Results for 'predicativity, Russell, Weyl, constructive mathematics'

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  1. Predicativity and Feferman.Laura Crosilla - 2017 - In Gerhard Jäger & Wilfried Sieg, Feferman on Foundations: Logic, Mathematics, Philosophy. Cham: Springer. pp. 423-447.
    Predicativity is a notable example of fruitful interaction between philosophy and mathematical logic. It originated at the beginning of the 20th century from methodological and philosophical reflections on a changing concept of set. A clarification of this notion has prompted the development of fundamental new technical instruments, from Russell's type theory to an important chapter in proof theory, which saw the decisive involvement of Kreisel, Feferman and Schütte. The technical outcomes of predica-tivity have since taken a life of their own, (...)
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  2. Predicativity and constructive mathematics.Laura Crosilla - 2022 - In Gianluigi Oliveri, Claudio Ternullo & Stefano Boscolo, Objects, Structures, and Logics. Cham (Switzerland): Springer.
    In this article I present a disagreement between classical and constructive approaches to predicativity regarding the predicative status of so-called generalised inductive definitions. I begin by offering some motivation for an enquiry in the predicative foundations of constructive mathematics, by looking at contemporary work at the intersection between mathematics and computer science. I then review the background notions and spell out the above-mentioned disagreement between classical and constructive approaches to predicativity. Finally, I look at possible (...)
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  3. Description, Construction and Representation. From Russell and Carnap to Stone.Thomas Mormann - 2006 - In Guido Imagire & Christine Schneider, Untersuchungen zur Ontologie.
    The first aim of this paper is to elucidate Russell’s construction of spatial points, which is to be <br>considered as a paradigmatic case of the "logical constructions" that played a central role in his epistemology and theory of science. Comparing it with parallel endeavours carried out by Carnap and Stone it is argued that Russell’s construction is best understood as a structural representation. It is shown that Russell’s and Carnap’s representational constructions may be considered as incomplete and sketchy harbingers of (...)
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  4. A Constructive Treatment to Elemental Life Forms through Mathematical Philosophy.Susmit Bagchi - 2021 - Philosophies 6 (4):84.
    The quest to understand the natural and the mathematical as well as philosophical principles of dynamics of life forms are ancient in the human history of science. In ancient times, Pythagoras and Plato, and later, Copernicus and Galileo, correctly observed that the grand book of nature is written in the language of mathematics. Platonism, Aristotelian logism, neo-realism, monadism of Leibniz, Hegelian idealism and others have made efforts to understand reasons of existence of life forms in nature and the underlying (...)
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  5. The Constitution of Weyl’s Pure Infinitesimal World Geometry.C. D. McCoy - 2022 - Hopos: The Journal of the International Society for the History of Philosophy of Science 12 (1):189–208.
    Hermann Weyl was one of the most important figures involved in the early elaboration of the general theory of relativity and its fundamentally geometrical spacetime picture of the world. Weyl’s development of “pure infinitesimal geometry” out of relativity theory was the basis of his remarkable attempt at unifying gravitation and electromagnetism. Many interpreters have focused primarily on Weyl’s philosophical influences, especially the influence of Husserl’s transcendental phenomenology, as the motivation for these efforts. In this article, I argue both that these (...)
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  6. (1 other version)Russell’s Many Points.Thomas Mormann - 2009 - In Alexander Hieke & Hannes Leitgeb, Reduction: Between the Mind and the Brain. Frankfurt: Ontos Verlag. pp. 11--239.
    Bertrand Russell was one of the protagonists of the programme of reducing “disagreeable” concepts to philosophically more respectable ones. Throughout his life he was engaged in eliminating or paraphrasing away a copious variety of allegedly dubious concepts: propositions, definite descriptions, knowing subjects, and points, among others. The critical aim of this paper is to show that Russell’s construction of points, which has been considered as a paradigm of a logical construction überhaupt, fails for principal mathematical reasons. Russell could have known (...)
