Results for 'Mathematical Metaphors'

895 found
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  1. Mathematical Metaphors in Natorp’s Neo-Kantian Epistemology and Philosophy of Science.Thomas Mormann - 2005 - In Falk Seeger, Johannes Lenard & Michael H. G. Hoffmann (eds.), Activity and Sign. Grounding Mathematical Education. Springer.
    A basic thesis of Neokantian epistemology and philosophy of science contends that the knowing subject and the object to be known are only abstractions. What really exists, is the relation between both. For the elucidation of this “knowledge relation ("Erkenntnisrelation") the Neokantians of the Marburg school used a variety of mathematical metaphors. In this con-tribution I reconsider some of these metaphors proposed by Paul Natorp, who was one of the leading members of the Marburg school. It is (...)
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  2.  99
    Mathematical Knowledge, the Analytic Method, and Naturalism.Fabio Sterpetti - 2018 - In Sorin Bangu (ed.), Naturalizing Logico-Mathematical Knowledge. Approaches from Philosophy, Psychology and Cognitive Science. New York, Stati Uniti: pp. 268-293.
    This chapter tries to answer the following question: How should we conceive of the method of mathematics, if we take a naturalist stance? The problem arises since mathematical knowledge is regarded as the paradigm of certain knowledge, because mathematics is based on the axiomatic method. Moreover, natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some authors tried to (...)
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  3. The Directionality of Distinctively Mathematical Explanations.Carl F. Craver & Mark Povich - 2017 - Studies in History and Philosophy of Science Part A 63:31-38.
    In “What Makes a Scientific Explanation Distinctively Mathematical?” (2013b), Lange uses several compelling examples to argue that certain explanations for natural phenomena appeal primarily to mathematical, rather than natural, facts. In such explanations, the core explanatory facts are modally stronger than facts about causation, regularity, and other natural relations. We show that Lange's account of distinctively mathematical explanation is flawed in that it fails to account for the implicit directionality in each of his examples. This inadequacy is (...)
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  4.  43
    Sofia A. Yanovskaya: The Marxist Pioneer of Mathematical Logic in the Soviet Union.Dimitris Kilakos - 2019 - Transversal: International Journal for the Historiography of Science 6:49-64.
    K. Marx’s 200th jubilee coincides with the celebration of the 85 years from the first publication of his “Mathematical Manuscripts” in 1933. Its editor, Sofia Alexandrovna Yanovskaya (1896–1966), was a renowned Soviet mathematician, whose significant studies on the foundations of mathematics and mathematical logic, as well as on the history and philosophy of mathematics are unduly neglected nowadays. Yanovskaya, as a militant Marxist, was actively engaged in the ideological confrontation with idealism and its influence on modern mathematics and (...)
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  5. Mathematical Symbols as Epistemic Actions.De Cruz Helen & De Smedt Johan - 2013 - Synthese 190 (1):3-19.
    Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols (...)
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  6. The Mismeasure of Machine: Synthetic Biology and the Trouble with Engineering Metaphors.Maarten Boudry & Massimo Pigliucci - 2013 - Studies in History and Philosophy of Biological and Biomedical Sciences (4):660-668.
    The scientific study of living organisms is permeated by machine and design metaphors. Genes are thought of as the ‘‘blueprint’’ of an organism, organisms are ‘‘reverse engineered’’ to discover their func- tionality, and living cells are compared to biochemical factories, complete with assembly lines, transport systems, messenger circuits, etc. Although the notion of design is indispensable to think about adapta- tions, and engineering analogies have considerable heuristic value (e.g., optimality assumptions), we argue they are limited in several important respects. (...)
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  7. Why Machine-Information Metaphors Are Bad for Science and Science Education.Massimo Pigliucci & Maarten Boudry - 2011 - Science & Education 20 (5-6):471.
    Genes are often described by biologists using metaphors derived from computa- tional science: they are thought of as carriers of information, as being the equivalent of ‘‘blueprints’’ for the construction of organisms. Likewise, cells are often characterized as ‘‘factories’’ and organisms themselves become analogous to machines. Accordingly, when the human genome project was initially announced, the promise was that we would soon know how a human being is made, just as we know how to make airplanes and buildings. Impor- (...)
