Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.57 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 5. Transformation and Individuation in Giordano Bruno's Monadology. Dr. Edward P. ButlerIndependent ScholarPhD. in PhilosophyNew School for Social ResearchNew York City United StatesORCID iD: http://orcid.org/0000-0002-7403-4524E-Mail: epb223@gmail.com Abstract: The essay explores the systematic relationship in the work of Giordano Bruno (1548-1600) between his monadology, his metaphysics as presented in works such as De la causa, principio et uno, the mythopoeic cosmology of Lo spaccio de la bestia trionfante, and practical works like De vinculis in genere. Bruno subverts the conceptual regime of the Aristotelian substantial forms and its accompanying cosmology with a metaphysics of individuality that privileges individual unity (singularity) over formal unity and particulars over substantial forms without sacrificing a metaphysical perspective on the cosmos. The particular is individuated as a unique site of desire, continually transforming but able to entrain itself and others through phantasmatic 'bonding', the new source of regularity in Bruno's polycentric universe. Bruno thus tries to do justice to the demands of intelligibility as well as transformative eros. The essay concludes with a note on Bruno's geometry as it relates to his general conception of form. Keywords: Bruno, monadology, polycentricity, individuation, metaphysics, cosmology Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.58 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 Transformation and Individuation in Giordano Bruno's Monadology. Bruno's cosmos is frequently described as acentric, but I would argue that we should ratherconceive it as polycentric. Bruno himself describes the situation in more or less this way, stating inthe fourth of his Paris disputation theses of 1588 that no point in the universe is peripheral toanother without being for itself the center, with its own equal horizon (Bruno 1879, 1.1, 98). Thisdoctrine has its roots, of course, in the pseudo-Hermetic axiom from the Liber XXIV Philosophorumthat God is an infinite sphere, the centre of which is everywhere and the circumference nowhere.Bruno appropriates the axiom, however, in a form which is novel for the importance it accords to theperspectives of the individual centers, which have each their own horizon.i One might contrastNicholas of Cusa's version of the same axiom: "The structure of the world is such, as if she had hercenter everywhere and her circumference nowhere, as her circumference and her center is God, whois everywhere and nowhere," (De docta ignorantia II,12, trans. Jasper Hopkins). In the original axiom,God is none other than the polycentric sphere itself. In Cusa's version, God is everywhere andnowhere, and since God is the center and circumference of the world, the center of the world iseverywhere and its circumference nowhere. It is as if the abstract divine attribute of beingeverywhere and nowhere requires the universe to adopt a polycentric structure in order to orientitself to the divine. The polycentric structure is thus subordinated, becoming an image of aparadigmatic divine attribute. In the context of the disputation thesis, Bruno also casts the axiom asproviding the sole manner in which to conceive the universe so that it may accord with ParmenideanBeing, for the homogeneity required of Being by Parmenides would exist only from a singleperspective if the universe had a single center. The multiplicity of perspectives, then, must either beresolved into one, or they must each bear the totality.That Bruno has opted for the latter course is evidenced by his doctrine of indivisible spiritualsubstances, his monadology. According to Bruno's 1591 essay De triplici minimo, the substance ofthings is the minimum, of which there are three principal varieties: the general metaphysicalminimum or monad; the corporeal minimum or atom; and the geometrical minimum or point. Weneed only concern ourselves for now with the monad. The monad is at once the indivisible substanceof the soul and the essence of number, which is an accident of the monad insofar as the monaddetermines the species (Bruno 1889, 1.3, p. 139.3-4; 140.22-3). A hierarchy is thus established inwhich the monad is primary, then species, then number, number being essentially the repetition ofform. In Bruno's dialogue De la causa, principio et uno (1584), the doctrine of the monad, to whateverdegree he had formulated it at the time, is implied by the critique of Aristotelian substantial forms inwhich he engages. Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.59 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 In this dialogue Bruno speaks of the forms of species as mere "external" forms or form "inthe vulgar sense" which applies only to "the operations which appear in the subjects and proceedfrom them," (Bruno 1998, p. 48). Since these forms are but accidents of matter, they are in no sensesubstantial for Bruno at all, and therefore there are, for Bruno, no "corruptible substances" (46).What is for Bruno a "substantial form" is none other than the monad, the indivisible spiritualsubstance of the individual which transmigrates from species to species, although he does not use theterminology of monads in De la causa. Because he does not speak of monads in De la causa, theidentification of the spiritual or vital principle of the individual spoken of in this dialogue with themonad of De triplici minimo could, in principle, be questioned. But there are clear parallels in the wayBruno speaks of the two. The description of the "internal artificer" in De la causa, which constitutesthe animal from the heart