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  7. The Origins of the Propositional Functions Version of Russell's Paradox.Kevin C. Klement - 2004 - Russell: The Journal of Bertrand Russell Studies 24 (2):101–132.
    Russell discovered the classes version of Russell's Paradox in spring 1901, and the predicates version near the same time. There is a problem, however, in dating the discovery of the propositional functions version. In 1906, Russell claimed he discovered it after May 1903, but this conflicts with the widespread belief that the functions version appears in _The Principles of Mathematics_, finished in late 1902. I argue that Russell's dating was accurate, and that the functions version does not appear in the (...)
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  8. Introduction to Mathematical Logic, Edition 2021.Vilnis Detlovs & Karlis Podnieks - manuscript
    Textbook for students in mathematical logic. Part 1. Total formalization is possible! Formal theories. First order languages. Axioms of constructive and classical logic. Proving formulas in propositional and predicate logic. Glivenko's theorem and constructive embedding. Axiom independence. Interpretations, models and completeness theorems. Normal forms. Tableaux method. Resolution method. Herbrand's theorem.
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  9. Gödel Mathematics Versus Hilbert Mathematics. II Logicism and Hilbert Mathematics, the Identification of Logic and Set Theory, and Gödel’s 'Completeness Paper' (1930).Vasil Penchev - 2023 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 15 (1):1-61.
    The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...)
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  10. The 1900 Turn in Bertrand Russell’s Logic, the Emergence of his Paradox, and the Way Out.Nikolay Milkov - 2016 - Siegener Beiträge Zur Geschichte Und Philosophie der Mathematik 7:29-50.
    Russell’s initial project in philosophy (1898) was to make mathematics rigorous reducing it to logic. Before August 1900, however, Russell’s logic was nothing but mereology. First, his acquaintance with Peano’s ideas in August 1900 led him to discard the part-whole logic and accept a kind of intensional predicate logic instead. Among other things, the predicate logic helped Russell embrace a technique of treating the paradox of infinite numbers with the help of a singular concept, which he called ‘denoting phrase’. (...)
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  11. A mathematically derived definitional/semantical theory of truth.Seppo Heikkilä - 2018 - Nonlinear Studies 25 (1):173-189.
    Ordinary and transfinite recursion and induction and ZF set theory are used to construct from a fully interpreted object language and from an extra formula a new language. It is fully interpreted under a suitably defined interpretation. This interpretation is equivalent to the interpretation by meanings of sentences if the object language is so interpreted. The added formula provides a truth predicate for the constructed language. The so obtained theory of truth satisfies the norms presented in Hannes Leitgeb's paper 'What (...)
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  12. A Cantorian argument against Frege's and early Russell's theories of descriptions.Kevin C. Klement - 2008 - In Nicholas Griffin & Dale Jacquette, Russell Vs. Meinong: The Legacy of "on Denoting". London and New York: Routledge. pp. 65-77.
    It would be an understatement to say that Russell was interested in Cantorian diagonal paradoxes. His discovery of the various versions of Russell’s paradox—the classes version, the predicates version, the propositional functions version—had a lasting effect on his views in philosophical logic. Similar Cantorian paradoxes regarding propositions—such as that discussed in §500 of The Principles of Mathematics—were surely among the reasons Russell eventually abandoned his ontology of propositions.1 However, Russell’s reasons for abandoning what he called “denoting concepts”, and his (...)
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  13. VALIDITY: A Learning Game Approach to Mathematical Logic.Steven James Bartlett - 1973 - Hartford, CT: Lebon Press. Edited by E. J. Lemmon.
    The first learning game to be developed to help students to develop and hone skills in constructing proofs in both the propositional and first-order predicate calculi. It comprises an autotelic (self-motivating) learning approach to assist students in developing skills and strategies of proof in the propositional and predicate calculus. The text of VALIDITY consists of a general introduction that describes earlier studies made of autotelic learning games, paying particular attention to work done at the Law School of Yale University, called (...)
