Spinoza and Tuberculosis: His Disease and Devotion

[Tuberculosis can be a difficult disease to diagnosis. The following is working under the assumption that the diagnosis of “phthisis” for Spinoza’s long-running pulmonary problems is best understood as the disease tuberculosis.]

The Influence of Disease

It is interesting that of all the influential facts we seem to have about Spinoza’s life, his tuberculosis may be neglected only as much as his lens-grinding has been. Very little of how debilitating this disease can be, nor its chronic nature seems to be considered when framing a picture of Spinoza’s motivations for life decisions. At most his tuberculosis, called in biographies “phthisis” (its name derived from Greek) gives us a remote picture of a man made weak and coughing at times. Then there is the oft repeated, unsupported, yet romantically satisfying thought that he died not only of his TB, but also from inhalations of glass dust from his lens-grinding. The facts of the disease seldom seem to enter into the explanations for Spinoza’s decisions and life turns.

Spinoza’s early biographer Colerus tells us that Spinoza had been suffering from tuberculosis for more than 20 years when Spinoza died at the age of 44, in February of 1677:

Spinosa was a Man of a very weak Constitution, unhealthy and lean, and had been troubled with a Pthysick above twenty years, which oblig’d him to keep a strict course of Dyet, and to be extreamly sober in his Meat and Drink. Nevertheless, his Landlord, and the people of the House did not believe that he was so near his end, even a little while before he died, and they had not the least thought of it.

If we track backwards, this would place the first bout with tuberculosis very close to the date of his father’s death (March 28, 1654), and his taking over of the family firm (September 1654). Spinoza’s step mother, Esther, died only five months before his father did (October 14, 1653), after a year of serious illness, itself a year after Spinoza’s own sister Miriam had died. Tuberculosis is a highly contagious disease when symptomatic, (if living 24-hours-a-day exposed for two months it is estimated that you have a 50% chance of being infected).

To more fully picture the condition, the symptoms of active tuberculosis include:

– A cough which may last three or more weeks and may produce discolored or bloody sputum
– Unintended weight loss
– Fatigue
– Slight fever
– Night sweats
– Chills
– Loss of appetite
– Pain with breathing or coughing (pleurisy)

That Spinoza may have contracted tuberculosis from his father (or other family members), and may himself have become symptomatic in the year 1656 or so is not something that many people have considered. (To his credit, Nadler does momentarily bring up the idea that Spinoza may have suffered from the same thing that killed his step-mother (Spinoza: A Life, 155); why he notes the step-mother and not his father I do not know. These are years that we have very little historical record of, and a struggle with the illness may very well be a reason for this (the highest risk for developing of the disease is in the first two years after infection). When Spinoza applied for orphan status in March of ’56 (two years after his father died), and when the cherem is read against him in July of the same year, removing him from the community, having failed to pay the family firm’s imposta tax, he may indeed already have been tubercular, and perhaps even seriously so. This would make his excommunication something of a quarantine, not only of ideas, but also in a vividness of metaphor, of body and illness. A cutting off of an already diseased limb. We really need not go that far, though it should be considered. We have had such a variety of motivations projected onto Spinoza and his situation at this time, from Jonathan Israel’s thought that Spinoza was during this period attempting to be excommunicated by being outrageous simply to climb out from the burden of onerous debts, to Wim Klever’s notion that Spinoza at this point was so invested in his political and spiritual education with Van den Enden, long broken from the community, the excommunication was but a trifle. Either of these may be so, but if Spinoza had by now become symptomatic, his illness certainly would have played into his inability to run the firm to profit, or more significantly, his desire to no longer conduct that kind of vigorous business or to remain in the community of his youth. No matter the thesis for his excommunication and his change of attitude towards the values in life, the facts of an onset of a lethal diseased that might have killed many of his family members certainly would play an informing role.

