In the paper, it is investigated whether for real argument s the (s − 1)n+1 weighted Riemann zeta function ζ(n)(s) limits s ↓ 1 do exist. Here we will look only at n =0,1. The answer to the question could very well be that assuming existence of limits to be true gives a conflicting outcome. This result may support the possibility of what can be called incompleteness in concrete mathematics. Interestingly, the uncovered incompleteness occurs in an approximation-theoretical framework. (...) The key argument we employ in the paper revolves around the approximation of a l’H ˆopital limit. Only an “after the fact” alternative approach reorders the formulae in the derivation. This reordering is, in fact, based on a 0=1contradiction as starting point. However,the alternative 0=1based approach is not the limit approximation that is used in the flow of the derivation in the present paper. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.3 (2001) 437-438 [Access article in PDF] Michael V. Wedin. Aristotle's Theory of Substance: The Categories and Metaphysics Zeta. Oxford Aristotle Studies. New York: Oxford University Press, 2000. Pp. xiii + 482. Cloth, $55.00. Michael Wedin has written the equivalent for Aristotle of what biblical scholars would call a "harmony of the gospels." It is a wonderfully rich and argumentatively dense reconstruction (...) of Aristotle's two most important treatises on substance, the Categories and Metaphysics Zeta, works that many of our most able Aristotle scholars have declared irreconcilable.The first chapter, on "the plan" of the Categories, includes a sensible account of the role in that work of the "onymies," as Wedin calls homonymy, synonymy, and paronymy. The second chapter, which focuses on "nonsubstantial individuals" in the Categories, gives the most philosophically sophisticated reconstruction known to me of how Aristotle might have conceived this white in Socrates to be a nonrecurrent particular. Having myself contributed to the glut of recent scholarship on nonsubstantial individuals in the Categories, I have personal, as well as professional, reasons to praise the rigor and insight of this chapter.In Chapter 3 Wedin tries to pin down the ontological commitment of Aristotle's Categories. Since, if there were no primary substances there would not be anything else, the fundamental ontological commitment of the Categories is a commitment to primary substances. Individual nonsubstances exist just in case there are primary substances in which they inhere. As for species and genera of substances and species and genera of the nonsubstantial individuals that inhere in them, Wedin finds Aristotle curiously indifferent to their existence.Chapter 4, a transitional chapter, takes up a range of possible views on the relation between the Categories and Metaphysics Zeta. Incompatibilism is argued against, yet the arguments for compatibilism in recent commentaries are found to be insufficient. In the next chapter Wedin moves on to his own statement of, and justification for, compatibilism.The key to Wedin's compatibilist interpretation is the distinction he draws between being a substance and being the "substance-of" something. Zeta can then be seen to be supplementing, rather than revising, let alone contradicting, the Categories, if Zeta can be understood to be about the substance-of the primary substances of the Categories (157-8).Aristotle proposes in Z3 three candidates for what the substance of, say, Socrates, is, namely, his matter, his form, and the compound of the two. Aristotle settles on form and discusses form as essence in Z4 and Z5, which discussion Wedin takes up in his own [End Page 437] Chapter 6. Then in Chapter 7 Wedin takes on the enigmatic claim of Z6, "In the case of things that are primary and spoken of per se, it is clear that the thing and the essence of the thing are the same" (1032a4-6).Wedin makes Chapter 8, which is primarily a treatment of Z10 and Z11, a discussion of Aristotle on "compositional plasticity," that is, on whether, say, the form of human being might be realized in something other than flesh and bones. "[O]ne could grant," Wedin writes, that to be a human being is just to be a member of a determinate biological species and so to have a very specific material nature, and yet insist that the form of such creatures be realizable in quite different sorts of matter. Creatures so constituted would not be human beings but they would be entities with similar functional capacities and states... From the point of view of philosophy of mind, for example, what matters are the psychological capacities, functions, and states characteristic of persons. Just what these are is determined by a form—the form that happens to be realized in human matter. (340-41) In Chapter 9 Wedin turns to Z13, which, as he acknowledges, has often been thought to be the most confounding chapter in Zeta. Wedin draws on Z16 to help resolve the aporia with which Z13 ends (roughly this... (shrink)

Adolf Hurwitz’s estate contains a note from the early 1880s on the converse to Riemann’s proof of the functional equation for the zeta-function; this idea has later been elaborated by Hans Hamburger for a characterization of the zeta-function by its functional equation and by Eugène Cahen and Erich Hecke with respect to modular forms. In this note, we present Hurwitz’s reasoning and comment on the historical context.

This paper revisits one of the first models of analog computation, the General Purpose Analog Computer . In particular, we restrict our attention to the improved model presented in [11] and we show that it can be further refined. With this we prove the following: the previous model can be simplified; it admits extensions having close connections with the class of smooth continuous time dynamical systems. As a consequence, we conclude that some of these extensions achieve Turing universality. Finally, it (...) is shown that if we introduce a new notion of computability for the GPAC, based on ideas from computable analysis, then one can compute transcendentally transcendental functions such as the Gamma function or Riemann's Zeta function. (shrink)

