Results for 'Category theory'

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  1. Category Theory is a Contentful Theory.Shay Logan - 2015 - Philosophia Mathematica 23 (1):110-115.
    Linnebo and Pettigrew present some objections to category theory as an autonomous foundation. They do a commendable job making clear several distinct senses of ‘autonomous’ as it occurs in the phrase ‘autonomous foundation’. Unfortunately, their paper seems to treat the ‘categorist’ perspective rather unfairly. Several infelicities of this sort were addressed by McLarty. In this note I address yet another apparent infelicity.
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  2. Category Theory and Set Theory as Theories About Complementary Types of Universals.David P. Ellerman - 2017 - Logic and Logical Philosophy 26 (2):1-18.
    Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the (...)
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  3.  91
    How Category Theory Works.David Ellerman - manuscript
    The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions. The analysis extends directly to other concrete categories (groups, rings, vector spaces, etc.) where the objects are sets with a certain type of structure and the morphisms are functions that preserve that structure. Then the elements & distinctions-based definitions can (...)
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  4.  87
    Pluralist-Monism. Derived Category Theory as the Grammar of N-Awareness.Shanna Dobson & Robert Prentner - manuscript
    In this paper, we develop a mathematical model of awareness based on the idea of plurality. Instead of positing a singular principle, telos, or essence as noumenon, we model it as plurality accessible through multiple forms of awareness (“n-awareness”). In contrast to many other approaches, our model is committed to pluralist thinking. The noumenon is plural, and reality is neither reducible nor irreducible. Nothing dies out in meaning making. We begin by mathematizing the concept of awareness by appealing to the (...)
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  5. On Concrete Universals: A Modern Treatment Using Category Theory.David Ellerman - 2014 - AL-Mukhatabat.
    Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic (...)
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  6. The Importance of Developing a Foundation for Naive Category Theory.Marcoen J. T. F. Cabbolet - 2015 - Thought: A Journal of Philosophy 4 (4):237-242.
    Recently Feferman has outlined a program for the development of a foundation for naive category theory. While Ernst has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a ‘cookbook recipe’ is used (...)
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  7. On the Self-Predicative Universals of Category Theory.David Ellerman - manuscript
    This paper shows how the universals of category theory in mathematics provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. The paper also shows how the always-self-predicative universals of category theory provide the "opposite bookend" to the never-self-predicative universals of iterative set theory and thus (...)
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  8.  35
    Buddhist Thought on Emptiness and Category Theory.Venkata Rayudu Posina & Sisir Roy - forthcoming - In Monograph on Zero.
    Notions such as Sunyata, Catuskoti, and Indra's Net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nagarjuna considered two levels of reality: one called conventional reality and the other ultimate reality. Within this framework, Sunyata refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuskoti refers to the claim (...)
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  9. Abstract Artifact Theory About Fictional Characters Defended — Why Sainsbury’s Category-Mistake Objection is Mistaken.Zsófia Zvolenszky - 2013 - Proceedings of the European Society for Aesthetics Vol. 5/2013.
    In this paper, I explore a line of argument against one form of realism about fictional characters : abstract artifact theory, the view according to which fictional characters like Harry Potter are part of our reality, but, they are abstract objects created by humans, akin to the institution of marriage and the game of soccer. I will defend artifactualism against an objection that Mark Sainsbury considers decisive against it: the category-mistake objection. The objection has it that artifactualism attributes (...)
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  10. A One Category Ontology.L. A. Paul - forthcoming - In John A. Keller (ed.), Being, Freedom, and Method: Themes From the Philosophy of Peter van Inwagen. Oxford University Press.
    I defend a one category ontology: an ontology that denies that we need more than one fundamental category to support the ontological structure of the world. Categorical fundamentality is understood in terms of the metaphysically prior, as that in which everything else in the world consists. One category ontologies are deeply appealing, because their ontological simplicity gives them an unmatched elegance and spareness. I’m a fan of a one category ontology that collapses the distinction between particular (...)