outward (38), is exactly like the account in De triplici minimo, where Brunosays that "[w]e are what we are only by virtue of the indivisible spiritual substance around whichatoms are gathered and clustered as around a center. Through birth and development the creativespirit expands into the mass of which we consist by diffusing itself from the heart to which itsintermingled threads return like arrows. In this fashion the spirit returns by the same road downwhich it came and exits through the same door through which it entered," (Bruno 1889, 1.3, p. 143.5-12, trans. Atanasijevic 1972, p. 27f). The exit to which Bruno refers is, of course, death, when themonad severs its connection to the atomic construct of the body to continue its journey, which willlead it to constitute some other body in similar fashion. The descriptions of metempsychosis in thetwo texts are in every way parallel. The identity of the two doctrines, or the inferences we areentitled to draw from them regarding Bruno's affirmation of individual immortality, have only beenquestioned at all, I believe, due to certain basic misapprehensions, which I shall take up below; first,however, it is necessary to lay out more of Bruno's doctrine in positive fashion.Since the monad is the active principle behind and within the material form, it is this whichBruno, in De la causa, wishes to regard as the form in the proper sense, treating the Peripatetic form,which is the form of the species, as form in a merely relative or accidental sense, "just as whoeversays what I do or can do is not expressing my being and substance; that would be expressed by whosays what I am, insofar as I am myself, considered absolutely," (Bruno 1998, p. 60). Bruno is speakingof ultimate individuals when he remarks that Aristotle was quite aware that what would be regardedas the Peripatetic substantial form is a mere "logical construction" rather than "the principle ofnatural things," explaining "I believe he [Aristotle] fully realized it but could do nothing about it. Thisis why he says that the ultimate differences are unknown and cannot be expressed." The difficulty ofexpressing the difference of the monadic individuals from each other, when all of the things wewould normally use to distinguish them appear as accidents, should not however lead us to assumethat Bruno's individuals are not really distinct. Understanding this inner core of individuality is aninfinite problem for the intellect. As Bruno explains in De la causa, "when we aspire and strivetowards the principle and substance of things, we progress toward indivisibility ... let us not be led Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.60 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 into believing we can understand of the substance and essence more than what we can understandconcerning indivisibility" (95). Bruno, though otherwise most sympathetic toward them, criticizesthe "intellectual weakness" of Pythagoreans and Platonists in this regard for having unified beingsunder species, then genera, and then the highest genera into one being, a being which is, however,but a "vain thing," as Bruno calls it, for they are unable to render from this thing "a single principle ofreality and of being for all that is, as they have recognized a common concept and name for all thatwhich is expressible and intelligible," (96). The hypostatized Being Itself differs from the monad asprinciple in that 'the monad' is really each monad continuously constituting itself and informingmatter. But it is important to Bruno to maintain at the same time a metaphysical perspective whichdiscerns the unity in principles. From this perspective, "Pythagoras' method is better and purer thanPlato's, because unity is the cause and the reason for individuality and the point, and it is a principlewhich is more absolute and appropriate to universal being," (94; my emphasis).The manifold of monads is a paradox in that each monad is absolutely unique from the restbecause in it lies a first-person perspective around which the universe is disposed, and yet anycharacteristic by which we might hope to distinguish it from the rest is accidental and susceptible tochange. No such characteristic, even were it to endure for all time, could be the individuating qualityof such an individual. This is what Bruno means when he refers to the multiplication of individualswithin the species by accidents (e.g., at 96). The numerical multiplicity within any species is, bydefinition, a multiplicity which comes about through accidents, even if these accidents are notaccidents from another perspective, but specific differences. Note, in this respect, that Bruno speaksin the Sigillus sigillorum of the "second contraction", through which "matter, through number, isdetermined to this or that form," in terms strongly reminiscent of the language of bonding: "inferiornature ... through some habit of agreement and obedience, is collected together and ... renderedparticipant, either by a natural or a conceptual impulse..." (Bruno 1890, 2.2, p. 214).Individuality is thus irreconcilable with formal unity insofar as formal unity necessarilydisplaces individuality, making of it an accident when for Bruno individuality, and not the form of thespecies, is the true substance. We must not infer the unreality of individuality from the very factwhich makes individuality fundamental and primary in Bruno's metaphysics. The formaldetermination of individuality is, in this respect, unattainable. Thus Bruno says in De la causa that"[t]his absolute act, which is identical with absolute potency, cannot be comprehended by theintellect, except by way of negatives ... for when the intellect wants to understand, it must try to forman