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  14. A mathematical theory of truth and an application to the regress problem.S. Heikkilä - forthcoming - Nonlinear Studies 22 (2).
    In this paper a class of languages which are formal enough for mathematical reasoning is introduced. Its languages are called mathematically agreeable. Languages containing a given MA language L, and being sublanguages of L augmented by a monadic predicate, are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of those languages. MTT makes them fully interpreted MA languages which posses their own truth predicates. MTT is shown to conform well with the eight norms formulated for theories (...)
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  15. Arnošt Kolman’s Critique of Mathematical Fetishism.Jakub Mácha & Jan Zouhar - 2020 - In Radek Schuster, The Vienna Circle in Czechoslovakia. Springer. pp. 135-150.
    Arnošt Kolman (1892–1979) was a Czech mathematician, philosopher and Communist official. In this paper, we would like to look at Kolman’s arguments against logical positivism which revolve around the notion of the fetishization of mathematics. Kolman derives his notion of fetishism from Marx’s conception of commodity fetishism. Kolman is aiming to show the fact that an entity (system, structure, logical construction) acquires besides its real existence another formal existence. Fetishism means the fantastic detachment of the physical characteristics of real (...)
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  16. Unpacking the logic of mathematical statements.Annie Selden - 1995 - Educational Studies in Mathematics 29:123-151.
    This study focuses on undergraduate students' ability to unpack informally written mathematical statements into the language of predicate calculus. Data were collected between 1989 and 1993 from 61students in six small sections of a “bridge" course designed to introduce proofs and mathematical reasoning. We discuss this data from a perspective that extends the notion of concept image to that of statement image and introduces the notion of proof framework to indicate the top-level logical structure of a proof. For simplified informal (...)
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  17. Towards a Theory of Computation similar to some other scientific theories.Antonino Drago - manuscript
    At first sight the Theory of Computation i) relies on a kind of mathematics based on the notion of potential infinity; ii) its theoretical organization is irreducible to an axiomatic one; rather it is organized in order to solve a problem: “What is a computation?”; iii) it makes essential use of doubly negated propositions of non-classical logic, in particular in the word expressions of the Church-Turing’s thesis; iv) its arguments include ad absurdum proofs. Under such aspects, it is like (...)
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  18. A theory of truth for a class of mathematical languages and an application.S. Heikkilä - manuscript
    In this paprer a class of so called mathematically acceptable (shortly MA) languages is introduced First-order formal languages containing natural numbers and numerals belong to that class. MA languages which are contained in a given fully interpreted MA language augmented by a monadic predicate are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of these languages. MTT makes them fully interpreted MA languages which posses their own truth predicates, yielding consequences to philosophy of mathematics. MTT (...)
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  19. A Review of The Algebraic Approaches to Quantum Mechanics. Some Appraisals of Their Theoretical Importance.Antonino Drago - manuscript
    The main algebraic foundations of quantum mechanics are quickly reviewed. They have been suggested since the birth of this theory till up to last years. They are the following ones: Heisenberg-Born- Jordan’s (1925), Weyl’s (1928), Dirac’s (1930), von Neumann’s (1936), Segal’s (1947), T.F. Jordan’s (1986), Morchio and Strocchi’s (2009) and Buchholz and Fregenhagen’s (2019). Four cases are stressed: 1) the misinterpretation of Dirac’s algebraic foundation; 2) von Neumann’s ‘conversion’ from the analytic approach of Hilbert space to the algebraic approach of (...)
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  20. 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 for constructing categories, and it is explicitly (...)
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  21. On the Probability of Plenitude.Jeffrey Sanford Russell - 2020 - Journal of Philosophy 117 (5):267-292.
    I examine what the mathematical theory of random structures can teach us about the probability of Plenitude, a thesis closely related to David Lewis's modal realism. Given some natural assumptions, Plenitude is reasonably probable a priori, but in principle it can be (and plausibly it has been) empirically disconfirmed—not by any general qualitative evidence, but rather by our de re evidence.
