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.

Husserl’s notion of definiteness, i.e., completeness is crucial to understanding Husserl’s view of logic, and consequently several related philosophical views, such as his argument against psychologism, his notion of ideality, and his view of formal ontology. Initially Husserl developed the notion of definiteness to clarify Hermann Hankel’s ‘principle of permanence’. One of the first attempts at formulating definiteness can be found in the Philosophy of Arithmetic, where definiteness serves the purpose of the modern notion of ‘soundness’ and leads Husserl to (...) a ‘computational’ view of logic. Inspired by Gauss and Grassmann Husserl then undertakes a further investigation of theories of manifolds. When Husserl subsequently renounces psychologism and changes his view of logic, his idea of definiteness also develops. The notion of definiteness is discussed most extensively in the pair of lectures Husserl gave in front of the mathematical society in Göttingen (1901). A detailed analysis of the lectures, together with an elaboration of Husserl’s lectures on logic beginning in 1895, shows that Husserl meant by definiteness what is today called ‘categoricity’. In so doing Husserl was not doing anything particularly original; since Dedekind’s ‘Was sind und sollen die Zahlen’ (1888) the notion was ‘in the air’. It also characterizes Hilbert’s (1900) notion of completeness. In the end, Husserl’s view of definiteness is discussed in light of Gödel’s (1931) incompleteness results. (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)

The paper discusses Husserl’s notion of definiteness as presented in his Göttingen Mathematical Society Double Lecture of 1901 as a defense of two, in many cases incompatible, ideals, namely full characterizability of the domain, i.e., categoricity, and its syntactic completeness. These two ideals are manifest already in Husserl’s discussion of pure logic in the Prolegomena: The full characterizability is related to Husserl’s attempt to capture the interconnection of things, whereas syntactic completeness relates to the interconnection of truths. In the Prolegomena (...) Husserl argues that an ideally complete theory gives an independent norm for objectivity for logic and experiential sciences, hence the notion is central to his argument against psychologism. In the Double Lecture the former is captured by non-extendibility, that is, categoricity of the domain, from which, so Husserl assumes, syntactic completeness is thought to follow. In the so-called ‘mathematical manifolds’ the expressions of the theory are equations that are reducible to equations between elements of the theory. With such an equational reduction structure individual elements of the domain are given criteria of identity and hence they are fully determined. (shrink)

A classic result in the foundations of Yang-Mills theory, due to J. W. Barrett ["Holonomy and Path Structures in General Relativity and Yang-Mills Theory." Int. J. Th. Phys. 30, ], establishes that given a "generalized" holonomy map from the space of piece-wise smooth, closed curves based at some point of a manifold to a Lie group, there exists a principal bundle with that group as structure group and a principal connection on that bundle such that the holonomy map corresponds (...) to the holonomies of that connection. Barrett also provided one sense in which this "recovery theorem" yields a unique bundle, up to isomorphism. Here we show that something stronger is true: with an appropriate definition of isomorphism between generalized holonomy maps, there is an equivalence of categories between the category whose objects are generalized holonomy maps on a smooth, connected manifold and whose arrows are holonomy isomorphisms, and the category whose objects are principal connections on principal bundles over a smooth, connected manifold. This result clarifies, and somewhat improves upon, the sense of "unique recovery" in Barrett's theorems; it also makes precise a sense in which there is no loss of structure involved in moving from a principal bundle formulation of Yang-Mills theory to a holonomy, or "loop", formulation. (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.

For a standard Finsler F on a manifold M, the domain is the whole tangent bundle T M and the fundamental tensor g is positive-definite. However, in many cases, these two conditions hold in a relaxed form only, namely one has either a psuedo-Finsler metric or a conic Finsler metric. Our aim is twofold. First, we want to give an account of quite a few subtleties that appear under such generalizations, say, for conic pseudo-finsler metrics. Second, we aim (...) to provide some criteria that determine when a pseudo-Finsler metric F obtained as a general homogeneous combination of Finsler metrics and one-forms is again a Finsler-metric -- or, more precisely, that the conic domain on which g remains positive-definite. Such a combination generalizes the known -metrics in different directions. Remarkably, classical examples of Finsler metrics are reobtained and extended, with explicit computations of their fundamental tensors. (shrink)

Kant defined moral evil as reversing the order between self-love and morality. For many critics, however, his egoistically-orientated notion of self-love fails to make sense of the infinitely manifold incentives of evil under the human condition. Against this criticism, my article will re-interpret Kantian self-love and empirical self-conception from both the transcendental and empirical level, thus offering a transcendental grounding for the empirical manifestations of evil. In this way I will argue that we can explain rather sufficiently the infinite (...) manifoldness of evil incentives in real human life with Kant’s prima facie simplistic definition of evil. (shrink)

The paper traces the development and the role of syntactic reduction in Edmund Husserl’s early writings on mathematics and logic, especially on arithmetic. The notion has its origin in Hermann Hankel’s principle of permanence that Husserl set out to clarify. In Husserl’s early texts the emphasis of the reductions was meant to guarantee the consistency of the extended algorithm. Around the turn of the century Husserl uses the same idea in his conception of definiteness of what he calls “mathematical manifolds.” (...) The paper argues that the notion anticipates the notion of reduction in term rewrite theory in computer science. The role of the reduction for Husserl is, however, primarily epistemological: its purpose is to impart clarity to formal mathematics. (shrink)

This chapter reconstructs the account of the organization of unified definite manifolds that Husserl developed in his early logic of parts and wholes. I argue that Husserl’s conception of necessity gets fixed through the logic of fitness that is operative in his account of unified definite manifolds that are organized by symmetrical part/whole relations. Husserl’s logical account of necessity finds its ultimate justification in his theory of intentionality and is operative in his phenomenological methodology generally. Through this conception (...) of necessity of the way in which manifolds are unified and organized, Husserl radicalized and exploded the Kantian conception of the material a priori and distinguished among several kinds of a priori, e.g., the correlational a priori, a priori bound to the empirical, and pure material a priori. Husserl’s phenomenological account of the material a priori further clarifies the important differences with Kant’s approach to the problem of necessity. (shrink)