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  8.  58
    Animal Cognition, Species Invariantism, and Mathematical Realism.Helen De Cruz - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Academic. pp. 39-61.
    What can we infer from numerical cognition about mathematical realism? In this paper, I will consider one aspect of numerical cognition that has received little attention in the literature: the remarkable similarities of numerical cognitive capacities across many animal species. This Invariantism in Numerical Cognition (INC) indicates that mathematics and morality are disanalogous in an important respect: proto-moral beliefs differ substantially between animal species, whereas proto-mathematical beliefs (at least in the animals studied) seem to show more similarities. This (...)
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  9. Complements, Not Competitors: Causal and Mathematical Explanations.Holly Andersen - 2017 - British Journal for the Philosophy of Science:axw023.
    A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non- causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the (...)
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  10. Numerical Cognition and Mathematical Realism.Helen De Cruz - 2016 - Philosophers' Imprint 16.
    Humans and other animals have an evolved ability to detect discrete magnitudes in their environment. Does this observation support evolutionary debunking arguments against mathematical realism, as has been recently argued by Clarke-Doane, or does it bolster mathematical realism, as authors such as Joyce and Sinnott-Armstrong have assumed? To find out, we need to pay closer attention to the features of evolved numerical cognition. I provide a detailed examination of the functional properties of evolved numerical cognition, and propose that (...)
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  11.  56
    The Narrow Ontic Counterfactual Account of Distinctively Mathematical Explanation.Mark Povich - 2019 - British Journal for the Philosophy of Science:axz008.
    An account of distinctively mathematical explanation (DME) should satisfy three desiderata: it should account for the modal import of some DMEs; it should distinguish uses of mathematics in explanation that are distinctively mathematical from those that are not (Baron [2016]); and it should also account for the directionality of DMEs (Craver and Povich [2017]). Baron’s (forthcoming) deductive-mathematical account, because it is modelled on the deductive-nomological account, is unlikely to satisfy these desiderata. I provide a counterfactual account of (...)
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  12.  16
    Mathematical and Moral Disagreement.Silvia Jonas - forthcoming - Philosophical Quarterly.
    The existence of fundamental moral disagreements is a central problem for moral realism and has often been contrasted with an alleged absence of disagreement in mathematics. However, mathematicians do in fact disagree on fundamental questions, for example on which set-theoretic axioms are true, and some philosophers have argued that this increases the plausibility of moral vis-à-vis mathematical realism. I argue that the analogy between mathemat- ical and moral disagreement is not as straightforward as those arguments present it. In particular, (...)
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  13. Two Criticisms Against Mathematical Realism.Seungbae Park - 2017 - Diametros 52:96-106.
    Mathematical realism asserts that mathematical objects exist in the abstract world, and that a mathematical sentence is true or false, depending on whether the abstract world is as the mathematical sentence says it is. I raise two objections against mathematical realism. First, the abstract world is queer in that it allows for contradictory states of affairs. Second, mathematical realism does not have a theoretical resource to explain why a sentence about a tricle is true (...)
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  14. In Defense of Mathematical Inferentialism.Seungbae Park - 2017 - Analysis and Metaphysics 16:70-83.
    I defend a new position in philosophy of mathematics that I call mathematical inferentialism. It holds that a mathematical sentence can perform the function of facilitating deductive inferences from some concrete sentences to other concrete sentences, that a mathematical sentence is true if and only if all of its concrete consequences are true, that the abstract world does not exist, and that we acquire mathematical knowledge by confirming concrete sentences. Mathematical inferentialism has several advantages over (...)
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  15. Can Mathematical Objects Be Causally Efficacious?Seungbae Park - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (3):247–255.
    Callard (2007) argues that it is metaphysically possible that a mathematical object, although abstract, causally affects the brain. I raise the following objections. First, a successful defence of mathematical realism requires not merely the metaphysical possibility but rather the actuality that a mathematical object affects the brain. Second, mathematical realists need to confront a set of three pertinent issues: why a mathematical object does not affect other concrete objects and other mathematical objects, what counts (...)
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  16. Two Analogy Strategies: The Cases of Mind Metaphors and Introspection.Eugen Fischer - 2018 - Connection Science 30 (2):211-243.