With Fermat’s Last Theorem finally disposed of by Andrew Wiles in 1994, it’s only natural that popular attention should turn to arguably the most outstanding unsolved problem in mathematics: the Riemann Hypothesis. Unlike Fermat’s Last Theorem, however, the Riemann Hypothesis requires quite a bit of mathematical background to even understand what it says. And of course both require a great deal of background in order to understand their significance. The Riemann Hypothesis was first articulated by Bernhard Riemann in an address (...) to the Berlin Academy in 1859. The address was called “On the Number of Prime Numbers Less Than a Given Quantity” and among the many interesting results and methods contained in that paper was Riemann’s famous hypothesis: all non-trivial zeros of the zeta function, ζ(s) = ∞ n=1 n−s, have real part 1/2. Although the zeta function as stated and considered as a real-valued function is defined only for s > 1, it can be suitably extended. It can, as a matter of fact, be extended to have as its domain all the complex numbers (numbers of the form x + yi, where x and y √ −1) with the exception of 1 + 0i (at which point are real numbers and i =. (shrink)

New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point correlation function. Their behavior results from two different contributions. One corresponds to (universal) random matrix eigenvalue fluctuations, the other to diffusive or chaotic characteristics of the corresponding classical motion. A closed formula expressing spacing autocovariances in terms of classical dynamical zeta functions, including the Perron–Frobenius operator, (...) is derived. It leads to a simple interpretation in terms of classical resonances. The theory is applied to zeros of the Riemann zeta function. A striking correspondence between the associated classical dynamical zeta functions and the Riemann zeta itself is found. This induces a resurgence phenomenon where the lowest Riemann zeros appear replicated an infinite number of times as resonances and sub-resonances in the spacing autocovariances. The theoretical results are confirmed by existing “data.” The present work further extends the already well known semiclassical interpretation of properties of Riemann zeros. (shrink)

This volume contains the proceedings of the conference "Casimir Force, Casimir Operators and the Riemann Hypothesis – Mathematics for Innovation in Industry and Science" held in November 2009 in Fukuoka. The conference focused on the following topics: Casimir operators in harmonic analysis and representation theory Number theory, in particular zeta functions and cryptography Casimir force in physics and its relation with nano-science Mathematical biology Importance of mathematics for innovation in industry.

We construct Hrushovski–Kazhdan style motivic integration in certain expansions of ACVF. Such an expansion is typically obtained by adding a full section or a cross-section from the RV-sort into the VF-sort and some extra structure in the RV-sort. The construction of integration, that is, the inverse of the lifting map , is rather straightforward. What is a bit surprising is that the kernel of is still generated by one element, exactly as in the case of integration in ACVF. The overall (...) construction is more or less parallel to the main construction of Hrushovski and Kazhdan , as presented in Yin and Yin . As an application, we show uniform rationality of Igusa zeta functions for non-archimedean local fields with unbounded ramification degrees. (shrink)

We investigate the degree spectra of computable relations on canonically ordered natural numbers $$(\omega,<)$$ ( ω, < ) and integers $$(\zeta,<)$$( ζ, < ). As for$$(\omega,<)$$( ω, < ), we provide several criteria that fix the degree spectrum of a computable relation to all c.e. or to all$$\Delta _2$$ Δ 2 degrees; this includes the complete characterization of the degree spectra of so-called computable block functions that have only finitely many types of blocks. Compared to (...) Bazhenov et al. (in: LIPIcs, vol 219, pp 8:1–8:20, 2022), we obtain a more general solution to the problem regarding possible degree spectra on $$(\omega,<)$$ ( ω, < ), answering the question whether there are infinitely many such spectra. As for $$(\zeta,<)$$( ζ, < ), we prove the following dichotomy result: given an arbitrary computable relation R on$$(\zeta,<)$$( ζ, < ), its degree spectrum is either trivial or it contains all c.e. degrees. This result, and the proof techniques required to solve it, extend the analogous theorem for$$(\omega,<)$$ ( ω, < ) obtained by Wright (Computability 7:349–365, 2018), and provide initial insight to Wright’s question whether such a dichotomy holds on computable ill-founded linear orders. This article is an extended version of Bazhenov et al. (in: LIPIcs, vol 219, pp 8:1–8:20, 2022). (shrink)

The initial dilemma. I.1. The gradual rise of the Metaphysics. I.2. A bold contribution from textual history. I.3. A new perspective on late ancient commentaries. I.4. First philosophy or Metaphysics? I.5. Can tradition be ignored? II. ‘Being’ and οὐσία at the core of Aristotle’s theoretical research. II.1. Ontology as a science of ‘being’ in Aristotle: “What is X?” in the foreground. II.2. The first caveat: the copula function of Aristotle’s ‘being’. II.3. The definite article τό as quotation marks before (...) the flexed forms of ‘be’: τὸ ὄν, τὸ εἶναι, τὸ ἔστιν. II.4. Further explanations about Aristotle’s ‘being’. III. Οὐσία, the core of Aristotle’s theoretical philosophy. III.1. οὐσία and the criterion of pre‑eminence as Plato’s legacy. III.2. The dialectical roots of ontology. III.3. οὐσία from Zeta to Lambda. III.4. οὐσία as essence and οὐσία as substance. III.5. οὐσία as a syntactical core; the word’s etymology. III.6. οὐσία as the first sense of being in Aristotle’s first philosophy. III.7. Ontology as science, science of the science. IV. Historicizing: the semantic gap. IV.1. Editorial tradition: ontology and οὐσία as a fil rouge in the order of Metaphysics books. IV.2. οὐσία in the first century B.C. IV.3. οὐσία by Alexander of Aphrodisias. IV.4. Metaphysics and its purpose: the role of the Lambda book. IV.5. Being and οὐσία: a relationship lost over time. IV.6. The Aristotelian tradition as a way to cooperation. (shrink)