ABSTRACT. The paper compares the views of Edmund Husserl (1859-1938) and Charles Sanders Peirce (1839-1914) on mathematics around the turn of the century. The two share a view that mathematics is an independent and theoretical discipline. Both think that it is something unrelated to how we actually think, and hence independent of psychology. For both, mathematics reveals the objective and formal structure of the world, and both think that modern mathematics is a Platonist enterprise. Husserl and Peirce also share a (...) teleological conception of the development of mathematics: both view it to evolve towards a goal. This is where the primary difference between the two can be found: while for Husserl the goal of mathematics is to characterize definite manifolds, for Peirce it is to discover the real potential world as expressed by his conception of continuum. Peirce elaborates the continuum with the notion ‘potential aggregate,’ a totality of the series of uncountable sets (each created by Cantor’s theorem) briefly discussed and compared to Husserl’s notion of definite manifolds. (shrink)

Humeans have a problem with quantities. A core principle of any Humean account of modality is that fundamental entities can freely recombine. But determinate quantities, if fundamental, seem to violate this core principle: determinate quantities belonging to the same determinable necessarily exclude one another. Call this the problem of exclusion. Prominent Humeans have responded in various ways. Wittgenstein, when he resurfaced to philosophy, gave the problem of exclusion as a reason to abandon the logical atomism of the Tractatus with its (...) free recombination of elementary propositions. Armstrong promoted a mereological solution to the problem of exclusion; but his account fails in manifold ways to provide a general solution to the problem. Lewis studiously avoided committing to any one solution, trusting simply that, since Humeanism was true, there had to be some solution. Abandonment; failure; avoidance: we Humeans need to do better. -/- In this paper, I present what I take to be the best account of quantities, tailoring it where needed to meet Humean demands as well as my own prior commitment to quidditism, and my own comparativist inclinations. In short: determinables, not determinates, are the fundamental properties, and freely recombine; determinates arise from the instantiation of determinables in an enhanced world structure; determinate quantities may be local (in a sense to be explained), but they are not intrinsic. Is the account I end up with Humean? Not, unfortunately, as it stands: the problem of exclusion still rears its ugly head. After dismissing a failed attempt at a solution, I consider in the final section the two viable Humean options. One attributes the source of the necessary exclusions to conventional definition, the other attributes it to logic. The first is safe and familiar, but not a response I can accept given my other commitments. The second is more radical and less familiar; but I am convinced it is on the right track. I don’t have space to develop it much here, but I put it out for future research. (shrink)

Crises today occur in manifold variants. Cyberattacks, floods, wars, pandemics – the list of cases is ongoing. Academic literature recognizes them as “transboundary crises” (Ansell et al. 2010) or as “global polycrisis” (Homer-Dixon et al., 2022), referring to their transgressing, cascading and overlapping dynamics in both space and time. In this paper, we discuss how decisions are made at a local level in such dynamic, if not disruptive, environments. By combining DDM and crisis management literature, we illustrate how the (...) decision-making evolves when the crisis shows transboundary characteristics, that is, when cascading dynamics call for even more decisions (hence the “Hydra” metaphor referring to a monster in Greek mythology that multiplies its heads once it is being fought). The paper draws on a qualitative study on decision processes in local authorities and organizations in Germany during the Covid-19 pandemic. It can show (1) how these local actors build inter-organizational networks (e.g. task forces) in order to synchronize their decision processes against the background of changing federal requirements; (2) how, due to the duration of the pandemic, rather permanent decision systems developed; and (3) how these networks learn to sustain dynamic decision-making capacities in order to cope with crises following Covid-19, such as the effects of the war in the Ukraine or recent climate impacts. With these findings we contribute to an “integrative” conception of crisis in current crisis management literature that seeks definition in a dynamic process view rather than using either objective or subjective criteria. A DDM approach allows for a more detailed realization of this conceptual shift by representing the current “cascading disasters” as “cascading decision-making”. This understanding focuses on the active role decision-making plays as well as it reflects on the fact that decision-making in today’s crises always involves _others _making decisions, too. (shrink)

The requirement of gauge invariance for the Schwinger-DeWitt equations, interpreted as a manifestly covariant quantum theory for the evolution of a system in spacetime, implies the existence of a five-dimensional pre-Maxwell field on the manifold of spacetime and “proper time” τ. The Maxwell theory is contained in this theory; integration of the field equations over τ restores the Maxwell equations with the usual interpretation of the sources. Following Schwinger's techniques, we study the Green's functions for the five-dimensional hyperbolic field (...) equations for both signatures ± [corresponding to O(4, 1) or O(3, 2) symmetry of the field equations] of the proper time derivative. The classification of the Green's functions follows that of the four-dimensional theory for “massive” fields, for which the “mass” squared may be positive or negative, respectively. The Green's functions for the five-dimensional field are then given by the Fourier transform over the “mass” parameter. We derive the Green's functions corresponding to the principal part ΔP and the homogeneous function Δ 1 ; all of the Green's functions can be expressed in terms of these, as for the usual field equations with definite mass. In the O(3, 2) case, the principal part function has support for x2⩾τ2, corresponding to spacelike propagation, as well as along the light cone x2=0 (for τ=0). There can be no transmission ofinformation in spacelike directions, with this propagator, since the Maxwell field, obtained by integration over τ, does not contain this component of the support. Measurements are characterized by such an integration. The spacelike field therefore can dynamically establish spacelike correlations. (shrink)