Chekhov’s Example

Tuberculosis does not always head in a straight line, by my understanding. It can be recurrent. Chekov, for instance, who like Spinoza also suffered from the disease over a twenty-year period. A first onset expressed itself in an initial bout of fevers in December of 1883, and then three days of coughing up blood a year later in December of 1884. It was not until six years after these, from the strain of trans-Siberian travel, that again the disease seemed to surface, much more forcefully. Chekhov, like Spinoza, died in his 44th year, at the peak of his intellectual and creative powers. [Citing “Chekhov’s Chronic Tuberculosis” (1963), by Brian R. Clarke]. This is how one medical information website describes the nature of the disease’s chronic mechanism:

In addition, TB can spread to other parts of the body. The body’s immune (defense) system, however, can fight off the infection and stop the bacteria from spreading. The immune system does so ultimately by forming scar tissue around the TB bacteria and isolating it from the rest of the body. Tuberculosis that occurs after initial exposure to the bacteria is often referred to as primary TB. If the body is able to form scar tissue (fibrosis) around the TB bacteria, then the infection is contained in an inactive state. Such an individual typically has no symptoms and cannot spread TB to other people. The scar tissue and lymph nodes may eventually harden, like stone, due to the process of calcification of the scars (deposition of calcium from the bloodstream in the scar tissue). These scars often appear on x-rays and imaging studies like round marbles and are referred to as a granuloma. If these scars do not show any evidence of calcium on x-ray, they can be difficult to distinguish from cancer.

Sometimes, however, the body’s immune system becomes weakened, and the TB bacteria break through the scar tissue and can cause active disease, referred to as reactivation tuberculosis or secondary TB. For example, the immune system can be weakened by old age, the development of another infection or a cancer, or certain medications such as cortisone, anticancer drugs, or certain medications used to treat arthritis or inflammatory bowel disease. The breakthrough of bacteria can result in a recurrence of the pneumonia and a spread of TB to other locations in the body. The kidneys, bone, and lining of the brain and spinal cord (meninges) are the most common sites affected by the spread of TB beyond the lungs.

“experience had taught me”

At the very least, if Spinoza was showing symptoms of the disease as early as 1656, as Colerus’ very rough estimate would place them, Spinoza’s life decisions to not pursue wealth, but rather a life of philosophy, must be cast in a slightly different psychological light. Spinoza writes of his change of mind in The Emendation of the Intellect:

After experience had taught me that all the usual surroundings of social life are vain and futile; seeing that none of the objects of my fears contained in themselves anything either good or bad, except in so far as the mind is affected by them, I finally resolved to inquire whether there might be some real good having power to communicate itself, which would affect the mind singly, to the exclusion of all else; whether, in fact, there might be anything of which the discovery and attainment would enable me to enjoy continuous, supreme, and unending happiness.

I say “I finally resolved,” for at first sight it seemed unwise willingly to lose hold on what was sure for the sake of something then uncertain. I could see the benefits which are acquired through fame and riches, and that I should be obliged to abandon the quest of such objects, if I seriously devoted myself to the search for something different and new. I perceived that if true happiness chanced to be placed in the former I should necessarily miss it; while if, on the other hand, it were not so placed, and I gave them my whole attention, I should equally fail (Elwes translation).

This is thought to have been Spinoza’s earliest philosophical text, before the Short Treatise, Shirley placing its composition between the years 1657 and 1660. What, we may ask, was this “experience” that has taught Spinoza the futility of social life, the uncertainty of “fame and riches”. Are these generic experiences that all of us would have, or perhaps the particularities of watching his father die in tubercular fashion, after a life of substantial monetary and honorific gain? Or, more jarringly, was it the onset of the same disease, the same coughing up of blood, that he had seen his father and his step-mother succumb to? This would certainly have a life-turning effect. Spinoza continues in the opening of the Emendation, actually referencing the analogy of fatal illness and remedy as the very mode of his decision making:

For I saw that my situation was one of great peril and I was obliged to seek a remedy with all my might, however uncertain it might be, like a sick man suffering from a fatal malady, who, foreseeing certain death unless a remedy is forthcoming, is forced to seek it, for therein lies all his hope (Shirley translation).

Is this just a proximate reference, or is Spinoza speaking literally of his own onset of illness?

We see no evidence for debilitation in April of ’55 in the record of Spinoza’s subpoena and physical confrontation with the Alvares brothers. He is struck so hard his hat comes off, something which might afford a reference to physical weakness, but none is mentioned. In fact, from the vague description it seems that only the hat seems worse for wear, leaving the impression of a firm man. And in ’58, from Fra Tomás’ 1659 report to the Spanish Inquisition, we find Spinoza to have a handsome face “de buena cara” with light, clear, but perhaps pale skin, blanco. This would seem to put him in good health. The only thing I would mention is that in this report there is great contrast given between his very dark hair and eyes, and the paleness of his skin. Prado, in whose company Spinoza is in, has a “brownish” complexion on the other hand. While he may have been in good health at the time, the paleness of his skin may have been due to some convalescence. In 1659 he is described by another informant for the Inquisition as having a “well-formed body, thin, long black hair, a small moustache of the same color, a beautiful face”.

