Results for 'Point-free ontology'

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  1.  10
    Russell's Theories of Events and Instants from the Perspective of Point-Free Ontologies in the Tradition of the Lvov-Warsaw School.Andrzej Pietruszczak - 2024 - History and Philosophy of Logic 45 (2):161-195.
    We classify two of Bertrand Russell's theories of events within the point-free ontology. The first of such approaches was presented informally by Russell in ‘The World of Physics and the World of Sense’ (Lecture IV in Our Knowledge of the External World of 1914). Based on this theory, Russell sketched ways to construct instants as collections of events. This paper formalizes Russell's approach from 1914. We will also show that in such a reconstructed theory, we obtain all (...)
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  2.  9
    On the idea of point-free theories of space based on the example of Tarski’s Geometry of Solids.Grzegorz Sitek - 2022 - Philosophical Discourses 4:157-186.
    The paper presents the main idea of point-free theories of space based on Tarski's system of point-free geometry. First, the general idea of the so-called point-free ontology was discussed, as well as the epistemological and methodological reasons for its adoption. Next, Whitehead's method of extensive abstraction, which is the methodological basis for the construction of point-free theories of space, is presented, and the fundamental concepts of mereology are discussed. The main part (...)
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  3. Space, points and mereology. On foundations of point-free Euclidean geometry.Rafał Gruszczyński & Andrzej Pietruszczak - 2009 - Logic and Logical Philosophy 18 (2):145-188.
    This article is devoted to the problem of ontological foundations of three-dimensional Euclidean geometry. Starting from Bertrand Russell’s intuitions concerning the sensual world we try to show that it is possible to build a foundation for pure geometry by means of the so called regions of space. It is not our intention to present mathematically developed theory, but rather demonstrate basic assumptions, tools and techniques that are used in construction of systems of point-free geometry and topology by means (...)
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  4.  72
    Ontological Commitment and Free Logic.John Bacon - 1969 - The Monist 53 (2):310-319.
    From Parmenides to the present, philosophers have been attracted by characterizations of being as being uttered or utterable, formulated or formulable. But what for Parmenides was presumably a valid co-entailment between antecedently understood concepts reappears in contemporary thought as a proffered explication of what it is to be. Without presuming to discredit Parmenidean views in general, my purpose here is to examine certain members of a modern family of theories of existence that fall into place around Quine’s. Depending on the (...)
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  5. Incompatibilism and Ontological Priority in Kant's Theory of Free Will.Benjamin Vilhauer - 2008 - In Pablo Muchnik (ed.), Incompatibilism and Ontological Priority in Kant's Theory of Free Will.
    This paper concerns the role of the transcendental distinction between agents qua phenomena and qua noumena in Kant's theory of free will. It argues (1) that Kant's incompatibilism can be accommodated if one accepts the "ontological" interpretation of this distinction (i.e. the view that agents qua noumena are ontologically prior to agents qua phenomena), and (2) that Kant's incompatibilism cannot be accommodated by the "two-aspect" interpretation, whose defining feature is the rejection of the ontological priority of agents qua noumena. (...)
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  6. Points as Higher-order Constructs: Whitehead’s Method of Extensive Abstraction.Achille C. Varzi - 2021 - In Stewart Shapiro & Geoffrey Hellman (eds.), The Continuous. Oxford University Press. pp. 347–378.
    Euclid’s definition of a point as “that which has no part” has been a major source of controversy in relation to the epistemological and ontological presuppositions of classical geometry, from the medieval and modern disputes on indivisibilism to the full development of point-free geometries in the 20th century. Such theories stem from the general idea that all talk of points as putative lower-dimensional entities must and can be recovered in terms of suitable higher-order constructs involving only extended (...)
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  7.  13
    Ontological Terror: Blackness, Nihilism, and Emancipation.Calvin L. Warren - 2018 - Duke University Press.