In the first part of this article, Feferman outlines his ‘conceptual structuralism’ and emphasizes broad similarities between Parsons’s and his own structuralist perspective on mathematics. However, Feferman also notices differences and makes two critical claims about any structuralism that focuses on the “ur-structures” of natural and real numbers: it does not account for the manifold use of other important structures in modern mathematics and, correspondingly, it does not explain the ubiquity of “individual [natural or real] numbers” in that use. (...) In the second part, Feferman presents a summary of his reasons for the skepticism he has towards contemporary metamathematical investigations of set theory. That skepticism led him to reject the Continuum Problem as a definite mathematical one. He contrasts that attitude sharply to Parsons’s “great sympathy for the current explorations of higher set theory.”. (shrink)

In his Doppelvortrag, Edmund Husserl introduced two concepts of “definiteness” which have been interpreted as a vindication of his role in the history of completeness. Some commentators defended that the meaning of these notions should be understood as categoricity, while other scholars believed that it is closer to syntactic completeness. A detailed study of the early twentieth-century axiomatics and Husserl’s Doppelvortrag shows, however, that many concepts of completeness were conflated as equivalent. Although “absolute definiteness” was principally an attempt to characterize (...) non-extendible manifolds and axiom systems, an absolutely definite theory has a unique model and, thus, it is non-forkable and semantically complete. Non-forkability and decidability were formally delimited by Fraenkel and Carnap almost three decades later and, in fact, they mentioned Husserl as precursor of the latter. Therefore, this paper contributes to a reassessment of Husserl’s place in the history of logic. (shrink)

Classic epistemology is under manifold changes; its categories loose their traditional meanings and gain new ones. Civilization and cultural changes, especially in mass communication and scientific knowledge, make impossible to insist on the concept of knowledge entirely as a true and justified belief. Traditional concepts of individual and subjectivistically conceived agent as well as concept of objects (areas and domains) of human knowledge are to much restrictive and at the same time controversial. Epistemological (pure philosophical) meaning of them is (...) constantly confronted and changed by the scientific discoveries and definitions, coming especially from natural and social sciences (biology, neural sciences, psychology and social sciences). It is long-lasting and manifold process of naturalization that regards not only cognitive phenomena but epistemic categories and epistemological theories as well. The papers presents the concise model of the naturalized theory of human knowledge one can eliminate from different positions and theories. Today types of naturalized epistemology try to go beyond the strict and limited concept of naturalism (Quine’s naturalized epistemology) and go toward anti-scientific, more liberal understanding of it. Naturalizing epistemology opens, as it is argued in the paper, the new perspectives and prospects on human cognition and knowledge that are far from the classic concepts. (shrink)

The legal and normative openness of human rights allows for the integration of new subjects, arenas, violators, and protectors of human rights. Indigenous movements manage to use this flexibility and implement their claims within the human rights system. Yet, indigenous rights cause manifold discussions and ambiguities, all of which are related to the question of the concept of indigeneity. In spite of the endeavor for pragmatic and flexible approaches, scopes and implications of concepts of indigeneity need to be dealt (...) with. This paper discusses both scope and implications, starting from hegemonic criteria for a working definition of indigeneity. It shows how indigenous identity is inextricably linked to its non-indigenous other. Subsequently, indigenous human rights entail specific repercussions in indigeneity being a resource and an imperative. Those repercussions stem from indigeneity being simultaneously a source and target of indigenous human rights claims and from the self-referential duplication of the right to indigeneity for indigenes, respectively. The provided tools for an analysis of the ambiguities of indigenous human rights contribute to their further and more just development, implementation, and monitoring. (shrink)

We are in 1563, somewhere on a Brazilian beach about 100 kilometres north of what is now São Paulo. A young man in a cowled robe alone on the beach is writing a poem on the sand with the point of his stick. The hostage of a savage tribe for weeks, he struggles daily against manifold carnal temptations, personified in the voluptuous native women who come to visit him every evening in his hammock, and addresses his Latin verses to (...) the Virgin Mary in order to fortify his virtue. The threat of being killed and eaten by cannibals is nothing to him by comparison with the loss of his virginity. Recourse to his own original culture is the ultimate bulwark against contamination, the sign of resistance and strengthening of his identity. The definitive rejection of the Other is, in these circumstances, a survival reflex. (shrink)

In her recent work, Nancy Folbre undertakes an ambitious effort: constructing an intersectional political economy that aims to identify the common mechanisms and logic underpinning the many wrongs that characterise capitalism. In this paper, we focus on what we deem the three fundamental theoretical pillars of her approach. First, she challenges the oppression/exploitation distinction within Marxian political economy and proposes a broader definition of exploitation that can take manifold forms. Second, she questions the Marxian concept of class, and emphasises (...) the variety of forms of subordination and exploitation related to social identities that cannot be reduced to Marxian classes. Finally, she advocates a more comprehensive notion of the economy beyond a focus on capitalist relations of production. It is difficult to understate the theoretical relevance of these claims, which highlight the importance of various contemporary forms of injustice—of which the exploitation of workers by capitalists is only one. As a complement to the Marxian theory of exploitation and class, Folbre’s approach would broaden our understanding of oppressive social relations. Yet as an alternative to Marxian political economy, it is ultimately unconvincing: a shift of emphasis to ‘manifold exploitations’, social groups, and the economy does not yield a gain in analytical insight but rather an impoverishment of our conceptual toolbox. The struggle against capitalism is different from the struggle against patriarchy and racism, even if the ultimate aim should be the removal of all structures of oppression and domination. (shrink)

The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and (...) so on. Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years. -Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included. (shrink)