intelligible species, and to assimilate and to measure itself with that species," (Bruno 1998, p. 68).Notice that it is itself that the intellect measures with the species. This shows that the topic of theinquiry into the absolute act which is identical with absolute potency, is in some manner the self. Andsince it is the self in its very first-person character, it only recedes furth from view insofar as it ismeasured by one intelligible species or another, for it repels them from itself in the very act ofthinking them. By contrast, "the divine mind and the absolute unity, with no species, is that which Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.61 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 understands and that which is understood simultaneously," (95). Our attempts to grasp this absoluteunity conceptually can only express "what we can understand concerning indivisibility." Thesophistication with which we are capable of conceiving absolute indivisibility is the index of ourcapacity to frame the notion of the monad.The relationship of this 'form', that is, the monad, to the Peripatetic form is characterized byDicsono, a character in the dialogue: "Inasmuch as this form that you posit as principle is asubstantial form, it makes up a perfect species, is to itself its own genus, and is not, like thePeripatetic form, part of a species," (48). Each monadic individual is, as it were, a species unto itself.The monad has thus inherited the status Scholastics accorded to the angelic individual, except themonadic pseudo-species has its serial instantiations through the particular bodies that it fashions inits successive lives, bodies which may belong ex hypothesi to the most diverse natural species. In thisprocess, an indestructible form and indestructible matter collaborate to produce a destructiblecomposite. The form, Bruno explains, "possessing in itself the faculty of constituting the particulars ofinnumerable species ... restrict[s] itself in order to constitute an individual, and, on the other hand,the potency of indeterminate matter, which can receive any form whatsoever, finds itself limited to asingle species," (ibid.). The Peripatetic form, then, has been recast as the mediator between the unityof matter and the virtually infinite multiplicity of unique, unrepeatable form-bringing individuals.What is it in Bruno's new system that comes to occupy the space, so to speak, that wasoccupied in the old system by the Peripatetic form? I do not think that Bruno fully resolved this issue;but I would like to indicate where I think the systematic foundations can be found for a resolution ofthe issue on Bruno's own terms and in accord with the most original aspects of his thought. Bruno'smonadology, in granting a metaphysical foundation to individuality, does not commit him to thesimplistic assumption that phenomenal individuals possess a greater autonomy than they in fact do.The participation of individuals in specific forms is the clearest indication of the composite nature ofphenomenal individuals. Bruno speaks in the essay De magia of "a multitude of spirits and souls" inus (Bruno 1998, p. 137); more systematically, he explains in De vinculis that "everything that can bebound is composite in some way" (ibid., p. 160) and composition is needed in the binding agent aswell: "we are in no way forcefully captured by simple and absolute things," (167). Moreover, shiftingour focus from the personal to the collective operation of bonding, "it is easier to bind many ratherthan only one," (168). Bonding thus obeys its own logic complementary to that of the monadology, alogic of multiplicities rather than of units, in which monads participate not by virtue of theiruniqueness but by virtue of their inescapable entanglement with each other, an entanglement whichis equiprimordial with their uniqueness, for it begins from the moment that the monad, havingterminated its relationship with a previous atomic construct which can no longer support itsactivities, begins to bond atoms together into a new body expressing the present state of its desire.As Bruno says in De minimo, "It is a property of it [the minimum] to compose, increase, form, as wellas being composed, formed and increased to the maximum," (Bruno 1889, 1.3, p. 146). It is not the Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.62 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 soul alone which can be seen either as active or as passive, but anything insofar as it can be seen as anatural or rational product respectively, for nature is "numerable number" and "measurablemagnitude", reason a "numerating number" and "measuring magnitude" (ibid., p. 136).The desiring monad, as a natural being, bears the impressions of a history of previous bondsand so is no longer in this respect 'atomic' at all. The forms of species, therefore, insofar as they areactive principles in their own right, are active as phantasmata binding the desires of monads anddetermining the corporeal forms they construct. Hence the importance for Bruno of "heroic"individuals taking control, to the degree possible, of their own phantasmatic economy: as Luca Salzaremarks, the 'heroism' of Bruno's 'hero' "consists precisely in 'utilizing' these metamorphoses,instead of suffering them passively," (Salza 2007, p. 50 n. 42, trans. mine). This process has itsexemplar on the cosmic scale in the activities of Jupiter in Lo spaccio, which has the implication, ofcourse, that the forms of species are not themselves static, but engaged in evolutionary processes.This is not to ignore the activity of the specific form as a kind of corporeal individual in its own rightwhich has its perpetuity in the individuals of the species; Bruno