In cognitive science, there is a tacit norm that phenomena such as cultural variation or synaesthesia are worthy examples of cognitive diversity that contribute to a better understanding of cognition, but that other forms of cognitive diversity (e.g., autism, attention deficit hyperactivity disorder/ADHD, and dyslexia) are primarily interesting only as examples of deficit, dysfunction, or impairment. This status quo is dehumanizing and holds back much-needed research. In contrast, the neurodiversity paradigm argues that such experiences are not necessarily deficits but rather (...) are natural reflections of biodiversity. Here, we propose that neurodiversity is an important topic for future research in cognitive science. We discuss why cognitive science has thus far failed to engage with neurodiversity, why this gap presents both ethical and scientific challenges for the field, and, crucially, why cognitive science will produce better theories of human cognition if the field engages with neurodiversity in the same way that it values other forms of cognitive diversity. Doing so will not only empower marginalized researchers but will also present an opportunity for cognitive science to benefit from the unique contributions of neurodivergent researchers and communities. (shrink)

Husserl?s concept of imagination has been systematically presented in Husserliana XXIII, in which its manifold role has been set out. Through the different texts, the author shows that phantasy should be considered as one of the modifications of pure re-presentation. The article first tries to underline the distinction between Husserl?s deliberation on this phenomenon and the traditional concept of imagination. Second, it shows the fundamental moments of constitu?tional consciousness in order to relate the notion of imagination to perceptual apprehension. (...) At the very end, the notion of phantasy is connected with the idea of first philosophy and the question of possibil?ity of its realization. (shrink)

Manifold learning and effective model building are generally viewed as fundamentally different types of procedure. After all, in one we build a simplified model of the data, in the other, we construct a simplified model of the another model. Nonetheless, I argue that certain kinds of high-dimensional effective model building, and effective field theory construction in quantum field theory, can be viewed as special cases of manifold learning. I argue that this helps to shed light on all of (...) these techniques. First, it suggests that the effective model building procedure depends upon a certain kind of algorithmic compressibility requirement. All three approaches assume that real-world systems exhibit certain redundancies, due to regularities. The use of these regularities to build simplified models is essential for scientific progress in many different domains. (shrink)

Kant is the last classical practitioner of foundationalist epistemology in the Cartesian tradition, a tradition which saw the major problem of the theory of knowledge as one of providing a metaphysical account of the way in which the subjective contents of the individual mind come to have indubitable objective reference. But he is also the inaugurator of a very different approach to epistemology, one that sees methodology or rules of cognitive procedure as fundamental in determining the objectivity of knowledge. An (...) examination of Kant's reconstruction of the traditional form-matter distinction and his application of it to the manifold of intuition in the Critique of Pure Reason brings out the transitional character of his philosophy with particular force, and shows the immense impact of his work on the central epistemological issues of representation, explanation, and justification. While Kant continues to employ the traditional term Vorstellung , he extends its signification beyond that of a subjective mental content to an intersubjectively shared scheme of description. Where he adopts scholastic usage in referring to categories as concepts, he does not regard them as highest genera, but interprets them as rules of connection, thereby providing a logical framework suitable for functional, rather than essentialist explanation. Finally, while retaining in his transcendental psychology the conception of mental activity derivative of the older empirical psychology, Kant still manages to distinguish successfully the previously conflated questions of the causal origins vs. the grounds of justification of knowledge. Consideration of subsequent developments in regard to these issues in the light of Kant's work not only lends a certain amount of support to pragmatic conceptions of the nature of knowledge and its justification, but also suggests some promising directions for future epistemological investigation along evolutionary lines. (shrink)

In this note, we outline a definition of propositional manifold and logical cohomology. An application is also considered for mathematics: two Boole algebras of mathematical propositions are non equivalent if their two cohomologies are not isomorphic.