This book analyzes unobvious relations between historical definitions of the face and its contemporary usage in popular culture and social media, like Facebook or Instagram. Bringing together a wide range of methodologies, it includes essays from manifold disciplines of the humanities such as philosophy, literary and art criticism, media and television studies, game studies, sociology and anthropology. The authors focus on both metaphorical and material meanings of the face. They grapple with crucial questions about modernity, modern and postmodern subjectivity, (...) as well as with origins of certain linguistic terms and popular, colloquial phrases based on the concept of the face. (shrink)

This article criticizes Bourdieu's and Giddens's overintellectualizing accounts of human activity on the basis of Wittgenstein's insights into practical under standing. Part 1 describes these two theorists' conceptions of a homology between the organization of practices (spatial-temporal manifolds of action) and the governance of individual actions. Part 2 draws on Wittgenstein's discussions of linguistic definition and following a rule to criticize these conceptions for ascribing content to the practical understanding they claim governs action. Part 3 then suggests an alternative, Wittgensteinian (...) account of the homology between practices and actions that avoids this pitfall. (shrink)

The concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his works. Many authors have been misled by this term, placing it in the context of Husserl’s early period in Halle, while writing the Philosophy of Arithmetic, as a friend and colleague of Georg Cantor.Yet at the time, Husserl distanced himself explicitly from Cantor’s definition and rather took Bernhard Riemann as example, having studied and lectured extensively on Riemann’s theories of space. Husserl’s (...) Mannigfaltigkeitslehre would then not be a Cantorian set-theory, but come rather closer to topology. Then, in the Prolegomena, Husserl introduces the idea of a pure Mannigfaltigkeitslehre as a meta-theoretical enterprise which studies the relations among theories, e.g. how to derive or found one upon another. When Husserl announces that in fact the best example of such a pure theory of manifolds is what is actually practiced in mathematics, this sounds slightly misleading. The pure theory of theories cannot simply be the mathematics underlying topology, but should rather be considered as a mathesis universalis. Indeed, while this might not have been fully clear yet in 1900/1901, Husserl will explicitly tie together the notions of pure theory of manifolds and mathesis universalis. The mathesis universalis in this sense is formal, a priori and analytic, as theory of theory in general. It is an analysis of the highest categories of meaning and their correlative categories of objects. In my paper I try to understand the development of the notion of Mannigfaltigkeit in Husserl’s thought from its mathematical beginnings to its later central philosophical role, taking into account the mathematical background and context of Husserl’s own development. (shrink)

Laws of mechanics, quantum mechanics, electromagnetism, gravitation and relativity are derived as “related mathematical identities” based solely on the existence of a joint probability distribution for the position and velocity of a particle moving on a Riemannian manifold. This probability formalism is necessary because continuous variables are not precisely observable. These demonstrations explain why these laws must have the forms previously discovered through experiment and empirical deduction. Indeed, the very existence of electric, magnetic and gravitational fields is predicted by (...) these purely mathematical constructions. Furthermore these constructions incorporate gravitation into special relativity theory and provide corrected definitions for coordinate time and proper time. These constructions then provide new insight into the relationship between manifold geometry and gravitation and present an alternative to Einstein’s general relativity theory. (shrink)

Compactified Minkowski spacetime is suggested by conformal covariance of Maxwell equations, while E. Cartan's definition of simple spinors leads to the idea of compactified momentum space. Assuming both diffeomorphic to (S 3 × S 1 )/Z 2 , one may obtain in the conformally flat stereographic projection field theories both infrared and ultraviolet regularized. On the compact manifold themselves instead, Fourier integrals of wave-field oscillations would have to be replaced by Fourier series summed over indices of spherical eigenfunctions: n, (...) l, m, m′. Tentatively identifying those wave structures with spacetime itself (in the frame of Big-Bang) and/or with matter and radiation distribution, some large-scale (hydrogenic) and small-scale (lattice) space structures are conjectured. (shrink)

Corporate social responsibility has long been an issue for research and practice. More recently, in response to growing public scrutiny, it has also gained importance in the agribusiness sector. Research has highlighted a growing gap between public perceptions of farming and food production processes and the realities of modern agriculture and the food industry. This can threaten the reputation and legitimacy of companies operating in this sector. One proactive means for companies to meet societal expectations is to make an active (...) commitment to society and its needs by implementing a CSR policy. However, there is still no clear definition of CSR, and what important stakeholders actually expect from companies remains largely unknown. This paper focuses on consumers’ perception of CSR. Its objective is to explore a CSR policy design for German agribusiness based on Archie B. Carroll’s famous pyramid model. A consumer survey was conducted to evaluate the CSR demands society places on agribusiness companies. An explorative factor analysis was employed to discover the outline of the construct in the German agribusiness context. The results reveal that Carroll’s model, which was developed from a U.S. point of view, cannot be confirmed for German agribusiness. Instead of Carroll’s four responsibility groups, three areas of responsibility were identified: economic, internal and external. These results have manifold implications for CSR strategies in agribusiness firms and represent an important origin for future investigations on CSR in other countries as well as in specific agribusiness subsectors. (shrink)

The world is a unification of matter, energy and information. Subjectivity information is such information that subject receives, deals with and expresses. Subjectivity information can be classified to two categories by form: image and symbol. On the basis of ontology of ‘matter, energy and information——triunity’, this paper presents the definitions of symbol and image, points out the origin of them and brings forward the mechanism that men cognize symbols. Also, the paper classifies symbols in two ways: In one way, according (...) to essence, origin and function, symbols can be classified to three categories: image symbols, appellation symbols and digit symbols. In the other way, symbols can be classified to two categories: static symbols and dynamic symbols, according to the carriers. Moreover, the author discussed the respective advantages and characteristics of image and symbol, especially presented four important characteristics of symbols: 1) be derived from definitions; 2) rely on manifold brain activities; 3) discretization; 4) meaning congruence. In the end, the author pointed out the epoch-making significance of symbols in the process that animals evolved into men. (shrink)

