huygens, (it is unclear if he has just met him, or if Spinoza is answering in a condensed fashion, having not mentioned to Oldenburg this relationship before - he may even have known him since the summer of ’64 [letter 30A:"...I know that about a year ago he told me"]):

The book on microscopic observations is also in Huygens’ possession, but, unless I am mistaken, it is in English. He has told me wonderful things about these microscopes, and also about certain telescopes in Italy (letter 26).

Several prospective questions arise here. As mentioned, we are unsure if Spinoza has just met Huygens (Nadler brings up a counter argument beside the one that I suggest), so we cannot say if Spinoza was able to look at the book at the Huygens estate. At this point he seems only to have heard of it, but this may even be a polite deferment. If Spinoza did visit the estate and looked at its pages one certainly can imagine its impact upon the lens-grinder. He must have been mystified and pleased. There is a very good chance that its viewing set off a change in Spinoza’s thinking about his lenses, optics and the world, for by letter 32 in late November Spinoza is making metaphysical analogies that seem to appeal to microscopic observations, the “tiny worm living in blood”¹. This seems to suggest that somewhere in the summer of 1665 Spinoza became more focused on both the telescopic and the microscopic uses of lenses. Years later, after much experimentation, Huygens would finally admit that Spinoza was right that the smallest of lenses were best for microscopic viewing. Nadler suggests, via Klever, that Spinoza had a reputation for his telescopes and lenses as early as 1661, (“Borch’s Diary”, from A Life 182). Whether Spinoza in this summer decided to make new observations, or had already been making them, or if there were microscopes at Huygens’ estate, we cannot know.

Whether Spinoza was working with microscopes or not, the presence of the Micrographia at the Huygens estate, the likelihood that Spinoza would have seen its breath-taking layout (not to mention the possibility that Hooke’s generous and detailed description of how he made his lenses by a thread of glass was relayed to him), combined with Huygens own experiments with lens designs, lens lathes, and spherical aberration at the time, the summer of 1665 must have had a concerted conceptual and imaginative impact on Spinoza’s thinking and practices.

1. There is scientific context for the imagine of worms in blood: The “dust” on old cheese was found to be not dust at all but little animals, and swarms of minute worms were discovered tumbling about in vinager (Fontana 1646, Borel 1656, Kircher 1646). Kircher announced that the blood of fever victims also teemed with worms, and there was talk that they infested sores and lurked in the pustules of smallpox and scabies. (Ruestow, 38).




Also featured at Turning The Pages On-line: Ambroise Paré’s Oeuvres; Conrad Gesner’s Historiae Animalium and Andreas Vesalius’s De Humani Corporis Fabrica

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.



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