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  11. The Problem of Exclusion in Feminist Theory and Politics: A Metaphysical Investigation Into Constructing a Category of 'Woman'.Maya J. Goldenberg - 2007 - Journal of Gender Studies 16 (2):139-153.
    The precondition of any feminist politics – a usable category of ‘woman’ – has proved to be difficult to construct, even proposed to be impossible, given the ‘problem of exclusion’. This is the inevitable exclusion of at least some women, as their lives or experiences do not fit into the necessary and sufficient condition(s) that denotes group membership. In this paper, I propose that the problem of exclusion arises not because of inappropriate category membership criteria, but because of (...)
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  12. Realization Reductios, and Category Inclusion.Ronald P. Endicott - 2010 - Journal of Philosophy 107 (4):213-219.
    Thomas Polger and Laurence Shapiro argue that Carl Gillett's much publicized dimensioned theory of realization is incoherent, being subject to a reductio. Their argument turns on the fact that Gillett's definition of realization makes property instances the exclusive relata of the realization relation, while his belief in multiple realization implies its denial, namely, that properties are the relata of the realization relation on occasions of multiple realization. Others like Sydney Shoemaker have also expressed their view of realization in terms (...)
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  13.  74
    The Category of Mereotopology and Its Ontological Consequences.Saikeerthi Rachavelpula - 2017 - University of Chicago Mathematics Research Program 2017.
    We introduce the category of mereotopology Mtop as an alternative category to that of topology Top, stating ontological consequences throughout. We consider entities such as boundaries utilizing Brentano’s thesis and holes utilizing homotopy theory with a rigorous proof of Hausdorff Spaces satisfying [GEM]TC axioms. Lastly, we mention further areas of study in this category.
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  14. A Category Semantics.Paul Symington - 2018 - In Paul Hackett (ed.), Mereologies, Ontologies, and Facets: The Categorial Structure of Reality. New York: Lexington Books. pp. 65-85.
    In this paper, I present a categorial theory of meaning which asserts that the meaning of a sentence is the function from the actualization of some potentiality or the potentiality of some actuality to the truth of the sentence. I argue that it builds on the virtues of David Lewis’s Possible World Semantics but advances beyond problems that Lewis’s theory faces with its distinctly Aristotelian turn toward actuality and potentiality.
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  15. Hick, Pluralism and Category Mistake.Akbari Reza - 2009 - International Journal of Hekmat 1 (1):101-114.
    John Hick’s theory concerning plurality of religions is an ontologic pluralism according to which all religions are authentic ways for man to attain the "real an sich". Gods of religions are real as perceived and veridical hallucinations; while the “real an sich” has ineffable substantial and trans-categorical properties. Hick’s view suffers from several problems. As a second order analysis of religions, Hick’s view is not a correct one. To reject naturalism, it falls into an epistemological circle, where distinction between (...)
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  16. Adjoints and Emergence: Applications of a New Theory of Adjoint Functors. [REVIEW]David Ellerman - 2007 - Axiomathes 17 (1):19-39.
    Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality in mathematics. The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens. The central feature of an adjunction is what might be called “determination through universals” based on universal mapping properties. A recently developed “heteromorphic” (...)
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  17. Deixis Category as Favorable Syllabus Materials —A Critical Study in Sudan Practical Integrated National English.Mustafa Shazali Mustafa Ahmed Msm - unJuly 2011known - Theory and Practice in Language Studies (No. 7,):811-820.
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  18. Kripke’s Category Error: Why There Are No Necessary A Posteriori Propositions.Peter Ulric Tse - manuscript
    Kripke’s main argument against descriptivism is rooted in a category error that confuses statements about the world with statements about models of the world. It is only because of the ambiguity introduced by the fact that a single sentence can frame two different propositions, one necessary and the other a posteriori, that one reaches the mistaken conclusion that there can be necessary a posteriori truths. This ambiguity from language was carried over into modal logic by Kripke. However, we must (...)