The chemist Jeremias Benjamin Richter (1762–1807) coined the term “stoichiometry” and proposed the “law of definite proportions.” He is also commonly acknowledged as having been a student of Immanuel Kant (1724–1804). This paper demonstrates how Kant’s philosophy positively shaped Richter’s approach to chemistry in the _Anfangsgründe der Stöchiometrie_ (1792–1794) and outlines two ways in which Richter attempted to represent the chemical force in “pure intuition”: (1) “reductionistic forces,” in which qualitative features scale with the quantity of matter; and (2) (...) generalized “abstracted forces,” in which a plurality of dissolution- and bonding-properties are latent within the chemical in the manifold of space-time. (shrink)

In an accompanying paper Gomes, we have put forward an interpretation of quantum mechanics based on a non-relativistic, Lagrangian 3+1 formalism of a closed Universe M, existing on timeless configuration space \ of some field over M. However, not much was said there about the role of locality, which was not assumed. This paper is an attempt to fill that gap. Locality in full can only emerge dynamically, and is not postulated. This new understanding of locality is based solely on (...) the properties of extremal paths in configuration space. I do not demand locality from the start, as it is usually done, but showed conditions under which certain systems exhibit it spontaneously. In this way we recover semi-classical local behavior when regions dynamically decouple from each other, a notion more appropriate for extension into quantum mechanics. The dynamics of a sub-region O within the closed manifold M is independent of its complement, \, if the projection of extremal curves on \ onto the space of extremal curves intrinsic to O is a surjective map. This roughly corresponds to \, where \ is a linear projection. This criterion for locality can be made approximate—an impossible feat had it been already postulated—and it can be applied for theories which do not have hyperbolic equations of motion, and/or no fixed causal structure. When two regions are mutually independent according to the criterion proposed here, the semi-classical path integral kernel factorizes, showing cluster decomposition which is the ultimate aim of a definition of locality. (shrink)

How to define space-time singularities is a serious problem in general relativity. Schmidt's b-boundary construction was commonly regarded as leading to the best (and very elegant) definition of singularities: space-time is said to be singular if it contains at least one b-incomplete curve. Unfortunately, Bosshard (1976) and Johnson (1977) demonstrated that the b-boundary of the closed Friedman universe consists of the single point. This means that the initial and final singularieties (i.e., the beginning and the end of the Friedman world) (...) coincide. So far no remedy to cure this disaster was known. In the present paper, the author reviews the results obtained by himself and W. Sasin (1994) which clarify the problem. The closed Friedman space-time together with its singularities is not smooth manifold but it turns out to be a structured space which is a strong generalization of the manifold concept. Consequently, if the problem is considered within the correct category, i.e. the category of structured spaces, the patologies dissapear. If one remains within the space-time everything is all right. It is only if one attempts to „touch” the singularity (to extend the differential structure from the inside of space-time to the singularity) when the beginning and the end of the universe coalesce. From the perspective of the Demiurg creating the closed Friedman universe the cosmic history is but a single point. The methodological significance of this result is briefly discussed. (shrink)

The prominent Russian philosopher Nikolai Lossky and his ex-student Nicolai Hartmann shared many metaphysical and epistemological views, and Lossky is likely to have influenced Hartmann in adopting several of them. But, in the case of axiological issues, it appears that Lossky also borrowed from the axiologies of Hartmann and the latter's Cologne colleague, Max Scheler. The links between the theories of values of Scheler and Hartmann have been studied abundantly, but never in relation to Lossky. In this paper, I examine (...) the manifold relationships – similarities, differences, borrowings, criticisms, and possible influences – between Lossky's axiology and those of Scheler and Hartmann on four key interweaving issues: (1) their ontological realism with regards to the objectivity of values, (2) their epistemological theories of the intuition of values, (3) their ontological definitions of "value", i.e., whether values are relations, qualities, essences, powers, meanings, etc., and (4) their theories of the stratification of values. (shrink)

Scientific hypotheses may either predict particular unknown facts or accommodate previously-known data. Although affirmed predictions are intuitively more rewarding than accommodations of established facts, opinions divide whether predictive hypotheses are also epistemically superior to accommodation hypotheses. This paper examines the contribution of predictive hypotheses to discoveries of several bio-molecular systems. Having all the necessary elements of the system known beforehand, an abstract predictive hypothesis of semiconservative mode of DNA replication was successfully affirmed. However, in defining the genetic code whose biochemical (...) basis was unclear, hypotheses were only partially effective and supplementary experimentation was required for its conclusive definition. Markedly, hypotheses were entirely inept in predicting workings of complex systems that included unknown elements. Thus, hypotheses did not predict the existence and function of mRNA, the multiple unidentified components of the protein biosynthesis machinery, or the manifold unknown constituents of the ubiquitin–proteasome system of protein breakdown. Consequently, because of their inability to envision unknown entities, predictive hypotheses did not contribute to the elucidation of cation theories remained the sole instrument to explain complex bio-molecular systems, the philosophical question of alleged advantage of predictive over accommodative hypotheses became inconsequential. (shrink)

The demand for a concept—for a definition specifying what one means by a term (or, for a thing, what it actually consists of)—is a classical requirement of philosophy. As a rule, however, this demand can scarcely be satisfied, and there are good reasons for not wanting to satisfy it. For a definition is always a way of fixing something, and a concept is an intervention in the manifold diversity of things and phenomena that freezes them. The defense of the (...) diversity of the particular and, to speak with Adorno, of the nonidentical is also an aim of phenomenology. The demand for a concept and the preservation of phenomena therefore appear to be in conflict with one another. The idea of formulating a concept .. (shrink)

