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Tag Archives: Short Treatise on God

Checking Heidegger’s Hammer: The Pleasure and Direction of the Whirr

How to Philosophize With a Hammer (or better…Spinoza’s Hatchet)

Heidegger is credited with profound originality in his treatment of “the hammer”, something even it is said his critics have to doff their hat to. With this we cannot, and should not dispute. But, it may be enough to point out that approximately 265 years before there was Heidegger’s Hammer, there was a similar point made by Spinoza, in the carpenter’s hatchet. Spinoza indeed, as a actual craftsman who thought deeply about his tools, had a sort of Tool-Being analysis which might help us reflect upon the nature of distinction that Heidegger was making (and that those that follow him continue to make). The comparison of these tools I originally found here, but is in reference to the essay “Heidegger’s Hammer, Spinoza’s Hatchet” by Eccy de Jonge, apparently defunctly found here, but which I have not been able to read. Here are the two complimentary passages:


Seventhly, this knowledge also brings us so far that we attribute all to God, love him alone because he is the most glorious and the most perfect, and thus offer ourselves up entirely to him; for these really constitute both the true service of God and our own eternal happiness and bliss. For the sole perfection and the final end of a slave and of a tool is this, that they duly fulfill the task imposed on them. For example, if a carpenter, while doing some work, finds his Hatchet of excellent service, then this Hatchet has thereby attained its end and perfection; but if he should think: this Hatchet has rendered me such good service now, therefore I shall let it rest, and exact no further service from it, then precisely this Hatchet would fail of its end, and be a Hatchet no more. Thus also is it with man, so long as he is a part of Nature he must follow the laws of Nature, and this is divine service; and so long as he does this, it is well with him. But if God should (so to say) will that man should serve him no more, that would be equivalent to depriving him of his well-being and annihilating him; because all that he is consists in this, that he serves God.

The Short Treatise On God, Man and His-Well-Being, part II, chapter XVIII “On the Uses of the Foregoing”


[The] less we stare at the hammer-Thing, and the more we seize hold of it and use it, the more primordial does our relationship to it become, and the more unveiledly is it encountered as that which it is-as equipment … If we look at Things just ‘theoretically’, we can get along without understanding readiness-to-hand. But when we deal with them by using them and manipulating them, this activity is not a blind one; it has its own kind of sight, by which our manipulation is guided and from which it acquires its specific Thing character …

The ready-to-hand is not grasped theoretically at all, nor is it itself the sort of thing that circumspection takes proximally as a circumspective theme. The peculiarity of what is proximally ready-to-hand is that, in order to be ready-to-hand, it must, as it were, withdraw in order to be ready-to-hand quite authentically. That with which our everyday dealings proximally dwell is not the tools themselves. On the contrary, that with which we concern ourselves primarily is the work – that which is to be produced at the time; and this is accordingly ready-to-hand too. The work bears with it that referential totality within which the equipment is encountered.

 Being and Time, section 15, “The Being of Entities Encountered in the Environment,” under the Analysis of Environmentality and Worldhood in General 

First, I want to really thank the initial two authors for bringing the two selections into contact for me. It never had occurred to me that there would be so close an analogical connection between Spinoza and Heidegger, in text, though long I had sensed that Spinoza works to resolve something of the strained and willfully produced tension in Heidegger’s human-torqued universe of fundamental alienation. (Briefly I could say that metaphysics of alienation are naturalizations of political products, and as such work to make invisible the results of choices we have collectively made.) Spinoza’s insistence that human beings are not “a kingdom within a kingdom” seems a well suited antidote to Heidegger’s “thrownness” [Geworfenheit], in concrete terms.

How the Hammer and the Hatchet Touch

But let us look at the two passages and see if we can rough-cut the correspondences and divergences in such a way to see were the Heideggerian and Spinozian realms touch. Happily, each uses the example of a tool, Heidegger famously so, to illustrate a fundamental metaphysical realty. For Heidegger it is to point out just what readiness-to-hand is, and kind of invisible power of the efficacy of the tool (as Graham Harman will tell us, of any object), whose power defies conception, theorization, or presentation. When we cease to engage a tool, pausing to look at it and frame it (the move from ready-to-hand to present-at-hand), breaking it out of its assemblage of powerful action, the tool becomes strange for us. It recedes from our occupation of it. Its presencing veils it from us, like an apparitional cloak. Yet if we look to strip away this veil by taking up the tool again, and using it, as the veil fades, along with the increasing efficacy of tool in use, so does the object itself. What we are looking to grasp, in literal grasping, vanishes.