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  19. Bundle Theory with Kinds.Markku Keinänen & Tuomas E. Tahko - 2019 - Philosophical Quarterly 69 (277):838-857.
    Is it possible to get by with just one ontological category? We evaluate L.A. Paul's attempt to do so: the mereological bundle theory. The upshot is that Paul's attempt to construct a one category ontology may be challenged with some of her own arguments. In the positive part of the paper we outline a two category ontology with property universals and kind universals. We will also examine Paul's arguments against a version of universal bundle theory (...)
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  20. Instantiation in Trope Theory.A. R. J. Fisher - 2018 - American Philosophical Quarterly 55 (2):153-164.
    The concept of instantiation is realized differently across a variety of metaphysical theories. A certain realization of the concept in a given theory depends on what roles are specified and associated with the concept and its corresponding term as well as what entities are suited to fill those roles. In this paper, the classic realization of the concept of instantiation in a one-category ontology of abstract particulars or tropes is articulated in a novel way and defended against unaddressed (...)
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  21.  65
    Walter Benjamin's Critique of the Category of Aesthetic Form: 'The Work of Art in the Age of its Technological Reproducibility' From the Perspective of Benjamin's Early Writing.Alison Ross - 2015 - In Nathan Ross (ed.), The Aesthetic Ground of Critical Theory : New Readings of Benjamin and Adorno. London: Roman and Littlefield. pp. 83-97.
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  22. On Adjoint and Brain Functors.David Ellerman - 2016 - Axiomathes 26 (1):41-61.
    There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms that parses an adjunction into two separate parts. Then these separate parts can be recombined in a new way to define a cognate concept, the brain functor, to abstractly model the functions of perception and action of a brain. The treatment uses relatively simple (...)
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  23. A Sketch of a Sirenia: Meros Theory.Dan Kurth - manuscript
    This sketch of a perhaps future 'Elementary Theory of the Category of Mereological Sums (including Mereological Wholes and Parts)' relates to my previous papers "The Topos of Emergence" and "Intelligible Gunk". I assert that for successfully categorizing Mereology one has to start with a specific setting of gunk. In this paper we will give a sketch of a categorically version of particular mereological structures. I.e. we will follow the example of F.W.Lawvere’s “An elementary theory of the (...) of sets” -/- where he introduced a categorised version of set theory. We refer to sirenians mainly for the reason that they are the closest living relatives of elephants. -/- But they are also rather underestimated creatures - at the first moment rather dull and clumsy, but moving gracefully and elegant in their natural habitat.And some sailors already reckognized their bewitching attraction before we did.Yet we still think this sirenia is a modest creature compared with the elephant in the room. (shrink)
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  24. Toward a Theory of the Pragmatic A Priori. From Carnap to Lewis and Beyond.Thomas Mormann - 2012 - Rudolf Carnap and the Legacy of Logical Empiricism 16:113 - 132.
    The aim of this paper is make a contribution to the ongoing search for an adequate concept of the a priori element in scientific knowledge. The point of departure is C.I. Lewis’s account of a pragmatic a priori put forward in his "Mind and the World Order" (1929). Recently, Hasok Chang in "Contingent Transcendental Arguments for Metaphysical Principles" (2008) reconsidered Lewis’s pragmatic a priori and proposed to conceive it as the basic ingredient of the dynamics of an embodied scientific reason. (...)
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  25. Examining Philosophy of Technology Using Grounded Theory Methods.Mark David Webster - 2016 - Forum: Qualitative Social Research 17 (2).
    A qualitative study was conducted to examine the philosophy of technology of K-12 technology leaders, and explore the influence of their thinking on technology decision making. The research design aligned with CORBIN and STRAUSS grounded theory methods, and I proceeded from a research paradigm of critical realism. The subjects were school technology directors and instructional technology specialists, and data collection consisted of interviews and a written questionnaire. Data analysis involved the use of grounded theory methods including memo writing, (...)