    In _Ontological Terror_ Calvin L. Warren intervenes in Afro-pessimism, Heideggerian metaphysics, and black humanist philosophy by positing that the "Negro question" is intimately imbricated with questions of Being. Warren uses the figure of the antebellum free black as a philosophical paradigm for thinking through the tensions between blackness and Being. He illustrates how blacks embody a metaphysical nothing. This nothingness serves as a destabilizing presence and force as well as that which whiteness defines itself against. Thus, the function of (...)
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  8.  20
    The Phenomenon of Sentiments and Love in Non-human Animals from the Ontological Point of View of Mulla Sadra.Mirzaei Hamidreza - 2022 - Sophia 61 (2):331-344.
    In the whole universe, from the lowest beings to the highest ones, love permeates through the entire world of existence. Love is one of the hallmarks and perfections of existence in animals. This survey was done to illuminate and explain Mullah Sadra’s ontological viewpoint on the entity of sentiments and the inborn and innate love in the existence of non-human animals. The analytic and descriptive method was used to conduct this study and research. An animal is one of the creatures (...)
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  9.  19
    Free abelian lattice-ordered groups.A. M. W. Glass, Angus Macintyre & Françoise Point - 2005 - Annals of Pure and Applied Logic 134 (2-3):265-283.
    Let n be a positive integer and FAℓ be the free abelian lattice-ordered group on n generators. We prove that FAℓ and FAℓ do not satisfy the same first-order sentences in the language if m≠n. We also show that is decidable iff n{1,2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices.
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  10.  33
    Hintikka, Free Logician.Matthieu Fontaine - 2019 - Logica Universalis 13 (2):179-201.
    The combination of quantifiers with a semantics for epistemic operators in a modal framework is one of the major contributions of Hintikka in intensional logic. Hintikka’s starting point is his diagnosis of the failure of existential generalization and the substitution of identicals in terms of referential multiplicity. In this paper, I introduce Hintikka as a free logician. Indeed, Hintikka’s first-order epistemic logic is grounded on a logic free of ontological presuppositions with respect to singular terms. It is (...)
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  11.  28
    Erratum to “Free abelian lattice-ordered groups” [Ann. Pure Appl. Logic 134 (2–3) (2005) 265–283].A. M. W. Glass, Angus Macintyre & Françoise Point - 2016 - Annals of Pure and Applied Logic 167 (4):431-433.
  12.  5
    A free dialogical logic for surrogate reasoning.Juan Redmond - 2021 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 36 (3):297-320.
    This article aims to present a Free Dialogic Logic [FDL] as a general framework for hypothesis generation in the practice of modelling in science. Our proposal is based on the idea that the inferential function that models fulfil during the modelling process (surrogate reasoning) should be carried out without ontological commitments. The starting point to achieve our objective is that the scientific consideration of models without a target is a symptom that, on the one hand, the Applicability of (...)
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  13.  76
    Language, Ontology, and the Carnap-Quine Debate.Jonathan Surovell - 2017 - Philosophia 45 (2):811-833.
    On a widespread reading, the Carnap-Quine debate about ontology concerns the objectivity and non-triviality of ontological claims. I argue that this view mischaracterizes Carnap’s aims in “Empiricism, Semantics, and Ontology” : Carnap’s fundamental goal is to free up decisions about scientific language from constraints deriving from ontological doctrine. The contention, based on his internal/external distinction, that ontological claims are either meaningless or trivial was Carnap’s means to achieving this more fundamental goal. Setting the record straight on this (...)
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  14. The Ontology of Intentional Agency in Light of Neurobiological Determinism: Philosophy Meets Folk Psychology.Dhar Sharmistha - 2017 - Journal of the Indian Council of Philosophical Research 34 (1):129-149.