A similar thing seems to happen to Spinoza’s carpentry hatchet. While it is being used by the carpenter it is filled with hatchetness, performing all the hatchet-effects of what it is, but once it is retired from work, it no longer is a hatchet at all. Its very essence seems to retreat from the carpenter into a distinct but unspecified objecthood. How much are Heidegger and Spinoza pointing out similar things?

Let us dig into Spinoza’s illustration though so to see how deeply it cuts into Heidegger’s hammer example. The first thing to note is that Spinoza is using an analogy meant to describe both human, teleological action, and the ultimate ground of those actions, the ateleological actions of Substance. In that he is describing human action in which things are characteristically marked by their place in function, he seems to be touching on something quite close to Heidegger’s point. The object of the hatchet, even when being fully used by the carpenter, or when laid down and retired, is in surpass (or retreat) of either condition. The ultimate ground of the object is deeper than each, teleological action, or contemplative repose. It oscillates between hatchet-in-action and not-hatchet-in-inaction.

But there is a further dimension to Spinoza’s point, for by analogy the “carpenter” is not a functionally minded man, but God, Substance, Nature. And the use that the “hatchet” is put to is not to build a wall, house or chair, but simply to exist and express Substance. In this way the object is fully deployed when existing. It cannot be named because its function runs in every direction along the full web of interactions which it supports, and is supported by. So in existence, the object stands bright. radiating out all its possibility (though the human carpenter locked in his teleological perspective does not fully see it). And when the carpenter “God” lays the hatchet down, to retire it, it simply passes out of existence, though still having Being under an aspect of eternity. It is no longer deployed, no longer what it was, but its objecthood, as an essence, remains, de-nominated.

The Carpenter’s Hand

Yet, there is a bit of a trick here. Is it so for Spinoza that Heidegger’s general claim of two kinds of invisibility of objects, those invisibly in use, and those present in rest, are present in Spinoza’s example of the human carpenter? We can see that as the human carpenter looks to his hatchet he only grasps some aspect of it in the as-structure of its use, something that is a veil of its ultimate and active object-capacities. But is the hatchet also invisible when being used, and the carpenter concentrates on his work? I think that the whole of Spinozist philosophy works against just that kind of imagined and absolute invisibility.

First take in Graham Harman’s summation of the Principle of Invisibility  implied by Heidegger’s tool-analysis. Graham’s interpretation is important because it pushes to the limit the fully abstract character of Heidegger’s claims, and as such makes clear just where Heideggerian abstractions depart from the relevant world, forcing open a gap between a science fiction philosophy of objects, and an abstract philosophy of what matters.

Heidegger has shown that its [tool-being’s] first notable trait is its invisibility. As a rule, the more efficiently the tool the tool performs its function, the more it tends to recede from view: “The peculiarity of what is proximally ready-to-hand is that, in its readiness-to-hand, it must, as it were, withdraw [zurückziehen] in order to be ready-at-hand quite authentically.” But this familiar point is rarely grasped in a sufficiently rigorous way. It is not just that equipment is generally invisible as long as it is working properly. Such a notion could never surpass the level of empirical anecdote, and only invites free-wheeling attempts at contradiction (“but then we noticed that it worked a lot better if you stared right at the damn thing”). The truth is far more radical than this. In the first instance, there is an internal chasm between equipment and tool-being. The wrench as reality and the visible or tactile wrench are incommensurable kingdoms, solitary planes without hope of intersection. The function or action of a tool, its tool-being, is absolutely  invisible – even if the hammer never leaves my sight. Neither gazing at an object nor theorizing about an object is enough to lure its being from concealment (21) 

Tool-being: Heidegger and the Metaphysics of Objects, Graham Harman

I want to take up Graham Harman’s call for “sufficiently rigorous” grasping of the Heideggerian notion of withdrawl. I think it is important though, as fast as Graham wants to fly into things other than outright tools (bank accounts, mindless jingles, hairballs), to stay with tools. For its is from human experiences with tools that Heidegger derives much of the convincing power of his great abstraction. If we are to be rigorous about the claim, we must concentrate on the exact nature of the site of the illustration, and see if the general point being made  can  even find enough ground there. Once approved there, we then can track out all the translations into The Great Wide Open of any object whatsoever.