This exploratory study investigates the manifold conceptions of the internal auditing of risk culture prevalent among four influential actors of the financial sector—regulators, normalizers, consultants, and implementers. By inductive analysis of 20 interviews and 295 documents, we illustrate a two-step interpretive scheme utilized by the four actors in their IA approaches of risk culture: defining broad goals and designing visibility schemes. The visibility schemes were tied to the demarcation, measurement, as well as the IA data collection techniques of risk (...) culture. Our results indicate two dichotomous interpretations among the four actors concerning the IA of risk culture. The first interpretation, prevalent among regulators and implementers, promotes the control of risk culture primarily through verification. The second interpretation, adopted by consultants and normalizers, promotes the control of risk culture by IA along with the empowerment of employees through training programs. Our results not only contribute to understanding IA expansions, specifically to non-tangible domains such as risk culture but also enrich the literature exploring the mechanisms different stakeholders utilize to shape weakly professionalized IA practices. (shrink)

My initial scope will be limited: starting from a neurobiological standpoint, I will analyse how actions are possibly represented and understood. The main aim of my arguments will be to show that, far from being exclusively dependent upon mentalistic/linguistic abilities, the capacity for understanding others as intentional agents is deeply grounded in the relational nature of action. Action is relational, and the relation holds both between the agent and the object target of the action , as between the agent of (...) the action and his/her observer . Agency constitutes a key issue for the understanding of intersubjectivity and for explaining how individuals can interpret their social world. This account of intersubjectivity, founded on the empirical findings of neuroscientific investigation, will be discussed and put in relation with a classical tenet of phenomenology: empathy. I will provide an 'enlarged' account of empathy that will be defined by means of a new conceptual tool: the shared manifold of intersubjectivity. (shrink)

In this paper non-Hausdorff manifolds as potential basic objects of General Relativity are investigated. One can distinguish four stages of identifying an appropriate mathematical structure to describe physical systems: kinematic, dynamical, physical reasonability, and empirical. The thesis of this paper is that in the context of General Relativity, non-Hausdorff manifolds pass the first two stages, as they enable one to define the basic notions of differential geometry needed to pose the problem of the evolution-distribution of matter and are not in (...) conflict with the Einstein equations. With regard to the third stage, various potential conflicts with physical reasonability conditions are considered with a tentative conclusion that non-Hausdorff manifolds are more likely to pass this stage than is typically assumed. When dealing with some of these problems, the modal interpretation of non-Hausdorff manifolds is invoked, according to which they represent bundles of alternative possible spacetimes rather than single spacetimes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 537 tion of his three dialogues, and of course there are several references to Hume's intern= parable Dialogues. The bibliographic essay is useful with respect to general works and period pieces but unfortunately does little to help those who are seeking further help in understanding an individual writer. Professor France's work is an invaluable guide nevertheless for those who realize that authors, even philosophers, do not write (...) in a cultural vacuum. NICHOLASCAPALDI Queens College, CUNY Die Auseinandersetzung yon ldealismus und Realismus in Fichtes Wissenscha/tslehre. By Ingeborg Schfissler. (Frankfurt am Main: Vittorio Klostermann, 1972. Pp. 182. DM 24.50) For Fichte scholars this closely argued and well organized study of the foundations of Fichte's Wissenscha/tslehre is simply a must. American philosophers generally, however, will not become Fichte enthusiasts after reading this book. But this is not the fault of the authoress, but of Fichte. The key question which Dr. SchiJssler raises is, What role does realism play in Fichte's transcendental idealism? With this question in mind she examines Fichte's "foundation of the entire theory of science" of 1794-1795 and related matters, and the "theory of science" of 1804, together with the lecture of 1813. As Fichte originally saw the task of philosophy it was to explain theoretical, i.e., scientific, consciousness in terms of its own foundation. In 1804, however, the task was conceived as presentation of absolute truth; and in 1813, Fichte tried to understand the theory of science as a theory of appearances. Dr. Schfissler's thesis is that all three approaches are necessary; that, in fact, the changes in Fichte's conception of what a theory of science is or ought to be are grounded in the nature of transcendental philosophy itself. The book is not something one reads for relaxation; its sustained and detailed arguments militate against that. But it is a highly illuminating study, and well worth the effort of careful analysis. W. H. WE~mSTBR Florida State University The Manifold in Perception. Theories of Art.from Kant to Hildebrand. By Michael Pedro. (Oxford: Clarendon Press, 1972. Oxford-Warburg Studies) This is a survey of theories of art of Kant, Schiller, Herbart, Hildebrand, Schopenhauer and Fiedler. One may question the value of a re-statement of this sort, over simply another reading of the works of the authors themselves. Pedro's answer may be found in the Preface and again in a more extended statement in the conclusion. "German aesthetic theory from Kant through to the end of the nineteenth century seemed to contain valuable critical ideas quite absent from contemporary philosophical writing." Pedro's attempt has been to "re-locate notions in current use, like 'aesthetic detachment', within the sustained systematic discourse of which they were once part. This seemed a way both of uncovering a number of assumptions which have been constraining writing on art for some time, and of clarifying a number of crucial insights of earlier theorists." The author's account is almost entirely expository, its negative critical questions being limited almost exclusively to Herbart. Yet even here, when the author indicates that Herbart's theory of mind "exhibits certain very basic logical difficulties," he adds that 538 HISTORY OF PHILOSOPHY "they are difficulties which have a particular importance in the discussion of art.... " Podro's clarification is largely made through the asking of questions which the authors themselves did not ask and then suggesting answers to these questions in the light of what the authors did say. The two chapters on Schiller form the core of the book. Schiller's theory of art and aesthetic education of man is placed as central to Podro's account of an aesthetic tradition beginning with Kant and ending with Fiedler. The "tradition" detailed in Podro's book is described as having two underlying assumptions. The first was that any account of art must indicate distinctive or at least characteristic uses of our perception, uses which if not exclusive to art are at least necessary to it, and which are seen in art in a particularly striking way. The second assumption was that art involves our attitudes, in the sense of our serious purposes as... (shrink)