Chapters 10 and 11 are critical to the argument of Metaphysics Zeta: these chapters are concerned with the purification of form. Z.10 introduces the apparatus of part and whole and consists of an argument to the end that form and its parts have priority over the other internal structural components of c‐substances, i.e. matter and the compound of form and matter; while in Z.11 Aristotle argues that form and its parts cannot involve any admixture of matter. Wedin argues that (...) the causal role of form presupposes its purity: if form is to explain why a certain portion of matter constitutes a c‐substance of a given kind, then matter—whether this latter is understood as functional, or remnant matter—cannot already be contained in the form. This is the ‘purity thesis’, as Wedin calls it: matter cannot be included in the definitions of natural organisms, Wedin points out, because that would make the explanandum a part of the principle that explains it. Wedin also argues that form must be sufficiently complex to provide definitions of the natures of particular compounds, which are complex, even though form itself is a kind of universal. (shrink)

I compare Plato’s and Husserl’s accounts of the non-original appearance and the original with a focus on their methodologies for distinguishing between them and the phenomenological—i.e., the answer to the question of the what and how of their appearance—criteria that drive their respective methodologies. I argue that Plato’s dialectical method is phenomenologically superior to Husserl’s reflective method in the case of phantasmata that function as apparitions. Plato’s method has the capacity to discern the apparition on the basis of criteria (...) that appeal solely to its appearance, whereas Husserl’s method presupposes a non-apparent primitive distinction between the original qua primal impression and the phantasm as its reproductive modification. On the basis of Plato’s methodological superiority in this regard, I sketch a reformulation of the Husserlian approach to appearances guided by the original interrogative context of Plato’s dialectical account of the distinction between true and false appearances, eikones and phantasmata. (shrink)

What is the role of gestures within the wider problem of corporeity in Maurice Merleau‑Ponty? How do gestures exemplify and complicate the bodily experience? The aim of this article is to investigate the thematic of gesture in Merleau‑Ponty’s production, with particular attention to the Phenomenology of Perception (1945) and the lessons held at the Collège de France about institution, passivity and nature (1954–60), down to the final indirect ontology inThe Visible and the Invisible. Gestures could be understood as forms (Gestalten), (...) i.e. dynamic structures which express individual and collective behaviours, as well as institutions (Stiftungen), underlying the process of sedimentation and reactivation of meanings. In both cases, gestures have a heuristic or generative function: they shape the individual style in the encounter with the world through “typics” or recurring “motifs”. As a conclusion, the paper argues for the key‑role of gesture, in order to re‑think eidetic intuition as the grasping of operative and emotional essences. (shrink)

Is the relationship of self-moving (kinaesthesis) to itself a direct pre-reflective self-awareness, or is it mediated through an Other? This article attempts to address this question, taking the phenomenon of dance as a point of departure, since in dance, movement steps out of its everyday background function to become the principal theme. Rudolf zur Lippe extracts from a dance step of the dances of the Quattrocento, the posa, a concept of sensual reflection. Rather than a conceptual reflection, the posa (...) can be understood as an awareness of one’s own movement. In this article, in a dialogue between critical philosophy, dance science, and phenomenology, terms of a possible sensual reflection in dance will be discussed. (shrink)

This paper intends to identify the functions of the French particle “comme” (“like” in opposition to “as”) and “comme si” (“as if”) in the work of French contemporary philosopher Jean-Luc Marion, especially in L’idole et la distance (American translation: The Idol and Distance), Dieu sans l’être (American translation: God without Being), Étant donné (American translation: Being given) and De surcroît (American translation: In excess). The author of this paper focuses on the relation between phenomenology and theology in order to demonstrate (...) its complexity by an analysis of linguistic phenomenology. At the end of this analysis, the “saturated phenomenon”, as proposed by Jean-Luc Marion, becomes an important notion to understand the boundaries of both disciplines, phenomenology and theology. (shrink)

Jan Patočka thought travels on the parallel rails of a-subjective phenomenology and the care of the soul. For the most part, their parallel supportive function remains unproblematic. However, in order to appreciate the significance of Patočka’s contribution to the history of philosophy and the stakes of its undertaking, the alignment of the rails must be tested: how can a phenomenology, which strives to dislocate the subject from its experiential privilege, attempt to bring the soul into both the onto-epistemic as (...) well as the ethico-political epicentre? By revising Platonism, Patočka wagers an ambitious, fragile answer, which opens nothing less than the space of freedom. (shrink)

From the hermeneutics of facticity to phenomenological destruction, Heidegger’s constant effort has been to achieve a non-metaphysical, pre-theoretical methodology of philosophy. His ideas finally lead to the development of the method of formal indication. In this essay, I will consider first the methodological function of historical things, in order to illustrate the method of destruction. Then, I will explain the definition of philosophy from the point of view of formal indication, thereby showing how different this method is from traditional (...) philosophical methods. Finally, I will analyse the importance of this transformation of methodology, in order to reveal in which sense a concrete universality is possible and how it contributes to the foundation of the ontology of life. (shrink)

Theodor Lipps’ doctrine of empathy (Einfühlung) is enjoying renewed relevance today for two reasons. On the one hand, it offers heuristic potential in researching the functionality of mirror neurons. On the other hand, as many of the early phenomenologists gained their conceptions of empathy by examining Lipps’ related works, the presently widespread interest in empathy necessitates a re‑reading of Lipps in phenomenological circles. The critiques that phenomenology launches against Lipps, however, often remain bound to the established cliché interpretations of Lipps. (...) This article counters such shortsighted readings by differentiating four kinds of imitation in Lipps. The supposed persuasiveness of such critiques, as will be shown, is lost in light of this differentiation. (shrink)

