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The Conatus of the Body in Spinoza’s Physics

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In Part 3 of his Ethics, Baruch Spinoza identifies the conatus of the mind as ‘will’ and of the mind and body together as ‘appetite’/‘desire,’ but he does not identify the conatus of the body. This omission is curious, given that he describes
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  95  THE CONATUS OF THE BODY IN SPINOZA’S PHYSICS   Sean WINKLER  *   Abstract. In Part 3 of his  Ethics  , Baruch Spinoza identifies the conatus    of the mind as „will‟ and of the mind and body together as „appetite‟/„desire,‟ but he does not identify the conatus   of the body. This omission is curious, given that he describes „motion -and- rest‟ and conatus   in such ways that they appear to be one and the same thing. In this paper, however, I propose that motion-and-rest and conatus   (in the attribute of extension) can be understood as two distinct aspects, relational and singular, of Spinoza‟s theory of the individuation of bodies. In Section 1, I explain Spinoza‟s account of the body.  In Section 2, I reject the notion that the conatus   of the body is a principle of rectilinear inertia. In Section 3, I indicate that besides conatus  , Spinoza uses other terms throughout his texts to denote the concept of striving, each of  which alludes to a relational and singular aspect of his theory of individuation. In Section 4, I show that for Spinoza, motion-and-rest refers to the relational („preindividual‟) aspect of the body and that conatus   (in the attribute of extension) refers to the singular (individuated) aspect of the body.  Keywords:  Spinoza, physics, individuation, body, conatus  , inertia, motion, rest. Introduction In Part 3 of his  Ethics  , Baruch Spinoza identifies the conatus   [striving] of the mind as „will‟ and of the mind and body together as „appetite‟/„desire,‟ but he does not identify the conatus   of the body. 1  This omission is curious, because Spinoza identifies the body as “an unvarying relation of movement,” 2  and there is a clear similarity between his phrasing of his law of motion in Part 2, where he states that “a body in motion will continue to move until it is determined to rest by another body, and a body at rest continues to be at rest until it is determined to move by another body,” 3  and his phrasing of his doctrine of conatus   in Part 3, where he states that if conatus    “is not destroyed by an external cause, it will always continue to exist by that same power by which it now exists.” 4  These details could lead one to assume that in the attribute of extension, so- called „motion -and- rest‟ and conatus   are two terms for one and the same thing. However, Spinoza does not explicitly connect these two concepts in the  Ethics  . One might argue that Spinoza simply deferred to the work of contemporary physicists, and took it to be obvious that the conatus   of the body is motion-and-rest (or the tendency of motion-and-rest to persist). However, he meticulously cross-references his arguments in the  Ethics   and the connection between motion-and-rest *  Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium. E-mail: sean.winkler@student.kuleuven.be    Sean Winkler  –    The Conatus of the Body in Spinoza’s Physics   96 and conatus   would be a rather blatant connection for him to overlook. And while Spinoza was not a physicist, it would be a mistake to underestimate his knowledge of physics. 5  One of the two works that Spinoza published during his lifetime, his Principles of Cartesian Philosophy  , contains a detailed account of Cartesian physics. In addition to developing the scientific aptitudes required for lens-grinding, Spinoza carried out a number of scientific experiments of his own, for instance, on the compound nitre (potassium nitrate), 6  in optics 7  and in hydrostatics. 8  Furthermore, he maintains in an early letter to Willem van Blyenbergh that the  Ethics    “must be based on metaphysics and physics.” 9  So, if Spinoza avoided addressing the relationship between motion-and-rest and conatus   in the attribute of extension in the  Ethics  , it may be worth asking  whether he had a good reason for doing so. Moreover , Spinoza‟s physics remained an unfinished enterprise at the time of his death. 10  In a letter to Ehrenfried Walther von Tschirnhaus from January 1675, Spinoza appears to have expressed the intent to write a treatise on the subject. To  Tschirnhaus‟s question, “When shall we have your . . . general treatise on physics?” 11   Spinoza responds that “concerning motion . . . , since my views on these are not yet  written out in due order, I reserve them for another occasion.” 12  Unfortunately, Spinoza never had the opportunity to compose such a treatise and he died just two years later. Thus, instead of a Tractatus Physica  , we only have, what David Lachterman calls, the Physical Digression from Part 2 of the  Ethics   along with a select number of correspondences dedicated to the subject. Thus, one could argue that Spinoza may have had a new way of defining the relationship between motion-and-rest and conatus   in the attribute of extension (and thereby, the conatus   of the body), but was unable to develop his position due to his untimely death.  