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  26. Unifying Diseases From a Genetic Point of View: The Example of the Genetic Theory of Infectious Diseases.Marie Darrason - 2013 - Theoretical Medicine and Bioethics 34 (4):327-344.
    In the contemporary biomedical literature, every disease is considered genetic. This extension of the concept of genetic disease is usually interpreted either in a trivial or genocentrist sense, but it is never taken seriously as the expression of a genetic theory of disease. However, a group of French researchers defend the idea of a genetic theory of infectious diseases. By identifying four common genetic mechanisms (Mendelian predisposition to multiple infections, Mendelian predisposition to one infection, and major gene and (...)
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  27. A Methodological Note on Proving Agreement Between the Elementary Process Theory and Modern Interaction Theories.Cabbolet Marcoen - manuscript
    The Elementary Process Theory (EPT) is a collection of seven elementary process-physical principles that describe the individual processes by which interactions have to take place for repulsive gravity to exist. One of the two main problems of the EPT is that there is no proof that the four fundamental interactions (gravitational, electromagnetic, strong, and weak) as we know them can take place in the elementary processes described by the EPT. This paper sets forth the method by which it can (...)
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  28. Free Associations Mirroring Self- and World-Related Concepts: Implications for Personal Construct Theory, Psycholinguistics and Philosophical Psychology.Martin Kuška, Radek Trnka, Aleš A. Kuběna & Jiří Růžička - 2016 - Frontiers in Psychology (7):art.n. 981, 1-13.
    People construe reality by using words as basic units of meaningful categorization. The present theory-driven study applied the method of a free association task to explore how people express the concepts of the world and the self in words. The respondents were asked to recall any five words relating with the word world. Afterwards they were asked to recall any five words relating with the word self. The method of free association provided the respondents with absolute freedom to choose (...)
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  29. Theory Without Practice is Empty; Practice Without Theory is Blind: The Inherent Inseparability of Doctrine and Skills.Harold Anthony Lloyd - 2017 - In Linda H. Edwards (ed.), The Doctrine Skills Divide: Legal Education's Self-Inflicted Wound. Durham, NC, USA: pp. 77-90.
    This article maintains that the so-called theory-practice divide in legal education is not only factually false but semantically impossible. -/- As to the divide's falsity, practitioners have of course performed excellent scholarship and academics have excelled in practice. As to the divide's semantic impossibility, this article examines, among other things: -/- (1) the essential role of experience in meaning, -/- (2) the resulting inseparability of theory and practice in the world of experience, -/- (3) problems the divide shares (...)
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  30.  17
    Homotopy Type Theory and Structuralism.Teruji Thomas - 2014 - Dissertation, University of Oxford
    I explore the possibility of a structuralist interpretation of homotopy type theory (HoTT) as a foundation for mathematics. There are two main aspects to HoTT's structuralist credentials. First, it builds on categorical set theory (CST), of which the best-known variant is Lawvere's ETCS. I argue that CST has merit as a structuralist foundation, in that it ascribes only structural properties to typical mathematical objects. However, I also argue that this success depends on the adoption of a strict typing (...)
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  31. The Mathematical Theory of Categories in Biology and the Concept of Natural Equivalence in Robert Rosen.Franck Varenne - 2013 - Revue d'Histoire des Sciences 66 (1):167-197.
    The aim of this paper is to describe and analyze the epistemological justification of a proposal initially made by the biomathematician Robert Rosen in 1958. In this theoretical proposal, Rosen suggests using the mathematical concept of “category” and the correlative concept of “natural equivalence” in mathematical modeling applied to living beings. Our questions are the following: According to Rosen, to what extent does the mathematical notion of category give access to more “natural” formalisms in the modeling of living (...)
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  32. Information Theory’s Failure in Neuroscience: On the Limitations of Cybernetics.Lance Nizami - 2014 - In Proceedings of the IEEE 2014 Conference on Norbert Wiener in the 21st Century.
