One of the most striking innovations in Aristotle’s philosophical writing is also one of its most characteristic features. That feature is Aristotle’s idea that terms central to philosophy, including ‘cause’ [aition], ‘good’, and even the verb ‘to be’, are, as he likes to put it, “said in many ways.” To be sure, philosophers before Aristotle give some evidence of having recognized the phenomenon of being said in many ways. Plato, in particular, suggests that things in this world that we call (...) “just” are only namesakes of the Just Itself. But, beyond that, homonymy seems to have been, even for Plato, no more than a source of ambiguity for wordplay. Aristotle is apparently the first philosopher to propose a taxonomy of homonymy and to view the identification and analysis of homonymies as a genuinely philosophical project. (shrink)

Aristotle attaches particular significance to the homomyny of many of the central concepts in philosophy and science: that is, to the diversity of ways of being that are denoted by a single concept. Shields here investigates and evaluates Aristotle's approach to questions about homonymy, characterizing the metaphysical and semantic commitments necessary to establish the homonymy of a given concept. Then, in a series of case studies, he examines in detail some of Aristotle's principal applications of homonymy--to the body, sameness and (...) and oneness, life, goodness, and being. This first full-length study of a central aspect of Aristotle's thought will interest philosophers working in a number of areas. (shrink)

Let T be a strongly minimal theory with quantifier elimination. We show that the class of existentially closed models of T{“σ is an automorphism”} is an elementary class if and only if T has the definable multiplicity property, as long as T is a finite cover of a strongly minimal theory which does have the definable multiplicity property. We obtain cleaner results working with several automorphisms, and prove: the class of existentially closed models of T{“σi is an automorphism”: (...) i=1,2} is an elementary class if and only if T has the definable multiplicity property. (shrink)

Laurel Schneider takes the reader on a vivid journey from the origins of "the logic of the One" - only recently dubbed monotheism - through to the modern day, where monotheism has increasingly failed to adequately address spiritual, scientific, and ethical experiences in the changing world. In Part I, Schneider traces a trajectory from the ancient history of monotheism and multiplicity in Greece, Israel, and Africa through the Constantinian valorization of the logic of the One, to medieval and modern (...) challenges to that logic in poetry and science. She pursues an alternative and constructive approach in Part II: a "logic of multiplicity" already resident in Christian traditions in which the complexity of life and the presence of God may be better articulated. Part III takes up the open-ended question of ethics from within that multiplicity, exploring the implications of this radical and realistic new theology for the questions that lie underneath theological construction: questions of belonging and nationalism, of the possibility of love, and of unity. In this groundbreaking work of contemporary theology, Schneider shows that the One is not lost in divine multiplicity, and that in spite of its abstractions, divine multiplicity is realistic and worldly, impossible ultimately to abstract. (shrink)

Because of the transcendental emphasis of his critical works, Immanuel Kant has been criticised for not being able to accommodate the notion of multiplicity. This paper outlines a complex argument designed as a means to the rescue of Kant from this repudiation. To this end, the paper proposes a new, strong reading of the doctrine of aesthetic ideas that unveils the idiosyncratic play of the mental powers, constituted of two separate acts, that equips one to intuit an unnameable mark (...) that evades both empirical apprehension and logical comprehension. By analogy with the two types of cognition, stipulated in the Stufenleiter (and elsewhere), I shall suggest that the two distinct kinds of a feeling of pleasure, stirred up by the generation of an aesthetic idea, add an overlooked, aesthetic element that renders Kant a philosopher of multiplicity. (shrink)

I explore connections between social divisions and diversity within the self, while striving to differentiate internal diversity and multiplicity. When the person is understood as composite or multiple, she is seen as divided into several distinct agent-like aspects. This view is found in ancient, modern, and postmodern philosophy, psychology, poetry, and lay people's accounts of their experience. I argue for a conception of the self as diverse but not composite or multiple.