    The moot point of the Western philosophical rhetoric about free will consists in examining whether the claim of authorship to intentional, deliberative actions fits into or is undermined by a one-way causal framework of determinism. Philosophers who think that reconciliation between the two is possible are known as metaphysical compatibilists. However, there are philosophers populating the other end of the spectrum, known as the metaphysical libertarians, who maintain that claim to intentional agency cannot be sustained unless it is (...)
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  15.  20
    Ontological and Other Assumptions.Lloyd A. Wells & Sandra J. Rackley - 2007 - Philosophy, Psychiatry, and Psychology 14 (3):203-204.
    In lieu of an abstract, here is a brief excerpt of the content:Ontological and Other AssumptionsLloyd A. Wells (bio) and Sandra J. Rackley (bio)Fahrenberg and Cheetham have conducted an immensely thought-provoking study of the assumptions about human nature made by 800 students and pose a question about the future impact of these assumptions on individuals’ practice in professions including medicine and psychotherapy.This work represents a branch of “philosophical anthropology,” which considers assumptions people make about human nature. The authors used a (...)
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  16.  70
    Modelling ourselves: what the free energy principle reveals about our implicit notions of representation.Matt Sims & Giovanni Pezzulo - 2021 - Synthese 199 (3-4):7801-7833.
    Predictive processing theories are increasingly popular in philosophy of mind; such process theories often gain support from the Free Energy Principle —a normative principle for adaptive self-organized systems. Yet there is a current and much discussed debate about conflicting philosophical interpretations of FEP, e.g., representational versus non-representational. Here we argue that these different interpretations depend on implicit assumptions about what qualifies as representational. We deploy the Free Energy Principle instrumentally to distinguish four main notions of representation, which focus (...)
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  17.  47
    Radical Pluralism, Ontological Underdetermination, and the Role of Values in Species Classification.Stijn Conix - 2018 - Dissertation, University of Cambridge
    The main claim of this thesis is that value-judgments should play a profound role in the construction and evaluation of species classifications. The arguments for this claim will be presented over the course of five chapters. These are divided into two main parts; part one, which consists of the two first chapters, presents an argument for a radical form of species pluralism; part two, which comprises the remaining chapters, discusses the implications of radical species pluralism for the role of values (...)
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  18.  22
    Temporal Omniscience, Free will, and Their Logic.Lifeng Zhang - 2023 - Global Philosophy 33 (1):1-9.
    Taking divine omniscience as including temporal omniscience, which means God exists at all times and knows everything, I point out the fallacies in an incompatibilist argument. Syntactically, due to misapplication of the principle of substitutivity, this incompatibilist argument isn’t valid. Semantically, due to cancelation of a supposition on which God’s earlier belief depends, an agent’s alternative action won’t result in falsification of divine belief. Finally, by appealing to an eternalist conception of truth of proposition about the future, I argue (...)
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  19. πολλαχῶς ἔστι; Plato’s Neglected Ontology.Mohammad Bagher Ghomi - manuscript
    This paper aims to suggest a new approach to Plato’s theory of being in Republic V and Sophist based on the notion of difference and the being of a copy. To understand Plato’s ontology in these two dialogues we are going to suggest a theory we call Pollachos Esti; a name we took from Aristotle’s pollachos legetai both to remind the similarities of the two structures and to reach a consistent view of Plato’s ontology. Based on this theory, (...)
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  20.  62
    Perception Dualism and Free Will.Gang Chen - 2008 - Proceedings of the Xxii World Congress of Philosophy 42:13-42.
    This paper is to spell out a version of perception dualism, whose ontological description of the mind-body relation is stronger than property dualism but weaker than substance dualism, that is, to define mental events as perceptions from an internal point of view and physical events as perceptions from an external point of view, then, the author set out to tackle some long-persisting ontological issues in philosophy of mind, such as the psycho-physical interaction, the criterion of mind, the clash (...)
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  21.  33
    Point Atomism, Space and God, 1760–80.Karis Muller - 2007 - The European Legacy 12 (3):277-292.
