This study is about the Quality. Here I have dealt with the quality that differs significantly from the common understanding of quality /as determined quality/ that arise from the law of dialectics. This new quality is the quality of the quantity /quality of the quantitative changes/, noticed in philosophy by Plato as “quality of numbers”, and later developed by Hegel as “qualitative quantity. The difference between the known determined quality and qualitative quantity is evident in (...) the exhibit form of these two qualities. The exhibit form of the known determined quality from the law of dialectics /or it transformation/ is related with discreteness and abrupt changes. The exhibit form of the qualitative quantity /and it transformation/ is related with the continuity and gradual transition from one condition, to a different condition, without any abrupt changes. In my paper “Quality of the quantity”, I have argued that one of the most ancient implementation of quality of the number can be found in the dimensional mathematical model of point – line – surface – figure - introduced by Plato. The most whole presentation of the idea of quality of number in Plato is embeded in his teaching about the "eidical number". The quality of the quantity emerges as criteria for recognizing the difference between the eidical numbers and natural arithmetical number. The thesis concerning Plato is based on the The Unwritten Doctrine of Plato and one of the most original works in the history of philosophy written in the 20th century - “Arete bei Platon und Aristoteles” – “Arete in Plato and Aristotle” /Heidelberg 1959/ written by Hans Joachim Krämer. The new quality as the quality of the quantity /quality of the quantitative changes/, first noticed in philosophy by Plato as “quality of numbers” was developed in Hegel as “qualitative quantity”. Hegel proclaimed the Qualitative quantity, or Measure in the both of his Logics -The Science of Logic / the Greater Logic/ and The Lesser Logic/ Part One of the Encyclopedia of Philosophical Sciences: The Logic. In my paper I have offered the arguments that the concept of quality of the quantity should be enhanced with the adopted methodological approach of analogy with an implementation in the field of the Topology - Analysis Situs, developed by the Jules Henri Poincare. In the topology we could see homeomorphism as exhibit form of Quality on the Quantity. The explicit form of the quality of the quantity transformation is the continuous deformation – typically known in topology as homeomorphism. The concept of qualitative quantity is linked with the concept “structural stability” and nonequilibrum phase transition. The concept of structural stability is related with the topological homeomorphism. In his book “Synergetics: Introduction and Advanced Topics” /Springer, ISBN 3-540-40824/, in the Chapter 1.13. Qualitative Changes: General approach, p. 434-435, Hermann Haken explores and illustrate the structural stability with an example /figure 1.13, p.434/ given by of D'Arcy W. Thompson, the Scottish biologist, mathematician and classics scholar and pioneering mathematical biologist, Nobel Laureate in Medicine /1960/, the author of the book, On Growth and Form, /1917/. The quality of the quantity could be seen in the Herman Haken’s citation on the D'Arcy W. Thompson. My thesis is that the topological homeomorphism is the explicit form of the quality of the quantity transformation. The qualitative quantity change which becomes phenomenon, according to Émile Boutroux, is the subject of study in Cultural Phenomenology of Qualitative quantity. Our approach to this subject is Poincaré Model of the Subconscious Mind in Mathematics, which is the most suitable tool to unfold the arhetype of qualitative quantity. (shrink)

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda (...) ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Kim. (shrink)

The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the (...) former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions. (shrink)

The shape of the Earth's surface, its topography, is a fundamental dimension of the environment, shaping or mediating many other environmental flows or functions. But there is a major divergence in the way that topography is conceptualized in different domains. Topographic cartographers, information scientists, geomorphologists and environmental modelers typically conceptualize topographic variability as a continuous field of elevations or as some discrete approximation to such a field. Pilots, explorers, anthropologists, ecologists, hikers, and archeologists, on the other hand, typically conceptualize this (...) same variability in terms of hills and valleys, mountains and plains, barrows and trenches, that is, as (special sorts of) objects, with locations, shapes, and often names of their own. In this chapter, we sketch an approach to bridging this fundamental gap in geographic information infrastructure. (shrink)

It is a well-known fact that mathematics plays a crucial role in physics; in fact, it is virtually impossible to imagine contemporary physics without it. But it is questionable whether mathematical concepts could ever play such a role in psychology or philosophy. In this paper, we set out to examine a rather unobvious example of the application of topology, in the form of the theory of persons proposed by Kurt Lewin in his Principles of Topological Psychology. Our aim is (...) to show that this branch of mathematics can furnish a natural conceptual system for Gestalt psychology, in that it provides effective tools for describing global qualitative aspects of the latter’s object of investigation. We distinguish three possible ways in which mathematics can contribute to this: explanation, explication and metaphor. We hold that all three of these can be usefully characterized as throwing light on their subject matter, and argue that in each case this contrasts with the role of explanations in physics. Mathematics itself, we argue, provides something different from such explanations when applied in the field of psychology, and this is nevertheless still cognitively fruitful. (shrink)

In “Topology of Balasaguni’s Kutadgu Bilig: Thinking the Between,” Onur Karamercan focuses on the philosophical dimension of Kutadgu Bilig, a poetic work of Yūsuf Balasaguni, an 11th century Central Asian thinker, poet, and statesman. Karamercan pays special attention to the meaning of betweenness and, in the first step of his argument, discusses the hermeneutic and topological implications of the between, distingushing the dynamic sense of betweenness from a static sense of in-betweenness. He then moves on to analyze Balasaguni’s notion (...) of language, which he interprets as an early critique of the instrumental account of language and, by examining several selected fragments from Kutadgu Bilig, illustrates Balasaguni’s designation of language as an inexhaustible phenomenon. In the process, he also points to the possible parallels between Balasaguni’s and Heidegger’s ideas of language. In the final section of the article, building on his argument, Karamercan thematizes the margins of Turkic languages and of Islamic philosophy, suggesting that they need to be reexamined. He problematizes the very meaning of Asia itself by decentering what he calls “its internal East–West antagonism” and puts forth instead a framework based on in-betweenness reinterpreted from a topological perspective, proposing it as an alternative view which might help us make sense of the hermeneutic neighborhoods of Asian philosophies. (shrink)