    In Cybernetics (1961 Edition), Professor Norbert Wiener noted that “The role of information and the technique of measuring and transmitting information constitute a whole discipline for the engineer, for the neuroscientist, for the psychologist, and for the sociologist”. Sociology aside, the neuroscientists and the psychologists inferred “information transmitted” using the discrete summations from Shannon Information Theory. The present author has since scrutinized the psychologists’ approach in depth, and found it wrong. The neuroscientists’ approach is highly related, but remains unexamined. (...)
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  33.  30
    Set Theory and Structures.Neil Barton & Sy-David Friedman - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Springer Verlag.
    Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a (...) that fruitfully interrelates a `structural' perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)
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  34. Action Guidance is Not Enough, Representations Need Correspondence Too: A Plea for a Two-Factor Theory of Representation.Paweł Gładziejewski - 2015 - New Ideas in Psychology:doi:10.1016/j.newideapsych.2015..
    The aim of this article is to critically examine what I call Action-Centric Theories of Representation (ACToRs). I include in this category theories of representation that (1) reject construing representation in terms of a relation that holds between representation itself (the representational vehicle) and what is represented, and instead (2) try to bring the function that representations play for cognitive systems to the center stage. Roughly speaking, according to proponents of ACToRs, what makes a representation (that is, what is (...)
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  35. Brain Functors: A Mathematical Model for Intentional Perception and Action.David Ellerman - 2016 - Brain: Broad Research in Artificial Intelligence and Neuroscience 7 (1):5-17.
    Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it is split into two parts, a left and a right (...)
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  36. Biology and Theology in Malebranche's Theory of Organic Generation.Karen Detlefsen - 2014 - In Ohad Nachtomy & Justin E. H. Smith (eds.), The Life Sciences in Early Modern Philosophy. Oxford University Press. pp. 137-156.
    This paper has two parts: In the first part, I give a general survey of the various reasons 17th and 18th century life scientists and metaphysicians endorsed the theory of pre-existence according to which God created all living beings at the creation of the universe, and no living beings are ever naturally generated anew. These reasons generally fall into three categories. The first category is theological. For example, many had the desire to account for how all humans are (...)
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  37.  37
    Functorial Semantics for the Advancement of the Science of Cognition.Venkata Posina, Dhanjoo N. Ghista & Sisir Roy - 2017 - Mind and Matter 15 (2):161{184.
    Cognition involves physical stimulation, neural coding, mental conception, and conscious perception. Beyond the neural coding of physical stimuli, it is not clear how exactly these component processes constitute cognition. Within mathematical sciences, category theory provides tools such as category, functor, and adjointness, which are indispensable in the explication of the mathematical calculations involved in acquiring mathematical knowledge. More speci cally, functorial semantics, in showing that theories and models can be construed as categories and functors, respectively, and in (...)
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  38. Efimov K-Theory of Diamonds.Shanna Dobson - manuscript
    Motivated by Scholze and Fargues' geometrization of the local Langlands correspondence using perfectoid diamonds and Clausen and Scholze's work on the K-theory of adic spaces using condensed mathematics, we introduce the Efimov K-theory of diamonds. We propose a pro-diamond, a large stable (infinity,1)-category of diamonds D^{diamond}, a diamond spectra and chromatic tower, and a localization sequence for diamond spectra. Commensurate with the localization sequence, we detail three potential applications of the Efimov K-theory of D^{diamond}: to emergent (...)
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  39. Interpretation of Absolute Judgments Using Information Theory: Channel Capacity or Memory Capacity?Lance Nizami - 2010 - Cybernetics and Human Knowing 17:111-155.
    Shannon’s information theory has been a popular component of first-order cybernetics. It quantifies information transmitted in terms of the number of times a sent symbol is received as itself, or as another possible symbol. Sent symbols were events and received symbols were outcomes. Garner and Hake reinterpreted Shannon, describing events and outcomes as categories of a stimulus attribute, so as to quantify the information transmitted in the psychologist’s category (or absolute judgment) experiment. There, categories are represented by specific (...)