Classic publishing of Eastern philosophy, religion, and poetry. This is a facsimile edition of the work originally published in London by John Murray in 1940.

Traditionally, there have been two methods of deriving the theorems of geometry: the analytic and the synthetic. While the analytical method is based on the introduction of numerical coordinates, and so on the theory of real numbers, the idea behind the synthetic approach is to furnish the subject of geometry with a purely geometric foundation in which the theorems are then deduced by purely logical means from an initial body of postulates. The most familiar examples of the synthetic geometry are (...) classical Euclidean geometry and the synthetic projective geometry introduced by Desargues in the 17th century and revived and developed by Carnot, Poncelet, Steiner and others during the 19th century. The power of analytic geometry derives very largely from the fact that it permits the methods of the calculus, and, more generally, of mathematical analysis, to be introduced into geometry, leading in particular to differential geometry (a term, by the way, introduced in 1894 by the Italian geometer Luigi Bianchi). That being the case, the idea of a “synthetic” differential geometry seems elusive: how can differential geometry be placed on a “purely geometric” or “axiomatic” foundation when the apparatus of the calculus seems inextricably involved? To my knowledge there have been two attempts to develop a synthetic differential geometry. The first was initiated by Herbert Busemann in the 1940s, building on earlier work of Paul Finsler. Here the idea was to build a differential geometry that, in its author’s words, “requires no derivatives”: the basic objects in Busemann’s approach are not differentiable manifolds, but metric spaces of a certain type in which the notion of a geodesic can be defined in an intrinsic manner. I shall not have anything more to say about this approach. The second approach, that with which I shall be concerned here, was originally proposed in the 1960s by F. W. Lawvere, who was in fact striving to fashion a decisive axiomatic framework for continuum mechanics.. (shrink)

The logical theory of branching space-times, which provides a relativistic framework for studying objective indeterminism, remains mostly disconnected from discussions of space-time theories in philosophy of physics. Earman has criticized the branching approach and suggested “pruning some branches from branching space-time.” This article identifies the different—order-theoretic versus topological—perspective of both discussions as a reason for certain misunderstandings and tries to remove them. Most important, we give a novel, topological criterion of modal consistency that usefully generalizes an earlier criterion, and we (...) introduce a differential-geometrical version of branching space-times as a non-Hausdorff (generalized) manifold. (shrink)