In an article published in Prolegomena 2006, Christoph Schmidt-Petri has defended his interpretation and attacked mine of Mill’s idea that higher kinds of pleasure are superior in quality to lower kinds, regardless of quantity. Millian qualitative superiorities as I understand them are infinite superiorities. In this paper, I clarify my interpretation and show how Schmidt-Petri has misrepresented it and ignored the obvious textual support for it. As a result, he fails to understand how genuine Millian qualitative superiorities (...) determine the novel structure of Mill’s pluralistic utilitarianism, in which a social code of justice that distributes equal rights and duties takes absolute priority over competing considerations. Schmidt-Petri’s own interpretation is a non-starter, because it does noteven recognize that Mill is talking about different kinds of pleasant feelings, such that the higher kinds are intrinsically more valuable than the lower. I conclude by outlining why my interpretation is free of any metaphysical commitment to the “essence” of pleasure. (shrink)

Hobbes emphasized that the state of nature is a state of war because it is characterized by fundamental and generalized distrust. Exiting the state of nature and the conflicts it inevitably fosters is therefore a matter of establishing trust. Extant discussions of trust in the philosophical literature, however, focus either on isolated dyads of trusting individuals or trust in large, faceless institutions. In this paper, I begin to fill the gap between these extremes by analyzing what I call the (...) class='Hi'>topology of communities of trust. Such communities are best understood in terms of interlocking dyadic relationships that approximate the ideal of being symmetric, Euclidean, reflexive, and transitive. Few communities of trust live up to this demanding ideal, and those that do tend to be small (between three and fifteen individuals). Nevertheless, such communities of trust serve as the conditions for the possibility of various important prudential epistemic, cultural, and mental health goods. However, communities of trust also make possible various problematic phenomena. They can become insular and walled-off from the surrounding community, leading to distrust of out-groups. And they can lead their members to abandon public goods for tribal or parochial goods. These drawbacks of communities of trust arise from some of the same mecha-nisms that give them positive prudential, epistemic, cultural, and mental health value – and so can at most be mitigated, not eliminated. (shrink)

Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio of two heights, for example, (...) is a perceivable and measurable real relation between properties of physical things, a relation that can be shared by the ratio of two weights or two time intervals. Ratios are an example of continuous quantity; discrete quantities, such as whole numbers, are also realised as relations between a heap and a unit-making universal. For example, the relation between foliage and being-a-leaf is the number of leaves on a tree,a relation that may equal the relation between a heap of shoes and being-a-shoe. Modern higher mathematics, however, deals with some real properties that are not naturally seen as quantity, so that the “science of quantity” theory of mathematics needs supplementation. Symmetry, topology and similar structural properties are studied by mathematics, but are about pattern, structure or arrangement rather than quantity. (shrink)

Total ontological unification of matter at all levels of reality as a whole, its “grasp” of its dialectical structure, space dimensionality and structure of the language of nature – “house of Being” [1], gives the opportunity to see the “place” and to understand the nature of information as a phenomenon of Ontological (structural) Memory (OntoMemory), the measure of being of the whole, “the soul of matter”, qualitative quantity of the absolute forms of existence of matter (absolute states). “Information” (...) and “time” are multivalent phenomena of Ontological Memory substantiating the essential unity of the world on the “horizontal” and “vertical”. Ontological constructing of dialectics of Logos self-motion, total unification of matter, “grasp” of the nature of information leads to the necessity of introducing a new unit of information showing the ideas of dialectical formation and generation of new structures and meanings, namely Delta-Logit (Δ-Logit), qualitative quantum-prototecton, fundamental organizing, absolute existential-extreme. The simplest mathematical symbol represents the dialectical microprocessor of the Nature. Ontological formula of John A. Wheeler «It from Bit» [2] is “grasped” as the first dialectic link in the chain of ontological formulas → “It from Δ-Logit” → “It from OntoMemory” → “It from Logos, Logos into It”. Ontological Memory - core, semantic attractor of the new conceptual structure of the world of the Information Age, which is based on Absolute generating structure («general framework structure»), the representant of onto-genetic code and algorithm of the Universe. (shrink)

Integration sustainability outcomes give attention to construction ecology in the design review of urban environments to comply with Earth’s System that is composed of integral parts of the (i.e., physical, chemical and biological components). Naturally, exchange patterns of industrial ecology have consistent and periodic cycles to preserve energy flows and materials in Earth’s System. When engineering topology is affecting internal and external processes in system networks, it postulated the valence of the first-level spatial outcome (i.e., project compatibility success). These (...) instrumentalities are dependent on relating the second-level outcome (i.e., participant security satisfaction). The construction ecology-based topology (i.e., as feedback energy system) flows from biotic and abiotic resources in the entire Earth’s ecosystems. These spatial outcomes are providing an innovation, as entails a wide range of interactions to state, regulate and feedback “topology” to flow as “interdisciplinary equilibrium” of ecosystems. The interrelation dynamics of ecosystems are performing a process in a certain location within an appropriate time for characterizing their unique structure in “equilibrium patterns”, such as biosphere and collecting a composite structure of many distributed feedback flows. These interdisciplinary systems regulate their dynamics within complex structures. These dynamic mechanisms of the ecosystem regulate physical and chemical properties to enable a gradual and prolonged incremental pattern to develop a stable structure. The engineering topology of construction ecology for integration sustainability outcomes offers an interesting tool for ecologists and engineers in the simulation paradigm as an initial form of development structure within compatible computer software. This approach argues from ecology, resource savings, static load design, financial other pragmatic reasons, while an artistic/architectural perspective, these are not decisive. The paper described an attempt to unify analytic and analogical spatial modeling in developing urban environments as a relational setting, using optimization software and applied as an example of integrated industrial ecology where the construction process is based on a topology optimization approach. (shrink)