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  40. Mac Lane, Bourbaki, and Adjoints: A Heteromorphic Retrospective.David Ellerman - manuscript
    Saunders Mac Lane famously remarked that "Bourbaki just missed" formulating adjoints in a 1948 appendix (written no doubt by Pierre Samuel) to an early draft of Algebre--which then had to wait until Daniel Kan's 1958 paper on adjoint functors. But Mac Lane was using the orthodox treatment of adjoints that only contemplates the object-to-object morphisms within a category, i.e., homomorphisms. When Samuel's treatment is reconsidered in view of the treatment of adjoints using heteromorphisms or hets (object-to-object morphisms between objects (...)
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  41.  51
    Return of Power: Theory of a Cosmic Bridge to the Dialectical Overhuman.Hermes Varini - 2018 - In 6th Philosophy and Culture of the Information Society International Conference, Saint-Petersburg State University of Aerospace Instrumentation (SUAI), November 16-17, 2018. Saint-Petersburg, Russia: Saint-Petersburg State University of Aerospace Instrumentation (SUAI). pp. 23.
    Propounded in relation to a peculiar mode in the view of an oscillating or cyclic universe, the concept of Return of Power, or of ontic recurrence as further increase in ontic Power signifies the determination of the existing entity according to its own selective recurrence as dialectically exceeding a previous status. Based thus upon the assumption that the actual ontological existence of the entity lies in its own potentiated recurrence (for it is maintained that only what is able to return (...)
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  42. Warrant and Epistemic Virtues: Toward and Agent Reliabilist Account of Plantinga's Theory of Knowledge.Stewart Clem - 2008 - Dissertation, Oklahoma State University
    Alvin Plantinga’s theory of knowledge, as developed in his Warrant trilogy, has shaped the debates surrounding many areas in epistemology in profound ways. Plantinga has received his share of criticism, however, particularly in his treatment of belief in God as being “properly basic”. There has also been much confusion surrounding his notions of warrant and proper function, to which Plantinga has responded numerous times. Many critics remain unsatisfied, while others have developed alternative understandings of warrant in order to rescue (...)
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  43. A Brief Introduction to Transcendental Phenomenology and Conceptual Mathematics.Nicholas Lawrence - 2017 - Dissertation,
    By extending Husserl’s own historico-critical study to include the conceptual mathematics of more contemporary times – specifically category theory and its emphatic development since the second half of the 20th century – this paper claims that the delineation between mathematics and philosophy must be completely revisited. It will be contended that Husserl’s phenomenological work was very much influenced by the discoveries and limitations of the formal mathematics being developed at Göttingen during his tenure there and that, subsequently, the (...)
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  44.  16
    Philosophical Implications of Morris’ Semiotic Theory.Milos Bogdanovic - 2020 - Filozofija I Društvo 31 (1):108-125.
    The subject of this paper is Charles Morris’ semiotic theory that has as one of its major projects the unification of all sciences of signs. However, since the above project has proven to be unsuccessful, we will try to examine here the reasons that led to this. Accordingly, we will argue that to transcend the particularities of individual disciplines that he wanted to unify, Morris had to make certain ontological assumptions, instead of theoretical and methodological ones, that they could (...)
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  45. Evils, Wrongs and Dignity: How to Test a Theory of Evil.Paul Formosa - 2013 - Journal of Value Inquiry 47 (3):235-253.
    Evil acts are not merely wrong; they belong to a different moral category. For example, telling a minor lie might be wrong but it is not evil, whereas the worst act of gratuitous torture that you can imagine is evil and not merely wrong. But how do wrongs and evils differ? A theory or conception of evil should, among other things, answer that question. But once a theory of evil has been developed, how do we defend or (...)