    Analogical reasoning is often employed in problem-solving and metaphor interpretation. This paper submits that, as a default, analogical reasoning addressing these different tasks employs different mapping strategies: In problem-solving, it employs analogy-maximising strategies (like structure mapping, Gentner & Markman 1997); in metaphor interpretation, analogy-minimising strategies (like ATT-Meta, Barnden 2015). The two strategies interact in analogical reasoning with conceptual metaphors. This interaction leads to predictable fallacies. The paper supports these hypotheses through case-studies on ‘mind’-metaphors from ordinary discourse, and abstract (...)
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  17. Mathematical Platonism and the Nature of Infinity.Gilbert B. Côté - 2013 - Open Journal of Philosophy 3 (3):372-375.
    An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.
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  18.  55
    Mathematical Explanations and the Piecemeal Approach to Thinking About Explanation.Gabriel Târziu - 2018 - Logique Et Analyse 61 (244):457-487.
    A new trend in the philosophical literature on scientific explanation is that of starting from a case that has been somehow identified as an explanation and then proceed to bringing to light its characteristic features and to constructing an account for the type of explanation it exemplifies. A type of this approach to thinking about explanation – the piecemeal approach, as I will call it – is used, among others, by Lange (2013) and Pincock (2015) in the context of their (...)
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  19. Against Mathematical Convenientism.Seungbae Park - 2016 - Axiomathes 26 (2):115-122.
    Indispensablists argue that when our belief system conflicts with our experiences, we can negate a mathematical belief but we do not because if we do, we would have to make an excessive revision of our belief system. Thus, we retain a mathematical belief not because we have good evidence for it but because it is convenient to do so. I call this view ‘ mathematical convenientism.’ I argue that mathematical convenientism commits the consequential fallacy and that (...)
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  20.  21
    Syntactic Characterizations of First-Order Structures in Mathematical Fuzzy Logic.Guillermo Badia, Pilar Dellunde, Vicent Costa & Carles Noguera - forthcoming - Soft Computing.
    This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.
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  21. Rejecting Mathematical Realism While Accepting Interactive Realism.Seungbae Park - 2018 - Analysis and Metaphysics 17:7-21.
    Indispensablists contend that accepting scientific realism while rejecting mathematical realism involves a double standard. I refute this contention by developing an enhanced version of scientific realism, which I call interactive realism. It holds that interactively successful theories are typically approximately true, and that the interactive unobservable entities posited by them are likely to exist. It is immune to the pessimistic induction while mathematical realism is susceptible to it.
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  22.  83
    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 (...)
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  23.  10
    A Critical Assessment Of The Role Of The Imagination In Kant’s Exposition Of The Mathematical Sublime.Richard Stopford - 2007 - Postgraduate Journal of Aesthetics 4 (3):24-31.
    Kant argues in the Critique of Judgment (CJ) that there are two distinct modes of the sublime. This essay will concentrate on the mathematical mode. It is helpful to begin an examination of the mathematical sublime by elucidating the difference between logical estimation and aesthetic estimation; it is aesthetic estimation under strain, so Kant argues, that instigates the moment of the sublime. Logical estimation forms the cognitive basis of scientific calculations. He argues that scientific enquiry only requires an (...)
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  24. Multi-Level Selection and the Explanatory Value of Mathematical Decompositions.Christopher Clarke - 2016 - British Journal for the Philosophy of Science 67 (4):1025-1055.
    Do multi-level selection explanations of the evolution of social traits deepen the understanding provided by single-level explanations? Central to the former is a mathematical theorem, the multi-level Price decomposition. I build a framework through which to understand the explanatory role of such non-empirical decompositions in scientific practice. Applying this general framework to the present case places two tasks on the agenda. The first task is to distinguish the various ways of suppressing within-collective variation in fitness, and moreover to evaluate (...)
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  25. Mathematical Representation: Playing a Role.Kate Hodesdon - 2014 - Philosophical Studies 168 (3):769-782.
    The primary justification for mathematical structuralism is its capacity to explain two observations about mathematical objects, typically natural numbers. Non-eliminative structuralism attributes these features to the particular ontology of mathematics. I argue that attributing the features to an ontology of structural objects conflicts with claims often made by structuralists to the effect that their structuralist theses are versions of Quine’s ontological relativity or Putnam’s internal realism. I describe and argue for an alternative explanation for these features which instead (...)