The passage of Mill’s Utilitarianism that sets out the condition in which one pleasure has a superior quality than another stokes interpretive controversy. According to the Lexical Interpretation, Mill takes one pleasure, P1, to be of a superior quality than another, P2, if, and only if, the smallest quantity of P1 is more valuable than any finite quantity of P2. This paper argues that, while the Lexical Interpretation may be supported with supplementary evidence, the passage itself does not (...) rule out qualitative superiority without lexical dominance, as it only requires P1 to be more valuable than any quantity of P2 that it is possible for someone to experience. Some will object that this concession to opponents of the Lexical Interpretation still renders Mill’s condition for qualitative superiority too demanding to be plausible. However, if Mill’s qualitative rankings apply to higher-order pleasures taken in modes of existence as such rather than to the pleasures of different activities chosen from within these modes, the objection loses much of its force. One upshot is that Mill may have more to contribute to debates in contemporary population axiology than is usually acknowledged. (shrink)

In the author’s previous contribution to this journal (Rosen 2015), a phenomenological string theory was proposed based on qualitative topology and hypercomplex numbers. The current paper takes this further by delving into the ancient Chinese origin of phenomenological string theory. First, we discover a connection between the Klein bottle, which is crucial to the theory, and the Ho-t’u, a Chinese number archetype central to Taoist cosmology. The two structures are seen to mirror each other in expressing the psychophysical (...) (phenomenological) action pattern at the heart of microphysics. But tackling the question of quantum gravity requires that a whole family of topological dimensions be brought into play. What we find in engaging with these structures is a closely related family of Taoist forebears that, in concert with their successors, provide a blueprint for cosmic evolution. Whereas conventional string theory accounts for the generation of nature’s fundamental forces via a notion of symmetry breaking that is essentially static and thus unable to explain cosmogony successfully, phenomenological/Taoist string theory entails the dialectical interplay of symmetry and asymmetry inherent in the principle of synsymmetry. This dynamic concept of cosmic change is elaborated on in the three concluding sections of the paper. Here, a detailed analysis of cosmogony is offered, first in terms of the theory of dimensional development and its Taoist (yin-yang) counterpart, then in terms of the evolution of the elemental force particles through cycles of expansion and contraction in a spiraling universe. The paper closes by considering the role of the analyst per se in the further evolution of the cosmos. (shrink)

The town of Aksum is historically the richest tourist destination in Ethiopia. Thus, it is known for its cultural tourist attractions i.e. archaeological, religious and historical attractions. The objective of this study is to assess the supplies of micro and small scale enterprises to the tourism industry in the town. A qualitative research design was pursued in this study. Data were collected from primary and secondary sources. Interviews were conducted with purposely selected subjects as the main instrument of primary (...) data collection. In addition, field visits were conducted to observe the sites and take pictures. Both published and unpublished secondary sources were used, particularly for the literature review. Participants of this study were selected from the tourism and hotel industry, the Small Scale Enterprises Agency, micro and small scale enterprises, the Culture and Tourism Agency and other government offices. The Ethiopian Sustainable Tourism Development Project (ESTDP) was also consulted to assess the involvement of micro and small scale enterprises in the tourism sector. The findings indicate that micro and small scale enterprises have been divided into the five main economic sectors including agriculture, manufacturing, construction, trade and service sectors. The Ethiopian Sustainable Tourism Development Project has supported the enterprises in working with the tourism industry. The government’s role in organizing and supporting the enterprises however, seems to be weak. Some of the enterprises produce and sell their products to tourism institutions involved as frontline suppliers to the tourists. However, the enterprises are not well-organized and not strong enough to supply the required quantity and quality. Moreover, some of the enterprises don’t have any link with the tourism sector. The policy implications from this study indicate that local government in collaboration with private sectors and voluntary donors should support the local small enterprises to increase their capacity and improve their supplies. (shrink)

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory of rest (...) and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises. (shrink)

In this article, I examine two of the standard objections to forms of value hedonism. The first is the common claim, most famously made by Bradley and Moore, that Mill's qualitative hedonism is inconsistent. The second is the apparent problem for quantitative hedonism in dealing with malicious pleasures. I argue that qualitative hedonism is consistent, even if it is implausible on other grounds. I then go on to show how our intuitions about malicious pleasure might be misleading.

In this paper, I define and study an abstract algebraic structure, the dimensive algebra, which embodies the most general features of the algebra of dimensional physical quantities. I prove some elementary results about dimensive algebras and suggest some directions for future work.