This article, divided into two parts, traces and discusses two pairs of analogies invoked in Sanskrit literature to articulate the paradox of God’s oneness and multiplicity vis-à-vis the souls and the manifest world, reflecting the philosophical positions of pariṇāmavāda and vivartavāda. These are, respectively, the analogies of fire in wood and dairy products in milk, and moon/sun in pools of water and space in pots. Having introduced prevalent ideas about the status of the supreme principle vis-à-vis the souls and (...) creation in Śaivism, Sāṅkhya, and Vedānta, and having investigated instances of the first pair of analogies in multiple textual genres in Part I, here I turn to the discussion of the second set of analogies. Having proposed that the first set reflects the influence of pariṇāma-Vedānta on an early strand of the Śaiva textual corpus, I argue that the second set, attested prevalently in relatively late sources, betrays a Śaṅkarian origin, thereby suggesting a vivartavāda-Advaita Vedānta influence on the Śaiva corpus after the 9th or 10th century. (shrink)

The solution of the outer multiplicity problem in the tensor product of U(3) irreducible representations (irreps) developed by Biedenharn et al.(1–7) and realized through the well-known Draayer-Akiyama (DA) computer code(8) is extended to the quantum algebra Uq(3). An analytic formula for special stretched Uq(3) Wigner coefficients, $$\left\langle {(\lambda _1 \mu _1 ) H_1 , (\lambda _2 \mu _2 ) \varepsilon _2 \Lambda _2 m_2 \left| { (\lambda _3 \mu _3 ) H_3 } \right.} \right\rangle _{\max }^q $$ is derived (...) using a projection operator method.(9–10) In this expression Hi denotes the highest weight vector of the (λiμi) irrep; the subscript “max” means coefficients corresponding to a unit tensor operator with a maximal characteristic null space; and q is the usual quantum label so the standard U(3) Wigner coefficient, which is required in the DA code, can be obtained in the q→1 limit of the theory. To illustrate the theory, some Uq(3) Wigner coefficients for the tensor product (22)×(22) are calculated. The procedure for evaluating nonhighest weight Wigner Uq(3) coefficients follow the DA prescription. (shrink)

Sexual difference must be recognized in thought and human interactions to enable people to find their real source of jouissance. The Lacanian finding of ‘masculine phallic desire’ and ‘feminine libidinal desire’ in all human beings, irrespective of their biological sex-gender, paved the way for rethinking gender identities. It calls for reforming inter-human relations from the presently predominant utilitarian mode to the one based on love and recognition of the other. Gender is an arbitrary construct to serve the interests of males (...) in finding phallic sexual pleasure, power and recognition in their social life. Assertion of sexual difference and gender multiplicity will enable human beings to find the other human being as their actual desired object, beyond the pleasures offered by wealth, comforts and commodities. (shrink)

While research has focused on financial and social goals in impact investing, we add to the limited research that focuses on how individuals manage identity multiplicity, defined as three or more role identities. Based on our qualitative study of Christian impact investors, we develop a model of identity multiplicity work, explaining how individuals manage their multiple role identities to reduce identity tensions during the process of impact investing. We find individuals engaged in an interactive, ongoing three-step process of (...) identity multiplicity work: prioritizing one of their salient identities, managing their identity multiplicity interrelationships, and reinforcing their prioritized identity. Investors generally prioritized an identity that was neither financial nor social, but rather religious. We also find this identity work implemented through three novel mechanisms: shadowing, one identity casts a shadow over another thereby enabling the simultaneous pursuit of related goals; distinguishing, all identities are retained and at least a minimum threshold of role expectations are met; and surrendering, partial sacrificing of goals of one identity in favor of another identity based on an individual’s self-reflective importance of the role. Our findings offer new insights to multiple identities, impact investing and business ethics literatures. (shrink)