In the Syracusan embassy scene (Hdt. 7.153–63), both the Spartan and the Athenian envoys invoke the epic past to buttress their claims to the chief command; against this, Gelon pits the youthful vigour of his recent superpower, calling his army the "spring of Greece." However, intertextual links undermine the claims of all three and evoke the later fights for hegemony. This analysis sheds light on the way Herodotus uses the widespread juxtaposition of the Trojan and Persian Wars and helps to (...) assess the relation of his Histories to non-historiographical genres. (shrink)

Each of us distinguishes between himself and states of himself on the one hand, and what is not himself or a state of himself on the other. What are the conditions of our making this distinction, and how are they fulfilled? In what way do we make it, and why do we make it in the way we do?

The article investigates the relations between Hausdorff and non-Hausdorff manifolds as objects of general relativity. We show that every non-Hausdorff manifold can be seen as a result of gluing together some Hausdorff manifolds. In the light of this result, we investigate a modal interpretation of a non-Hausdorff differential manifold, according to which it represents a bundle of alternative space-times, all of which are compatible with a given initial data set.

Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and infinite-dimensional manifolds deeply similar. In this context the infinite-dimensional counterparts of simple notions such as basis, dual basis, orthogonal basis, etc. are shown to be closely related to the choice of a model. It is also shown that in this formalism a single tensor equation on an infinite-dimensional (...) manifold produces a family of functional equations on different spaces of functions. (shrink)

Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this setting, also called functional tensor equations, describe families of functional equations on various Hilbert spaces of functions. The principle of functional relativity is introduced which states that quantum theory (QT) is indeed a functional tensor theory, i.e., it can be described by (...) functional tensor equations. The main equations of QT are shown to be compatible with the principle of functional relativity. By accepting the principle as a hypothesis, we then explain the origin of physical dimensions, provide a geometric interpretation of Planck’s constant, and find a simple model of the two-slit experiment and the process of measurement. (shrink)

In the following interview with Manlio Iofrida, Aldo Giorgio Gargani retraces the fundamental moments and key phases of his intellectual development: his early childhood and adolescence in Genoa, strongly marked by the influence of his artist father and of the social context of the immediate post-war situation; his studies at the Scuola Normale Superiore in Pisa, and subsequently at the University of Oxford, which resulted to his first book on Wittgenstein; the achievement during the 1960s of a distinctive philosophical position (...) of his own, reflected in the publication of the book Il sapere senza fondamenti [Knowledge without Foundations]; the renewal of philosophical culture in Italy in the 1980s and 1990s, in which Gargani himself was one of the main protagonists; the return to an engagement with Wittgenstein, after a period in which he had dedicated himself principally to literary questions and concerns, one pursued specifically in the context of the new issues raised at the beginning of the 21st century. This historical and autobiographical reconstruction of his intellectual career is accompanied at every turn by philosophical reflections on our contemporary situation and by specific critical responses to other contemporary philosophical trends and developments: the interview thus constitutes a telling summation of the fundamental themes and aspects of the author’s thought in general. (shrink)

The problem of ‘collective unity’ in the transcendental philosophies of Kant and Husserl is investigated on the basis of number’s exemplary ‘collective unity’. To this end, the investigation reconstructs the historical context of the conceptuality of the mathematics that informs Kant’s and Husserl’s accounts of manifold, intuition, and synthesis. On the basis of this reconstruction, the argument is advanced that the unity of number – not the unity of the ‘concept’ of number – is presupposed by each transcendental philosopher (...) in their accounts of the transcendental foundation of manifold, intuition, and synthesis. This presupposition is ultimately traced to Kant’s and Husserl’s responses to Hume’s philosophy of human understanding and the critical limits of what Kant calls the ‘qualitative’ unity of transcendental consciousness. These critical limits are exposed in both philosophers’ attempts to account for that ‘qualitative’ unity on the basis of the ‘quantitative’ unity of number. (shrink)