Aristotle defines motion as such: ‘The fulfillment of what exists potentially, in so far as it exist potentially, is motion.’ (Phy., Γ, 1, 201a10-11) He defines it again in the same chapter: ‘It is the fulfillment of what is potential when it is already fully real and operates not as itself but as movable, that is motion. What I mean by ‘as’ is this: Bronze is potentially a statue. But it is not the fulfillment of bronze as bronze which is (...) motion.’ (Phy., Γ, 1) 2) Motion: not a real thing Aristotle believes that ‘there is no such thing as motion over and above the things’ that is supposed to mean that motion cannot be something else than his categories: ‘It is always with respect to substance or to quality or to quantity or to place that what changes changes. But it is impossible to find anything common to these which is neither ‘this’ not quantum nor quale nor any of the other predicates. Hence neither will motion and change have reference to something over and above the things mentioned, for there is nothing over and above them.’ (Phy., Γ, 1, 200b32-201a3) In fact, it is what is moved that is a reality for Aristotle and not the motion itself: ‘Motion is known because of that which is moved, locomotion because of that which is carried. What is carried is a real thing, the movement is not.’ (Phy., Δ, 11) 3) Three items in each motion Aristotle distinguishes three items in each motion (Phy., E, 4): a) ‘That which’ moves; (Note: It is this item that makes a motion a unitary motion. (Phy., Δ, 11)) e.g. a man or gold b) ‘That in which’ the movement occurs; e.g. a place or an affection c) ‘That during which’ the movement takes place; e.g. time Based on the second item, Aristotle distinguishes three kinds of motion: quantitative, qualitative and local which are in respect of the three categories of quantity, quality and place. (Phy., E, 1) However, Aristotle speaks of four things in respect of which change takes place adding substance to the three mentioned categories. (Phy., Γ, 1, 200b32-35) It seems it is based on the differentiation of that in which motion takes place in these four types that Aristotle distinguishes four kinds of motion. (Phy., Γ, 1, 201a11-15): a) Alteration: the motion of what is alterable qua alterable b) Increase and decrease: the motion of what can be increased and what can be decreased c) Coming to be and passing away: the motion of what come to be and pass away d) Locomotion: the motion of what can be carried away Alteration happens in qualities, increase and decrease in quantities, coming to be and passing away in substances and locomotion in place. 4) Problem of motion as an element Discussing why Pythagoreans put motion in their column of indefinites, Aristotle somehow hints to the problem of understanding motion due to its non-elemental character: ‘The reason why they put motion into these genera is that it is thought to be something indefinite and the principles in the second column are indefinite because they are privative: none of them is either ‘this’ or ‘such’ or comes under any of the other modes of predication. The reason in turn why motion is thought to be indefinite is that it cannot be classed simply as a potentiality or as an actuality- a thing that is merely capable of having a certain size is not undergoing change, nor yet a thing that is actually of a certain size, and motion is thought to be a sort of actuality, but incomplete. The reason for this view being that the potential whose actuality it is is incomplete. This is why it is hard to grasp what motion is. It is necessary to class it with privation or with potentiality or with sheer actuality, yet none of these seems possible. There remains then the suggested mode of definition, namely that it is a sort of actuality, or actuality of the kind described, hard to grasp, but not incapable of existing.’ (Phy., Γ, 2, 201b24-) It becomes a real difficulty when it is asked whether the motion is in the mover or in the movable: ‘The solution of the difficulty that is raised about the motion-whether it is in the movable- is plain. It is the fulfillment of this potentiality, and by the action of that which has the power of causing motion; and the actuality of that which has the power of causing motion is not other than the actuality of the movable, for it must be the fulfillment of both. A thing is capable of causing motion because it can do this, it is a mover because it actually does it. But it is on the movable that it is capable of acting. Hence there is a single actuality of both alike, just as one to two and two to one are the same interval, and the steep ascent and the steep descent are one- for these are one and the same, although they can be described in different ways. So it is with the mover and the moved.’ (Phy., Γ, 3) This is not, however, the solution: ‘This view has a dialectical difficulty. Perhaps it is necessary that the actuality of the agent and that of the patient should not be the same. The one is ‘agency’ and the other ‘patiency’; and the outcome and the completion of the one is an ‘action’, that of the other a ‘passion.’ Since then they are both motions, we may ask: in what are they, if they are different? Either (a) both are in what is acted on and moved, or (b) the agency is in the agent and the patiency in the patient. … Now in alternative (b), the motion will be in the mover, for the same statement will hold of ‘mover’ and ‘moved.’ Hence either every mover will be moved, or, through having motion, it will not be moved. If on the other hand (a) both are in what is moved and acted on- both the agency and the patiency (e.g. both teaching and learning, though they are two, in the learner), then, first, the actuality of each will not be present in each, and, a second absurdity, a thing will have two motions at the same time. How will there be two alterations of quality in one subject towards one definite quality? The thing is impossible: the actualization will be one.’ (Phy., Γ, 3) This leads Aristotle to another problem, the problem of one identical actualization for two different things: ‘But (someone will say) it is contrary to reason to suppose that there should be one identical actualization of two things which are different in kind. Yet there will be, if teaching and learning are the same, and agency and patiency. To teach will be the same as to learn, and to act the same as to be acted on- the teacher will necessarily be learning everything that he teaches, and the agent will be acted on. One may reply: (1) It is not absurd that the actualization of one thing should be in another. Teaching is the activity of a person who can teach, yet the operation is performed on some patient- it is not cut adrift from a subject, but is of A on B. (2) There is nothing to prevent two things having one and the same actualization, provided the actualizations are not described in the same way, but are related as what can act on what is acting. (3) Nor is it necessary that the teacher should learn, even if to act and to be acted on are one and the same, provided they are not the same in definition (as ‘raiment’ and ‘dress’), but are the same merely in the sense in which the road from Athens to Thebes are the same, as has been explained above.’ (Phy., Γ, 3) And he continues: ‘For it is not things which are in a way the same that have all their attributes the same, but only such as have the same definition. But indeed it by no means follows from the fact that teaching is the same as learning, that to learn is the same as to teach, any more than it follows from the fact there is one distance between two things which are at a distance from each other, that the two vectors AB and BA, are one and the same. To generalize, teaching is not the same as learning, or agency and patiency, in the full sense, though they belong to the same subject, the motion; for the ‘actualization’ of X in Y’ and the ‘actualization of Y through the actualization of X’ differ in definition.’ (Phy., Γ, 3) . (shrink)