Husserl focused perhaps more than any other philosopher on the relationship between philosophy and psychology. This problem was important to him because the European project of universal science must include sciences of consciousness that address questions of meaning, value and purpose so crucial for humanity. This paper provides a sketch of the later Husserl’s thinking on this issue in order to clarify the relationships among transcendental philosophy as the mother of the sciences, psychology as the foundational mental science, and the (...) various regional sciences of persons. Radicalizing and extending the transcendental tradition to free philosophy from naturalism, Husserl developed methods and fundamental concepts for understanding consciousness in its distinctive world constituting function. In parallel fashion, Husserl traced the historical failures of psychology to its naturalistic philosophy, from which he liberated the discipline by means of phenomenological reflections on the intentional property of its subject matter. This pure focus on mental processes resulted in the clarification of the transcendental phenomenological foundation of psychology as well as a recognition of the paradoxical manner in which psychological processes are both world constituting and mundanely present in the lives of persons. The apperceptive synthesis of transcendental consciousness and mundane embodiment in the identification of the person is proposed as essential for a non-naturalistic, intentional psychology, which provides appropriate concepts and the method of intentional analysis for such sciences of persons as sociology, history, literary studies, and religious studies. The problems, means, and inevitable inadequacies of communicating transcendental insights in language are discussed. Analysis of the complexity of living persons discloses their transcendental dimension in the manifolds their mundane activities and in their products, including use, cultural, and art objects as well as social institutions. Attention is drawn to resources in phenomenology beyond Husserl and in the genuine psychological intuitions of non-phenomenologists for generating non-naturalistic, phenomenologically grounded person sciences. (shrink)

This paper explores how whiteness as the transcendental norm shapes the meaning structure of Black-being-in-the-world. If home is a place, a site, a dwelling of acceptance, where one is allowed to feel safe, to relax, to let one’s guard down, then being Black in white supremacist America is anathema to being at home for Black people. Indeed, to be Black is to be a stranger, something “strange,” “scary,” “dangerous,” an “outsider.” To be Black within white America belies what it means (...) to dwell, to reside, to rest. In other words, one’s sense of racialized Black embodiment remains on guard, unsettled, hyperalert. Phenomenologically, there is a profound sense of alienation, where one’s racialized body is ostracized and shunned. On this score, I examine, within the mundane context of an elevator, how the dynamics of intersubjectivity and sociality are strained through the dynamics of the white gaze. The white gaze, among other things, functions to police the meaning of the Black body and attempts to de-subjectify Black embodiment. In this way, the only real perspective is white. Black bodies are deemed devoid of a perspective on the world as there is no subjectivity, no sense of agential meaning making. One might say that Black people, on this view, constitute an essence, a typified mode of being. Unlike the existentialist thesis where existence precedes essence, Black people are locked into an objecthood, a fungible and fixed essence. This racial and racist myth is what, for Schutz, would collapse the importance that he places on intersubjectivity and sociality. Indeed, within this paper, I delineate the threatening, necro-political dimensions of whiteness that I experienced after writing the well-known article “Dear White America.” That experience cemented, for me, and for many other readers, what it means to occupy the residence of whiteness, an abode that can take one’s life in the blink of an eye. The experience of the racialized stranger means walking a tightrope, a precarious situation where one flirts with death, where one’s body is deemed hypersexual, inferior, frightening, and monstrous. Based upon this construction, the white body is deemed the site of virtue, safety, deliverer, protector of all things white and pure. Think here of “the white man’s burden” or the idea of “white manifest destiny.” Stain, blemish, taint, and defilement are indelible markers of the stranger. And based upon the logics of racial purity, one must extinguish the “vermin,” the “criminals,” the “rapists.” While I don’t explore this within the paper, Schutz scholars will immediately recognize the genocidal implications of what would have been at stake for Schutz had he not escaped Adolf Hitler’s anti-Semitic gaze and his Anschluss of Austria. My sense is that Schutz would have understood not just the horrors of white racism but would appreciate the necessity of theorizing the need to rethink home as existentially capacious and intersubjectively vibrant. I conclude this paper by thinking through the concept of “breakdown”, delineating its spatial, phenomenological, and subjectively embodied implications. Breakdown, as I use the term, upends forms of white racialized habituation, creating possible embodied psychic space for what I term un-suturing, which involves undoing the machinations of white safety in the face of alterity, where the stranger invokes wonder and self-critique. (shrink)

The enumeration of the “principal passions” in the articles 53 to 67 of the Passions of the Soul is generally regarded as laborious and unclear. This article opposes to this view and proposes elements to make sense of Descartes’ enumerative procedure. First, it clarifies the nature and function of what is called “ordered enumeration”: it amounts to a methodical act of collecting which must not be confused with a cognitive sequence based on determinate principles. The article also suggests that (...) the paragraph 52 of the Passions provides relevant indications to account for the structure of Descartes’ discourse. Indeed, different ordering criteria can be deduced from the under­standing of what the emotional object is, and from Descartes’ emotional subject as a “mind-body union” put into motion by passion. The article finally insists on Descartes’ main novelty: his forty “principal passions” are not exclusively centered on the ego and his desire; on the contrary, the enumeration makes room for other human beings who, being emotional subjects in their own right, play an active role in the develop­ment of the subject’s sentimental experience. (shrink)