    This paper compares and contrasts the main metaphysical and religious ideas of the eighteenth-century political theorist and chemist Joseph Priestley (1733–1804) with those of his correspondent Ruder Boscovic (1711–1787), astronomer, poet, mathematician, diplomat and Jesuit priest. It points out the theological differences between the two thinkers resulting from the divergent ontological and metaphysical implications of the theory of point atomism that they shared. This theory they placed in a wider context, considering both its limits and its value as a (...)
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  22.  75
    Super-Humeanism and free will.Michael Esfeld - 2019 - Synthese 198 (7):6245-6258.
    Super-Humeanism is an even more parsimonious ontology than Lewisian standard Humean metaphysics in that it rejects intrinsic properties. There are point objects, but all there is to them are their relative positions and the change of them. Everything else supervenes on the Humean mosaic thus conceived. Hence, dynamical parameters come in on a par with the laws through their position in the best system. The paper sets out how Super-Humeanism has the conceptual means to reject van Inwagen’s consequence (...)
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  23.  8
    Chimera of Naturalism and Free Will.Anton V. Kuznetsov - 2023 - Epistemology and Philosophy of Science 60 (1):221-240.
    This article is devoted to the analysis of arguments from empirical science against free will. Its main purpose is to reveal their deep anti-naturalism. This anti-naturalism lies in the use of a concept of free will that cannot be the subject of naturalistic consideration, as well as in the various explanatory and ontological paradoxes that arguments from empirical science lead in case when someone is trying to generalize the explanatory principles underlying them. At the beginning of the article, (...)
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  24.  33
    Essays in Ontology (review).Avrum Stroll - 1964 - Journal of the History of Philosophy 2 (2):285-287.
    In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 285 than" which is both immanent and transcendent, a kind of "coincidentia oppositorum" beyond logic and definition. It is the realm of the "person" within which, although the tragic conflict is not resolved, there arises the free self from whose non-dual perspective the unity and eternity of life are seen. Within this realm the individual gains an illumination the result of which is "amor fad," his (...)
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  25.  18
    Captiveness and Openness as Ontological Intuitions in Works of H. Bergson.Maksim F. Litvinov & Литвинов Максим Федорович - 2023 - RUDN Journal of Philosophy 27 (2):332-344.
    The research focuses on the problem of freedom from that point of view which puts captiveness by being and openness to being in the middle of non-dialectical examination. This perspective clarifies not only the major course of Bergson’s thought, but also the subsequent incorrect shift to the pole of openness in the hermeneutical interpretation of facticity, implemented by Heidegger. The work is conventionally divided into two parts. The first one inquires about specifics of the method used by Bergson. It (...)
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  26.  5
    Essays in Linguistic Ontology.Jack Kaminsky - 1977 - Southern Illinois University Press.
    “Metaphysical questions relating to what ex­ists do not seem to fade away” notes Jack Kaminsky in this book, which takes as its starting point the Quinian view that we de­termine what exists by means of the formal systems we construct to explain the world. This starting point, Kaminsky points out, is not novel; philosophers have often tried to construct formal systems, and from these systems they have been able to deduce what can be said to exist. Contemporary formal (...)
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  27.  41
    Francisco Suárez on the Ontological Status of Divine Action.R. J. Matava - 2016 - American Catholic Philosophical Quarterly.
    It has recently been argued that God’s causation of human free choices is best understood in light of Aquinas’s teaching on creation. Such a position is attractive because it provides a way of avoiding the compatibilism of classical interpretations of Aquinas. However, this position may be subject to other flaws. In fact, Francisco Suárez explicitly rejects the view that God’s creative causality can be understood either as the divine essence or as a predicamental relation of the created effect to (...)
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  28.  26
    Levinas Faces Kant, Hegel and Heidegger: Debates of Contemporary Philosophy on Ontology.Ye Xiushan & Zhang Lin - 2008 - Frontiers of Philosophy in China 3 (3):438 - 454.