In The Equilibrium Manifold, noted economic scholar and major contributor to the theory of general equilibrium Yves Balasko argues that, contrary to what many textbooks want readers to believe, the study of the general equilibrium model did not end with the existence and welfare theorems of the 1950s. These developments, which characterize the modern phase of the theory of general equilibrium, led to what Balasko calls the postmodern phase, marked by the reintroduction of differentiability assumptions and the application of (...) the methods of differential topology to the study of the equilibrium equation. Balasko's rigorous study demonstrates the central role played by the equilibrium manifold in understanding the properties of the Arrow-Debreu model and its extensions. Balasko argues that the tools of differential topology articulated around the concept of equilibrium manifold offer powerful methods for studying economically important issues, from existence and uniqueness to business cycles and economic fluctuations. After an examination of the theory of general equilibrium's evolution in the hundred years between Walras and Arrow-Debreu, Balasko discusses the properties of the equilibrium manifold and the natural projection. He highlights the important role of the set of no-trade equilibria, the structure of which is applied to the global structure of the equilibrium manifold. He also develops a geometric approach to the study of the equilibrium manifold. Applications include stability issues of adjustment dynamics for out-of-equilibrium prices, the introduction of price-dependent preferences, and aspects of time and uncertainty in extensions of the general equilibrium model that account for various forms of market frictions and imperfections. Special effort has been made at reducing the mathematical technicalities without compromising rigor. The Equilibrium Manifold makes clear the ways in which the postmodern" developments of the Arrow-Debreu model improve our understanding of modern market economies. (shrink)

Mimesis is configured in many ways. Its manifold senses require the doubling of sense, such that it designates both what is commonly displayed to the senses and what intrinsically cannot be so displayed. As Gadamer insists in his criticism of Hegel, the work of art is no mere bearer of meaning that can subsist apart from it and that could be transferred to some other vehicle. This is, then, the first of the four moments that constitute Gadamer's deconstruction of (...) mimesis. Mimesis is transformation. This redetermination constitutes the second moment in the Gadamerian deconstruction of mimesis. The third deconstructive moment involves reconstruing the duality of mimesis, displacing the image/original relation that was definitive for traditional concepts of mimesis. The fourth claims that in the artwork, there is not only a manifestation but also a sheltering of sense, which stabilizes and secures the sense that mimesis has also set free. (shrink)

This paper develops and defends three related forms of relationism about spacetime against attacks by contemporary substantivalists. It clarifies Newton's globes argument to show that it does not bear on relations that fail to determine geodesic motions, since the inertial effects on which Newton relies are not simply correlated with affine structure, but must be understood in dynamical terms. It develops remarks by Sklar and van Fraassen into relational versions of Newtonian mechanics, and argues that Earman does not show them (...) to trivialize the debate. (shrink)

Claims that our species is an “evolutionary success” typically do not feature prominently in academic articles. However, they do seem to be a recurring trope in science popularization. Why do we seem to be attracted to viewing human evolution through the lense of “success”? In this chapter we discuss how evolutionary success has both causal-descriptive and ethical-normative components, and how its ethical status is ambiguous, with possible hints of anthropocentrism. We also place the concept of “success” in a wider context (...) of biological thought, contrasting it with two other value-laden concepts: evolutionary progress and human uniqueness. Claiming the human species to be an evolutionary success is ostensibly grounded in metrics such as the dominance or the size of the human population, but often goes beyond this, suggesting that humans are a unique species or the pinnacle of evolutionary progress. (shrink)

Over the last fifteen years, the largely American tradition of process theology has moved in new directions as it has been lured into sustained engagements with French poststructuralism. Roland Faber’s The Divine Manifold is perhaps the most impressive example of this new shape that process thought is taking on in the twenty-first century. For those who would dismiss Whitehead’s philosophy as outdated or irrelevant to our present context, Faber’s Manifold offers a startlingly novel interpretation of the great metaphysician (...) and a series of complex arguments for his continuing importance. By entangling Whitehead’s metaphysics with the poststructuralism of Gilles Deleuze, Faber reveals what process thought could... (shrink)

We point out that a certain complex compact manifold constructed by Lieberman has the dimensional order property, and has U-rank different from Morley rank. We also give a sufficient condition for a Kahler manifold to be totally degenerate (that is, to be an indiscernible set, in its canonical language) and point out that there are K3 surfaces which satisfy these conditions.