This problem has been discussed extensively in the secondary literature, 13  but in this paper, I propose that motion-and-rest and conatus   can be understood as two distinct aspects, relational and singular, of Spinoza‟s theory of the ind ividuation---i.e., the individual identity and persistence---of bodies. In Spinoza‟s system, finite individuals are not individuated in isolation from one another. Rather, they are „co - individuated,‟ so to speak, meaning that a given finite individual and its environment (other individuals) are differentiated from one another simultaneously. Based on this model, I maintain that the individuation of the body requires a relational (or, to borrow Gilbert Simondon‟s term, „preindividual‟) aspect, motion -and-rest, and a singular (individuated), aspect, conatus   (again, in the attribute of extension). In Section 1, I explain Spinoza‟s account of the body.  In Section 2, I reject the notion that the conatus   of the body is a principle of rectilinear inertia, as in the work of René Descartes. In Section 3, I indicate that besides conatus  , Spinoza uses other terms throughout his texts to denote the concept of striving, each of which alludes to a relational and singular aspect of his theory of individuation. In Section 4, I show that for Spinoza, motion-and-rest refers to the relational (preindividual) aspect of the body and that conatus   refers to the singular (individuated) aspect of the body. In order to develop my argument, I draw from Spinoza‟s Physical Digression in P art 2 of the  Ethics  , as well as relevant passages in Spinoza‟s other texts and letters.     Society and Politics Vol. 10, No. 2(20)/November 2016   97   1. The Body as an Unvarying Relation of Motion In Part 3 of the  Ethics  , Spinoza refers to conatus    as “nothing but the actual essence of the thing itself.” 14  Since will is the actual essence of the mind, and since appetite/desire is the actual essence of the mind and body together, I must begin by trying to discern what Spinoza may have meant by the actual essence of the „body.‟ In the  Ethics  , he defines the body as “a mode that expresses in a definite and determinate  way God‟s essence insofar as he is considered as an extended thing.” 15  One cannot begin to properly understand this definition, without understanding his denial of the existence of a vacuum. 16  For Spinoza, the very concept of a vacuum is a contradiction. In a letter to Henry Oldenburg from 1663, he comments on Robert Boyle‟s ambivalence towards the theory, saying: “I do not know why he calls the impossibility of a vacuum a hypothesis, since it clearly follows from the fact that nothing has no properties.” 17  He states in the Short Treatise on God, Man and His Well-Being   that a  vacuum is a basic contradiction in terms, because there cannot be “something positive and yet no body.” 18  He presents this same refutation of the theory of a vacuum consistently throughout his oeuvre: there can be no place where bodies stop and space begins. 19  Through his denial of a vacuum, Spinoza is led to maintain that the physical universe is a single, absolutely infinite individual that consists of an infinite series of contiguous bodies. Spinoza demonstrates that bodies are: 1) infinitely divisible, 2) composed of greater and lesser infinites, and 3) parts of an indefinitely expansive individual. In the words of Nicolas Malebranche, “no thing but infinities are found everywhere.” 20   The first kinds of individuals that Spinoza introduces in his Physical Digression are the simplest bodies, or the elements of the physical world. One could take Spinoza‟s use of the superlative, „simplest,‟ to m ean that he holds to a brand of atomism, or a theory that elemental particles are indivisible, but also possess mass and  volume. Spinoza, however, maintains that space is a plenum and in the context of 17 th -century physics, denying a vacuum was essentially one and the same as denying atomism. For atoms to be distinct entities, they could not be separated by other bodies, but by space devoid of body alone. 21   A concept of simplest bodies, thus, seems rather out of place in the context of Spinoza‟s system, as  it establishes conditions in which no fundamental element is discernible, or at the very least, isolable. Bodies are, in principle, divisible ad infinitum  . 22  Could simplest bodies, then, be akin to Cartesian corpuscles, elemental particles that possess mass and volume, but which are infinitely divisible? 23  Or are they more equivalent to Leibnizian monads? 24  Spinoza explicitly rejects the concept of vortices  which describe the internal motion of Cartesian corpuscles. 25  The latter option must be ruled out in light of the fact that simplest bodies are not souls, as Leibnizian monads are. 26   Although Jacob Adler and Lachterman maintain that the concept of simplest bodies functions as a placeholder for Spinoza, 27  it seems that this concept can be interpreted in one of two ways, namely, as 1) infinitesimals or vanishing quantities or 2) oscillations. The first interpretation has been defended by H.F. Hallet and Gilles Deleuze who argue that simplest bodies function as a limit concept. 28  If bodies are infinitely divisible, then simplest bodies must be those quantities of body that   Sean Winkler  –    The Conatus of the Body in Spinoza’s Physics   98 approach nothingness in the process of continual division. This has invited comparisons to Gottfried Wilhelm Leibniz‟s infinitesimals or Sir Isaac Newton‟s  vanishing quantities. 