In the chapter of Difference and Repetition entitled ‘Ideas and the synthesis of difference,’ Deleuze mobilizes mathematics to develop a ‘calculus of problems’ that is based on the mathematical philosophy of Albert Lautman. Deleuze explicates this process by referring to the operation of certain conceptual couples in the field of contemporary mathematics: most notably the continuous and the discontinuous, the infinite and the finite, and the global and the local. The two mathematical theories that Deleuze draws upon for this purpose (...) are the differential calculus and the theory of dynamical systems, and Galois’ theory of polynomial equations. For the purposes of this paper I will only treat the first of these, which is based on the idea that the singularities of vector fields determine the local trajectories of solution curves, or their ‘topological behaviour’. These singularities can be described in terms of the given mathematical problematic, that is for example, how to solve two divergent series in the same field, and in terms of the solutions, as the trajectories of the solution curves to the problem. What actually counts as a solution to a problem is determined by the specific characteristics of the problem itself, typically by the singularities of this problem and the way in which they are distributed in a system. Deleuze understands the differential calculus essentially as a ‘calculus of problems’, and the theory of dynamical systems as the qualitative and topological theory of problems, which, when connected together, are determinative of the complex logic of different/ciation. (DR 209). Deleuze develops the concept of a problematic idea from the differential calculus, and following Lautman considers the concept of genesis in mathematics to ‘play the role of model ... with respect to all other domains of incarnation’. While Lautman explicated the philosophical logic of the actualization of ideas within the framework of mathematics, Deleuze (along with Guattari) follows Lautman’s suggestion and explicates the operation of this logic within the framework of a multiplicity of domains, including for example philosophy, science and art in What is Philosophy?, and the variety of domains which characterise the plateaus in A Thousand Plateaus. While for Lautman, a mathematical problem is resolved by the development of a new mathematical theory, for Deleuze, it is the construction of a concept that offers a solution to a philosophical problem; even if this newly constructed concept is characteristic of, or modelled on the new mathematical theory. (shrink)

A condensed summary of the adventures of ideas (1990-2020). Methodology of evolutionary-phenomenological constitution of Consciousness. Vector (BeVector) of Consciousness. Consciousness is a qualitative vector quantity. Vector of Consciousness as a synthesizing category, eidos-prototecton, intentional meta-observer. The development of the ideas of Pierre Teilhard de Chardin, Brentano, Husserl, Bergson, Florensky, Losev, Mamardashvili, Nalimov. Dialectic of Eidos and Logos. "Curve line" of the Consciousness Vector from space and time. The lower and upper sides of the "abyss of being". The existential (...) tension of being. Five reference “points” (existential-extremum) - world events in the evolution of Consciousness from “homo habilis” to “homo sapiens sapiens”. “Prometheus Effect". Inversion and reversion of Сonsciousness. "Open" and "closed" Сonsciousness. Consciousness and Self-Consciousness. Protogeometer: fall in the future, in the "EgoLand". The problem of justification/substantiation of mathematics (knowledge) is an ontological problem. The crisis of ontology and ontological limits of cognition. Ontological structure of space. The project of constructive dialectic ontology. The methodology of dialectical-ontological construction (modeling): conceptual-figure synthesis, total unification of matter, coincidence of ontological opposites, primordial Meta-Axioma and Superprinciple, vector (bivector) of the absolute state (states) of matter (absolute forms of existence). The ontological "celestial triangle" (Plato). Ontological invariants of the Universum and their ontological paths. Ontological and gnoseological dimensions of space. Triune (ontological) space of nine gnoseological dimensions: absolute rest (linear state, "Continuum")+ absolute motion (absolute vortex, "Discretuum") + absolute becoming (absolute wave, "Dis-Continuum"). Primordial generating structure: ontological framework, ontological carcass and ontological foundation. Ontological (structural, cosmic) memory - the semantic core of the conceptual construction of the Universum being as an eternal process of generation of new meanings and structures. Consciousness is an absolute (unconditional) attractor of meanings, a univalent phenomenon of ontological memory, which manifests itself at a certain level of the Universum being. Ontological space-MatterMemory-Ontological time (S-MM-T). Ontological Rhythm and Cycle. The nature and structure of ontological time. Natural (absolute) determinism. (shrink)

Abstract: Public procurement is the acquisition of right goods, works and services required to satisfy certain needs at the right time, from the right supplier, in the right quantities, in the right quality, and at the right price. Worldwide it accounts 10% – 30 % of GNP while in Tanzania it accounts for about more 45% of the total budget. Appropriate procurement system in the public sector is a tool for achieving political, economic and social goals. The research examined the (...) impact of the capacity building on the performance of LGAs procurement function, was conducted in Tanzania to the four regions in 2018, comprised a sample size of 224 respondents from eight Local Government Authorities (LGAs). Qualitative and quantitative data were collected, employed the case study method intended to the Evaluate Assessment of Capacity Building Programme on the Performance of LGAs procurement functions. The study revealed that procurement functions have improved because of the intervention of capacity building such as the improvement of the; Use and application of PPA and PPR, use and application of Procurement Planning, use and application of Contract Management and Administration, use procurement record keeping and reporting, use and application of PMIS & Other Procurement Systems, appropriate Tendering Process. Also, the researchers have revealed challenges hindering LGAs procurement system such as; lack training, unpredictable funds flow and political interference. Moreover, based on the contributions attributed by the capacity building further research can be undertaking to measure the impact of capacity building in the other areas apart from procurement field such as; health, agriculture, good governance and so on. In addition to that, another research can be undertaken to assess the factors hindering the performance of LGAs procurement system. (shrink)

This study aimed to understand the preserved elements of self-identity in persons with moderate to severe dementia attributable to Alzheimer’s disease. A semi-structured interview was developed to explore the narrative self among residents with dementia in a residential care facility and residents without dementia in an independent living setting. The interviews were transcribed verbatim from audio recordings and analyzed for common themes, while being sensitive to possible differences between the groups. The participants with dementia showed evidence of self-reference even though (...) losses in explicit memory were evident. The most noticeable difference between the two groups was time frame reference. Nonetheless, all participants showed understanding of their role in relationships and exhibited concrete preferences. Our findings suggest that memory loss and other cognitive deficits associated with moderate to severe dementia do not necessarily lead to a loss of “self.”. (shrink)

The current technical report presents the partial results of the quantitative analysis of the research project, after the review of 247 gambling websites. It is focused on and discusses the usage of the math terms specific to gambling in the reviewed sample. In particular, the fifth technical report discusses the usage of math terms associated with the game of slots, as found in the reviewed sample.