“Myth” comprises the first chapter of the book, The Logic of the Imagination, by Miki Kiyoshi.In this chapter Miki analyzes the significance of myth (shinwa) as possessing a certain reality despite being “fictions.” He begins by broadening the meaning of the imagination to argue for a logic of the imagination that involves expressive action or poiesis (production) in general, of which myth is one important product. The imagination gathers in myth material from the environing world lived by the social collectivity. (...) Its formation of images (Bilder) expresses the pathos of a people vis-a-vis their environment, but myth also contains elements of logos in the form of intellectual representations and figures. And their combination becomes expressed externally by stimulating and guiding action. In this way Miki argues that myths contain both emotive and kinetic elements, which by moving people to action, are capable of making history. Thus rooted in the symbiosis between individual and social and between society and environment, myth possesses a “historical creativity.” And he also argues that myths can be present with a sense of reality at any epoch in history, even today, wherever and whenever their primeval power is felt to function, “drawing out” a new reality, a new world, out of the natural world. (shrink)

In the years after the first circulation of Sidereus Nuncius, Galileo’s Padua anti-Copernican colleague, the staunch Aristotelian philosopher, Cesare Cremonini, published a book on ‘traditional’ cosmology, Disputatio de coelo in tres partes divisa which puzzled the Roman authorities of the Inquisition and the Index much more than any works on celestial novelties and ‘neo-Pythagorean’ astronomy. Cremonini’s disputation on the heavens has the form of an over-intricate comment of Aristotle’s conceptions, in the typi­cally argumentative style of Scholasticism. Nonetheless, it immediately raised (...) the concern of Cardinal Bellarmin, the Pope and other Inquisitors. At a close reading, Cremonini’s interpretation of Aristotle’s cosmos proved radically anti- Christian. It represented a radicalization of Pomponazzian Alexandrism. In fact, Cremonini did not only circulate Aristotelian principles used by Pom­ponazzi to argue for the soul’s mortality. He also wiped away all transcendence from the Aristotelian cosmos. In fact, he marginalized the function of the motive Intelligences by explaining heavenly motions through the action of animal-like inseparable souls although he did not erase nor reduced all Intelligences to only one, in accordance with Alexander. Also, he put at the center of Aristotle’s cosmos the idea of its eternity, a thesis which he explicitly connected with the rejection of the idea of God the Creator. Cremonini assumed that the univer­sal efficiens, that is the efficient cause of all motion and change in the world, is nothing but the first heaven. As a result of this radically naturalist reading of Aristotle, he banned God from the cosmos, reduced Him to the final cause of the world, and deprived Him of any efficiency and will. This essay on less ex­plored sources of Renaissance astronomical debates considers the institutional, cultural and religious setting of Cremonini’s teaching and conceptions. It as­sesses the reasons for his troubles with the religious authorities, and the politi­cal support he was granted by the Serenissima Republic of Venice inspite of the scandalous opinions he circulated as a university professor. My reconstruction of his views is based on the Disputatio de coelo of 1613 and later works, which are directly connected with cosmo-theological polemics with the religious au­thorities: his Apologia dictorum Aristotelis de quinta coeli substantia and the unpublished book De coeli efficientia, two manuscript copies of which are preserved in the libraries of Padua and Venice. (shrink)

Simondon’s poorly examined theory of imagination reveals a number of interesting possibilities. On the one hand, by grounding the function of images within the idea of a cycle, it provides an attempt of reconciliation between the assumptions that privilege either reproduction or creativity. On the other hand, his view might also be conceived as a serious alternative to various theoretical stances that characterize the problem of imagination strictly within a dichotomy between individual subject and social imaginaries. The paper proposes (...) a reading of Simondon’s lectures given between 1965 and 1966 in Sorbonne in the broader context of his philosophy and outlines the role of imagination that exceeds imagining subject as well as establishing the mode of correlation with associated milieu, which performs the conditioning of its potentiality. Rejecting the primacy of representation, Simondon’s take enables one to draw the conclusion that imagination can be attributed to all living beings and conceived as the function of life. (shrink)

In the practical philosophy of the Discours de la Méthode, before the theoretical metaphysics of Part Four and the Meditationes, Descartes gives us an inductive argument that his method, the procedure and cognitive psychology, is veracious at its inception. His evidence, akin to his Scholastic predecessors, is God, a maximally perfect being, established an ontological foundation for knowledge such that reason and nature are isomorphic. Further, the method, he tells us, is a functional definition of human reason; that is, like (...) other rationalists during this period, he holds the structure of reason maps onto the world. The evidence for this thesis is given in what I call the groundwork to Descartes’ philosophical system, essentially the first half of the Discours, where, through a series of examples in the preamble of Part Two, he, step-by-step, ascends from the perfection of artifacts through the imposition of reason to the perfection of a constituent’s use of her cognitive faculties, to God perfecting and ordering reality. Finally, he descends, establishing the structure of human reason, which undergirds and entails the procedure of the method. (shrink)

Alfred Schutz elaborated Edmund Husserl’s term of appresentation to a particular theory of appresentational relations comprising “marks”, “signs”, “symbols” and “indications”. Even though Schutz implied the existence of other such relations, it was Husserl who drew a line between appresentation and proof. Following this differentiation, this paper aims to constitutionally analyse the everyday life phenomenon of proof and to describe its structure by consulting William James’ term of “knowledge about” as well as by discussing Schutz’ theory of relevance. With reference (...) to Husserl’s Logical Investigation and by contrasting proof with indication it is shown that proof is appresentationally constituted through reflectively bringing the polythetical elements of clear, distinctive and consistent knowledge about, functioning as interpretational relevance, into the centre of topical awareness. (shrink)