would, in this regard, doubtlessagree with the judgment of Lucretius (I. 196-7; 584-92)-but this is only a stability, a durabilitywithin the processes of metamorphosis. The revolution Jupiter carries out is no simple process,either, but involves an economy. First, he places in the sky objects of intellectual contemplation, andthen he sends incarnated phantasms into the world. The phantasms removed from the heavens mustgo somewhere; hence Jupiter sends them into the world, making them ethical problems. As heavenlyimages, they were like lenses coloring the natural light in ways whose contingency was masked bythe fantasy of the primum mobile. By returning them to the world, Jupiter re-establishes their immanence, just as Bruno shatters the immutable stasis of the medieval cosmos. Dissolving this stasiswas the prerequisite for a transformative understanding of the cosmos.Bruno has been characterized as 'anti-humanist' for depriving the human species of theprivilege accorded it in the hierarchical cosmos on account of its rationality; and indeed, he states inthe Cabala that it is possible "that many animals have more understanding and a much moreenlightened intellect than man," and are only inferior insofar as they lack the proper limbs: all thethings "that signify human grandeur and excellence, and make man truly the victory over the otherspecies ... All this ... refers primarily not so much to the style of mind, as to that of the hand, organ ofthe organs," (Bruno 2002, p. 57f). There is, within Bruno's system, however, a different, subtler sortof privilege to which humans are heir. That which is more complex is less limited in the sorts ofbonds into which it may enter (Bruno 1998, p. 159). This introduces, in turn, an "indeterminateness,"as Bruno calls it, within the species. Humans are thus more indeterminate in their desires thanhorses and the species 'human' is itself less determinate. Self-love, on the other hand, tends to limitthe types of bonds into which the subject can enter to those which are "natural to them." Self-loveinvolves the desire to maintain the form of the body one occupies at the moment, and thus excludes Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.63 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 bonds incompatible with that form. Self-love is not, however, uniform in its action; rather, Brunoexplains that while a thing strives out of self-love to preserve itself as it presently is, it strives as well"to be completely developed in itself." And since for Bruno "everything can be produced fromeverything," (ibid., p. 44) this means that it is also in accord with the monad's self-love to experienceother forms of life. The complexity of the human form of life gives it an indefiniteness allowing thehuman form it to be a more stable expression of the inherently restless desire of the monadicindividual.As Bruno puts it in De magia, "nothing is so incomplete, defective or imperfect, or, accordingto common opinion, so completely insignificant that it could not become the source of great events.Indeed, on the contrary," he stresses, "a very large disintegration into such components must occur for an almost completely new world to be generated from them" (Bruno 1998, p. 111, my emphasis). Herewe see the connection between the philosophical project of metaphysics of individuality and theproject of social renovation that Bruno imagined. The "disintegration" of the Ptolemaic andAristotelian cosmos into its radical components, namely the multitude of individual desiring monadsand the atomic sea of matter, is essential to free the space for an account of bonding in general,because it forces us to account for the immense multitude of different bonds which constitute thecosmos, as well as to analyze apparently integral individuals to discern their internal compositionand the consequent degree of stability they exhibit.I referred above to certain misapprehensions that have helped, along with Bruno's ownfrequent obscurity, of course, to frustrate the proper appreciation of Bruno's monadology. One suchmisapprehension is that because Bruno speaks of a universal intellect or world soul, he does notintend the living things whose constitution he describes in De la causa to be really distinctindividuals who retain an identity-however problematic-from one embodiment to another. Thisinterpretation has been argued particularly forcefully by Ramon Mendoza (2002). Mendoza seems toconceive the 'universal intellect' as a thinker, when the latter seems for Bruno to embody merely the intelligible order of the universe: viz., e.g., the identification of the universal intellect with a harmony,or a special form of light, in De triplici minimo (Bruno 1889, 1.3, p. 170f). Light is an important topicin Bruno: it is at once one of the four irreducible principles of reality, together with "water or theabyss or the Styx," "dryness or atoms or earth," and "spirit or air or soul," (De magia, Bruno 1998, p.118); and with darkness one of the twin principles of the "mathematical" world, (ibid., 109); but alsoan accident (113). Hilary Gatti has also remarked on an "evolving" tendency of Bruno's thought,reflected in the late fragment De rerum principiis (1590), "to eliminate from his discourse ... anyreference to the universal intellect," (Gatti 2010, p. 103).If we are to speak of a universal agency in Bruno, and in a manner consistent with the rest ofhis thought, surely this agency must belong rather to matter: "That principle is most perfect whichwishes [vult] to become all things ... and this is universal matter ... There is nothing outside of matter Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.64 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 