Yet as we have seen from the example of Chekhov, an attack of tuberculosis does not necessarily leave one debilitated for life. The body’s immune system can indeed isolate the infection, and return one to health, even robust health, only to be susceptible to the disease later, at times of great stress or weakness. Assuming that his disease was that of tuberculosis, one cannot conclude that Spinoza’s health was never robust, as some have thought.

The Beginnings of “Isolation” and a Conserve of Roses

A great deal of investigative imagination and analysis has gone into the question as to why Spinoza left Amsterdam for the much more quiet Rijnsburg in 1661. Gullan-Whur suspects that something had frightened Spinoza in a way that the excommunication had not, perhaps something to do with the Spanish Inquisition. Perhaps an increasing pressure from Dutch authorities and Jewish reaction made it unsafe for Spinoza to continue his Amsterdam life, some feel. And there is the account of a knife attack outside the theatre, if it is to be believed. Alternately, some think that he went to Rijnsburg to be closer to the Collegiant movement. Spinoza’s very good, generous friend Jarig Jelles bought a large new house on the Herengracht in Amsterdam in 1660, but Spinoza did not move in. First he moved to near  “near ” Ouderkerk, and then to Rijnsburg near Leiden’s university. Why? It is mentioned that his move towards isolation was so that he could be away from distractions from friends, so that he could concentrate on his work, and this is no doubt true. But is it too much to notice that his withdrawal from friends and the air of the city may have been really a question of health? Was it not that tuberculosis struck him again, and it is was in full view of his mortality, and even questions of contagiousness, a theoretical need for fresh air, that brought him to concentrated isolation?

By September 1661 he writes to Oldenburg that his Short Treatise, (one may say his most overtly spiritual work) is still a work in progress. There is no hint of his illness in their correspondence. In the winter of ’62/’63 he has the company of Johannes Caesarius, who is living with him, helping him in a none-too-satisfactory fashion with the geometrical treatment of Descartes’ philosophy. Gullan-Whur reads Caesarius to be Jan Casier, a student of Van den Enden’s school, now a young, Dutch Reformed ordinand (1642-77). As a collaborative biographical note of perhaps significant correspondence during this period, Adriaan Koerbagh, Spinoza’s friend and comrade in spirit of the same age, had received his doctor of medicine from nearby Leiden University in 1659, with a dissertation on the causes of Tuberculosis, Disputio medica unauguralis de Phthisi. In 1661, the year that Spinoza moved to Rijnsburg, Koerbagh became a Doctor of Law, again at nearby Leiden, and in Koerbagh’s later political trial he admits that he had discussed philosophical matters with Spinoza numerous times in the years 1661-63. Having conducted a study of the causes of tuberculosis, one wonders if Koerbagh had ever seen Spinoza as a patient. Or if Adriaan himself had tuberculosis which weakened him (as he would died only within a few months of being sentenced to prison and hard labor in 1669). Along this thin line of argument, is it a coincidence that a conserve of roses is the only conserve mentioned in Koerbagh’s Bloemhof  (1668). The suppressed Bloemhof  was a 672 page dictionary of terms written by Adriaan and his brother, meant to demystify the use of foreign phrases and technical jargon, putting into the vernacular the verbal obfuscations by which eclesiastical, medical and legal “experts” carried out much of its authority over the common man. In June 1665 it is for a conserve of roses that Spinoza says he is waiting (Letter 28), writing to the physician Johan Bouwmeester who was an intimate of Adriaan Koerbagh. Spinoza had visited his friends in Amsterdam earlier in the year, and during his visit to the city he seems to have suffered a recurrence of his tuberculosis:

At the same time I also expected some of the conserve of roses which you promised, although now for a long time felt better. On leaving there, I opened a vein once, but the fever did not abate (although I was somewhat more active even before the bloodletting because of the change of air, I think). But I suffered two or three times with tertian fever, though by good diet I have at last rid myself of it and sent it packing. Where it went I know not, but I don’t want it back.