It is well known that the set of algebraic numbers (let us call it A) is countable. In this paper, instead of the usage of the classical terminology of cardinals proposed by Cantor, a recently introduced methodology using ①-based infinite numbers is applied to measure the set A (where the number ① is called grossone). Our interest to this methodology is explained by the fact that in certain cases where cardinals allow one to say only whether a set is countable (...) or it has the cardinality of the continuum, the ①-based methodology can provide a more accurate measurement of infinite sets. In this article, lower and upper estimates of the number of elements of A are obtained. Both estimates are expressed in ①-based numbers. (shrink)

Quantities like mass and temperature are properties that come in degrees. And those degrees (e.g. 5 kg) are properties that are called the magnitudes of the quantities. Some philosophers (e.g., Byrne 2003; Byrne & Hilbert 2003; Schroer 2010) talk about magnitudes of phenomenal qualities as if some of our phenomenal qualities are quantities. The goal of this essay is to explore the anti-physicalist implication of this apparently innocent way of conceptualizing phenomenal quantities. I will first argue for a metaphysical thesis (...) about the nature of magnitudes based on Yablo’s proportionality requirement of causation. Then, I will show that, if some phenomenal qualities are indeed quantities, there can be no demonstrative concepts about some of our phenomenal feelings. That presents a significant restriction on the way physicalists can account for the epistemic gap between the phenomenal and the physical. I’ll illustrate the restriction by showing how that rules out a popular physicalist response to the Knowledge Argument. (shrink)

Imagination is necessary for scientific practice, yet there are no in vivo sociological studies on the ways that imagination is taught, thought of, or evaluated by scientists. This article begins to remedy this by presenting the results of a qualitative study performed on two systems biology laboratories. I found that the more advanced a participant was in their scientific career, the more they valued imagination. Further, positive attitudes toward imagination were primarily due to the perceived role of imagination in (...) problem-solving. But not all problem-solving episodes involved clear appeals to imagination, only maximally specific problems did. This pattern is explained by the presence of an implicit norm governing imagination use in the two labs: only use imagination on maximally specific problems, and only when all other available methods have failed. This norm was confirmed by the participants, and I argue that it has epistemological reasons in its favour. I also found that its strength varies inversely with career stage, such that more advanced scientists do (and should) occasionally bring their imaginations to bear on more general problems. A story about scientific pedagogy explains the trend away from (and back to) imagination over the course of a scientific career. Finally, some positive recommendations are given for a more imagination-friendly scientific pedagogy. (shrink)

This paper intends to further the understanding of the formal properties of (higher-order) vagueness by connecting theories of (higher-order) vagueness with more recent work in topology. First, we provide a “translation” of Bobzien's account of columnar higher-order vagueness into the logic of topological spaces. Since columnar vagueness is an essential ingredient of her solution to the Sorites paradox, a central problem of any theory of vagueness comes into contact with the modern mathematical theory of topology. Second, Rumfitt’s recent (...) topological reconstruction of Sainsbury’s theory of prototypically defined concepts is shown to lead to the same class of spaces that characterize Bobzien’s account of columnar vagueness, namely, weakly scattered spaces. Rumfitt calls these spaces polar spaces. They turn out to be closely related to Gärdenfors’ conceptual spaces, which have come to play an ever more important role in cognitive science and related disciplines. Finally, Williamson’s “logic of clarity” is explicated in terms of a generalized topology (“locology”) that can be considered an alternative to standard topology. Arguably, locology has some conceptual advantages over topology with respect to the conceptualization of a boundary and a borderline. Moreover, in Williamson’s logic of clarity, vague concepts with respect to a notion of a locologically inspired notion of a “slim boundary” are (stably) columnar. Thus, Williamson’s logic of clarity also exhibits a certain affinity for columnar vagueness. In sum, a topological perspective is useful for a conceptual elucidation and unification of central aspects of a variety of contemporary accounts of vagueness. (shrink)

Since antiquity well into the beginnings of the 20th century geometry was a central topic for philosophy. Since then, however, most philosophers of science, if they took notice of topology at all, considered it as an abstruse subdiscipline of mathematics lacking philosophical interest. Here it is argued that this neglect of topology by philosophy may be conceived of as the sign of a conceptual sea-change in philosophy of science that expelled geometry, and, more generally, mathematics, from the central (...) position it used to have in philosophy of science and placed logic at center stage in the 20th century philosophy of science. Only in recent decades logic has begun to loose its monopoly and geometry and topology received a new chance to find a place in philosophy of science. (shrink)

We now found nine new topologies, such as: NonStandard Topology, Largest Extended NonStandard Real Topology, Neutrosophic Triplet Weak/Strong Topologies, Neutrosophic Extended Triplet Weak/Strong Topologies, Neutrosophic Duplet Topology, Neutrosophic Extended Duplet Topology, Neutrosophic MultiSet Topology, and recall and improve the seven previously founded topologies in the years (2019-2023), namely: NonStandard Neutrosophic Topology, NeutroTopology, AntiTopology, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. They are called avantgarde topologies because of their innovative (...) forms. (shrink)

The aim of this paper is to show that (elementary) topology may be useful for dealing with problems of epistemology and metaphysics. More precisely, I want to show that the introduction of topological structures may elucidate the role of the spatial structures (in a broad sense) that underly logic and cognition. In some detail I’ll deal with “Cassirer’s problem” that may be characterized as an early forrunner of Goodman’s “grue-bleen” problem. On a larger scale, topology turns out to (...) be useful in elaborating the approach of conceptual spaces that in the last twenty years or so has found quite a few applications in cognitive science, psychology, and linguistics. In particular, topology may help distinguish “natural” from “not-so-natural” concepts. This classical problem that up to now has withstood all efforts to solve (or dissolve) it by purely logical methods. Finally, in order to show that a topological perspective may also offer a fresh look on classical metaphysical problems, it is shown that Leibniz’s famous principle of the identity of indiscernibles is closely related to some well-known topological separation axioms. More precisely, the topological perspective gives rise in a natural way to some novel variations of Leibniz’s principle. (shrink)