Content externalism and vehicle externalism (what-externalism and how—externalism) or more commonly known as the thesis of extended mind, are said to be two totally independent views that ”diverge sharply” (Stanford encyclopedia). There are advocates, adversaries but also ag nostics about the extended mind thesis. The approach has been much debated and the controversies about vehicle externalism are importantly manifold. I am not going into any of them. My aim is different and fo cused on why and how content externalism (...) is characterized by vehicle externalists. Content externalism is labelled by extended mind theorists as: merely causal, taxonomic (Wilson), reactionary (Rowlands), passive (Clark), while vehicle externalism is: constitutive, radical and active. Since content externalists (to my knowledge) have not reacted to a rather negative presentation of their ideas, I restrict myself to showing that many of vehicle externalist (VE) presented views about content externalism (CE) are partly unjustified, not definitive and even wrong. I zoom on the following: 1. CE being ‘merely’ causal. 2. Active vs. Passive distinc tion, 3. CE being behaviourally inert. (shrink)

Relative to any point in time, how many possible futures are there? For example, it may rain tomorrow, or again it may not. So it would appear that relative to today, there are at least two possible futures, one involving rain tomorrow and the other not. Of course only one of these two future states of affairs will take place, and in that sense there is only one actual future, though there may be many possible futures. The only hypothesis under (...) which there is, for every instant in time, only one possible future, is the hypothesis of universal Laplacean determinism, and this hypothesis has had little to recommend it since the advent of quantum physics. Furthermore, although among the many possible futures relative to any given moment in time there is only one which will become actual, no distinguishing mark separates this one from its fellows at the given moment. So it would appear that what confronts the world at each moment in time is an undifferentiated multiplicity of possible futures. But this multiplicity, though at first sight admittedly frightening in its implications, may be put to good philosophical use: as will be seen it yields natural and convincing definitions of the notions of physical necessity and possibility. On the other hand, alternative definitions of these notions are obtainable which do not make use of the manifold of possible futures, and these also will be presented. The paper will be in two parts, the first dealing with the concepts of physical possibility and necessity, and the second presenting a formal calculus of necessary and sufficient conditions in which the physical modalities find their place. (shrink)

By taking into account some texts published between the first and the second edition of the Critique of Pure Reason that have been neglected by most of those who have dealt with the deduction of the categories, I argue that the core of the deduction is to be identified as the ‘almost single inference from the precisely determined definition of a judgment in general’, which Kant adumbrates in the Metaphysical Foundations in order to ‘make up for the deficiency’ of the (...) A-deduction. Whereas the first step of the B-deduction is an attempt to show that the manifold of an intuition belongs to the ‘necessary unity of self-consciousness’ by means of the synthesis of the understanding, the second step has the task of showing that the very same synthesis is responsible for the spatio-temporal unity of the manifold. Thus, Kant's ‘answer to Hume’ is that no spatio-temporal objects of experience at all are merely ‘given’, independently of the conceptual activities of the understanding. Against the established view I substantiate the claim that with this ‘almost single inference’ of the second proof step the distinction between judgments of perception and judgments of experience consequently vanished from Kant's thinking. (shrink)

Socrates did not claim to know many things, but one of the things that he insisted he did know with certainty was that there is a genuine distinction between knowledge and true opinion. Socrates maintained that unless this distinction held, inquiry would be pointless. Such a claim would seem to pre-suppose knowledge of what it means to know, an ability to specify the ground of the distinction between knowledge and true opinion. However, the attempt to bring the manifold forms (...) of knowledge under a unified definition in the Theaetetus ends in perplexity. (shrink)

L’épistémologie ouverte de Gilbert Durand a permis, depuis ses origines, il y a déjà 50 ans, non seulement un approfondissement dans l’étude du mythe dans les œuvres de culture, à partir de ces deux notions clés, que sont la mythocritique et la mythanalyse, mais également une pluridisciplinarité, de plus en plus poussée, entre les dites sciences humaines et les sciences en général. C’est, en définitive, grâce à l’imago-centrisme inhérent à cette méthode archétypologique qu’elle est devenue un horizon mythodologique au pluriel, (...) pour mieux étudier l’humain. For 50 years, Durand’s epistemology has both enhanced our understanding of cultural myths through the key notions of “myth-criticism” and “myth-analysis” and allowed multi-disciplinary collaborations between the social sciences and sciences proper. In sum, the central role Durand’s theoretical positions assign to “the image” has given rise to a manifold “myth-dology” now central in the study of human nature. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Christopher Norris IMAGE AND PARABLE: READINGS OF WALTER BENJAMIN Marxist literary criticism is a house with many mansions, most of diem claiming a privileged access to the great central chamber of history and truth. Only the most blinkered polemicist could nowadays attack "Marxist criticism" as if it presented a uniform front or even a clearly delineated target. Differences of oudook have developed to a point where debates within Marxism (...) are often more highly charged and polarized man anything brought to bear by its downright opponents. These differences will seem a crippling liability only from the viewpoint of a hard-line determinist creed which insists both on the rightness of its own reductive methodology and on a one-track notion of historical necessity and reason. The alternative, as New Left theorists have argued, is to examine the diversity of present-day Marxist thinking and show how its manifold traditions take rise from various backgrounds of political and cultural development. Perry Anderson's Considerations on Western Marxism is one such attempt to "situate" the work of thinkers like Sartre, Almusser, and Adorno in terms of their beleaguered position as left intellectuals outside the active mainstream of any revolutionary movement.1 Another example is Terry Eagleton's Criticism and Ideology, a book which sets out to rethink the bases of a Marxist-theoretical approach to English literary history.2 Eagleton, like Anderson, takes it as axiomatic that no such critique can get underway without first coming to terms with the problems and dilemmas which others have faced in trying to make new sense of a communal enterprise. For Eagleton this means a diagnostic treatment of the gaps and significant sUences which have marked the texts of those — like Arnold or Leavis — engaged in a class-based mystification ofliterary history and values. The critique extends to what Eagleton sees as the inbuilt problems of a homespun British Marxism, whedier of the crudely determinist variety (Caudwell) or the "left-Leavisite" amalgam of radical mêmes and traditionalist assumptions represented by Raymond Williams. Eagleton's approach lays claim to a power of unmasking die 15 16Philosophy and Literature latent ideology at work both in literary and critical texts. Ramer than simply collapse that distinction — as desired by the current post-structuralists, with whom he is wholly out of sympadiy — Eagleton strives to articulate the different structures and relations of discourse which situate criticism vis-à-vis literary history. He proposes a Marxist "science of the text" which would bring out its ideological modes of production, inscribed in the twists and unconscious blind-spots of meaning where a project comes up against its own impossibility. Criticism "deconstructs" the literary text, but not (like the Yale deconstructors) with a view to breaking down all possible distinctions between literature and commentary, merging both in the infinite freeplay of signs. For Eagleton there is indeed a knowledge of die text which stands at a definite remove from its object, just as literature itself"works" and transforms the raw stuffoflived ideology, mus offering it up to critical knowledge. Eagleton's theory of literary production was worked out in response to a powerful new current of Marxist thought, associated mainly with the French philosopher Louis Akhusser. What mis program involved, very briefly, was a rigorous re-reading of Marx's texts, aimed at defining their precise theoretical structure and die place within mem of such concepts as "knowledge," "ideology," and "structure" itself. Only thus could Marxist science attain the clarity and grasp of its own first principles which would set it apart from other, deviant or "ideological" discourses. This meant drawing a firm critical line (or "epistemological break") between the early, humanist Marx and the later productions —including Das Kapital— where his thought took on the full rigor of its scientific basis. Such a theory, in Althusser^ words, "makes it possible to distinguish a word from a concept, to distinguish the existence or non-existence of a concept behind a word, to discern the existence of a concept by a word's function in the dieoretical discourse...." 3 This structuralist reading of the Marxist text is intended as an immanent critique, a means of salvaging the essential Marx from fhose elements in his... (shrink)