Carefully we note that for Heidegger the two occluded states of invisible action (equipment) and veiled repose are the famously the two states of working and broken tool:

Equipment in action operates in an inconspicuous usefulness, doing its work without our noticing it. When the tool fails, its unobtrusive quality is ruined. There occurs a jarring of reference, so that the tool becomes visible as what it is: “The contexture of reference and thus the referential totality undergoes a distinctive disturbance which forces us to pause.” There is thus a double life of equipment – tool in action, tool in disrepair. These two planes would seem never to intersect, since the visibility of the tool immediately marks it’s cessation as equipment. But in fact, their point of intersection provides what amounts to the central theme for Heidegger’s career: namely, the as-structure. Through the “as,” the two worlds actually turn out to exist only in communion, in constant intersection with one another… (Harman 45)

Now we all know exactly what Heidegger is talking about. We are working away, concentrating on the nails, the wood-finish, thinking about lunch, hammering away, and the hammer is very close to being “invisible” (if we are a good enough carpenter). But then if the handle fractures, it sends up a vibration to the hand that suddenly shocks it into visibility, but as a hammer, as we look at it that is somehow lost. Beautiful, excellent poetic description of some aspects of what it is like to use a hammer, it kind of passes between these two states. I wish to bring up an objection though which hopefully will not fall too much into the category of “free-wheeling” “empirical anecdote” for a reader such Graham, for I already find Heidegger’s analogical binary a bit too free-wheeling on its own right. The objection to invisibility is not as Graham states it, “but then we noticed that it worked a lot better if you stared right at the damn thing” but it is much more radical than that.

The Texture of Communication

And that is, for a great variety of tools (and I will come to suspect, perhaps all tools and therefore objects), Heidegger and his radix purifier, has left out an entire dimension of visibility, the way that visibility and workability actually coincide together. In their pursuit of irreconcilable binaries something important has been lost, and their entire reductive, categorical claim depends upon the exhaustabilty of its split. Heidegger wants withdrawal to be the very mark of the authenticity of readiness-to-hand, but if anyone has used a tool that excels in its capacities, one understands that there is a way that the tool leaps into visibility that has nothing to do with repose or reflection or theorization. A musician who picks up a Stradivarius and pulls the bow, whether for the first time, or 1,00oth, has something of the instrument’s depth that reverberates with its very surplus of the mere functionality of the thing, a surplus that feeds back into its very function and performance. A baseball player who lifts and swings the right maple-wood bat, testing out is character of distribution, a character which fills his hands, has a presencing of the object which is conditioned upon its very performance. Swinging the bat in its arc, the bat only “disappears” in the most restrictively defined notion of sense. Instead the bat continually reports and manifests because of its mutuality with the human body. A racecar driver that is prostheticallyextended to the road through an expert suspension system, does not actually feel the suspension system become invisible in its performance, but rather the suspension is cybernetically feedback into the horizon of the body as a constitutive factor in the performance itself, making itself known as a series of limits and expressions. This is known as the “feel” of an instrument, not as the last visible vestige of  a tool’s inefficiency, but the very live, material connectivity to the world. As much as Heidegger (and perhaps even more Graham Harman) may want to divide an object into “working” invisibility and “broken” (in)visibility, there is a profound aspect of “working” which is made up of the very substance of revealed and composite com-munication, which means literally “to divide up within one, to share”. As such there is a variability of consubstantial change (the violin becomes the musician, the musician the violin) which oscillates between the parts, such that we can say that the parts are “seen” by each other. We certainly admit that the violin can indeed disappear before the music, the car before the road, but in no way is there a categorical link between efficacy of performance and invisibility. In the very fact that objects regularly become visible through their performability, the charge of their expressivity. This visibility of expression might indeed get us to pause, and to do as Graham says, look at the object, and notice its performance in it own right, but this is distinct from the expressive inter-relationship itself, the way that the very effective performance of a tool, and instrument, a prosthetic, depends upon the inter-relatability of the combination of our parts with its parts. We do not only notice our body when it breaks down. In fact, and dancer knows, inhabits with great visibility its own body, increment by increment, capacity by capacity, in such a way that the dance itself becomes visible, as an excellence.

So why did Heidegger (and Graham) miss this (or subdivide it into non-importance), and what does this have to do with what Spinoza says? Well, the problem is that each of the former are looking for binaries that will be locked against each other and that is because they come from an intellectual heritage of Idealism which wants to profoundly assert subject/object, Being/Non-Being, object/object dichotomies (CCC). When each looks at a tool they want to see how it can break into two, and only two pieces. In fact though, once Graham has isolated out this neat binary of the hammer, its supposed broken and unbroken parts, he wants to get as far away as possible from actual tools, real world human actions altogether:

I will argue that Heidegger’s tool-analysis has nothing to do with any kind of “pragmaticism,” or indeed with any theory of human action at all. Instead the philosophy of Heidegger forces us to develop a ruthless inquiry into the structure of objects themselves, and to a greater extent than even he himself would have endorsed (15).