The thorny issue of the created status of eternal verities, a hypothesis initially promulgated by Descartes in his 1630 correspondence with Mersenne, generated widespread debates across confessional lines in 17th century philosoph­ical and theological circles. At stake was not only the necessary or contingent status of these truths, and thus God’s relationship with creation, but also the very nature of the Deity. This was certainly the case for the Cambridge Platonists Henry More and Ralph Cudworth. Both were early advocates of (...) Descartes’ philosophy, while still critical of some of its assumptions. The doctrine of the creation of eternal truths represents such an instance, and it was a highly sensitive topic for both. I shall propose a scholastic context in which to situate some of their ideas in order to shed some light on how this issue was addressed in More and Cudworth. The position where eternal truths are arbitrarily instantiated by the mere fiat of God is avoided by the Cambridge Platonists in two ways. First, the immutable, necessary, and eternal status of these ideas is safeguarded by the premise that they are intrinsic to the divine essence insofar as it is intellectual. We shall see that this raises a question concerning their precise ontological status. Second, the function of these ideas as the framework of the created order is guaranteed by the perfec­tion of the divine will. This will require a clarification of the causal relationships existing between eternal truths, God, and the realm of creation. (shrink)

The particularly significant theory of the symbol of Alfred Schutz is based on a combination of the two perspectives of phenomenological individualism and pragmatic realism. This theory on the one hand explains processes of symbolic meaning constitution from a phenomenological viewpoint, specifically following Edmund Husserl. On the other hand it demonstrates the functioning of symbols through pragmatic social action, which is relevant for symbolic reality construction. The paper elaborates both perspectives within the Schutzian theory of the symbol with reference to (...) diverse interpretations of Franz Kafka’s novel The Castle. It outlines the decisive capacity of symbols to overcome and harmonize diverse and often contradictory meanings that are expressed and at the same time united by the symbol itself. (shrink)

Historia, as both a type of critical inquiry and a source of information about nature and the human world, is a key category in Spinoza’s Tractatus theologico-politicus. In this work, the Latin word cannot be simply and invariably translated as “history,” not even if we add the proviso that its meaning wavers inevitably between “history” and “story,” for its semantic range is too broad and complex. At the two ends of the semantic spectrum we have the impartial report, on the (...) one hand, and the creations of sheer fantasy, on the other. Historia may therefore denote the detached observation of nature and the philological analysis of a text, but it can also refer to the free exercise of the imagination in a variety of narrative contexts. While Spinoza denies that the inquiry resulting from historia and its products may have true cognitive value, he acknowledges that historia plays a fundamental role in society and politics. The reason is that historia and the imagination are bound up together by a special relationship. This is apparent at all levels of the historical engagement with reality, but is particularly true in the case of religion, moral norms and belief systems, for in this variegated domain the link between imagination and historia functions as the connective tissue that keeps societies united and functioning. This specific nexus of imagination and historia is Spinoza’s original contribution to the early modern notion of “moral certainty.” More importantly, it is only at this level that Spinoza grants a modicum of intelligibility to the ‘historical’ productions of the imagination, be they signa, revelationes, or even nugae. The fact remains, though, that to a certain extent humans keep having a distorted grasp of reality, indeed hallucinate, even when their ‘historical’ accounts of reality are socially and politically productive. Here the key element is the notion of fictional continuity based on a socially constructed trust in narrative accounts of reality: the imagination turns reality into stories, but in so doing it keeps the otherwise constitutively hallucinatory nature of humans at bay and under control. Perceptibilitas, that is, the ability to provide acceptable cognitive solutions between intelligible knowledge and moral certainty, is ultimately what defines the contribution of the imagination to the human work of knowledge. (shrink)

Aristotelian imagination is widely understood as a psychological power by which retained perceptual states recur in consciousness. According to this view, imagination is decaying sense, a part of the psyche that is parasitic on perceptual acts for its content. This paper disputes this reading and provides an alternative account of Aristotle’s concept of imagination. I argue that Aristotelian imagination is a power of the psyche that is both productive like intellect, and presentational like perception. Unlike perception and intellect, however, imagination (...) does not correctly discriminate among beings, and thus cannot be relied upon to give one knowledge of the world. When one accepts this alternative conception of Aristotelian imagination, it becomes clear how it can take on the peculiar epistemic function of allowing a particular serve as the vehicle of a universal thought. This paper argues that Aristotle’s explanation of valid judgments in geometry depends on the imagination to allow the perception of a particular diagram to give rise to the intellectual grasp of a general proposition. (shrink)

This paper suggests that Alfred Schutz’s account of systems of typi­fication together with Sara Ahmed’s account of the proximity of the stranger allows for a different understanding of social integration. The paper proposes to rethink the political and social relationship of the in-group and the stranger, approached through the face-to-face encounter between an integration counselor and an immigrant. The encounter offers a disruption of what is taken for granted by the in-group and functions as a catalyst for a system of (...) reference to appear at all. Through Ahmed’s account on the familiarity and proximity of the stranger, I argue that integration practices are considered to produce, rather than translate, a coherent system of reference for an in-group. The institutionalization of social integration is consequently risking concealing the “unintegratable” stranger rather than offering a solution for the more epistemological dimensions of social exclusion that we find in the experience of sameness and difference. (shrink)