For most of the twentieth century, anthropologists understood themselves as ethnographers. The art of anthropology was the fieldwork-based description of faraway others—of how social structures secretly organized the living-together of a given society, of how a people had endowed the world surrounding them with cultural meaning. While the poetics and politics of anthropology have changed dramatically over the course of a century, the basic equation of anthropology with ethnography—as well as the definition of the human as a social and cultural (...) being—has remained so evident that the possibility of questioning it occurred to hardly anyone. In After Ethnos Tobias Rees endeavors to decouple anthropology from ethnography—and the human from society and culture—and explores the manifold possibilities of practicing a question-based rather than an answer-based anthropology that emanates from this decoupling. What emerges from Rees's provocations is a new understanding of anthropology as a philosophically and poetically inclined, fieldwork-based investigation of what it could mean to be human when the established concepts of the human on which anthropology has been built increasingly fail us. (shrink)

Within the bosom of the humanities philosophy reposes and, as an academic field, it is ever so often criticized for its aloofness. In a recent book, Roudometof and Dessi (2022, 9-10) politely quip that philosophy’s engagement with the “glocal” has been “resilient,” transacted mostly “without encroaching on other fields.” Philosophy’s ostensible remoteness stems in part from its institutional affiliation with, cultivation and deployment of often forbiddingly technical tools of logical analysis. Although the academic field comprises a manifold of specialities, (...) with resentment often arising against prohibitively technical branches, I narrow my focus to an understanding of “philosophy” as an activity engrossed in logical analysis, and I will plead as defence of this avowed postulation that by so doing, operationally as it were, I can argue that philosophy can make critical and salutary contributions to the burgeoning field of glocalization studies, which is so ably canvassed in the book edited by Roudometof and Dessi. Notwithstanding the promissory note offered above, and since my definition of philosophy may seem unduly restrictive, it is incumbent on me to disambiguate across related notions and to make an initial case as to both the plausibility and arguable pay-offs from taking philosophy in the way I just adumbrated. This is a substantive issue as it relates to a case I will be making as to what philosophy may have to offer to the study of glocalization. (shrink)

Whether poetry gives knowledge or not is a question that has been debated from a variety of perspectives, depending on how a society or a culture defines knowledge, and on the function it ascribes to poetry in relation to that definition. The civilizations of Asia and the Middle East have generally taken the line that poetry deals primarily with affects, emotions and feelings. The West has had a more complicated history of responses. One way of making sense of this history (...) is to map rival claims as split over the idea of scientific knowledge, where it affects notions of the poetic function. The mapping, through all its manifold branches, gives clear indications that claims to knowledge – both those made on behalf of poetry, and those denied to poetry – depend more on assumptions, predispositions and cultural conditioning than on rational argument or critical debate. The resulting variety also suggests that the cultural relativism that affects such debates is unlikely to arrive at resolutions except of the contingent kind. (shrink)

We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein’s general relativity in a non-Riemannian Finsler space. This approach is based on the geometrization of quantum mechanics proposed in Tavernelli and combines quantum and gravitational effects into a global curvature of the Finsler space induced by the quantum potential associated to the matter quantum fields. In order to make this theory compatible with general relativity, the quantum effects are described in (...) the framework of quantum field theory, where a covariant definition of ‘simultaneity’ for many-body systems is introduced through the definition of a suited foliation of space-time. As in Einstein’s gravitation theory, the particle dynamics is finally described by means of a geodesic equation in a curved space-time manifold. (shrink)