Calvino’s apology of multiplicity starts with the exposure, revealed by his take on typically modern novels, of some fundamental contradictions underlaying the modern quest for knowledge, which are definitely not alien to our day education. Then, when Calvino goes on to explore how twentieth century literature transcended those difficulties, he provides us with a valuable inspiration for how education could cope with its ambiguous relation to knowledge, still deeply rooted in the modern approach. Guided by Calvino’s readings, we are (...) shown that literature can succeed in its epistemological (r)evolution. Meanwhile, education, as it seems, is still struggling to overcome its entanglement with the unreachable goal of teaching everything about everything, to cope with the infinity and complexity of that everything, making reflecting upon education’s epistemological stance in the twenty-first century very much a necessity, one that I will try to pursue in the following pages After a methodological introduction, the paper starts by placing Calvino’s examination of beautiful, yet unsuccessful literary attempts at an exhaustive account of the world in the context of education, to show how their unattainable ambitions are mirrored in pedagogical practice, pointing out to the “modern spirit” underlying both the aforementioned novels’ and contemporary education’s relation to knowledge. Then, with the help of J. Rancière’s take on education, I will try and make educational sense of Calvino’s account of Bouvard and Pécuchet failed quest to know everything there is to be known, and relate it to the particular model of knowledge at work in education, one that needs to be questioned. Finally, I will draw on Calvino’s praise of “the contemporary novel as (…) a method of knowledge” (SM, p. 105), and particularly on his analysis of Perec’s masterpiece La Vie mode d’emploi, and his rehabilitation of the idea of arbitrariness, to outline some reflections about how an educational multiplicity, where “everything is in everything” could come to life (Rancière, 1991, p. 26). (shrink)

This article sets out to analyse some of the most basic elements of our number concept - of our awareness of the one and the many in their coherence with multiplicity, succession and equinumerosity. On the basis of the definition given by Cantor and the set theoretical definition of cardinal numbers and ordinal numbers provided by Ebbinghaus, a critical appraisal is given of Frege’s objection that abstraction and noticing (or disregarding) differences between entities do not produce the concept of (...) number. By introducing the notion of subject functions, an account is advanced of the (nominalistic) reason why Frege accepted physical, kinematic and spatial properties (subject functions) of entities, but denied the ontic status of their quantitative properties (their quantitative subject function). With reference to intuitionistic mathematics (Brouwer, Weyl, Troelstra, Kreisel, Van Dalen) the primitive meaning of succession is acknowledged and connected to an analysis of what is entailed in the term ‘Gleichzahligkeit’ (‘equinumerosity’). This expression enables an analysis of the connections between ordinality and cardinality on the one hand and succession and wholeness (totality) on the other. The conceptions of mathematicians such as Frege, Cantor, Dedekind, Zermelo, Brouwer, Skolem, Fraenkel, Von Neumann, Hilbert, Bernays and Weyl, as well as the views of the philosopher Cassirer, are discussed in order to arrive at an assessment of the relation between ordinality and cardinality (also taking into account the relation between logic and arithmetic) - and on the basis of this evaluation, attention is briefly given to the definition of an ordered pair in axiomatic set theory (with reference to the set theory of Zermelo-Fraenkel) and to the defmition of an ordered pair advanced by Wiener and Kuratowski. (shrink)

The concept of multiplicity describes the fluid nature of identity and experience in the wake of postmodernity. Yet the question of how we negotiate and maintain our identities, despite our multiplicities, requires phenomenological clarification. I suggest that recognition of multiplicity needs to be combined with an acknowledgement of continuity, however minimal. I maintain that this continuity is evidenced in our pre-reflective self-awareness, embodiment and habitual activities. Our authorship of life narratives and our ability to deliberate and shape our (...) identities takes place against the background of our lived, prereflective experience. I develop the notion of prereflective self-awareness using the work of Sartre, Heidegger and Merleau-Ponty. I suggest that prereflective self-awareness, embodiment and habitual activity are themselves shaped by our participation in sociocultural frameworks that give meaning to our lives. (shrink)