At this time Spinoza has just moved from Rijnsburg to Voorborg near the Hague. Likely having finished first drafts of parts I and II of a then tripart Ethica, he makes a break and begins his work on the Politico-Theological Treatise. Spinoza distinctly associates the “air” of Amsterdam with the onset of his illness. It would appear likely that this causal belief was consistent in his life, and thus part of his reason for moving out of Amsterdam in the first place. One can also ask, something I’ve not seen considered, was the renewed attack of his disease in some way linked to the much discussed break from the Ethics, and his turn to political issues of the day?

Voorburg, Not So Quiet

At this point I would like to take up some of the psychological criticism aimed at Spinoza by his biographer Gullan-Whur. In making her assessment of a certain flaw in Spinoza’s self-perception she provides us with a rather telling description of the house Spinoza moved into in Voorburg. She points out that although Spinoza, in her opinion, plays the role of the isolated sage, being crankily troubled by intrusions, he moved into one of the most bustling, connected locations in all of Voorburg:

Voorburg was a rural village, but Benedictus had not chosen to live in a peaceful part of it, for the Kerkstraat houses, huddled on a terrace and generally having only a gable loft above their ground floors, were flanked by the market place and a boat-servicing harbour beside the Vliet. Yet, whole this lodging was feverishly cacophonous compared with sleepy Katwijkerlaan, he never complained…nothing was easier that getting to any Dutch city from Voorburg. The philosopher could leave home almost at the ringing of the horse-boy’s bell to catch the trekschuit. Voorburg being on the way to everywhere (the canal system joined the River Schie at Delft, and continued south to Rotterdam and Dordrecht), he should have foreseen a continuous flow of callers (154-155)

She goes onto conclude that Spinoza himself does not own up to his own emotional needs for company, caught up in the production of his own image. I might suggest that Gullan-Whur has severely misread Spinoza’s contradictory needs for isolation and for contact. This essentially is the mindset of the chronically, if sporatically, ill. Rather than this being a profound conflict of conscience, or the inability for Spinoza to understand his own needs, Spinoza’s tuberculosis and his philosophical/scientific endeavours required both isolation and contact. Indeed I would suggest that it was likely the disease that forced Spinoza to reconsider his life, and it was this ever-present relationship to his own body and mortality that made his rationalist philosophy most concerned with the freedoms of the body. Gullan-Whur’s example of reading the man is actually instructive for all interpretations which ignore his physical histories. In fact I would think that all of Spinoza’s metaphysical positions on the body should benefit from being seen in the light of  a possible continual threat and experience of tuberculosis.

Summation

It is persuasive to infer, and least as persuasive as any other reasoning I have encountered, that Spinoza’s father and step-mother indeed died of tuberculosis, and that Spinoza had contracted the illness from them. On average, people have a 50 % chance of becoming infected with tuberculosis if they are in close contact eight hours a day for six months. If Colerus’s estimate is right that Spinoza had struggled with the disease for more than twenty years, this would put his first attack right at the decisive years of the late 50s, as Spinoza was forming his new political and theological relationships with Van den Enden and Prado, leaving behind the family business. (By stating this length as more than 20 years, Colerus at the very least seems to want to place the illness before Spinoza’s milestone move from Amsterdam.) This encounter with a disease that may have killed his father and step-mother surely would have shaped the decisions Spinoza was making. And the resultant dedication to philosophy, science and selective isolation should not be considered outside of this persistent awareness of both his disease and the effects it may have had on others. All the complexities of influence that we can convincingly conjure up may very well pale to the experience of the fatal fever and cough a year after you watched your father and step-mother, and perhaps even sister, pass under similar conditions. It is agreed that this is a time of plagues, and the death of family members and close friends, certainly by 1664 was not uncommon. This does not mitigate the personal effect the disease would have had upon Spinoza in the determinative years of 1655-1658, not to mention the consequences of managing the disease over a lifetime.

Why the timing and substance of the disease has not been well considered by biographers and interpreters of Spinoza’s life, I do not quite understand, except for the recognizable need to comprehend the man in terms of much vaster, more abstract historical and intellectual factors.

Spinoza’s Letter 39: Descartes’ Silence

I post Letter 39 here, for reference. 

Letter 39

To the humane and sagacious Jarig Jelles, from B.d.S.

[The Original, written in Dutch, is lost. It may be the text reproduced in the Dutch edition of the O.P. The Latin is a translation.]