He says this I think because he feels that Heidegger gives us conceptual capacity to be ruthless and transgress the human realm and give full rights to objects as things themselves, to make them each a miniature neutron star bombarding us with unknown energies. But the problem is that he runs a bit too fast from the human realm, and has not inspected the full vibrancy of tool use itself, the way in which tools necessarily employ visibility through performance.

The De-Centered Human in the Use of Mechanism

Counter to this I place Spinoza who like Graham also had a philosophical bent to de-centralize humans (nothing that Heidegger shares). Additionally, instead of using hammers as abstract, and quite theoretical objects like Heidegger, Spinoza was a craftsman of great care and precision. Much of his days was spent thinking about, choosing and using tools. A process which relied upon the manual improvements that come from a craftsman’s hand. One might say that as adept as Heidegger was at metaphysical reasoning, Spinoza was at instrument making (leaving his own metaphysics aside). His practice as lens-grinder was necessarily laborious and technique rich, relying upon not only precise measurement and material choice, but also harmonious and embodied physical labor. And with his hand-ground lenses he made some of the more respected microscopes and telescopes of his day:

A Spring-pole lens grinding lathe, mid 17th century

I believe much of his metaphysics was causally derived from his experiences with tools and their projects [An example]. If anyone would have concluded through a real life engagementwithtools that tools become categorically invisible when they perform well, it would have been Spinoza. It was precisely the opposite. Spinoza’s interaction with the glass blank and his lathe produced in him a shattering of the very human/world divide that enrapture’s Heideggerian disjointed universe of veilings. Likely, it was the distinct way that tools become visible in the very fabric of their performance (and not as an after thought, though that too), that Spinoza realized that human beings must be tools like all other things, and that only by the lived combination of powers, in manifesting displays of created self-determinations, that human beings experience a (relative) freedom. For this reason, human beings (and all things) become more perfect, more active, and most importantly in Heideggerian terms, have more being, to the degree that they combine with the manifestation of others. And tool use, tool-combination, is an irreplaceable aspect of this freedom. Performance is visibility.

So when Graham attempts to minimize the actual states of human consciousness under ultimate questions of visibility and performance, setting up two worlds…:

Someone might object that the tool is always invisible “only in a certain respect” rather than absolutely. And sure enough, a table obviously does not vanish into the ether once it begins to function as a support for plates and apples. But this complaint once again presupposes the idea of the table as a natural object, proportions of its reality momentarily visible and others unseen. On the contrary, it is not the chance fluctuations of human attention that determine whether the ready-to-hand is invisible or not. To say that the tool is unseen “for the most part” is ultimately superfluous, even incorrect. Whatever is visible of the table is in any given instant can never be its tool-being, never  its ready-to-hand. However deeply we meditate on the table’s act of supporting solid weights, however tenaciously we monitor its presence, any insight that is yielded will always be something quite distinct from this act itself.

(The Weight of Fleeting Thoughts)

…I feel in his quest to over shoot the concrete example and ascend to universalizing abstractions, he he misses the determining aspect of human action. It is not its the “humanness” of human action, or even its subjective character that makes it what it is. Rather it is exactly the incremental “fluctuations of human attention” that indeed do make up the degrees of power of ontological change. Spinoza I think would indeed agree that when using a tool or object or condition we as teleologically oriented beings do not fully grasp it, that there is a degree of invisibility (and also that when we nominalize it in a system of use and reference, particularly those of functional definition, we also have inadequate ideas, and it surpasses us). But what he would refuse is that our combination with other objects necessarily and categorically forecloses their visibility. Instead, it is our very participation with them that their internal natures are communicated to us, revealedly, in our bodies, because our bodies have become mutual. The reason for this is twofold. One is that, because Heidegger’s Idealist derived object-consciousness of definition of mental action has to be abandoned if we are ever to let go of a human-centric philosophy of the world, ultimately whether an object is not before our “mind’s eye” or not, whether we are locked in on the Stradivarius or not, is not a true measure of visibility. Mental action is not a picture-making, or picture-defined process. Mental action is revelation through both internal experience (across bounds) and expressional freedom to self-determine. The second reason for this is found in Spinoza’s treatment of just those “chance fluctuations” that Graham is so quick to dismiss as anything important.  Heidegger is talking about big things, not whether one’s mind lights upon the length of a table or the timbre of a cord played.