or without matter," (Bruno 1998, p. 173). Even spiritual agencies are treated by Bruno as incorporealmatter, and there is nothing in Bruno corresponding to the distinction between sublunar andcelestial matter.ii The "immanent rational principle in matter" that Mendoza (2002, p. 278) correctlynotes differentiates Bruno's atomism from the Epicurean doctrine is thus simply this desireimmanent to matter and its laws,iii which form the substance of Bruno's inquiry into bonding. BrunoPinchard, who recognizes the crucial significance of the work on bonding to the final state of Bruno'ssystem, contrasts Bruno on just this point with Malebranche, in whom we may discern the outlines ofMendoza's interpretation of Bruno. For Malebranche, though like Bruno rejecting the hierarchicalcosmos of the Middle Ages, replaces it with a monism in which "[w]e are in effect only united immediately to God, and it is from this union that bonds"-i.e., relations between monads-"result,which are invisible in their basis," (Pinchard 2007, p. 98). Pinchard recognizes here "a dilemmarationalism will never escape," namely of either "reducing the bond to the relation", and thus to theunity of the entire system of relations, which becomes the sole genuine subject-"the systems ofrelation will be the systems of absolute reason," (92)-or, and this is Bruno's choice, "recognizing thepowers of the bond" as "an occult power of which I am at once the instigator and the victim," (100).The point here is not the "occultism" per se, but rather the mysterious depth accorded the individualsubject by rendering the bond concrete as the subject's active or passive power; it is this whichMendoza resists in Bruno's doctrine of metempsychosis.Accordingly, when Bruno states in the Cabala that the specific essence in the human "isidentical with that of flies, marine oysters and plant, and any other thing that is animated or has asoul" (Bruno 2002, p. 56), a necessary corollary to the metempsychosis doctrine he plainly endorseselsewhere, e.g., in Lo spaccio, in which humans we see about us now "have been or are about to bepigs, horses, asses, eagles, or whatever else" (Bruno 2004, p. 78), Mendoza is forced to interpret this categorial unity of souls as a numerical unity, through the false inference that "if man's soul isidentical with that of those living beings, there must be only one soul in all of them, which can be noother than the unique and singular soul of the world," (Mendoza 2002, p. 289). This is the veryAristotelian logic of individuation through form that Bruno resists, however, in placing the ultimateprinciple of individuation beyond form as such. The multiplicity of forms an individual assumesthrough metempsychosis thus function as a sort of eidetic variation to disclose, negatively, theineffable unity irreducible to any of them, the unity that can be identified only with the desire thatruns like a thread through all of them, a unique trajectory at the heart of every living thing, thatwhich Bruno calls "the divinity, the hero, the demon," and, most tellingly, "the particular god [il dio particolare]" (Bruno 2004, p. 77).A similar issue arises by way of the reference, in De triplici minimo, to God as the Monad ofMonads (Bruno 1879, 1.3, p. 146.30). Atanasijevic, in her study of De triplici minimo, criticizes Brunofor failing to specify the relation between the monads and the Monad of Monads (Atanasijevic 1972,p. 31). Ernesto Schettino, similarly, while recognizing that "the absolute physical minima"-i.e., of Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.65 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 corporeal or incorporeal matter-"are the authentic substance" (Schettino 2002, p. 315), worriesabout "[h]ow to reconcile ... the existence of these physical infinite minima, which would eachbecome an absolute in itself, with the unity of the maximum?" (319). Unlike Mendoza, Schettinorecognizes that forcing this reconciliation through "a super Unity (or 'suprasubstantial' substance) of matter-soul of the world-nature-universeand so on," (ibid.) is unsatisfactory. Schettino suggests-correctly, I believe-that the "transits between minima and maximum" (321) are to be conceived asan "expansion or self-unfolding on the part of the atom ... filling infinity with an infinite motion(which would mean unlimited speed) tantamount to immobility" (320), but is uneasy with thissolution. Schettino's substantive concerns lie, first, in the status of space in the account, which liesoutside the synthesis; and, second, Bruno's respect for "the awareness of our finitude andgnoseological limitations with respect to God's infinity" (ibid.). A full consideration of the formermust take into account Bruno's geometry, on which see below; however, we can say in advance thatthe indifference of Brunian space to forms (Bönker-Vallon 2007, p. 67-71), the essential corollary ofits polycentricity, forecloses any simple identity between this infinite atom and any empiricalconsciousness as passive configuration of the self rather than as the product of the activity of theinfinite will, for the empirical consciousness is always a species-consciousness. In a certain sense wemay say that the physical and gnoseological problem find their common solution in the Nolan'smonadology.With respect to the problem as Atanasijevic poses it, Bruno does not specify a relationbetween the monads and the Monad of Monads because these are not entities which can be positedupon a single plane. From one perspective there is simply the Monad per se; from the other, there aresimply the innumerable individual incorporeal and corporeal monads. Similarly, in De vinculis Brunoexplains that the "universal force of bonding ... cannot be