One of the aims of the encyclical "Laudato Si’" is to help us “marvel at the manifold connections existing among creatures”, to show how we are also involved, and to motivate us thereby to care for our common home. Are there new dimensions of beauty available to us today because of recent advances in biology? In this paper I seek to answer this question by first recalling the basic criteria for beauty, as expressed by Aristotle and Aquinas, and then (...) evaluating their applicability as regards three ways in which some prominent twentieth century philosophers of biology have sought to overcome the limitations of reductionism. The overall argument refers especially to the works of Jakob von Uexküll and Georges Canguilhem. The results indicate that harmony, proportion, and integrity in the natural order should be more evident than ever before, especially as regards the way the organism and its environment codetermine each other. This insight allows a deeper appreciation of the message of "Laudato Si’". (shrink)

Studies have failed to yield definitive evidence for the existence and/or role of well-defined chaotic attractors in real brain systems. Tsuda's transients stabilized on unstable manifolds of unstable fixed points using mechanisms similar to Ott's algorithmic “control of chaos” are demonstrable. Grebogi's order in preserving “strange nonchaotic” attractor with fractal dimension but Lyapounov is suggested for neural network tasks dependent on sequence.

In the mid seventeenth century, European scholars on the frontline of philosophical discussions corresponded and exchanged their works in manuscript or in print, as they had always done, but a strong trend towards publishing their work in the vernaculars and towards translating each other’s works between vernaculars was building up. The French mathematician Guillaume du Verdus had become friends with the English philosopher Thomas Hobbes, and ambitioned to translated the latter’s English Leviathan into French. In spite of all his endeavours (...) and of Hobbes’s friendly support, he could not become proficient enough in English to safely translate the book, hence his decision to translate the Latin De Cive, an earlier work of political philosophy by Hobbes. What can explain this choice? How were modern languages taught in early modern Europe? Was Du Verdus’s decision to translate Hobbes mainly due to philosophical or ideological reasons? How can we contextualise such choices from internal and external evidence? (shrink)

The article deals with the lines along which manifold senses of horizonedness emerge and their reference to potentiality as a starting-point. The first section examines Gurwitsch's analyses of field-potentialities and margin-potentialities in the light of distinctions drawn by Husserl in terms of latency and patency. It is contended that Husserl's concept of latency encompasses both modes of potentiality. The second section shows how the world- horizon functions as a background- horizon and alternation- horizon conceived of as the two fundamental (...) modes of non-thematic consciousness. In this respect, an attempt is made to link this theme with Gurwitsch's description of the acquisition of the character of positional index as a worldly existent. The third section is concerned with how potentiality develops into an all-encompassing domain that can be anticipated as an ideal totality and into a pregiven ground, and outlines an approach to the complementarity of this threefold characterization. This development falls out of Gurwitsch's framework for the analysis of horizonedness. The article concludes with a characterization of the encasement-of-one-in-another of horizons. Reasons are suggested for the application of some ideas of Gurwitsch on thematic transformation to this sequence of levels. (shrink)

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov}, \cite{Kryukov1} is further analyzed. The main subject here is a comparison of the ordinary and the string bases of eigenvectors of a linear operator as introduced in \cite{Kryukov}. It is shown that the string basis of eigenvectors is a natural generalization of its classical counterpart. It is also shown that the developed formalism forces us to consider any Hermitian operator with continuous spectrum as a restriction to a space of square integrable functions (...) of a self-adjoint operator defined on a space of generalized functions. In the formalism functional coordinate transformations preserving the norm of strings are now linear isometries rather than the unitary transformations. (shrink)

We present a modernized proof, with a modification by M.A. Shtan’ko, of the Markov theorem on the unsolvability of the homeomorphy problem for manifolds. We then discuss a proof of the S.P. Novikov theorem on the unrecognizability of spheres for n≥5, from which we obtain a corollary about unrecognizability of all manifolds of dimension at least five. An analogous argument then proves the unrecognizability of stabilizations of all four-dimensional manifolds. We also give a brief overview of known results concerning algorithmic (...) recognizability of three-dimensional manifolds. (shrink)