But Spinoza has it right, as he expresses in the General Definition of the Affects:

But it should be noted that, when I say a greater or lesser force of existing than before, I do not understand that the Mind compares its Body’s present constitution with a past constitution, but that the idea which constitutes the form of the affect affirms of the body something which really involves more or less reality than before (E3, General Definition of the Affects)

It is precisely in the moment to moment fluctuations of the mental life that the moment to moment ontological fluctuations of the power of the human body and mind are found. Each and every moment, each trace of thought to another thought, is veridically linked to increases and diminishments of the person’s capacity to act in the world. The Principles of Invisibility and Veiledness which Spinoza has some affinity toward, are cross slashed with vectors of raw power ruled by the experience of Joy. It is for this reason that Spinoza speaks of the excellent service of his hatchet. We human beings are already, as tool-beings of Substance, fully expressing ourselves unto our contingent causal matrix. We are at full service to Being. But through the following of Joy and the reading of the expressive power of other tool-beings, in increasingly self-determined assemblage, we can acquire more being, more freedom, more Joy. It is the very visibility that is experienced with tool performance, the way that a violin sings, and must sing, in order to be a playable violin, in order for our fingers to combine with it, that points us between Heidegger’s twin realms, making ourselves more visible.

In a certain sense Spinoza realizes that we are both external to events as human beings, and internal to them. Which is to say that because human beings do not comprise a kingdom within the kingdom of Being, but rather ultimately are expressions of it, though our passings between Heideggerian veiled and invisible realms seems to lock ourselves in, the greatest portion of our capacity to ingest our abstactions seems to be that like a water-mammal: when we go under the surface in performance with objects and they seem to recede into optical invisibility, because we too are made of the same stuff (the same primary connections between body and mind) and thus are in communication with it, when things appear to vanish into equipment, this is livingly so as an expressive state such that our growingly extensive bodies become inhabited across their dimension with perception and internal revelation. Subcutaneously there is conscious revelation in the experience of powers and Joys such that never is that world in-cognizant. We become what we know in action because we are already conjoined to it, however confusedly.

For those who want a world that is fractured, alienating, eruptive, weird, schizophrenic, I believe that there is plenty of room for that on the lived Spinozist plane of affective, bodily cybernetic reveal. There are disruptive paths that leap between local minima, that makes of one object the surprising neutron star of rays and beams. What is important though is not to naturalize our alienations as metaphysical boundaries in their own right, and so to see that the bridgings between this ontological moment so constituted by your relations, and the ones they follow, can rightfully have a path as vectored and free as our capacity to grasp and combine as we can make it. There can be no real hiding when we are part of the hidden, by degrees.

The “Corporeal Equation” of 1:3: What Makes A Body for Spinoza?

If a Body Catch a Body Comin’ Through the Rye

I have always been fascinated by Spinoza’s defintion of a body as found in the Second Part of the Ethics. Not because it reflected some proto-physics, but because it allowed a radical revisioning of what defined boundaries between persons, and between persons and things. What seems implicit in such a definition is that something of a cybernetic recusivity surrounds and defines any isolated “part” of the Universe, yet, a recursivity that only comes clear by taking a perspective. One understands that really for Spinoza the entire Universe composes a single such body.

Here is Spinoza’s famous Ethics  defintion, and an even more elementary and bold one from his much earlier Short Treatise on God, Man and His Well-Being (KV)

Ethics: When a number of bodies of the same or different magnitude form close contact with one another through the pressure of other bodies upon them, or if they are moving at the same or different rates of speed so as to preserve an unvarying relation of movement among themselves, these bodies are said to be united with one another and all together to form one body or individual thing, which is distinguished from other things through this union of bodies (E2p13a2d)

KV: Every particular corporeal thing [lichaamelijk ding] is nothing other than a certain ratio [zeekere proportie] of motion and rest.

Yet, such a vision for Spinoza is more than an instructive imaginary relation, it indeed is a proto-physics, a concrete real which must be accepted as such. There is a certain sense in which Spinoza’s conception of a body must be reconciled with the “facts” of contempory physics if we are to geta stronger impression of the truth of his metaphysics and psychology. As Spinoza wrote to Blyenbergh, “Ethics, … as everyone knows, ought to be based on metaphysics and physics” (Ep 38). At a general level, in Spinoza’s own terms, if his physics is radically wrong this may pose serious doubts as to his Ethics (an entirely rationalist reading of his philosophy notwithstanding). And concordantly, one might assume, new information in physics could have a rippling effect across his philosophy and Ethics.