designated by one name," but only positedwith respect to "agents" such as "God, demons, souls, animals, nature, chance, luck and, finally, fate"(Bruno 1998, p. 145). Here diverse agents may be known according to their manners of bonding,while Bruno resists fully hypostatizing this universal, and hence subordinating the discrete agents,preferring to give an account of the activities classified as 'bonding'. Note, as well, that these bondingagencies are not all monads; bonding does not presuppose a subject intending to bind. Bruno'stheory of bonding does not presuppose an underlying unity of one-in-all-on the contrary, it isprecisely removing this presupposition which frees the space for an account of "bonding in general";but nor does it yield to an uncritical empiricism.The passage I cited above from the essay on bonding is significant for showing that Brunoenvisioned a comprehensive theory of things which at the same time allowed for a real plurality ofagents and perspectives. As he says in the very first sentence of De vinculis: "Anyone who has thepower to bind must to some degree have a universal theory of things in order to be able to bindhumans" (ibid.). The most binding theory therefore would, by embracing the very multiplicity ofdesires and perspectives without deforming them, succeed in harnessing them, just as the Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.66 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 polycentric universe alone can make the universe itself a Parmenidean intelligible. At the same time,however, Bruno strongly resists any reductionistic methodology, "for it is a sign of an ambitious,presumptuous, envious and vain mind to wish to persuade others that there is only one way toinvestigate and to attain knowledge of nature" (De la causa, Bruno 1998, p. 62). Bruno's monadologyis thus an ambitious attempt to meet both these conditions: universal in scope, but non-reductionistic, and the resulting high degree of abstraction explains some of the difficultycommentators have had understanding, e.g., Bruno's diagrams, the polyvalence of which has finallybeen recognized by Arielle Saiber (2005), a subject to which I would devote some words inconclusion.Bruno's general concept of form cannot be treated without specific reference to his accountof geometrical form. Bruno regards geometrical form as in some sense the ground of all others, as wesee for instance in De la causa where he remarks that the triangle as "the first finite and first limitedthing," is "the primary foundation of every limited and configurated thing" (Bruno 1998, p. 97). Withthis in mind, we can look at Bruno's geometry in a different light; specifically, as an adjunct to hismonadology-and in this light, what seems to render Bruno's geometry unfit to function as ageometry in the narrow sense, that is, as geometry in the sense familiar to us, is just what makes ituseful on this broader stage.Bruno's geometry is, we may say, his account of the nonindifference of space. Commentatorshave remarked on the indifference of space for Bruno relative to Aristotelian qualitative space, whichgave a fixed direction to elemental motion, an absolute 'up' and 'down' for all things; but space is notindifferent as an expression of monadic desire. Monads form bonds, and bonding determines space,or rather, spaces appropriate to the bonds themselves. In Bruno's geometry, figures have no uniformmeasure, but rather each one must be measured according to its gnomon, the number of minimawhich are in the smallest figure of its type. Hence a circle's minimum increase in size comes aboutthrough the addition of six minima, while a triangle requires three minima, a square four. No figurecan grow through the addition of one single minimum (Atanasijevic 1972, p. 50ff). Hence, a figure ismade up, not of isolated monads, but of a monadic collective. Such a collective, in itsnondecomposability, forms a kind of monad in its own right.The determination of figures according to diverse minima represents a complement toBruno's well-known appropriation of the Cusan proofs of the identity of different figures in theinfinite. For the doctrine of minima means that it is impossible to equate one sort of figure withanother, even when the parts of one figure are equal in number to the parts of another; the rejectionof a common finite measure for figures has the additional consequence that there are no irrationalquantities (Atanasijevic 1972, p. 81; 110f). Having rejected number, an accident of species, as acommon measure for figures, different figures can only be equated in the infinite, that is, in theinfinite sphere of which each monad is the center. To translate back into the terms of metaphysics, Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.67 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 the diverse figures are equivalent just insofar as each can be seen as the contingent shape of theinfinite will of some given monad.Bruno extends this same reasoning on incommensurability in an attempt to solve Zeno'sparadox about Achilles and the tortoise. The paradox arises, in Bruno's judgment, from the attempt tocompare incommensurable minima: the minimum of time and of motion, the minimum of impulsiveforce and the minimum of movement produced. A homogeneous measure can only be imposed uponthese diverse species artificially and for practical purposes (Atanasijevic 1972, pp. 32-37). Bruno'ssolution indicates that there are more species of minima than just the metaphysical monad, thegeometrical point, and the corporeal atom. We may thus posit that there are in turn, within theseclasses of minima, stable and irreducible structures like the figures within geometry, such as distinct'figures' of