The paper investigates how formal/informal networks of scientists, while facilitating the scientific West-East transfer in the Cold War context, shaped the scientific field of sexology by imposing personal scientific credos, in a particular national context. The paper shows that in the Cold War context, sexual science was present in Communist Romania, but neither as imitation of the regional scholarship, nor as a simple reproduction of western advancements in the field. The post-war Romanian scholarship in the field of sexology was the (...) result of scientific interests of Stefan Milcu – long time party protégée and respected member of the international scientific community – and of its personal circle that included remarkable personalities such as Victor Săhleanu or Tudor Stoica. Presenting the public with information about sexual and re­productive functions, and sometimes even elaborated descriptions of sexual techniques, certainly was never meant to enhance the individual gratification or provoke any form of sexual revolution. The Romanian production of sex/educational manuals and of sexology works was part of a state policy towards a better, stable, family life, aiming for collective and social happiness. (shrink)

Social opposition to instituted policies and practices marks the sites of resistance that populate the contemporary political landscape. Animated by the prospects of a better and more just world, the emancipatory ambitions of social and political movements bring to the fore discrepancies between ideologically congealed power relations and habits of thought and the subversive function of utopian expectations. Paul Ricoeur reminds us that our participation in society is invariably punctuated by our experiences of reality’s noncongruence with imaginative alternatives we (...) can project and upon which we can act. After explaining how literary fictions open spaces for reworking reality, I set out the imagination’s analogous power on the political plane. The struggles with which social and political movements are engaged seek to transform established conventions. Hence, like literary works, these movements aim at refashioning the existing order of reality from within. Protest movements attest to how struggles for recognition combat systemic injustices by holding out the prospect of a different and better future. Consequently, these movements exemplify the power that springs from individuals acting in consort, as evidenced by recent protests against the Trump administration. Conversely, violence destroys power. In view of the way that future expectations animate the force of the present, I therefore argue that dystopic representations of authoritarian regimes in Margret Atwood’s The Handmaid’s Tale and George Orwell’s 1984 fulfill a critical, social function as apocalyptic harbingers of political corruption and deceit. As such, these dystopian novels intensify the force that the present has as a time of crisis and decision. (shrink)

This paper aims to show the logical consistency between the subjective and the intersubjective constitution of meaning in Alfred Schutz by revealing his insight into the dynamic character of reality. In reconstructing what is implied by the proposition “the problem of meaning is a time problem,” this paper reveals that the interrelationship between the past and the present, namely “becoming,” is fundamental to meaning-constitution. By critically introducing the Bergsonian view of the tension between the durée and its symbolization, Schutz thematizes (...) our meaningful reality in the fluidity. From this perspective, the intersubjective world is characterized as a continuous dynamic reality taken for granted by the actors. While subjectivity, as a function of articulating experiences in becoming, is a condition of the intersubjective world, the intersubjective process enables the taken-for-grantedness of subjective reality. Schutzian phenomenology may lead to a theory of the complexity and uncertainty of social reality. (shrink)

__ Inclusive education is complex, multi-faceted and ever-changing and to date there has been no fixed definition of what is meant by the term ‘inclusion’, leading to confusion about what inclusive education actually means in practice. This key text introduces readers to the underlying knowledge and wider complexities of inclusion and explores how this can relate to practice. Considering inclusion as referring to _all_ learners, it surveys the concept of inclusive practice in its broadest sense and examines its implementation in (...) a variety of educational institutions. Throughout the book, international contributors consider this broader concept to critically evaluate the realities of practically implementing inclusive objectives. Each chapter assesses key theories and concepts alongside a range of examples to encourage students to think critically and reappraise their own experience as learners. Key topics covered include: • studying the definition of inclusion • the relevance of pedagogy in inclusive practice • how to lead and manage for inclusion • the issue of inclusion in early years, primary, secondary and post-16 settings • inclusive practice for families • international perspectives on inclusive practice. Fully illustrated with tasks, case studies, discussion questions and recommended reading, _Inclusive Education_ is essential reading for second and third year students looking to extend their research and writing, and to develop their critical and reflective thinking. (shrink)