It is not my aim here to explore these wider meta-questions, but rather to for a moment pause upon a change in my own thinking. I had always taken Spinoza’s above defintions just as I explained, fantastic frameworks for revisioning the world as it common-sensically and historically has come down to us, intellectual opportunities for instance to see the connections between bodies in a Batesonian or an Autopoietic sense. This still remains. But I came to realize that when Spinoza is thinking about a “certain ratio” (as Shirley translates) or a “fixed manner” (Curley), he is thinking of something quite quantifiable, something numeric. I had of course loosely thought that this was the case, but until recently I had never strictly thought about it.

Spinoza’s Objection

There is an interesting, rather provocative point in Spinoza’s letters to Oldenburg, as he is reporting back to this Secretary of the Royal Society on the progress of his brilliant neighbor Christiaan Huygens. It seems apparent from what Spinoza reports that he has had intermittent, but somewhat substantive discussions on not only optics and lens-grinding, but also on physics. Huygens, by what history tells, had corrected Descartes’ rules of motion, and done so through experiment. Huygens was quite interested in the rules of motion for he had invented the pendulum clock way back in 1656 (the same year he had discovered the rings and a moon of Saturn), and for a decade was focused on improving it. Spinoza reports back to Oldenburg Huygens’ disagreement with Descartes, but tantalizingly also speaks of his own disagreement, in particular, with the sixth rule of motion:

Spinoza: “It is quite a long time since he [Huygens] began to boast that his calculations had shown that the rules of motion and the laws of nature are very different from those given by Descartes, and that those of Descartes are almost all wrong…I know that about a year ago he told me that all his discoveries made by calculation regarding motion he had since found verified by experiment in England. This I can hardly believe, and I think that regarding the sixth rule of Motion in Descartes, both he and Descartes are quite in error.” (Letter 30A)

Oldenburg: “When you speak of Huygens’ Treatise on Motion, you imply that Descartes’ Rules of motion are nearly all wrong. I do not have to hand the little book which you published some time ago on ‘Descartes’ Principia demonstrated in geometrical fashion’. I cannot remember whether you there point out that error, or whether you followed Descartes closely to gratify others.” (Letter 31)

Spinoza: “As to what you say about my hinting that the Cartesian Rules of motion are nearly all wrong, if I remember correctly I said that Mr. Huygens thinks so, and I did not assert that any of the Rules were wrong accept the sixth, regarding which I said I thought that Mr. Huygens too was in error.” (Letter 32)

Many commentators have not been able to make much headway when interpreting Spinoza’s objection to Descartes sixth rule of motion, for at the very least, it seems woven to his other rules, and the objection should have spread far wider than this, as in the case with Huygens. Alan Gabbey (The Cambridge Companion ) for instance simply finds it nonsensical. And Lachterman in “The Physics of Spinoza’s Ethics”, really almost avoids the issue altogether. (Wim Klever has taken the question directly on in “Spinoza and Huyges: A Diversified Relationship Between Two Physicists”, tying it to a Cartesian difficulty in explaining cohension, while Rivaud finds what seems to be an untenable conceptual connection between speed and essence in his “La physique de Spinoza”.)

I certainly am not one here to solve the question, but it did get me thinking about how Spinoza conceived of a body, and what a “certain ratio” meant to him.

Descartes’ Sixth Rule of Motion and Spinoza’s Defintion of a Body in the Short Treatise

Below is the sixth rule of motion to which Spinoza found objection. It essentially describes what would ideally happen if two bodies of the same size, one in motion and one at rest, struck. Descartes suggests that if the moving body had four (4) degrees of speed before impact, after impact the ratio would be 1:3, with the body at rest taking on one (1) degree of speed, the bodies rebounding:

Descartes:51. Sixth rule.
Sixthly, if body C at rest were most accurately equal to body B moved toward it, it would be partly impelled by B and would partly repel it in the contrary direction. That is, if B were to approach C with four degrees of speed, it would communicate to C one degree and with the three remaining would be reflected in the opposite direction.

Huygens reportedly showed through experiments at the Royal Society that instead all the degrees of speed would be imparted to the body at rest, and the intially moving body would then be stopped, and it was to this, as well as to Descartes’ rule that Spinoza expressed an unspecified objection. But this is not the ultimate point here for me. I was rather struck by an early note on Spinoza’s defintion of a body found in the Short Treatise , which proposes the same ratio of 1:3 that Descartes used to illustrate his sixth rule, here below stated as the ratio of motion to rest, and not as “degrees of speed”:

Spinoza: Short Treatise, notes to the Preface to Part II:

12. As soon, then, as a body has and retains this proportion [a proportion of rest and motion which our body has], say e.g., of 1 to 3, then that soul and that body will be like ours now are, being indeed constantly subject to change, but none so great that it will exceed the limits of 1 to 3; though as much as it changes, so much does the soul always change….