This article traces an emergent tension in an interdisciplinary public health project called Weather Health and Air Pollution. The tension centered on two different kinds of data of air pollution: monitored and modeled data. Starting out with monitoring and modeling practices, the different ways in which they enacted air pollution are detailed. This multiplicity was problematic for the WHAP scientists, who were intent on working across disciplines, an initiative driven primarily by the epidemiologists who imbued the project with meaning (...) and value as the protagonists of “health.” To work collaboratively implies a stable, singular, and shared research object, however: one kind of data, one version of air pollution. In detailing two attempts by researchers to address the inadequacies of modeled and monitored data, this article explores the ways in which difference and multiplicity were negotiated and transformed. In doing so, this article suggests that it is the mobility and instability of data that are particularly fruitful for exploring the facilitation and enactment of new realities, while also making explicit the emergent problematics and partialities which inevitably result. (shrink)

The book describes the ways in which American thinkers and artists in the first two decades of the twentieth century challenged notions that a single principle ...

Taking its direction from references to Black and Indigenous struggles present in Leonard Harris’ oeuvre, this chapter turns to politicized acts of resistance among Black and Indigenous communities. More specifically, the essay traces the functions of cultural pluralism, value relativism, and representative heuristics within solidarity work that enact logics of resistance to settler colonization and anti-Black racism, among other forms of oppression. Through this analysis, we see that Harris’ views about insurrection and normativity entail that both oppression and resistance are (...) the result of multiplicitous forms of agency. (shrink)

This article, divided into two parts, traces and discusses two pairs of analogies invoked in Sanskrit literature to articulate the paradox of God’s oneness and multiplicity vis-à-vis the souls and the manifest world, reflecting the philosophical positions of pariṇāmavāda and vivartavāda. These are, respectively, the analogies of fire in wood and dairy products in milk, and moon/sun in pools of water and space in pots. In Part I, having introduced prevalent ideas about the status of the supreme principle vis-à-vis (...) creation in Śaivism, Sāṅkhya, and Vedānta, I investigate instances of the first pair of analogies in multiple textual genres, and especially in Śaiva literature from South and Southeast Asia, to highlight the influence of pariṇāma-Vedānta on the Śaiva textual corpus. Arguing that the distribution of the two pairs of analogies may cast some light on the relationship between different strands of dualistic and non-dualistic scriptures, I propose that the first pair could be traced back to the “formative” period of Śaivism—that is, prior to the emergence of the fully dualistic Śaiva Saiddhāntika corpus known to us. (shrink)

An analysis of biological selection aimed at deriving a mechanism-independent definition removes Hull et al.'s obligatory requirement for replication of the carriers of information, under conditions, such as those obtaining in the nervous system, where the information content of a carrier can be modified without duplication by an amount controlled by the outcome of interactions with the environment.

A prominent argument for the immateriality of the soul is the so-called "Achilles Argument", which relies on the claim that the soul is simple or indivisible. It was not widely used in the Aristotelian tradition, however. But a version of the argument played a crucial role in Suárez’s contention that a human being contains only one unitary soul. On an alternative view that was widespread at the time, living substances may contain several souls, such as a sensitive and a rational (...) soul in the case of human beings. Suárez holds that the powers of the soul are really distinct from each other and from the soul itself. At the same time, the actions of the different powers of the soul influence each other, as when a loud noise distracts me from doing philosophy or when my intellect relies on my imagination for mental images. Suárez argues that this interaction between powers requires that they are all are "rooted" [radicatae] in one single soul. (shrink)

How has multiplicity superseded impossibility in philosophical challenges to artificial consciousness? I assess a trajectory in recent debates on artificial consciousness, in which metaphysical and explanatory challenges to the possibility of building conscious machines lead to epistemological concerns about the multiplicity underlying ‘what it is like’ to be a conscious creature or be in a conscious state. First, I analyse earlier challenges which claim that phenomenal consciousness cannot arise, or cannot be built, in machines. These are based on (...) Block’s Chinese Nation and Chalmers’ Hard Problem. To defuse such challenges, theorists of artificial consciousness can appeal to empirical methods and models of explanation. Second, I explain why this naturalistic approach produces an epistemological puzzle on the role of biological properties in phenomenal consciousness. Neither behavioural tests nor theoretical inferences seem to settle whether our machines are conscious. Third, I evaluate whether the new challenge can be managed through a more fine-grained taxonomy of conscious states. This strategy is supported by the development of similar taxonomies for biological species and animal consciousness. Although it makes sense of some current models of artificial consciousness, it raises questions about their subjective and moral significance. (shrink)