Work of elderly is a controversial problem. The introduction of protection of old age in form of pensions and retirement caused shaping in modern societies qualitatively new social category of persons in post-working age. Growth of human life-span with simultaneous lack of the principle changes of pensionable age inflicts grow in quantity of persons’ using welfare benefits. Growing costs of seniors livelihood lead to transformations in socio-economical structures as well as forcing them to engage in activities that will help (...) increase their social participation, including the lengthening of their professional activity. It seems that the nowadays processes of dematerialization of work combined with the shaping of knowledge-based economy and the movement of third-age universities largely enable the achievement of these objectives. Article aims to approximate the results of qualitative analysis of elderly economic activity in Bialystok conducted in the context of social capital research. Study describes main factors that restrict work opportunities for older people, as well as their hidden resources and potential workplaces. ** Wykonywanie pracy zarobkowej przez osoby starsze jest zagadnieniem kontrowersyjnym. Wprowadzenie zabezpieczenia starości w formie rent i emerytur sprawiło, że w społeczeństwach nowoczesnych ukształtowała siȩ jakościowo nowa kategoria społeczna składaj¸a}ca siȩ z osób w wieku poprodukcyjnym. Wzrost długości życia ludzkiego przy jednoczesnym braku zasadniczych zmian progów wieku emerytalnego sprawia, że ilość osób korzystaj¸a}cych ze świadczeń rośnie. Zwiȩkszaj¸a}ce siȩ koszty utrzymania seniorów prowadz¸a} do szeregu przemian w strukturach społeczno-ekonomicznych oraz wymuszaj¸a} podejmowanie działań, które pozwol¸a} na wzrost ich uczestnictwa społecznego, w tym na wydłużanie ich aktywności zawodowej. Wydaje siȩ, że zachodz¸a}ce współcześnie procesy dematerializacji pracy ł¸a}czone z kształtowaniem siȩ gospodarki opartej na wiedzy oraz ruch uniwersytetów trzeciego wieku w znacznej mierze umożliwiaj¸a realizacjȩ tych celów. Artykuł ma na celu przybliżenie wybranych wyników jakościowych analiz aktywności ekonomicznej ludzi starych w Białymstoku prowadzonych w kontekście badań nad kapitałem społecznym. Określone zostały podstawowe czynniki ograniczaj¸ace możliwości wykonywania pracy przez ludzi starych, jak również ich ukryte zasoby i potencjalne miejsca pracy. (shrink)

Experimental philosophy brings empirical methods to philosophy. These methods are used to probe how people think about philosophically interesting things such as knowledge, morality, and freedom. This paper explores the contribution that qualitative methods have to make in this enterprise. I argue that qualitative methods have the potential to make a much greater contribution than they have so far. Along the way, I acknowledge a few types of resistance that proponents of qualitative methods in experimental philosophy might (...) encounter, and provide reasons to think they are ill-founded. (shrink)

The aim of this paper is to elucidate the relationship between Aristotelian conceptual oppositions, commutative diagrams of relational structures, and Galois connections.This is done by investigating in detail some examples of Aristotelian conceptual oppositions arising from topological spaces and similarity structures. The main technical device for this endeavor is the notion of Galois connections of order structures.

I analyze the meaning of mass in Newtonian mechanics. First, I explain the notion of primitive ontology, which was originally introduced in the philosophy of quantum mechanics. Then I examine the two common interpretations of mass: mass as a measure of the quantity of matter and mass as a dynamical property. I claim that the former is ill-defined, and the latter is only plausible with respect to a metaphysical interpretation of laws of nature. I explore the following options for (...) the status of laws: Humeanism, primitivism about laws, dispositionalism, and ontic structural realism. (shrink)

Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity.

This is a revised version of the introductory essay in C. Eschenbach, C. Habel and B. Smith (eds.), Topological Foundations of Cognitive Science, Hamburg: Graduiertenkolleg Kognitionswissenschaft, 1994, the text of a talk delivered at the First International Summer Institute in Cognitive Science in Buffalo in July 1994.

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...) are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge. (shrink)

Irigaray’s engagement with Aristotelian physics provides a specific diagnosis of women’s ontological and ethical situation under Western metaphysics: Women provide place and containership to men, but have no place of their own, rendering them uncontained and abyssal. She calls for a reconfiguration of this topological imaginary as a precondition for an ethics of sexual difference. This paper returns to Aristotelian cosmological texts to further investigate the topologies of sexual difference suggested there. In an analysis both psychoanalytic and phenomenological, the paper (...) rigorously traces a teleological and oedipal narrative implicit in the structure of the Aristotelian cosmos, in which desire for the mother is superseded by love for the father. Further, the paper argues that this narrative is complicated by certain other elements in the Aristotelian text—aporias involving the notion of boundary and the relationship between space and time, the fallenness of the feminine, and the ineliminably aleatory qualities of matter. The paper concludes that such elements may provide material for disrupting this teleology of gender, opening onto not merely an ethics of sexual difference, but providing space and place for a proliferation of non-normative, queer, transgender and intersex modes of sexed and gendered subjectivity. (shrink)

The paper interprets the concept “operator in the separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined in the “classical” quantum mechanics) by that of “quantum information”. As far as wave function is the characteristic function of the probability (density) distribution for all possible values of a certain quantity to be measured, the definition of quantity in quantum mechanics means any unitary change of the probability (density) distribution. It can be represented as a particular case (...) of “unitary” qubits. The converse interpretation of any qubits as referring to a certain physical quantity implies its generalization to non-Hermitian operators, thus neither unitary, nor conserving energy. Their physical sense, speaking loosely, consists in exchanging temporal moments therefore being implemented out of the space-time “screen”. “Dark matter” and “dark energy” can be explained by the same generalization of “quantity” to non-Hermitian operators only secondarily projected on the pseudo-Riemannian space-time “screen” of general relativity according to Einstein's “Mach’s principle” and his field equation. (shrink)

This second technical report shows some partial results for the variables of the proposed statistical analysis and a discussion about some changes in sampling. In what concerns the qualitative analysis of content, the report presents the general predominant tendencies that get contoured with the first two samples.