Most humane Sir,

Various obstacles have hindered me from replying any sooner to your letter. I have looked at and read over what you noted regarding the Dioptica of Descartes. On the question as to why the images at the back of the eye become larger or smaller, he takes account of no other cause than the crossing of the rays proceeding from the different points of the object, according as they begin to cross one another nearer to or further from to eye, and so he does not consider the size of the angle which the rays make when they cross one another at the surface of the eye. Although this last cause would be principle (sit praecipua ) to be noted in telescopes, nonetheless, he seems deliberately to have passed over it in silence, because, I imagine, he knew of no other means of gathering rays proceeding in parallel from different points onto as many other points, and therefore he could not determine this angle mathematically.

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.

For because a circle is everywhere the same, it has the same properties everywhere. 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. So the case is as you describe; that is, if no account is taken of anything except the focal lenth of the eye or of the telescope, we should be obliged to manufacture very long telescopes before we could see objects on the moon as distinctly as those on earth. But as I have said, the chief consideration is the size of the angle made by the rays issuing from different points when they cross one another at the surface of the eye. And this angle also becomes greater or less as the foci of the glasses fitted in the telescope differ to a greater or lesser degree. If you desire to see the proof of this I am ready to send it to you whenever you wish.

Voorburg, 3 March 1667

[trans. Samuel Shirley altered]

Benedicti de Spinoza opera quotquot reperta sunt quotquot reperta sunt By Benedictus de Spinoza, Baruch Spinoza, Johannes van Vloten, Jan Pieter Nicolaas Land

 

Spinoza’s Blunder and the Spherical Lens

Did Spinoza Understand the Law of Refraction?

 

In seeking to uncover the nature of Spinoza’s lens-grinding practices, and the competence of his optical knowledge, I believe I may have uncovered another small, but perhaps significant mis-translation of the text. The text is letter 39, written to Jelles (March 1667)), wherein Spinoza explains the insufficiency of Descartes treatment of the cause by which objects appear smaller or larger on the back of the eye. Spinoza points out that in La dioptrique Descartes fails to consider the angle of incidence of the rays at the surface of the lens, and only considers “the crossing of the rays proceeding from different points of the object” at various distances from the eye. I believe that there are subtle epistemological issues that come with this point, and which Spinoza has in mind, but for now it is best to pay attention to what follows this complaint.

Spinoza suspects that Descartes has fallen intentionally silent on this factor, in part because Descartes has it within his plan to promote the importance of the hyperbolic lens, a reported improvement upon spherical lenses. Hyperbolic lenses, which Descartes championed and tried at great length to produce in an automated way, by the time of Spinoza’s writing had proven to be impossible to manufacture. Yet here Spinoza objects to them at the geometrical level. Spinoza argues that their means of collecting light rays, due to their aspherical nature, was less proficient than that of spherical lenses. I shall have to leave this immediate comparison of lens shapes aside, as well, to narrow our attention to a reported blunder Spinoza makes in his explanation, a blunder that has lead some to conclude that Spinoza really could not have had much comprehension of theoretical optics at all. He might have known how to make lenses, but was unclear as to how they worked. The charge is that he didn’t even understand the law of refraction: the principle relation between the angle of incidence and the refractive properties of a lens medium, derived by Descartes to explain the main insufficiency of spherical lenses: spherical aberration. 

Spinoza draws a diagram to help explain to Jelles just what the advantages of spherical lenses are. It depicts what Spinoza regards as a natural product of its symmetry, the capacity to focus rays that are parallel along its infinite number of axes, across its diameter, to a point opposite:

This is how Spinoza describes the relation, as translated by Shirley, (a wonderful translator):

For the circle, being everywhere the same, has everywhere the same properties. For example, the circle ABCD has the property that all the rays coming from the direction A and parallel to the axis AB are refracted at its surface in such a manner that they all thereafter come together at point B. Likewise, all the rays coming from the direction C and parallel to the axis CD are refracted at the surface in such a way that they all come together at point D. This can be said of no other figure, although hyperbolae and ellipses have infinite diameters

Now this description has lead notable, modern critics to conclude that Spinoza seems to have failed to understand the Law of refraction altogether, for in seeking to raise the value of the figure of the circle Spinoza has attributed properties to it that appear to ignore just that law. Principle here is the apparent, unqualified claim, “the circle ABCD has the property that all [parallel] rays coming from direction A…are refracted [at] point B”:

This is how Alan Gabbey articulates the failure on Spinoza’s part, and the reasonable conclusion to be drawn from it:

One’s immediate suspicions of error is readily confirmed by a straightforward application of Descartes Law of refraction. For the circle to have to the dioptrical property Spinoza claims, the refractive index of the glass would have to be a function of the angle of incidence [Gabbey secures his point with a footnote of the formula], a condition of which there is not the slightest hint in the letter. In his next letter [March 25, 1667] to Jelles, who asked for clarification, Spinoza explained that light rays from a relatively distant object are in fact only approximently parallel, since they arrive as “cones of rays” from different points on the object. Yet he maintains the same property of the circle in the case of ray cones, apparently unaware of the importance of the “[other] figures” [the famous “Ovals of Descartes”] that Descartes had constructed in Book 2 of La Géométrie to provide a general solution to the problem of spherical aberration [Ep 40]. I suggest on these grounds alone that though Spinoza may well have written a treatise on the rainbow [which he allegedly burned shortly before his death: Spinoza 1985b: 8], it is very unlikely that he wrote Stelkonstige Reekening van den Regenboog (“Spinoza’s Natural Science and Methodology” in The Cambridge Companion to Spinoza, 154)

For me what is at issue is not Gabbey’s concern as to whether Spinoza wrote the particular treatise on rainbows or not; it is the general appraisal of Spinoza’s aptitude in the theoretical optics of his day. Just what did Spinoza understand? Gabbey’s point rests on the slender idea that Spinoza does not seem to be able to even conduct “a straightforward application of Descartes’ Law of refraction”.

The problem arises I think from a slight neglect in the translation, the loss of the word “if”. I do not know what translation Gabbey was using, but if he was working from the Latin I believe he made a similar mistake. This is the Latin taken from his Opera:

Nam quia circulus idem ubique est, easdem ubique proprietates habet. Si, exempli causa, circulus A B C D hanc possideat proprietatem, ut radii omnes, axi A B paralleli, a parte A venientes, ad eum modum in ejus superficie refringantur, ut postea omnes simul in puncto B coeant; omnes quoque radii, axi C D paralleli, a parte C venientes, ita in superficie refringentur, ut simul in puncto D conveniant; id quod de nulla alia figura affirmare licet, licet Hyperbolae ac Ellipses infinitas habent diametros (the conditionals emphasized)

Key is to note that Spinoza has shifted into a hypothetical subjunctive. It is not as Shirley translates: “For example, the circle ABCD has the property that…” (though Shirley’s translation does not wholly obscure my point). The line reads “If, for example, circle ABCD should have the property that…”. It is not an assertion. This small difference has lasting effects on the nature of the point that Spinoza is trying to make. He is not attempting to say that circle ABCD, and therefore all circles, has the general property that ALL rays that are parallel to ANY of its axes, would be refracted to a point opposite. This would be absurd, and as a lens-maker and user he would know this. He is saying that given that this particular circle, as it represents a lens, can be said to have this property that all rays [all rays so depicted] come from direction A and do refract to a point opposite B, then another set of rays, at the same angle of incidence to a different axis would be refracted to another point in just the same manner [C to D].

Thus, what Gabbey mistakes as a general definition of the capacities of a spherical lens, ANY spherical lens, is actually for Spinoza a description that has two levels of comprehension. The first level is manifest and actual, the second is abstract and geometrical. At the manifest level circle ABCD is understood to be a description of a hypothetical, though real lens, with specific properties and focal points (here the Law of refraction is simply assumed); at the second level, given the acceptance of the first level, there a general property of ALL spherical lenses due to their geometry. This property is: if the index of refraction allows the focusing of a set of rays at a range of angles of incidence to a particular axis (as drawn), so that they meet at one point, the same will be said of other such axes of the arc. The loss of the hypothetical “If” in translation makes it appear that Spinoza is making a much broader claim about sphericals which simply ignores the Law of refraction. He is not.

Here is the text in a translation more sensitive to the conditional (wording suggested by S. Nadler):

For because a circle is everywhere the same, it has the same properties everywhere. 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.

The construction of his thought is: “if this can be said of this particular figure, it can be said of no other figure, hyperbola and ellipse included”. We can see that part of the problem of translation lies with the very condensed way in which Spinoza is employing the subjunctive. His hypothetical has two levels of comprehension. To repeat, the figure ABCD is being treated as a real world manifestation, and so has particular properties such as the limitations granted to it by its index of refraction as being made of glass, but also it is taken to be an illustration of an abstract property of spherical shapes in general. It is both general and particular, and, as such, it is quite easy to miss both aspects, as Alan Gabbey and others seem to have done.