With the assumption of inactivation of small traits in bacteriophages “chromosomes” by ultraviolet irradiation the probability of multiplicity reactivation of irradiated phages is calculated. The result appears to be in agreement with the experimental results ofDulbecco.In the mathematical treatment of the problem a distinction is made between ordinary genes, with probability of inactivation negligible relative to the probability of inactivation of the whole phage, and a few vulnerable centers or genes whose probability of inactivation is not negligible. The hypothesis (...) of the existence of vulnerable centers appears necessary in order to explainDulbecco's experimental results.Postulant que de petites sections des „chromosomes” du bactériophage sont inactivés par l'irradiation ultraviolette, on a calculé la probabilité de réactivation par infection multiple des bactériophages traités par les rayons ultraviolets. Les résultats obtenus s'accordent avec les résultats expérimentaux de M.Dulbecco.Dans la tractation mathématique des problèmes une distinction a été faite entre les gènes ordinaires — dont la probabilité d'inactivation prise individuellement peut Être négligée relativement à la probabilité d'inactivation du phage entier — et quelques centres vulnérables ou gènes dont la probabilité d'inactivation ne pourrait Être négligée.L'hypothèse de l'existance des centres vulnérables s'est démontrée nécessaire à l'explication des résultats expérimentaux de M.Dulbecco.Die Wahrscheinlichkeit der Reaktivation durch multiplen Infektionen ist unter Voraussetzung, dass die Ultraviolett-Bestrahlung kleine Teile der Bakteriophagenchromosomen inaktiviert, berechnet. Das Ergebnis entspricht den experimentellen ResultatenDulbecco's.In der mathematischen Behandlung des Problems ist ein Unterschied gemacht worden zwischen gewöhnlichen Genen — wovon jeder eine geringe Wahrscheinlichkeit der Inaktivierung hat, in Bezug auf die Wahrscheinlichkeit der Inaktivierung der ganzen Bakteriophage — und einige verletzbare Stellen oder Genen, wovon die Wahrscheinlichkeit der Inaktivierung grössenordnungsmÄssig höher liegt. Die Hypothese über die verletzbaren Stellen war notwendig um die experimentellen ResultateDulbecco's zu erklÄren. (shrink)

it is not unusual to interpret Friedrich Nietzsche’s philosophy, or some of his claims, as a therapeutic thought nowadays.1 Nietzsche’s perspectivism, style, and controversial doctrines are supposed to do something, rather than merely teach or state a theoretical position. The legitimacy of this action and its actual goal are far from self-evident, however. This paper tackles the problem from the perspective of a fundamental tension, which is at work underneath Nietzsche’s project since The Birth of Tragedy: that is, the tension (...) between multiplicity and singularity, respectively personified, in that book, by the figures of Dionysus and Apollo. When it comes to ethics, this dimension of Nietzsche’s thought is... (shrink)

We extend prior research of deceitful behavior by studying the reactions of those who are targets of deception and how a specific attribute of communication media, cue multiplicity , influences such reactions. We report on a laboratory experiment involving dyads asked to engage in a stock share purchase exercise. We find that when a broker is perceived to act deceitfully by the buyer, the buyer reacts with negative affect (anger) which provokes subsequent acts of revenge against the broker. Importantly, (...) we find that media with higher cue multiplicity attenuate buyer anger as well as lessen the propensity for the buyer to seek retaliatory acts of revenge. We further find that moral anger mediates the effect of buyers’ perceived deception on revenge. (shrink)