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  46.  34
    Confusing the "Confusion Matrix": The Misapplication of Shannon Information Theory in Sensory Psychology.Lance Nizami - 2012 - Acta Systemica 12 (1):1-17.
    Information flow in a system is a core cybernetics concept. It has been used frequently in Sensory Psychology since 1951. There, Shannon Information Theory was used to calculate "information transmitted" in "absolute identification" experiments involving human subjects. Originally, in Shannon's "system", any symbol received ("outcome") is among the symbols sent ("events"). Not all symbols are received as transmitted, hence an indirect noise measure is calculated, "information transmitted", which requires knowing the confusion matrix, its columns labeled by "event" and its (...)
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  47.  27
    Is Uncertainty Reduction the Basis for Perception? Errors in Norwich’s Entropy Theory of Perception Imply Otherwise.Lance Nizami - 2010 - Proceedings of the World Congress on Engineering and Computer Science 2010 (Lecture Notes in Engineering and Computer Science) 2.
    This paper reveals errors within Norwich et al.’s Entropy Theory of Perception, errors that have broad implications for our understanding of perception. What Norwich and coauthors dubbed their “informational theory of neural coding” is based on cybernetics, that is, control and communication in man and machine. The Entropy Theory uses information theory to interpret human performance in absolute judgments. There, the continuum of the intensity of a sensory stimulus is cut into categories and the subject is (...)
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  48.  21
    Perfectoid Diamonds and N-Awareness. A Meta-Model of Subjective Experience.Shanna Dobson & Robert Prentner - manuscript
    In this paper, we propose a mathematical model of subjective experience in terms of classes of hierarchical geometries of representations (“n-awareness”). We first outline a general framework by recalling concepts from higher category theory, homotopy theory, and the theory of (infinity,1)-topoi. We then state three conjectures that enrich this framework. We first propose that the (infinity,1)-category of a geometric structure known as perfectoid diamond is an (infinity,1)-topos. In order to construct a topology on the (infinity,1)- (...) of diamonds we then propose that topological localization, in the sense of Grothendieck-Rezk-Lurie (infinity,1)-topoi, extends to the (infinity,1)-category of diamonds. We provide a small-scale model using triangulated categories. Finally, our meta-model takes the form of Efimov K-theory of the (infinity,1)-category of perfectoid diamonds, which illustrates structural equivalences between the category of diamonds and subjective experience (i.e.its privacy, self-containedness, and self-reflexivity). Based on this, we investigate implications of the model. We posit a grammar (“n-declension”) for a novel language to express n-awareness, accompanied by a new temporal scheme (“n-time”). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? We also examine the notion of “self” within our framework. A new model of personal identity is introduced which resembles a categorical version of the “bundle theory”: selves are not substances in which properties inhere but (weakly) persistent moduli spaces in the K-theory of perfectoid diamonds. (shrink)
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  49.  54
    গণিত দর্শন Gonit Dorshon.Avijit Lahiri - manuscript
    This article, written in Bengali ('Gonit Dorshon' means `philosophy of mathematics' ), briefly reviews a few of the major points of view toward mathematics and the world of mathematical entities, and interprets the philosophy of mathematics as an interaction between these. The existence of these different points of view is indicative that mathematics, in spite of being of universal validity, can nevertheless accommodate alternatives. In particular, I review the alternative viewpoints of Platonism and Intuitionism and present the case that in (...)
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  50. Canonical Maps.Jean-Pierre Marquis - 2018 - In Elaine Landry (ed.), Categories for the Working Philosophers. Oxford, UK: pp. 90-112.
    Categorical foundations and set-theoretical foundations are sometimes presented as alternative foundational schemes. So far, the literature has mostly focused on the weaknesses of the categorical foundations. We want here to concentrate on what we take to be one of its strengths: the explicit identification of so-called canonical maps and their role in mathematics. Canonical maps play a central role in contemporary mathematics and although some are easily defined by set-theoretical tools, they all appear systematically in a categorical framework. The key (...)
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