A systematic effort is here made to express some of the general results of quantum mechanics in a conceptual form closer to ordinary language than is the case with most modern physics. Many of the implications of the theory appear much more clearly thereby, in particular the fact that the laws of quantum mechanics are only statistical propositions about classes, not referring to individual objects. Conversely, the microscopic structure of an object cannot be precisely defined in quantum mechanical terms. To (...) say that an object has a definite microscopic structure is an operationally meaningless statement; it is on the same level as saying in relativity that a selected coordinate system is “at rest.” This raises the need for a “theory of matching”: What is the best statement about the structure of an object, given that the tools of description are only statistical? A technique is known for this: the theory of inductive probabilities. There is no longer one true description but a manifold of statistical descriptions, some of which have a greater likelihood of being satisfactory than others. The main concrete application of this type of conceptual reasoning lies in its power to clean out the speculative underbrush which so far has prevented the transition from theoretical physics to theoretical biology. (shrink)

The historical evolution of the homotopy concept for paths illustrates how the introduction of a concept (be it implicit or explicit) depends upon the interests of the mathematicians concerned and how it gradually acquires a more satisfactory definition. In our case the equivalence of paths first meant for certain mathematicians that they led to the same value of the integral of a given function or that they led to the same value of a multiple-valued function. (See for instance [Cau], [Pui], (...) [Rie].) Later this dependency upon given functions is dropped (by Jordan for surfaces, by Riemann and most explictly by Poincaré) and this leads to a concept which depends only upon the manifold. It thus becomes a concept which belongs to topology. As a consequence of this hesitant evolution, there was at first a confusion between concepts and hence no attention to relations between them. At a later stage these relations were investigated, as for instance the fact that homotopy equivalence implies homology equivalence: in1882, Klein gave an example of a closed curve on a surface which is the boundary of a part of the surface but could not be shrunk to a point. In 1904, Poincaré explicitly said that this curve is “homologue à zéro” (null homologous), but not “équivalent à zéro” (null homotopic). Poincaré obtains the homologies from the fundamental group by allowing changes in the order of the terms in the “équivalences”. This means also that the equivalences imply homologies but not vice versa. From a methodological standpoint, this situation of using properties without asking about relations between them or without even properly defining them is reminiscent of mathematics of a century earlier. An example is the way differentiability was used for the differentiation of functions without consciously questioning the properties of this concept until in the nineteenth century examples were given by Bolzano (1834), Weierstrass (1872), Riemann (1854) and others of functions which are continuous but nowhere differentiable [Kli]. Another example is the use eighteenth-century mathematicians made of series without inquiring about the validity of the operations they used on them. Another aspect which had its influence was the success of algebraic methods in topology which explains the preference for theories with “base point” and constrained deformation even though free deformation is a more natural concept. As we can see the evolution of the homotopy concept for paths did not progress without impediments. It also had an influence on the evolution of the abstract group concept and the basic principle of equivalence. These aspects make it a history which is not only intrinsically interesting (how did homotopic paths come to be?), but also because it illustrates relations between different branches of mathematics. (shrink)

A formulation of relativistic quantum mechanics is presented independent of the theory of Hilbert space and also independent of the hypothesis of spacetime manifold. A hierarchy is established in the nondistributive lattice of physical ensembles, and it is shown that the projections relating different members of the hierarchy form a semigroup. It is shown how to develop a statistical theory based on the definition of a statistical operator. Involutions defined on the matrix representations of the semigroup are interpreted in (...) terms ofCPT conjugations. The theory of particles of spin one-half and systems with higher spin is developed from first principles. Methods are also developed for defining energy, momentum, orbital angular momentum, and weighted spacetime coordinates without reference to a manifold. (shrink)

Noncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller than the scale—and ultimately the concept of a point—makes sense in such a theory. We argue that it does not, in two interrelated ways. In the context of Connes’ spectral triple approach, we show that arbitrarily small regions are not definable in the formal sense. While in the scalar (...) field Moyal–Weyl approach, we show that they cannot be given an operational definition. We conclude that points do not exist in such geometries. We therefore investigate (a) the metaphysics of such a geometry, and (b) how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry. (shrink)

In this article, we discuss expertise by considering the activity of reading. Cognitive scientists have traditionally conceptualised reading as a single, well-defined task, namely the decoding of letter sequences into meaningful sequences of speech sounds. This definition captures a core feature of the reading activity at the computational level, but it is an overly narrow model of how reading behaviour occurs in the real world. We propose a more expansive model of expertise. In our view, expertise in general is best (...) conceptualised as a distributed process that takes place within a cultural-cognitive ecosystem. Our model allows for a more inclusive view of expertise in reading. We argue that reading is better understood as a manifold task domain that admits multiple reasonable criteria for evaluating performance. We draw on ethnographic data to show how our model allows for a wider appreciation of what expertise in reading amounts to in educational contexts. (shrink)

The Hamiltonian structure of General Relativity (GR), for both metric and tetrad gravity in a definite continuous family of space-times, is fully exploited in order to show that: i) the "Hole Argument" can be bypassed by means of a specific "physical individuation" of point-events of the space-time manifold M^4 in terms of the "autonomous degrees of freedom" of the vacuum gravitational field (Dirac observables), while the "Leibniz equivalence" is reduced to differences in the "non-inertial appearances" (connected to gauge (...) variables) of the same phenomena. ii) the chrono-geometric structure of a solution of Einstein equations for given, gauge-fixed, initial data (a "3-geometry" satisfying the relevant constraints on the Cauchy surface), can be interpreted as an "unfolding" in mathematical global time of a sequence of "achronal 3-spaces" characterized by "dynamically determined conventions" about distant simultaneity. This result stands out as an important conceptual difference with respect to the standard chrono-geometrical view of Special Relativity (SR) and allows, in a specific sense, for an "endurantist" interpretations of ordinary physical objects in GR. (shrink)