…14. But when other bodies act so violently upon ours that the proportion of motion [to rest] cannot remain 1 to 3, that means death, and the annihilation of the Soul, since this is only an Idea, Knowledge, etc., of this body having this proportion of motion and rest.

What is striking to me is that such an elementary numerical value for the definition of a body would occur to Spinoza in this context. Alan Gabbey wants us to point out that this ratio of 1:3 is found in editorial notes, and my not even be of Spinoza’s hand, though I am unsure if Spinoza would have allowed such a strong example to slip through if it was alien to his thinking. Provocative is that the context for this proposed illustration of a “corporeal equation” (as Matheron has named it), of 1 to 3, is that it is the human body that is being discussed and not abstract solids such as those Descartes discusses in his physics. Even if Spinoza does not imagine that the human body might actually retain such an elementary 1:3 ratio of motion to rest, somewhere in his conception of the human body there is an affinity to such an simple math. One for instance would not be describing a super computer whose mark would be its complexity, and turn to such a number. It would appear that at least figuratively Spinoza at the time of the Short Treatise  thought of the human body as elementarily composed such that its conatus expressed a homeostasis that was comprehesible and simple. The numerical value of 1 to 3 held perhaps a rhetorical attraction.

By the time of Spinoza’s geometrical treatment of Descartes’ philosophy, the proposed illustrative values that Descartes included in his rules for motion are no longer there. Spinoza generalizes them apart from any particular equation. One could see in this perhaps already a distancing from some of Descartes’ assertions, and Oldenburg tells Spinoza that he looked over Spinoza’s exposition of Descartes to see signs of his disagreement, finding none.

What the sixth rule Meant for Spinoza

For my part, if we take Descartes’ sixth rule at face value, and imagine the interaction between two bodies of the same size, one at rest, one in motion, we get a glimpse into the kind of change Spinoza thinks makes a body. For once the supposed transfer of a degree of speed occurs, the two bodies are now in communication. As long as they are not interacted with by other bodies their ratio will remain 1:3, and they would be considered an “individual”. And if one of those bodies interacted with another body so as to change its speed, immediately one realizes that if the idea of a single body is to be preserved the definition of parts needs to be expanded so that the ratio is to be expanded across a host of interactions. One sees how the definition of a body as a body is entirely contingent upon how you calculate.

Wim Klever finds in Spinoza’s 1665 objection to Descartes’ sixth rule (made almost 4 years after the writing of the Short Treatise ) a testament to Spinoza’s thorough-going commitment to a physics of immanence. This could be. But one could also imagine the case that Spinoza had been caught up in a conversation with Huygens at the Hofwijck estate and was entirely caught off guard by Huygens’ sweeping dismissal of Cartesian physics, which up to that point had been a touchstone for most scientific thinking in Europe. Spinoza’s objection to the sixth rule may have only been a reaction, one that prudently and instinctively placed himself between Descartes and Huygens, on a single point, a point he could not elaborate on.

But what was it about Huygens’ correction to Descartes which may have also given Spinoza pause, especially if Descartes’ rule for the transfer of motion between two equal bodies, one moving, one at rest helped frame Spinoza’s general notion of what makes a body? Would it not be that there was a complete tranfer of motion from one to the other, that one stopped and the other started? Because Spinoza envisioned bodies moving together in community, and integrated communication of impinging interactions that could be analyzed either in terms of their recursive cohensions (for instance how the human body can be studied solely in terms of its own internal events, as one might say, immanent to their essence), or in terms of extrinsic interactions which “through the pressure of other bodies” cause these internal events, the intuitional notion that a body in motion would deliver all of its motion to another body at rest, and not be rebounded simply defied the over all picture of what Spinoza imagined was happening.

I suggest that somewhere in the genealogy of Spinoza’s thought about what defines a body he found Descartes sixth rule quite suggestive. The idea that two bodies which do not seem to be in communication, one moving, one unmoving, (an essential perceptual differential which allows us to distinguish one thing from another in the world), suddenly can appear in communication from the change they bring about in each other in collision, now departing at a ratio of speeds, helped Spinoza psychologically and causally define the concrete yet contingent composition of an individual. The corporeal equation of 1 to 3 standing in for the possibility of mathematical determination which could conceptually unite any two parts in a single body, given the right analysis.