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  22. Non-Archimedean Preferences Over Countable Lotteries.Jeffrey Sanford Russell - 2020 - Journal of Mathematical Economics 88 (May 2020):180-186.
    We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.
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  23. Responsibility, Naturalism and ‘the Morality System'.Paul Russell - 2013 - In David Shoemaker, Oxford Studies in Agency and Responsibility, Volume 1. Oxford: Oxford University Press UK. pp. 184-204.
    In "Freedom and Resentment" P.F. Strawson, famously, advances a strong form of naturalism that aims to discredit kcepticism about moral responsibility by way of approaching these issues through an account of our reactive attitudes. However, even those who follow Strawson's general strategy on this subject accept that his strong naturalist program needs to be substantially modified, if not rejected. One of the most influential and important efforts to revise and reconstruct the Strawsonian program along these lines has been provided by (...)
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  24. The Problem of Evil and Replies to Some Important Responses.Bruce Russell - 2018 - European Journal for Philosophy of Religion 10 (3):105-131.
    I begin by distinguishing four different versions of the argument from evil that start from four different moral premises that in various ways link the existence of God to the absence of suffering. The version of the argument from evil that I defend starts from the premise that if God exists, he would not allow excessive, unnecessary suffering. The argument continues by denying the consequent of this conditional to conclude that God does not exist. I defend the argument against Skeptical (...)
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  25. Composition as Abstraction.Jeffrey Sanford Russell - 2017 - Journal of Philosophy 114 (9):453-470.
    The existence of mereological sums can be derived from an abstraction principle in a way analogous to numbers. I draw lessons for the thesis that “composition is innocent” from neo-Fregeanism in the philosophy of mathematics.
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  26. Reciprocity and reputation: a review of direct and indirect social information gathering.Yvan I. Russell - 2016 - Journal of Mind and Behavior 37 (3-4):247-270.
    Direct reciprocity, indirect reciprocity, and reputation are important interrelated topics in the evolution of sociality. This non-mathematical review is a summary of each. Direct reciprocity (the positive kind) has a straightforward structure (e.g., "A rewards B, then rewards A") but the allocation might differ from the process that enabled it (e.g., whether it is true reciprocity or some form of mutualism). Indirect reciprocity (the positive kind) occurs when person (B) is rewarded by a third party (A) after doing a good (...)
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  27. The Politics of the Third Person: Esposito’s Third Person and Rancière’s Disagreement.Matheson Russell - 2014 - Critical Horizons 15 (3):211-230.
    Against the enthusiasm for dialogue and deliberation in recent democratic theory, the Italian philosopher Roberto Esposito and French philosopher Jacques Rancière construct their political philosophies around the nondialogical figure of the third person. The strikingly different deployments of the figure of the third person offered by Esposito and Rancière present a crystallization of their respective approaches to political philosophy. In this essay, the divergent analyses of the third person offered by these two thinkers are considered in terms of the critical (...)
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  28. Indefinite Divisibility.Jeffrey Sanford Russell - 2016 - Inquiry: An Interdisciplinary Journal of Philosophy 59 (3):239-263.
    Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of (...)
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  29. Numbers without Science.Russell Marcus - 2007 - Dissertation, The Graduate School and University Center of the City University of New York
    Numbers without Science opposes the Quine-Putnam indispensability argument, seeking to undermine the argument and reduce its profound influence. Philosophers rely on indispensability to justify mathematical knowledge using only empiricist epistemology. I argue that we need an independent account of our knowledge of mathematics. The indispensability argument, in broad form, consists of two premises. The major premise alleges that we are committed to mathematical objects if science requires them. The minor premise alleges that science in fact requires mathematical objects. The (...)