The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...) and (3) the specific forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology – the proof of Alexander’s theorem – is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identified above brings to the emergence of philosophically relevant features in the practice of topology: the need for a revision in the definition of criteria of validity, the interest in tracking the operations that are performed on the notation, and the constant and fruitful back-and-forth from one representation to another in dealing with mathematical content. Finally, some suggestions for further research are given in the conclusions. (shrink)

The production of scientific instruments in America was neither a postwar phenomenon nor dramatically different from that of several other developed countries. It did, however, undergo a step-change in direction, size and style during and after the war. The American scientific instrument industry after 1945 was intimately dependent on, and shaped by, prior American and European experience. This was true of the specific genres of instrument produced commercially; to links between industry and science; and, just as importantly, to manufacturing practices (...) and cultures. I will argue that, despite the new types of instrument commercialized after the war, this historical continuity of links with science and scientists guided and constrained the design and manufacture of these products. Nevertheless, new designers, manufacturers and customers gradually transformed the culture of scientific instruments in the second half of the century. -/- This chapter deals with a subset of the American instrument industry, namely the measuring and monitoring instruments manufactured for scientific use. Even with the specification of ‘scientific’ instruments, however, these borders are rather artificial and unclear: instrument making from the seventeenth through the twentieth century has generally involved the fabrication of both standard products and custom-made devices for scientific use.2 In this context of sales quantities, ‘scientific’ instruments have often been defined as low-volume, special-order or custom devices. In a similar vein, ‘scientific’ instruments were commonly distinguished from ‘production’ instruments by context of usage, namely their very absence from – and indeed irrelevance to – production environments. This demarcation according to customer and environment was mirrored in at least one furth er respect: the training of their users. The classification into ‘scientific’ and ‘engineering’ applications was as fluid as the relationship between American universities and technical industries themselves.Despite these complementary definitions, the notion of the ‘scientific instrument’ was beginning to prove inadequate even at the turn of the twentieth century, and dramatically so when discussing the post-Second World War period. Definitions altered qualitatively after the Second World War in at least three further ways: (a) new genres of device altered the scope of the scientific instrument; (b) the contribution of State and military sponsorship of new forms of instrument became significant; and, (c) the postwar demand for specialist instruments increased rapidly, owing to wartime innovation, new applications and new customers. I will explore the evolution of instrument manufacturing in this changing context of new technology, funding, development and markets. (shrink)

The aim of this paper is to show that topology has a bearing on Leibniz’s Principle of the Identity of Indiscernibles (PII). According to (PII), if, for all properties F, an object a has property F iff object b has property F, then a and b are identical. If any property F whatsoever is permitted in PII, then Leibniz’s principle is trivial, as is shown by “identity properties”. The aim of this paper is to show that topology can (...) make a contribution to the problem of giving criteria of how to restrict the domain of properties to render (PII) non-trivial. In topology a wealth of different Leibnizian principles of identity can be defined - PII turns out to be just the weakest topological separation axiom T0 in disguise, stronger principles of can be defined with the aid of higher separation axioms Ti, i > 0. Topologically defined properties have a variety of nice features, in particular they are stable in a natural sense. Topologically defined properties do not have a monopoly on defining “good” properties. In the final section of the paper it is show that the topological approach is closely related to Gärdenfors’s approach of conceptual spaces based on the concept of convexity. (shrink)

The current study evaluates qualitatively how the mathematical dimension of gambling is reflected in the content of gambling websites. A number of gambling websites have been reviewed for their content in that respect. A statistical analysis recorded the presence of the mathematical dimension of gambling and its forms in the content of the participating websites, and a qualitative research study analyzed and assessed the quality of the content with respect to that dimension. The technical reports associated with this study (...) describe the methods used in the processes of review and content analysis, details of the processes, and the specific challenges and difficulties that they posed. (shrink)

Proponents of ontic conceptions of explanation require all explanations to be backed by causal, constitutive, or similar relations. Among their justifications is that only ontic conceptions can do justice to the ‘directionality’ of explanation, i.e., the requirement that if X explains Y , then not-Y does not explain not-X . Using topological explanations as an illustration, we argue that non-ontic conceptions of explanation have ample resources for securing the directionality of explanations. The different ways in which neuroscientists rely on multiplexes (...) involving both functional and anatomical connectivity in their topological explanations vividly illustrate why ontic considerations are frequently (if not always) irrelevant to explanatory directionality. Therefore, directionality poses no problem to non-ontic conceptions of explanation. (shrink)

In this paper, I present a general theory of topological explanations, and illustrate its fruitfulness by showing how it accounts for explanatory asymmetry. My argument is developed in three steps. In the first step, I show what it is for some topological property A to explain some physical or dynamical property B. Based on that, I derive three key criteria of successful topological explanations: a criterion concerning the facticity of topological explanations, i.e. what makes it true of a particular system; (...) a criterion for describing counterfactual dependencies in two explanatory modes, i.e. the vertical and the horizontal; and, finally, a third perspectival one that tells us when to use the vertical and when to use the horizontal mode. In the second step, I show how this general theory of topological explanations accounts for explanatory asymmetry in both the vertical and horizontal explanatory modes. Finally, in the third step, I argue that this theory is universally applicable across biological sciences, which helps to unify essential concepts of biological networks. (shrink)

This essay explores various problematical aspects of Descartes' conservation principle for the quantity of motion (size times speed), particularly its largely neglected "dual role" as a measure of both durational motion and instantaneous "tendencies towards motion". Overall, an underlying non-local, or "holistic", element of quantity of motion (largely derived from his statics) will be revealed as central to a full understanding of the conservation principle's conceptual development and intended operation; and this insight can be of use in responding (...) to some of the recent and traditional criticisms of Descartes' physics. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine – (...) Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)