    Levinas subverts the traditional "ontology-epistemology," and creates a "realm of difference," the realm of "value," "ethic," and "religion," maintaining that ethics is real metaphysics. According to him, it is not that "being" contains the "other" but the other way round. In this way, the issues of ethics are promoted greatly in the realm of philosophy. Nonetheless, he does not intend to deny "ontology" completely, but reversed the relationship between "ontology (theory of truth)" and "ethics (axiology)," placing the (...)
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  29.  61
    Why determinism in physics has no implications for free will.Michael Esfeld - unknown
    This paper argues for the following three theses: There is a clear reason to prefer physical theories with deterministic dynamical equations: such theories are both maximally simple and maximally rich in information, since given an initial configuration of matter and the dynamical equations, the whole evolution of the configuration of matter is fixed. There is a clear way how to introduce probabilities in a deterministic physical theory, namely as answer to the question of what evolution of a specific system we (...)
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  30.  31
    Buses and Breaking Point: Freedom of Expression and the ‘Brexit’ Campaign.Andrew Reid - 2019 - Ethical Theory and Moral Practice 22 (3):623-637.
    In the aftermath of the ‘Brexit’ referendum two pieces of campaign material used by the successful Leave campaign proved controversial: a slogan on the side of a bus fallaciously implying that leaving the EU would necessarily free up £350 million a week for the NHS; and a poster stating that Britain was at “Breaking Point” – purportedly due to an influx of migrants – that was redolent of Nazi propaganda. This paper analyses and develops some criticisms that were (...)
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  31. Modelling ourselves: what the debate on the Free Energy Principle reveals about our implicit notions of representation.Matthew Sims & Giovanni Pezzulo - 2021 - Synthese 1 (1):30.
    Predictive processing theories are increasingly popular in philosophy of mind; such process theories often gain support from the Free Energy Principle (FEP)—a nor- mative principle for adaptive self-organized systems. Yet there is a current and much discussed debate about conflicting philosophical interpretations of FEP, e.g., repre- sentational versus non-representational. Here we argue that these different interpre- tations depend on implicit assumptions about what qualifies (or fails to qualify) as representational. We deploy the Free Energy Principle (FEP) instrumentally to (...)
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  32.  90
    Has the Ontological Argument Been Refuted?William F. Vallicella - 1993 - Religious Studies 29 (1):97 - 110.
    Suppose we say that a deductive argument is probative just in case it is valid in point of logical form, possesses true premises, and is free of informal fallacy. We can then say that an argument is normatively persuasive for a person if and only if it is both probative and has premises that can be accepted, without any breach of epistemic propriety, by the person in question. If the premises of a probative argument would be accepted by (...)
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  33. Point-Free Geometry and Verisimilitude of Theories.Giangiacomo Gerla - 2007 - Journal of Philosophical Logic 36 (6):707-733.
    A metric approach to Popper's verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some of (...)
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  34.  91
    Levinas faces Kant, Hegel and Heidegger: Debates of contemporary philosophy on ontology[REVIEW]Xiushan Ye - 2008 - Frontiers of Philosophy in China 3 (3):438-454.
    Levinas subverts the traditional “ontology-epistemology,” and creates a “realm of difference,” the realm of “value,” “ethic,” and “religion,” maintaining that ethics is real metaphysics. According to him, it is not that “being” contains the “other” but the other way round. In this way, the issues of ethics are promoted greatly in the realm of philosophy. Nonetheless, he does not intend to deny “ontology” completely, but reversed the relationship between “ontology (theory of truth)” and “ethics (axiology),” placing the (...)
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  35. Monistic Idealism May Provide Better Ontology for Cognitive Science: A Reply to Dyer.Amit Goswami - 1995 - Journal of Mind and Behavior 16 (2):135-150.