Wedin discusses Aristotle's claims in Metaphysics Zeta 6 that the essence of a thing is to be sought among its per se attributes, and that each thing that is primary and spoken of per se, e.g. primary substance, is the same as its essence. Wedin argues that the Zeta 6 Thesis, i.e. that the essence of a thing is the thing's immediate essence, is a crucial requirement of the explanatory role of essence as the substance of c‐substances. According (...) to Wedin, Aristotle introduces this requirement in order to establish that a thing's essence cannot depend on another essence. Form must be the essence; if form cannot explain the nature of the thing of which it is the form, there would be the threat of a regress of explanatory forms. At the end of the chapter, Wedin considers the problem that the identity of a thing and its essence is a requirement that can be met by non‐substance items, but he denies that this leads to a dilution of the conception of substance. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.2 (2003) 267-268 [Access article in PDF] Myles Burnyeat. A Map of "Metaphysics" Zeta. Pittsburgh, PA: Mathesis Publications, 2001. Pp. x + 176. Paper, $25.00. Burnyeat's map is an ambitious attempt to establish two claims about Zeta: that Aristotle employs an unusual, non-linear form of argument in Zeta, and that the discussion in Zeta is on two levels, one (...) abstract and "logical" and another specific and "metaphysical." In addition to looking at Zeta, chapter by chapter, Burnyeat examines the other works that provide the context for Zeta—the Organon for the logical level of explanation and the rest of the Metaphysics for the metaphysical level. Burnyeat argues that Aristotle's metaphysical project culminates in the theology of'Lambda, for which the metaphysics of Zeta has prepared us. The goal is to "map" or sketch the evidence for these claims rather than provide definitive arguments for them.A brief introductory chapter presents the main themes of the book. This is followed by an even briefer chapter that sets out the four routes (or independent sections of Zeta), viz. Z 3; Z 4-6, 10-11 with Z 7-9, 12; Z 13-6; and Z 17 with H 1. On all four routes, a logical discussion moves to a metaphysical discussion of form and matter.The third chapter on "signposts" is the lengthiest of all and takes the reader through the chapters of Zeta in order. It is also the most map-like of the chapters, as it requires that the reader have a copy of the Metaphysics ready to hand. Burnyeat follows other commentators in treating Zeta 7-9 and Zeta 12 as later insertions; he does, however, argue that the former and probably the latter were added by Aristotle. Chapters 7-9 are integral to the argument of Zeta, as they provide a diachronic view of artifacts and substantial beings (37). [End Page 267] Rejecting the prominence assigned Z 13 by several recent commentators, Burnyeat reads Z 13 in context with chapters 14-6. "The task of Z 13-6 is to show how the idea that substantial being is a universal such as human leads eventually, after suitable refinements and restrictions, to the conclusion that substantial being is form" (54). Wrapping up the discussion of Zeta, Burnyeat concludes that the goal of Zeta's two-level approach has been to show how logical concepts should be used to search for form.This leads directly to a chapter on the Organon. Burnyeat argues that none of the treatises making up the Organon are metaphysical; all employ an abstract (logical) mode of analysis. Even if written at different times, these treatises belong together because they are all methodological. Since form and matter belong to the metaphysical level, in the Analytics Aristotle "follows a deliberate policy of excluding form and matter" (97).In the final chapter, Burnyeat returns to the Metaphysics and considers Zeta in the context of the other books. Three "chunks," viz. books ABGE, ZHQ, and MN are briefly surveyed. The topics of Zeta are then considered in relation to Lambda. Several chapters, viz. D1 and Z1; D3 and Z 7-9, are found to have the same concerns. Burnyeat concludes with a fanciful muqo~ (story) about a dying Aristotle hastily writing a culminating metaphysical treatise.Burnyeat gives us a map—a map to prompt questions; he does not attempt to delve into many of the interpretative puzzles that have exercised other interpreters of Zeta. Thus, this book stands as a helpful counterbalance to a certain kind of scholarship on Zeta. The two interpretative claims, however, that are at the heart of Burnyeat's enterprise stand in need of further justification. One of these, the non-linearity of Zeta, seems to be too weak to support substantive claims. Burnyeat defines non-linearity as holding when "it is not the case that the successive chapters build continuously upon the results of their predecessors" (4). He then cites a few examples of linearity, e.g., Physics II. Yet the vast majority of Aristotelian... (shrink)

Aristotle's views on the fundamental nature of reality are usually taken to be inconsistent. The two main sources for these views are the Categories and the central books of the Metaphysics, particularly book Zeta. In the early theory of the Categories the basic entities of the world are concrete objects such as Socrates: Aristotle calls them 'primary substances'. But the later theory awards this title to the forms of concrete objects. Michael Wedin proposes a compatibilist solution to this long-standing (...) puzzle, arguing that Aristotle is engaged in quite different projects in the two works. The theory of Metaphysics Zeta is meant to explain central features of the standing doctrine of the Categories, and so presupposes the essential truth of the early theory. The Categories offers a theory of underlying ontological configurations, while book Zeta gives form the status of primary substance because it is primarily the form of a concrete object that explains its nature, and this form is the substance of the object. So when the late theory identifies primary substance with form, it appeals to an explanatory primacy that is quite distinct from the ontological primacy that dominates the Categories. Wedin's new interpretation thus allows us to see the two treatises as complementing each other: they are parts of a unified history of substance. (shrink)

The classic logical positivist account of historical explanation, putting forward what is variously called the "regularity interpretation" (#Gardiner, The Nature of Historical Explanation), the "covering law model" (#Dray, Laws and Explanation in History), or the "deductive model" (Michael #Scriven, "Truisms as Grounds for Historical Explanations"). See also #Danto, Narration and Knowledge, for further criticisms of the model. Hempel formalizes historical explanation as involving (a) statements of determining (initial and boundary) conditions for the event to be explained, and (b) statements of (...) general laws that imply that whenever events of the kind described in (a) occur, an event of the kind to be explained will take place. He admits that in practice historians rarely explain historical events in this way, but instead give only fragmentary "explanation sketches." Such sketches can, however, be "scientifically acceptable," providing it points to where "more specific statements" are to be found (351). An interesting aspect of the article is its "late" positivist, proto‑Kuhnian assertion that "the separation of 'pure description' and 'hypothetical generalization and theory construction' in empirical science is unwarranted" (356). But Hempel does not work out the wider implications of this important conclusion. It is also worth noting that he himself was not much interested in the philosophy of history; other authors took up his model and discussed it within that context. Usefully discussed by #Ricoeur, Time and Narrative, 1:112‑17. (shrink)

This book explains the relationship between intelligence and environmental complexity, and in so doing links philosophy of mind to more general issues about the relations between organisms and environments, and to the general pattern of 'externalist' explanations. The author provides a biological approach to the investigation of mind and cognition in nature. In particular he explores the idea that the function of cognition is to enable agents to deal with environmental complexity. The history of the idea in the work (...) of Dewey and Spencer is considered, as is the impact of recent evolutionary theory on our understanding of the place of mind in nature. (shrink)

Frank A. Lewis presents a close study of book Zeta of Aristotle's Metaphysics, one of his most dense and controversial texts, commonly understood to contain his deepest thoughts on the definition of substance and related metaphysical issues. Lewis argues that Aristotle returns to the causal view of primary substance from his Posterior Analytics.