To really make clear Spinoza’s point, as he sees it, one just has to overlay his circle with the figure of a hyperbolic, and assume, as Spinoza does, that both sets of parallel rays (A and C) would be refracted to a single point (B and D). The hyperbolic lens simply would not have the same property:

 

There are several issues at stake here, some of them optical, some epistemological, some pragmatic, most of which must be left aside for the moment. It is my purpose to expose that Spinoza is making a point about the capacities of spherical lenses. We are to understand, under his proposed description, that these are lenses that are capable of focusing rays at a mutuality of angles of incidence by virtue of the geometrical properties of their class.

Although a surface reading of Spinoza’s diagram and description seems to present an elementary blunder, and may lead to the conclusion that he did not even understand how the Law of refraction was to be applied, a closer reading shows, at the very least, that he was intimately aware of Descartes’ law, and how Descartes attempted to solve the problem of spherical aberration. Key to understanding Spinoza’s approach was that he considered spherical aberration itself to be incidental to the limitations of lens use. Most likely he thought of lenses as devices, and the slight blurring at the edges of focus to be endemic to them. In this he followed closely his friend in correspondence, mathematician Johannes Hudde, who in his now lost treatise, Specilla circularia, argued just this conclusion. Instead of accepting Descartes’ attempt to define a mathematical point of focus, and construct a lens to achieve it, Hudde claimed that the point of focus of a lens is what he called a “mechanical point”. And it is precisely this “mechanical point” notion of focus that Spinoza has in mind when he speaks of rays meeting up at points B or D in his figure, (he uses the phrase in the following letter of clarification to Jelles, letter 40). Spinoza may have been on the wrong side of the argument, but to decide that he was unfamiliar with the argument itself in a fundamental way would be incorrect.

There is an additional piece of evidence of Spinoza’s theoretical familiarity with the application of the Law of refraction. We have the historical fact that he was in conversation and likely visitation with Christiaan Huygens in the summer of 1665, just as Huygens was working out his solution to spherical aberration using solely spherical lenses in composite. Huygens was bent on solving the aberration problem in a non-Cartesian way, as he meant to publish in his Dioptrics. In letter 30A to Oldenburg, as Spinoza responds to the Royal Society secretary’s urgings for an update on Huygens’s progress, despite Spinoza’s love of the spherical lens he expresses his doubts that Huygens would solve the problem that Descartes thought he had solved with hyperbolics:

The problem which he says he is trying to solve in Dioptics is as follows: Is it possible to arrange the lenses in telescopes in such a way that the deficiency in one will correct the deficiency in the other, and thus bring it about that all parallel rays passing through the objective lens will reach the eye as if they converge on a mathematical point? As yet this seems to me impossible. Further, throughout his Dioptrics, as I have both seen and gathered from him (unless I am mistaken), he treats only spherical figures. (quoted on October 7, 1665).

By the time that Oldenburg had read this Huygens indeed had solved much of problem of spherical aberration using two spherical lenses. (He would improve upon his solution later.) While it is likely Spinoza did not know of Huygens’s success – as he kept his discoveries close to the vest – Spinoza most certainly had discussed with Huygens, and seemingly read in the draft of the Dioptrics itself, the theoretical nature of the pursuit. He likely understood the issue that was at hand, most particularly the failure of Descartes to provide a practical solution to the problem of aberration, and how the Law of refraction itself might be used to overcome this aberration. It is noteworthy that Spinoza denies the possibility of Huygens’s aim in the context of his working solely spherical figures.

Given these factors of a theoretical correspondence with Hudde, the reading of Hudde’s treatise, and also Spinoza’s personal exchange with Huygens, the closer translation of letter 39 attests to a proficiency of optical knowledge far greater than what Alan Gabbey allows. Spinoza did seem to be more than familiar with the “importance” of Descartes figures, in particular, with the disappointments of that importance, at least as far as they were understood in his day. Central though to the issue of the “if” and the subjunctives that follow, is that the conditional itself assumes Spinoza’s own “mechanical point” (Hudde) notion of the focus of a lens. When Spinoza says, if circle ABCD has the property that certain parallel rays would meet at point B, he means at “mechanical point” B. Granting that they meet at such a mechanical point, other such rays must meet in a similar fashion at other points, as due to the nature of a circle, and this could not be said of Descartes’ other figures.

[For a Full Treatment of Spinoza’s Letters 39 and 40: Deciphering Spinoza’s Optical Letters ]