    This is a response to Michael Dyer's Commentary on Goswami's Quantum-Based Theory of Consciousness and Free Will, a theory that I will call idealist science - a science based on the primacy of consciousness rather than matter. First, I review Dyer's main points: there is no need for idealist science since cognitive science can explain whatever human phenomena idealist science purports to explain; and idealist science offers nothing new, such as, new methodology or experimental prediction. I then review some (...)
     
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  36. W poszukiwaniu ontologicznych podstaw prawa. Arthura Kaufmanna teoria sprawiedliwości [In Search for Ontological Foundations of Law: Arthur Kaufmann’s Theory of Justice].Marek Piechowiak - 1992 - Instytut Nauk Prawnych PAN.
    Arthur Kaufmann is one of the most prominent figures among the contemporary philosophers of law in German speaking countries. For many years he was a director of the Institute of Philosophy of Law and Computer Sciences for Law at the University in Munich. Presently, he is a retired professor of this university. Rare in the contemporary legal thought, Arthur Kaufmann's philosophy of law is one with the highest ambitions — it aspires to pinpoint the ultimate foundations of law by explicitly (...)
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  37.  20
    The Actuality of Sartre's Free Will Conception.Peter Kampits - 2015 - Labyrinth: An International Journal for Philosophy, Value Theory and Sociocultural Hermeneutics 17 (2):39-48.
    The main Sartrean concepts and theses of freedom of will and unlimited responsibility, which seemed for many already outdated, are gaining actually interest in respect to the recent results in brain research. The main objective of the paper is to reevaluate Sartre's free will conception trying to answer the question: How would Sartre who, in the time of his existentialist phase during which his radical theory of freedom received its most pointed articulation, was familiar with psychological theories of determinism, (...)
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  38.  12
    The Promise of Martin Luther’s Political Theology: Freeing Luther from the Modern Political Narrative.Candace L. Kohli - 2018 - Journal of the Society of Christian Ethics 38 (2):202-203.
    In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Promise of Martin Luther's Political Theology: Freeing Luther from the Modern Political Narrative by Michael Richard LaffinCandace L. KohliThe Promise of Martin Luther's Political Theology: Freeing Luther from the Modern Political Narrative Michael Richard Laffin NEW YORK: BLOOMSBURY / T&T CLARK, 2016. 272 pp. $121.00Is Christianity antagonistic of the political, as Machiavelli, Rousseau, and Nietzsche have all claimed? Michael Laffin argues against this position for "the life-affirming, (...)
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  39.  21
    Point-free topological spaces, functions and recursive points; filter foundation for recursive analysis. I.Iraj Kalantari & Lawrence Welch - 1998 - Annals of Pure and Applied Logic 93 (1-3):125-151.
    In this paper we develop a point-free approach to the study of topological spaces and functions on them, establish platforms for both and present some findings on recursive points. In the first sections of the paper, we obtain conditions under which our approach leads to the generation of ideal objects with which mathematicians work. Next, we apply the effective version of our approach to the real numbers, and make exact connections to the classical approach to recursive reals. In (...)
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  40.  69
    Point-free Foundation of Geometry and Multivalued Logic.Cristina Coppola, Giangiacomo Gerla & Annamaria Miranda - 2010 - Notre Dame Journal of Formal Logic 51 (3):383-405.
    Whitehead, in two basic books, considers two different approaches to point-free geometry: the inclusion-based approach , whose primitive notions are regions and inclusion relation between regions, and the connection-based approach , where the connection relation is considered instead of the inclusion. We show that the latter cannot be reduced to the first one, although this can be done in the framework of multivalued logics.
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  41.  23
    Point-free geometry, ovals, and half-planes.Giangiacomo Gerla & Rafał Gruszczyński - 2017 - Review of Symbolic Logic 10 (2):237-258.
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  42.  17
    Measures in Euclidean Point-Free Geometry (an exploratory paper).Giuseppina Barbieri & Giangiacomo Gerla - forthcoming - Logic and Logical Philosophy:1-20.