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  30. The Structure of Gunk: Adventures in the Ontology of Space.Jeffrey Sanford Russell - 2008 - In Dean Zimmerman, Oxford Studies in Metaphysics: Volume 4. Oxford University Press UK. pp. 248.
    Could space consist entirely of extended regions, without any regions shaped like points, lines, or surfaces? Peter Forrest and Frank Arntzenius have independently raised a paradox of size for space like this, drawing on a construction of Cantor’s. I present a new version of this argument and explore possible lines of response.
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  31. Signs, Toy Models, and the A Priori.Lydia Patton - 2009 - Studies in History and Philosophy of Science Part A 40 (3):281-289.
    The Marburg neo-Kantians argue that Hermann von Helmholtz's empiricist account of the a priori does not account for certain knowledge, since it is based on a psychological phenomenon, trust in the regularities of nature. They argue that Helmholtz's account raises the 'problem of validity' (Gueltigkeitsproblem): how to establish a warranted claim that observed regularities are based on actual relations. I reconstruct Heinrich Hertz's and Ludwig Wittgenstein's Bild theoretic answer to the problem of validity: that scientists and philosophers can depict the (...)
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  32. A NEW PHILOSOPHICAL FOUNDATION OF CONSTRUCTIVE MATHEMATICS.Antonino Drago - manuscript
    The current definition of Constructive mathematics as “mathematics within intuitionist logic” ignores two fundamental issues. First, the kind of organization of the theory at issue. I show that intuitionist logic governs a problem-based organization, whose model is alternative to that of the deductive-axiomatic organization, governed by classical logic. Moreover, this dichotomy is independent of that of the kind of infinity, either potential or actual, to which respectively correspond constructive mathematical and classical mathematical tools. According to this (...)
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  33. Dead Letters.Russell Ford - 2013 - LIT: Literature Interpretation Theory 24 (4):299-317.
    This essay considers Richard Calder’s Dead trilogy as an important contribution to the argument concerning how pornography’s pernicious effects might be mitigated or disrupted. Paying close attention to the way that Calder uses the rhetoric of fiction to challenge pornographic stereotypes that have achieved hegemonic status, the essay argues that Calder’s trilogy provides an important link between debates about pornography and contemporary philosophical discussions of alterity and community. Finally, it argues that, for Calder, sexuality is implicitly predicated on a reconceptualization (...)
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  34. Language Teachers’ Pedagogical Orientations in Integrating Technology in the Online Classroom: Its Effect on Students’ Motivation and Engagement.Russell de Souza, Rehana Parveen, Supat Chupradit, Lovella G. Velasco, Myla M. Arcinas, Almighty Tabuena, Jupeth Pentang & Randy Joy M. Ventayen - 2021 - Turkish Journal of Computer and Mathematics Education 12 (10):5001-5014.
    The present study assessed the language teachers' pedagogical beliefs and orientations in integrating technology in the online classroom and its effect on students' motivation and engagement. It utilized a cross-sectional correlational research survey. The study respondents were the randomly sampled 205 language teachers (μ= 437, n= 205) and 317 language students (μ= 1800, n= 317) of select higher educational institutions in the Philippines. The study results revealed that respondents hold positive pedagogical beliefs and orientations using technology-based teaching in their language (...)
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  35. Foundations of Metaphysical Cosmology : Type System and Computational Experimentation.Elliott Bonal - manuscript
    The ambition of this paper is extensive: to bring about a new paradigm and firm mathematical foundations to Metaphysics, to aid its progress from the realm of mystical speculation to the realm of scientific scrutiny. -/- More precisely, this paper aims to introduce the field of Metaphysical Cosmology. The Metaphysical Cosmos here refers to the complete structure containing all entities, both existent and non-existent, with the physical universe as a subset. Through this paradigm, future endeavours in Metaphysical Science could thus (...)
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  36. Do Goedel's incompleteness theorems set absolute limits on the ability of the brain to express and communicate mental concepts verifiably?Bhupinder Singh Anand - 2004 - Neuroquantology 2:60-100.
    Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth (...)
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  37. Hume: An Intellectual Biography by James Harris. [REVIEW]Paul Russell - 2016 - Notre Dame Philosophical Reviews 1.
    James A. Harris's biography of David Hume is the first such study to appear since Ernest Mossner's The Life of David Hume (1954). Unlike Mossner, Harris aims to write a specifically "intellectual biography", one that gives "a complete picture of Hume's ideas" and "relates Hume's works to the circumstances in which they were conceived and written" (vii). Harris's study turns on four central theses or claims about the character of Hume's thought and how it is structured and developed. The claims (...)
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  38. Analysis and dialectic: studies in the logic of foundation problems.Joseph Russell - 1984 - Hingham, MA, USA: Distributors for the U.S. and Canada, Kluwer Academic Publishers. Edited by Paul Russell.
    This book was completed by the early 1960s and published in 1984 but it has not lost its topicality, for it contains an important re-assessment of the relations of two main streams of contemporary philosophy - the Analytical and the Dialectic. Adherents and critics of these traditions tend to assurnethat they are diametrically opposed, that their roots, concerns and approaches contradict each other, and that no reconciliation is possible. In contradistinction Russell derives both traditions from the common root of the (...)
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  39. Clarke's 'Almighty Space' and Hume's Treatise.Paul Russell - 1997 - Enlightenment and Dissent 16:83-113.
    The philosophy of Samuel Clarke is of central importance for an adequate understanding of Hume’s Treatise.2 Despite this, most Hume scholars have either entirely overlooked Clarke’s work, or referred to it in a casual manner that fails to do justice to the significance of the Clarke-Hume relationship. This tendency is particularly apparent in accounts of Hume’s views on space in Treatise I.ii. In this paper, I argue that one of Hume’s principal objectives in his discussion of space is to discredit (...)
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  40. Buying Logical Principles with Ontological Coin: The Metaphysical Lessons of Adding epsilon to Intuitionistic Logic.David DeVidi & Corey Mulvihill - 2017 - IfCoLog Journal of Logics and Their Applications 4 (2):287-312.
    We discuss the philosophical implications of formal results showing the con- sequences of adding the epsilon operator to intuitionistic predicate logic. These results are related to Diaconescu’s theorem, a result originating in topos theory that, translated to constructive set theory, says that the axiom of choice (an “existence principle”) implies the law of excluded middle (which purports to be a logical principle). As a logical choice principle, epsilon allows us to translate that result to a logical setting, where one (...)
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  41. Sobre o significado da função proposicional no Tractatus de Wittgenstein.Rafael dos Reis Ferreira - 2016 - Dissertation, University of Campinas
    The analysis of logical predication has long philosophical tradition in which one of the central subjects of study is the analysis of the logical form of the proposition. We contemporaneously can say that the way more well-finished of logic predication is propositional function. Historically, the propositional function arises as a logical analysis of the proposition scheme resulting from the convergence of mathematics and logic between the XIX and XX centuries. Two of the main responsible for this convergence were Gottlob (...)
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  42. Russell’s method of analysis and the axioms of mathematics.Lydia Patton - 2017 - In Sandra Lapointe & Christopher Pincock, Innovations in the History of Analytical Philosophy. London, United Kingdom: Palgrave-Macmillan. pp. 105-126.
    In the early 1900s, Russell began to recognize that he, and many other mathematicians, had been using assertions like the Axiom of Choice implicitly, and without explicitly proving them. In working with the Axioms of Choice, Infinity, and Reducibility, and his and Whitehead’s Multiplicative Axiom, Russell came to take the position that some axioms are necessary to recovering certain results of mathematics, but may not be proven to be true absolutely. The essay traces historical roots of, and motivations for, (...)