time or force.Bruno applies this reasoning to the senses as well, each of which judges according to its ownmeasure (ibid., p. 59f). Bruno's reflections on finite geometry demonstrate that the realm of thefigure or form is incommensurable with the realm of monads, an incommensurability which isimmediately manifest in the contrast between the integral monad and the senses by means of whichit knows the world, for each sense has, as it were, its own minimum or measure. There can be, inother words, no solipsism of sensation, because the monad is not the measure of its own sensation:sensation is not private, but essentially collective. In general, the point, which corresponds ingeometry to the monad in metaphysics, is only conceivable as a non-detachable, purely relativemoment in the gnomon of some species. The 'unit' of form is therefore really a whole or set while themetaphysical unit, being indivisible, thus eludes determination by any universal characteristics.Indeed, Bruno's concern with incommensurability is a motive for his geometrical inquiries,as Saiber notes, for "[u]nlike in algebra and trigonometry, in geometry the notion ofincommensurability can be formulated without contradiction," (Saiber 2005, p. 47). One might saythat this distinguishes Bruno's approach to geometry from his models in antiquity, but only if onefails to take account of the 'philosophical' arithmetic Plato envisions at Philebus 56de, in contrast tothe mundane arithmetic of indifferent units. Incommensurability is important to Bruno because onlyby recognizing different minima as generically, and not only specifically, diverse is a genuine theoryof bonding possible, for a true bond requires genuine multiplicity, and things bonded cannot beprimordially one, at least not in the respect in which they bond.The fundamental division in Bruno's monadology is thus between the partless that is itself apart of some whole, as the minima in a collective, and the partless that is not a part, monads as ends, termini (De Minimo IV, Cap. VII (Bruno 1889, 1.3, p. 284.11-13). This is not a division of entities, butof modes of bonding-thus a line may be regarded as either a minimum (of extension) or a terminus(between plane figures) (ibid. 284.20-25). The distinction between minima and termini is that Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.68 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 between, on the one hand, the immanent bond of parts in a whole (or system) to the "first part" orminimum measuring that system, and to each other through its mediation; and on the other hand, theterminus as transcendent moment of application of a measure. Thus Angelica Bönker-Vallon notesthat Bruno transforms Cusa's doctrine of the coincidence of contraries by placing this coincidence-e.g., of the straight line and the curve-in the termini of the contraries, and thus internal to geometry.Bruno thus operationalizes Cusa's reflections: "If for the Cusan all of mathematics could be finite andthe consideration of the infinite nothing more than a symbolic aid (manuductio) for the knowledge ofGod, by nature unknowable, Bruno interprets the coincidence of qualitatively diverse opposites asthe unity of quantitative extremes," (Bönker-Vallon 2007, p. 70, trans. mine). Figures areincommensurable except in the infinite, but the infinite is no longer transcendent, but immanent,practical.Saiber notes that Bruno introduces an element of temporal, even narrative constitution intothe geometrical figure. Speaking of the diagrams in Articuli adversus mathematicos and De minimo,Saiber remarks on the narratives through which Bruno constructs the figures: "He often makes hisexplanations of how to draw a figure into stories with actual characters, not mere letters or symbols.His diagrams are the results of these stories; they are the products of a series of events; they areactual narratives and dynamic happenings," (Saiber 2005, p. 49). The narrative construction of thediagram helps to highlight that the geometrical figure as such is in fact for Bruno a complex bondingrendered in an abstract form; and this helps us to appreciate his geometrical finitism. The minimacomposing a figure do not look inward, so to speak, toward the more simple, but outward, to thecomplex encounters of which the figure is a sign. The finite line's divisibility into a finite number ofminima signifies that it is not itself straight, but angled, virtually bent at each point at which it mightbreak off into a new trajectory; a straight line is thus two lines in precise opposition, the contingentresolution of this internal conflict. Such a perfect opposition resolves itself into the perfect circle,which is identical to the infinite, perfectly straight line (Articuli adv. math., Memb. VI, Art. 61ff (Bruno1889, 1.3, pp. 33-36)). "In most instances of coincidentia oppositorum," however, as Saiber remarks,"there is not perfect coincidence or perfect repulsion, and the intersection of these two entitieseventually settles into an acute or obtuse angle of agreement," (Saiber 2005, p. 91). While much hasbeen said about the notion of coincidentia oppositorum in Bruno, not enough, perhaps, has been saidabout the failure of coincidence and its productivity, that which sends the monad restlessly off intoits next encounter, its next transformation.The point of syntheses such as the "dolphins on forest treetops and wild boars under therocks of the sea" (De gli eroici furori, Argomento, 13), therefore, is not to dissolve differences into a coincidentia oppositorum leading all things to an undifferentiated unity, but rather the productivevitality of the incongruous union, the failure of coincidence, the failure of identity, which in turndemands