    We face with the question of a suitable measure theory in Euclidean point-free geometry and we sketch out some possible solutions. The proposed measures, which are positive and invariant with respect to movements, are based on the notion of infinitesimal masses, i.e. masses whose associated supports form a sequence of finer and finer partitions.
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  43.  20
    A Study in Grzegorczyk Point-Free Topology Part I: Separation and Grzegorczyk Structures.Rafał Gruszczyński & Andrzej Pietruszczak - 2018 - Studia Logica 106 (6):1197-1238.
    This is the first, out of two papers, devoted to Andrzej Grzegorczyk’s point-free system of topology from Grzegorczyk :228–235, 1960. https://doi.org/10.1007/BF00485101). His system was one of the very first fully fledged axiomatizations of topology based on the notions of region, parthood and separation. Its peculiar and interesting feature is the definition of point, whose intention is to grasp our geometrical intuitions of points as systems of shrinking regions of space. In this part we analyze separation structures and (...)
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  44.  55
    Special Issue on Point-Free Geometry and Topology.Cristina Coppola & Giangiacomo Gerla - 2013 - Logic and Logical Philosophy 22 (2):139-143.
    In the first section we briefly describe methodological assumptions of point-free geometry and topology. We also outline history of geometrical theories based on the notion of emph{region}. The second section is devoted to concise presentation of the content of the LLP special issue on point-free theories of space.
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  45.  23
    A Study in Grzegorczyk Point-Free Topology Part II: Spaces of Points.Rafał Gruszczyński & Andrzej Pietruszczak - 2019 - Studia Logica 107 (4):809-843.
    In the second installment to Gruszczyński and Pietruszczak we carry out an analysis of spaces of points of Grzegorczyk structures. At the outset we introduce notions of a concentric and \-concentric topological space and we recollect some facts proven in the first part which are important for the sequel. Theorem 2.9 is a strengthening of Theorem 5.13, as we obtain stronger conclusion weakening Tychonoff separation axiom to mere regularity. This leads to a stronger version of Theorem 6.10. Further, we show (...)
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  46. Towards a Point-free Account of the Continuous.Geoffrey Hellman & Stewart Shapiro - 2012 - Iyyun 61:263.
  47.  43
    On the T 1 axiom and other separation properties in constructive point-free and point-set topology.Peter Aczel & Giovanni Curi - 2010 - Annals of Pure and Applied Logic 161 (4):560-569.
    In this note a T1 formal space is a formal space whose points are closed as subspaces. Any regular formal space is T1. We introduce the more general notion of a formal space, and prove that the class of points of a weakly set-presentable formal space is a set in the constructive set theory CZF. The same also holds in constructive type theory. We then formulate separation properties for constructive topological spaces , strengthening separation properties discussed elsewhere. Finally we relate (...)
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  48.  19
    A comparison of two systems of point-free topology.Rafał Gruszczyński & Andrzej Pietruszczak - 2018 - Bulletin of the Section of Logic 47 (3):187.
    This is a spin-off paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk’s point-free topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was inspired by the Grzegorczyk’s system, and which is its variation. Our aim is to compare the two approaches and show that they are slightly different. Except for pointing to dissimilarities, we also demonstrate that the theories coincide in presence of axiom stipulating non-existence of (...)
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  49.  38
    On some peculiar aspects of the constructive theory of point-free spaces.Giovanni Curi - 2010 - Mathematical Logic Quarterly 56 (4):375-387.
    This paper presents several independence results concerning the topos-valid and the intuitionistic predicative theory of locales. In particular, certain consequences of the consistency of a general form of Troelstra's uniformity principle with constructive set theory and type theory are examined.
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  50.  29
    Mathematical Features of Whitehead’s Point-free Geometry.Annamaria Miranda & Giangiacomo Gerla - 2008 - In Michel Weber and Will Desmond (ed.), Handbook of Whiteheadian Process Thought. De Gruyter. pp. 119-130.
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