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  26. Adaptive Landscapes, Phenotypic Space, and the Power of Metaphors[REVIEW]Massimo Pigliucci - 2008 - Quarterly Review of Biology 83 (3):283-287.
    Metaphors play a crucial role in both science in particular and human discourse in gen- eral. Plato’s story of the cave—about people shackled to a wall and incapable of perceiv- ing the world as it really is—has stimulated thinking about epistemology and the nature of reality for more than two millennia. But metaphors can also be misleading: being too taken with Plato’s story has cost philosophers endless discussions about how to access the world “as it is,” until Kant (...)
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  27. Mathematical Modelling and Contrastive Explanation.Adam Morton - 1990 - Canadian Journal of Philosophy 20 (Supplement):251-270.
    Mathematical models provide explanations of limited power of specific aspects of phenomena. One way of articulating their limits here, without denying their essential powers, is in terms of contrastive explanation.
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  28. Kant on Mathematical Construction and Quantity of Matter.Jennifer McRobert - manuscript
    Kant's special metaphysics is intended to provide the a priori foundation for Newtonian science, which is to be achieved by exhibiting the a priori content of Newtonian concepts and laws. Kant envisions a two-step mathematical construction of the dynamical concept of matter involving a geometrical construction of matter’s bulk and a symbolic construction of matter’s density. Since Newton himself defines quantity of matter in terms of bulk and density, there is no reason why we shouldn’t interpret Kant’s Dynamics as (...)
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  29.  36
    Review – Mathematical Doodlings. [REVIEW]Karl Pfeifer - 2017 - Metapsychology Online Reviews 21 (45):n.p..
    A review of Geoffrey Marnell, Mathematical Doodlings: Curiosities, conjectures, and challenges.
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  30. Wittgenstein on Mathematical Identities.André Porto - 2012 - Disputatio 4 (34):755-805.
    This paper offers a new interpretation for Wittgenstein`s treatment of mathematical identities. As it is widely known, Wittgenstein`s mature philosophy of mathematics includes a general rejection of abstract objects. On the other hand, the traditional interpretation of mathematical identities involves precisely the idea of a single abstract object – usually a number –named by both sides of an equation.
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  31.  24
    Mathematical Modeling of Biological and Social Evolutionary Macrotrends.Leonid Grinin, Alexander V. Markov & Andrey V. Korotayev - 2014 - In History & Mathematics: Trends and Cycles. Volgograd,Russia: Uchitel Publishing House. pp. 9-48.
    In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological data and an analogy with macrosociological models, we suggest (...)
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  32. The Indefinite Within Descartes' Mathematical Physics.Françoise Monnoyeur-Broitman - 2013 - Eidos: Revista de Filosofía de la Universidad Del Norte 19:107-122.
    Descartes' philosophy contains an intriguing notion of the infinite, a concept labeled by the philosopher as indefinite. Even though Descartes clearly defined this term on several occasions in the correspondence with his contemporaries, as well as in his Principles of Philosophy, numerous problems about its meaning have arisen over the years. Most commentators reject the view that the indefinite could mean a real thing and, instead, identify it with an Aristotelian potential infinite. In the first part of this article, I (...)
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  33.  85
    Book Reviews: Claude P. Bruter (Editor), Mathematics in Art: Mathematical Visualization in Art and Education.Walter Carnielli - 2004 - Logic and Logical Philosophy 13:163-166.
    Claude P. Bruter (editor), Mathematics in Art: Mathematical Visualization in Art and Education, Springer-Verlag, New York, 2002, pp. X + 337, ISBN 3-540-43422-4.
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  34.  52
    The Philosophical Implications of the Loophole-Free Violation of Bell’s Inequality: Quantum Entanglement, Timelessness, Triple-Aspect Monism, Mathematical Platonism and Scientific Morality.Gilbert B. Côté - manuscript
    The demonstration of a loophole-free violation of Bell's inequality by Hensen et al. (2015) leads to the inescapable conclusion that timelessness and abstractness exist alongside space-time. This finding is in full agreement with the triple-aspect monism of reality, with mathematical Platonism, free will and the eventual emergence of a scientific morality.
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  35.  20
    Mathematical Thinking Undefended on The Level of The Semester for Professional Mathematics Teacher Candidates. Toheri & Widodo Winarso - 2017 - Munich University Library.