transformation, as in Bruno's emblem from the Furori of a phoenix burning in the sun,which bears the motto neque simile, nec par, "neither similar, nor equal," on which Saiber comments Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.69 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70 that "the hero in his process of transformation, or even transmutation ... is neither similar nor equalto that with which he is uniting," and hence between them, contrary to the thesis of "mystical union","[t]here is intersection and acquaintance, but no fusion ... Two lines meeting on a plane do notbecome one and the same line, but an angle, a joining of discrete vectors," (Saiber 2005, p. 92f).Similarly, the emblem of a boy's face burning in flames and a phoenix flying overhead bears themotto Fata obstant, "Their fates run contrary," and a poem that reads in part "I by Cupid, you byPhoebus are enflamed"; in this way Saiber explains that "Bruno shows how two opposing entitiescoincide in the general concept of 'fire', but are, ultimately, on different courses," (ibid., 98f).What is from a certain perspective the failure of mathematics is thus for Bruno an advantage.He does not want mathematics to enter into a privileged relationship of approximation towardempirical objects. He prefers analogical relationships, such as those between geometry and grammar(Saiber 2005, p. 53 and n. 115), the source of the geometrical-rhetorical syntheses Saiber uncovers inBruno's works, because of their lack of closure. Hence when Bruno severs the bond of necessitybetween a word's form and its meaning (De Compositione Imaginum, I, Cap. X (Bruno 1889, 2.3, pp.113-115), it is because he would promote an infinity of languages, not because he wishes tosubordinate language's material diversity to an inner identity. Indeed, the privilege Bruno accords in De Magia to hieroglyphic scripts over alphabetic ones is not because in their 'natural' resemblance tothings they represent a unity above and beyond the conventional signs of alphabetic scripts, but rather because they are more plastic to investment by the individual, so that "each person, by the dictate of his own inspiration or by the impulse of his own spirit ... characterizes for himself each symbol according to his own impulse, and as the divine spirit personally exerts certain powers which are not expressed in any explicit language, speech or writing," (Bruno 1998, p. 214). By not being fixed to a phonetic vehicle in the way an alphabetic script is, the hieroglyphic script is better suited to express that itinerant linguistic agency which forms 'bodies' for itself just as the indivisible soul-unit forms for itself one animal body after another. References:  Atanasijevic, K. (1972). The Metaphysical and Geometrical Doctrine of Bruno, trans. George Tomashevich. St.Louis: Warren H. Green  Bönker-Vallon, A. (2007). "L'unité divine et la structure mathématique de la nature: le développement dessciences naturelles chez Giordano Bruno." Pp. 59-72 in P. Magnard, ed.  Bruno, G. (1879-1891). Jordani Bruni Nolani opera latine conscripta publicis sumptibus edita, 3 vols. Neapoli:D. Morano [1.1 (1879), 1.3 (1889), 2.2 (1890), 2.3 (1889)]  -(1998). Cause, Principle and Unity and Essays on Magic, trans. and ed. Robert de Lucca and Richard J.Blackwell. Cambridge: Cambridge University Press  -(2002). The Cabala of Pegasus, trans. Sidney L. Sondergard & Madison U. Sowell. New Haven, CT: YaleUniversity Press Vol 3 No 2 (2015) ISSUE – JUNE ISSN 2347-6869 (E) & ISSN 2347-2146 (P) Page no.70 Transformation and IndividuationDr. Edward P. Butler Page No. 57-70  -(2004). The Expulsion of the Triumphant Beast, trans. Arthur D. Imerti. Lincoln, NE: University ofNebraska Press  Catana, L. (2005). The Concept of Contraction in Giordano Bruno's Philosophy. Aldershot: Ashgate.  Gatti, H. ed. (2002). Giordano Bruno: Philosopher of the Renaissance. Aldershot: Ashgate  -(2010). Essays on Giordano Bruno. Princeton, NJ: Princeton University Press  Magnard, P. ed. (2007). Fureurs, héroïsme et métamorphoses. Louvain: Peeters  Mendoza, R. (2002). "Metempsychosis and Monism in Bruno's nova filosofia." Pp. 273-297 in Gatti, ed.  Pinchard, B. (2007). "Au péril des liens." Pp. 91-105 in Magnard, ed.  Saiber, A. (2005). Giordano Bruno and the Geometry of Language. Aldershot: Ashgate  Salza, L. (2007). "Nature et homme dans la 'mutation vicissitudinale'." Pp. 37-56 in Magnard, ed.  Schettino, E. (2002). "The Necessity of the Minima in the Nolan Philosophy." Pp. 299-325 in Gatti, ed. Notes: i Note that Leo Catana, in his otherwise perspicuous study The Concept of Contraction in Giordano Bruno's Philosophy, does not note the significance of this passage for Bruno's doctrine of the "contraction of the horizoninto the center" from his Sigillus sigillorum (Bruno 1890, 2.2, p. 182f) despite the consequences that apolycentric reading would have for the very meaning of an 'ascent' from multiplicity to unity (Catana 2005, pp.10-13).ii On "incorporeal matter", see the fourth dialogue of De la causa.iii Cf. Schettino, who speaks more judiciously of "an intrinsic and absolute rational structure that allows for thetransits between minima and maximum, a rationality that must be determined beginning from the minima,because ... they are its foundation," (Schettino 2002, p. 321; my emphasis). CITE THIS ARTICLE:Transformation and Individuation in Giordano Bruno's Monadology. CITATION FORMATAPA:Butler, E. (2015). Transformation and Individuation in Giordano Bruno's Monadology. SO C R A T E S, 3(2), 57-70. Retrieved fromhttp://www.socratesjournal.com/index.php/socrates/article/view/143 FOR MORE CITATION FORMATS PLEASE VISIT:http://www.socratesjournal.com/index.php/socrates/rt/captureCite/143/