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  43. Where the Shape of the Egg Comes From?Marvin E. Kirsh - manuscript
    The shape of the egg is proposed to be the consequence of synergistic actions from the transmission of forces derived from instinctual motions and energy matter conversions that act to obstruct the grounding and neutralization of energy emissions by limiting in size the physical domain of self witness. A philosophy and theory associating, atemporal in nature, form and emergence is evolved from logical considerations for the construction of a mathematical/geometrical model of the egg that is generated from a template construed (...)
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  44. Three Dogmas of First-Order Logic and some Evidence-based Consequences for Constructive Mathematics of differentiating between Hilbertian Theism, Brouwerian Atheism and Finitary Agnosticism.Bhupinder Singh Anand - manuscript
    We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- (...)
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  45. Toward a Humean True Religion: Genuine Theism, Moderate Hope, and Practical Morality by Andre C. Willis. [REVIEW]Paul Russell - 2017 - Journal of the History of Philosophy 55 (1):168-169.
    Andre Willis argues that although Hume is generally credited with being a “devastating critic” of religion, it is a mistake to view Hume solely in these terms or to present him as an “atheist.” This not only represents a failure to appreciate Hume’s “middle path” between “militant atheists and evangelical theists”, it denies us an opportunity to “enhance” our understanding and appreciation of the positive, constructive value of religion through a close study of Hume’s views. Willis’s study presents Hume (...)
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  46. Filosofia Analitica e Filosofia Continentale.Sergio Cremaschi (ed.) - 1997 - 50018 Scandicci, Metropolitan City of Florence, Italy: La Nuova Italia.
    ● Sergio Cremaschi, The non-existing Island. The chapter discusses how the cleavage between the Continental and the Anglo-American philosophies originated, the (self-)images of both philosophical worlds, the converging rediscoveries from the Seventies, and recent ecumenic or anti-ecumenic strategies. I argue that pragmatism provides an important counter-instance to the familiar self-images and the fashionable ecumenic or anti-ecumenic strategies. The conclusions are: (i) the only place where Continental philosophy exists (as Euro-Communism one decade ago) is America; (ii) less obviously, also analytic philosophy (...)
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  47. Bertrand Russell on Logical Constructions: Matter as a Logical Construction from Sense-data.Mika Suojanen - 2020 - AL-Mukhatabat 36:13-33.
    The notion of logical construction was used by Bertrand Russell in the early 20th century, which originally comes from A. N. Whitehead. Russell said that matter as a mind-independent thing can only be known by description. He also argued that matter is a logical construction of sense-data. However, this leads to an incoherent view of the direct or indirect connection between a mind and the external world. The problem examining is whether a collapsing house is a logical construction of the (...)
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  48. Russell's Paradox in Appendix B of the Principles of Mathematics : Was Frege's response adequate?Kevin C. Klement - 2001 - History and Philosophy of Logic 22 (1):13-28.
    In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his (...)
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  49. THE HISTORICAL SYNTAX OF PHILOSOPHICAL LOGIC.Yaroslav Hnatiuk - 2022 - European Philosophical and Historical Discourse 8 (1):78-87.
    This article analyzes the historical development of the philosophical logic syntax from the standpoint of the unity of historical and logical methods. According to this perspective, there are three types of logical syntax: the elementary subject-predicate, the modified definitivespecificative, and the standard propositional-functional. These types are generalized in the grammatical and mathematical styles of logical syntax. The main attention is paid to two scientific revolutions in elementary subject-predicate syntax, which led to the emergence of modified definitive-specific and standard propositional-functional syntaxes (...)
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  50. Plato’s Metaphysical Development before Middle Period Dialogues.Mohammad Bagher Ghomi - manuscript
    Regarding the relation of Plato’s early and middle period dialogues, scholars have been divided to two opposing groups: unitarists and developmentalists. While developmentalists try to prove that there are some noticeable and even fundamental differences between Plato’s early and middle period dialogues, the unitarists assert that there is no essential difference in there. The main goal of this article is to suggest that some of Plato’s ontological as well as epistemological principles change, both radically and fundamentally, between the early and (...)
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