    Mathematical thinking skills are very important in mathematics, both to learn math or as learning goals. Thinking skills can be seen from the description given answers in solving mathematical problems faced. Mathematical thinking skills can be seen from the types, levels, and process. Proportionally questions given to students at universities in Indonesia (semester I, III, V, and VII). These questions are a matter of description that belong to the higher-level thinking. Students choose 5 of 8 given problem. (...)
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  36. Chasing Individuation: Mathematical Description of Physical Systems.Zalamea Federico - 2016 - Dissertation, Paris Diderot University
    This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the set of observables of a physical system, be it classical or quantum, is described by a Jordan-Lie algebra. From the geometric point of view, the space of states of any system is described by a uniform Poisson space with transition probability. Both these (...)
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  37.  78
    The "Artificial Mathematician" Objection: Exploring the (Im)Possibility of Automating Mathematical Understanding.Sven Delarivière & Bart Van Kerkhove - 2017 - In B. Sriraman (ed.), Humanizing Mathematics and its Philosophy. Cham: Birkhäuser. pp. 173-198.
    Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer.
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  38. Mathematical Shortcomings in a Simulated Universe.Samuel Alexander - 2018 - The Reasoner 12 (9):71-72.
    I present an argument that for any computer-simulated civilization we design, the mathematical knowledge recorded by that civilization has one of two limitations. It is untrustworthy, or it is weaker than our own mathematical knowledge. This is paradoxical because it seems that nothing prevents us from building in all sorts of advantages for the inhabitants of said simulation.
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  39.  98
    On Similarities Between Biological and Social Evolutionary Mechanisms: Mathematical Modeling.Leonid Grinin - 2013 - Cliodynamics: The Journal of Theoretical and Mathematical History 4:185-228.
    In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. This is more or less identical with the working of the collective learning (...)
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  40. Review of Macbeth, D. Diagrammatic Reasoning in Frege's Begriffsschrift. Synthese 186 (2012), No. 1, 289–314. Mathematical Reviews MR 2935338.John Corcoran - 2014 - MATHEMATICAL REVIEWS 2014:2935338.
    A Mathematical Review by John Corcoran, SUNY/Buffalo -/- Macbeth, Danielle Diagrammatic reasoning in Frege's Begriffsschrift. Synthese 186 (2012), no. 1, 289–314. ABSTRACT This review begins with two quotations from the paper: its abstract and the first paragraph of the conclusion. The point of the quotations is to make clear by the “give-them-enough-rope” strategy how murky, incompetent, and badly written the paper is. I know I am asking a lot, but I have to ask you to read the quoted passages—aloud (...)
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  41. Review Of: Hodesdon, K. “Mathematica Representation: Playing a Role”. Philosophical Studies (2014) 168:769–782. Mathematical Reviews. MR 3176431.John Corcoran - 2015 - MATHEMATICAL REVIEWS 2015:3176431.
    This 4-page review-essay—which is entirely reportorial and philosophically neutral as are my other contributions to MATHEMATICAL REVIEWS—starts with a short introduction to the philosophy known as mathematical structuralism. The history of structuralism traces back to George Boole (1815–1864). By reference to a recent article various feature of structuralism are discussed with special attention to ambiguity and other terminological issues. The review-essay includes a description of the recent article. The article’s 4-sentence summary is quoted in full and then analyzed. (...)
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  42.  80
    1983 Review in Mathematical Reviews 83e:03005 Of: Cocchiarella, Nino “The Development of the Theory of Logical Types and the Notion of a Logical Subject in Russell's Early Philosophy: Bertrand Russell's Early Philosophy, Part I”. Synthese 45 (1980), No. 1, 71-115.John Corcoran - 1983 - MATHEMATICAL REVIEWS 83:03005.
    CORCORAN RECOMMENDS COCCHIARELLA ON TYPE THEORY. The 1983 review in Mathematical Reviews 83e:03005 of: Cocchiarella, Nino “The development of the theory of logical types and the notion of a logical subject in Russell's early philosophy: Bertrand Russell's early philosophy, Part I”. Synthese 45 (1980), no. 1, 71-115 .