29  The comparison is not unbecoming given Spinoza‟s concept of quantities that cannot be accurately expressed by any number in Ep. 12, a concept  which Leibniz himself expressed great admiration for. 30  Although the nature of such quantities are a matter of considerable dispute in the context of mathematics, in the context of Spinoza‟s physics, simplest bodies can be no more than useful abstractions for performing mathematical calculations as Leibniz and Newton treat them. 31  Otherwise, they would have to be individuals defined strictly by their external relationships, or as Alexandre Matheron and Lee Rice note, individuals with an outside, but no inside, which seems inconceivable. 32  Thus, simplest bodies would not be real entities in this reading, but relative from one perspective to another.  The interpretation of simplest bodies as oscillations can be found in the work of Martial Gueroult, who emphasizes Spinoza‟s definition of simplest bodies as those “which are distinguished from one another solely by motion -and-rest, quickness and slowness.” 33  According to Gueroult, simplest bodies are indeed like Cartesian corpuscles. He maintains, however, that Spinoza‟s  definition creates a problem. If simplest bodies are strictly defined by a pattern of motion, they can only manifest as a single pattern, otherwise, they would not be simple. A change in the pattern, of course,  would result in a change of the identity of the simplest body. Any collision between a simplest body and another body, however, would result in a transfer of force that  would interrupt this pattern of motion and, consequently, change the identity of the simplest body. Since simplest bodies are constantly in contact with other bodies, they  would be in perpetual flux. 34  Thus, if they are defined by an internal pattern of motion, it cannot manifest as a vortex, as in Cartesian corpuscles, but only as periodic  vibration or oscillation as in Christiaan Huygens‟s simple pendulums. 35   This oscillation is defined by the following formula: t    = 2π √ l  /  g  ,  where t stands for the duration of a single oscillation, l   for the length of the pendulum, and  g   for the acceleration of gravity. 36  In order to develop a pendulum for clocks that could reliably keep time, Huygens turned to the concept of the isochrone curve, or a curve that no matter  where an object was dropped from, would reach the lowest point of the curve in the same amount of time. He discovered that such a curve was a cycloid, or the curve formed by tracing a circle as it rolls like a wheel along a straight line: Fig. 1 37     Society and Politics Vol. 10, No. 2(20)/November 2016   99   In the absence of intervening forces like friction, the period of motion of a pendulum along a cycloid ideally will remain the same in spite of losses in momentum after when the clock is first set. 38  For Gueroult, applying this formula of isochronic oscillation to the concept of simplest bodies allows each simplest body to maintain the same pattern of motion, even when encountered by other bodies. 39   Treating simplest bodies as corpuscles, however, is problematic for Gueroult‟s interpretation given Spinoza‟s rather non -committal attitude towards Huygens‟s pendulums. 40  Moreover, if the logic of the simple pendulum holds, while it allows for a steady pattern of motion during collisions, this does not hold for division, as changes in length alter the period of motion. If bodies are, in fact, infinitely divisible and simplest bodies are indivisible, the latter would not be bodies. While Gueroult contends that simplest bodies are neither hard, nor soft, nor fluid, they could not possess mass or volume either. 41  This would mean that simplest bodies are, quite simply, nothing. Given the implausibility of the second reading, then, simplest bodies should not be understood as real at all, but as hypothetical entities, specifically as infinitesimal or vanishing quantities, according to the first reading.  The second kind of individuals that Spinoza introduces in the Physical Digression are composite bodies, which he defines as follows: [w]hen 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. 42  Composite bodies are compounds, produced in the aggregation of either simplest or other composite bodies. They can be categorized according to three different states of matter: hard, soft and liquid. While Spinoza defines only these three in the  Ethics  , there is no reason to assume that he meant for this list to be exhaustive. In Ep. 6, for instance, Spinoza twice refers to vapours, indicating the possibility that he also considered there to be a gaseous state. 43  The concluding postulates of the Physical Digression suggest that Spinoza may have restricted himself to liquid, soft and hard bodies as these are the three types of composite bodies he saw as making up the human body. 44   Regardless, hard describes those “bodies whose parts maintain close contact along large areas of their surfaces,” while bodies are soft “whose parts maintain contact along small surface areas” and, finally, those bodies are liquid “whose parts are in a state of motion among themselves.” 45  If bodies can be divided ad infinitum  , they must be composed of an infinite number of parts. However, this introduces the inverse problem of division. Spinoza says that if an infinite length is measured in feet, it will have to consist of an infinite number of feet; and if it is measured in inches, it will consist
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