Burned at the stake for heresy, Giordano Bruno (1548-1600) was one of the Renaissance's more controversial thinkers. Current scholarship tends to read Bruno as either a Neo-Platonist who ultimately collapses reality to an overarching unity, or as an eclectic thinker whose disparate and disjointed musings are essentially incoherent. By closely and critically examining Bruno's writings this book demonstrates that Bruno was very much in the spirit of Modernity in that he tried to explain philosophically the possibility of the coexistence of (...) unity and multiplicity (difference) through the «then-scientific» logic of the coincidence of opposites. His metaphysics, cosmology and ethical thinking are to be understood through this underlying logic of coincidence, thereby rendering Bruno neither an absolute Neo-Platonist nor unintelligible. (shrink)

This work argues from a social-theoretical perspective for the view that every concept of 'gender' remains bound to reproduction. As every culture is interested in its continuity, it distinguishes individuals according to their assumed possible contribution to reproduction and so develops a fundamental dual classification. Subsequent gender categories are necessarily derived from this one. The conceptual and empirical arguments for this thesis are illustrated through an imagined dystopia. There I envision under what conditions a complete dissociation of the concepts 'sex' (...) and 'gender' from the old dual distinction would be possible and in what way a multiplicity of genders would be accomplished. (shrink)

This work argues from a social-theoretical perspective for the view that every concept of 'gender' remains bound to reproduction. As every culture is interested in its continuity, it distinguishes individuals according to their assumed possible contribution to reproduction and so develops a fundamental dual classification. Subsequent gender categories are necessarily derived from this one. The conceptual and empirical arguments for this thesis are illustrated through an imagined dystopia. There I envision under what conditions a complete dissociation of the concepts 'sex' (...) and 'gender' from the old dual distinction would be possible and in what way a multiplicity of genders would be accomplished. (shrink)

This unpublished 1990 preprint argues that a crucial distinction in discussions of the many-worlds interpretation of quantum mechanics (MWI) is that between versions of the interpretation positing a physical multiplicity of worlds, and those in which the multiplicity is merely psychological, and due to the splitting of consciousness upon interaction with amplified quantum superpositions. It is argued that Everett's original version of the MWI belongs to the latter class, and that most of the criticisms leveled against the MWI, (...) in particular that it is illogical or incoherent, are not valid against such "psychological-multiplicity" versions. Attempts to derive the quantum-mechanical probabilities from the many-worlds interpretation are reviewed, and Everett's initial derivation is extended in an attempt to show that these are the unique possible probabilities. But there remains a challenge for proponents of the MWI: to show that their interpretation requires probabilities, rather than merely nonprobabilistic indeterminacy. A 2002 preface, revised in 2004, briefly discusses the extent to which I still agree with the claims in the paper. While its derivation of probabilities used, and failed to justify, noncontextuality, I still agree with the paper's general interpretation of the MWI, though not with the MWI itself. (shrink)

In this paper, I present a new reading of Simone de Beauvoir’s first major work, L’Invitée ( She Came to Stay ), in order to reveal the text as a vital place of origin for feminist phenomenological philosophy. My reading of L’Invitée departs from most scholarly interpretations of the text in three notable respects: (1) it is inclusive of the “two unpublished chapters” that were excised from the original manuscript at the publisher’s request, (2) it takes seriously Beauvoir’s claim that (...) phenomenological philosophy is often better expressed in novels than essays or treatises, and (3) it views the novel’s main characters, Françoise and Xavière, as one woman who has multiple, contradictory, excessive selves. Thus approached, L’Invitée provides us with a thick description of one woman’s embodied consciousness and thereby shows us with specificity what a consciousness whose underlying structures reflect sexual difference looks like. This consciousness not only experiences itself as being both gendered, categorized, disciplined, and defined and in excess of these genders, categories, disciplines, and definitions at the same time, but also experiences its own self-relation through the presence of multiple selves who are each simultaneously attracted to and negating of the other. As such, the defining features of this consciousness involve experiences that I have respectively labeled “ontological multiplicity” and “auto-jealousy.”. (shrink)