But when Spinoza encountered Huygens’ thorough dispatch of Cartesian mechanics we can suspect that Spinoza came in contact with his own theoretical disatisfactions with Descartes. As we know, Spinoza was part of a small cadre of mathematicians and thinkers which found dissatisfaction with Descartes idealized optics, something that no doubt formed part of his discussions with fellow-lense grinding and instrument maker Christiaan Huygens. And too, Spinoza likely felt that though Descartes’ mechanics provided an excellent causal framework for rational explanations of the world, his determinations lacked experimental ground. It would seem to me that Spinoza’s objection to the sixth rule of motion poses something of a revelation into the indeterminancy of Spinoza’s physics. The sixth rule may have played a constructive role in his imagination of what a body must be, but in particular in view of Huygens’ confirmed rejection of the rule, it became simply insufficient. Spinoza’s physical conception of a body stands poised between a Cartesian rational framework of causal interaction and mechanism, which proves lacking in specifics, and the coming Newtonian mechanics of force. However, in such a fissure, one does have to place Spinoza’s notion of immanence.

Autopoiesis Comes?

Signficantly, and something which should not be missed, is that the definition from axiom 2 of proposition 13 of Part 2 above is not the only conclusive one that Spinoza provides in the Ethics. Lemma 4 under axiom 3 actually provides a view of the body which does not require that the parts themselves remain in a fixed ratio to each other. Rather, it is only the ratio itself that must be preserved:

If from a body, or an individual thing composed of a number of bodies, certain bodies are separated, and at the same time a like number of other bodies of the same nature take their place, the individual thing will retain its nature as before, without any change in its form [forma].

This allows us to see that by the time of his writing of the Ethics, Spinoza’s notion of ratio, the aim of his mechanics, is far from what Newton would develop. The causal histories traceable through interactions between bodies certainly were signficantly important for Spinoza, but it was the preservation of a mode of interaction which really concerned Spinoza’s focus. That all the bodies that compose and individual could conceivably be replaced, without that individual being considered as changed (as for instance we know of nearly every cell of the human body), is something that Newtonian physics would not enumerate. It is within this conception of preservation that I think Spinoza’s mechanical conceptions have to be framed, in the entirety of an effect between bodies, the cohesiveness of the modal expression.

One need only turn to something like Autopoietic theory (both those of life by Maturana and Varela, and suggestively of social forms by Luhmann) to see a lineage given from Spinoza’s Lemma 4 description:

The defintion of a living thing understood to be a self-producing machine:  “An autopoietic machine is a machine organized (defined as a unity) as a network of processes of production (transformation and destruction) of components which: (i) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and (ii) constitute it (the machine) as a concrete unity in space in which they (the components) exist by specifying the topological domain of its realization as such a network.” (Maturana, Varela, 1980, p. 78)

On the difference between “organization” and “structure”:  “…[I]n a toilet the organization of the system of water-level regulation consists in the relations between an apparatus capable of detecting the water level and another apparatus capable of stopping the inflow of water. The toilet unit embodies a mixed system of plastic and metal comprising a float and a bypass valve. This specific structure, however, could be modified by replacing the plastic with wood, without changing the fact that there would still be a toilet organization.”
(Maturana & Varela, 1987, p. 47)

Where Lies Spinoza’s Physics?

Spinoza’s immanent connection between physics and metaphysics in a turn toward a decisive ethics, is one in which any outright mechanics must be understood beyond simply A causes B, and the appropriately precise mathematical calculation of what results. If Spinoza’s physics (and even its relationship to Descartes who preceded him, and Newton who followed him) is to be understood, it is this recursive relationship between parts that has to be grasped, the way in which parts in communication can be analyzed in two ways, along a differential of events internal to a horizon, and events external to that horizon, interior and exterior, even with a view to the conceived totality. It seems that it is this replaceable nature of body-parts in composite that qualifies Spinoza’s physics as interpretively distinct, and what allows it to place within the domain of cause not only questions of material interaction, but also psychology and belief, and ultimately social values of good and bad. 

What it seems that Spinoza was most concerned with in his assessment of a physics is the kinds of concrete reactions which ground our selective ability to usefully distinguish one thing from another, a usefulness that ever trades on the community of rational explanations with share with others. The result of this physics is an ultimate ground upon which we can and do build our own mutual body of social wholes, our own physics of decisions and distinctions. Physics both ground and distinguish us for Spinoza, always suggesting an anatomy of joined, contiguous parts; it is an anatomy that guides the effortless butcher’s knife that ideally, knowingly, seldom would need sharpening.