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  43.  39
    Review Of: Garciadiego, A., "Emergence Of...Paradoxes...Set Theory", Historia Mathematica (1985), in Mathematical Reviews 87j:01035.John Corcoran - 1987 - MATHEMATICAL REVIEWS 87 (J):01035.
    DEFINING OUR TERMS A “paradox" is an argumentation that appears to deduce a conclusion believed to be false from premises believed to be true. An “inconsistency proof for a theory" is an argumentation that actually deduces a negation of a theorem of the theory from premises that are all theorems of the theory. An “indirect proof of the negation of a hypothesis" is an argumentation that actually deduces a conclusion known to be false from the hypothesis alone or, more commonly, (...)
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  44. Mathematical Thought in the Light of Matte Blanco’s Work.Giuseppe Iurato - 2013 - Philosophy of Mathematics Education Journal 27:1-9.
    Taking into account some basic epistemological considerations on psychoanalysis by Ignacio Matte Blanco, it is possible to deduce some first simple remarks on certain logical aspects of schizophrenic reasoning. Further remarks on mathematical thought are also made in the light of what established, taking into account the comparison with the schizophrenia pattern.
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  45.  30
    Mathematical Electron Model and the SI Unit 2017 Special Adjustment.Malcolm J. Macleod - manuscript
    Following the 26th General Conference on Weights and Measures are fixed the numerical values of the 4 physical constants ($h, c, e, k_B$). This is premised on the independence of these constants. This article discusses a model of a mathematical electron from which can be defined the Planck units as geometrical objects (mass M=1, time T=2$\pi$ ...). In this model these objects are interrelated via this electron geometry such that once we have assigned values to 2 Planck units then (...)
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  46.  68
    Mathematical Nature of Reality, Plus Gravitation-Electromagnetism Unification, Derived From Revised Gravitational Tidal Forces and Mass-From-Gravity Concept.Rodney Bartlett - manuscript
    This article had its beginning with Einstein's 1919 paper "Do gravitational fields play an essential role in the structure of elementary particles?" Together with General Relativity's statement that gravity is not a pull but is a push caused by the curvature of space-time, a hypothesis for Earth's ocean tides was developed that does not solely depend on the Sun and Moon as Kepler and Newton believed. It also borrows from Galileo. The breakup of planets and asteroids by white dwarfs, neutron (...)
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  47. Mathematical Deduction by Induction.Christy Ailman - 2013 - Gratia Eruditionis:4-12.
    In attempt to provide an answer to the question of origin of deductive proofs, I argue that Aristotle’s philosophy of math is more accurate opposed to a Platonic philosophy of math, given the evidence of how mathematics began. Aristotle says that mathematical knowledge is a posteriori, known through induction; but once knowledge has become unqualified it can grow into deduction. Two pieces of recent scholarship on Greek mathematics propose new ways of thinking about how mathematics began in the Greek (...)
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  48. Retrieving the Mathematical Mission of the Continuum Concept From the Transfinitely Reductionist Debris of Cantor’s Paradise. Extended Abstract.Edward G. Belaga - forthcoming - International Journal of Pure and Applied Mathematics.
    What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? -/- The double-edged purpose of the present study is to save from the (...)
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  49.  31
    Can We Have Mathematical Understanding of Physical Phenomena?Gabriel Târziu - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (1):91-109.
    Can mathematics contribute to our understanding of physical phenomena? One way to try to answer this question is by getting involved in the recent philosophical dispute about the existence of mathematical explanations of physical phenomena. If there is such a thing, given the relation between explanation and understanding, we can say that there is an affirmative answer to our question. But what if we do not agree that mathematics can play an explanatory role in science? Can we still consider (...)
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  50. On Some Considerations of Mathematical Physics: May We Identify Clifford Algebra as a Common Algebraic Structure for Classical Diffusion and Schrödinger Equations?Elio Conte - 2012 - Advanced Studies in Theoretical Physics 6 (26):1289-1307.
    We start from previous studies of G.N. Ord and A.S. Deakin showing that both the classical diffusion equation and Schrödinger equation of quantum mechanics have a common stump. Such result is obtained in rigorous terms since it is demonstrated that both diffusion and Schrödinger equations are manifestation of the same mathematical axiomatic set of the Clifford algebra. By using both such ( ) i A S and the i,±1 N algebra, it is evidenced, however, that possibly the two basic (...)
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