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  1. Artistic Mediation in Mathematized Phenomenology.Robert Prentner & Shanna Dobson - manuscript
    Mathematics has a long track record of refining the concepts by which we make sense of the world. For example, mathematics allows one to speak about different senses of "sameness", depending on the larger context. Phenomenology is the name of a philosophical discipline that tries to systematically investigate the first-personal perspective on reality and how it is constituted. Together, mathematics and phenomenology seem to be a good fit to derive statements about our experience that are, at the same time, well-defined, (...)
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  2. Algunos tópicos de Lógica matemática y los Fundamentos de la matemática.Franklin Galindo - manuscript
    En este trabajo matemático-filosófico se estudian cuatro tópicos de la Lógica matemática: El método de construcción de modelos llamado Ultraproductos, la Propiedad de Interpolación de Craig, las Álgebras booleanas y los Órdenes parciales separativos. El objetivo principal del mismo es analizar la importancia que tienen dichos tópicos para el estudio de los fundamentos de la matemática, desde el punto de vista del platonismo matemático. Para cumplir con tal objetivo se trabajará en el ámbito de la Matemática, de la Metamatemática y (...)
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  3. El Programa original de David Hilbert y el Problema de la Decibilidad.Franklin Galindo & Ricardo Da Silva - 2017 - Episteme NS: Revista Del Instituto de Filosofía de la Universidad Central de Venezuela 37 (1):1-23.
    En este artículo realizamos una reconstrucción del Programa original de Hilbert antes del surgimiento de los teoremas limitativos de la tercera década del siglo pasado. Para tal reconstrucción empezaremos por mostrar lo que Torretti llama los primeros titubeos formales de Hilbert, es decir, la defensa por el método axiomático como enfoque fundamentante. Seguidamente, mostraremos como estos titubeos formales se establecen como un verdadero programa de investigación lógico-matemático y como dentro de dicho programa la inquietud por la decidibilidad de los problemas (...)
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  4. Математизирането на историята: число и битие.Vasil Penchev - 2013 - Sofia: BAS: ISSk (IPR).
    The book is a philosophical refection on the possibility of mathematical history. Are poosible models of historical phenomena so exact as those of physical ones? Mathematical models borrowed from quantum mechanics by the meditation of its interpretations are accomodated to history. The conjecture of many-variant history, alternative history, or counterfactual history is necessary for mathematical history. Conclusions about philosophy of history are inferred.
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  5. Hale and Wright on the Metaontology of Neo-Fregeanism.Matti Eklund - 2016 - In Marcus Rossberg & Philip A. Ebert (eds.), Abstractionism.
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  6. Demostraciones «tópicamente puras» en la práctica matemática: un abordaje elucidatorio.Guillermo Nigro Puente - 2020 - Dissertation, Universidad de la República Uruguay
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  7. গণিত দর্শন Gonit Dorshon.Avijit Lahiri - manuscript
    This article, written in Bengali ('Gonit Dorshon' means `philosophy of mathematics' ), briefly reviews a few of the major points of view toward mathematics and the world of mathematical entities, and interprets the philosophy of mathematics as an interaction between these. The existence of these different points of view is indicative that mathematics, in spite of being of universal validity, can nevertheless accommodate alternatives. In particular, I review the alternative viewpoints of Platonism and Intuitionism and present the case that in (...)
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  8. Maddy On The Multiverse.Claudio Ternullo - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Berlin: Springer Verlag. pp. 43-78.
    Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...)
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  9. 关于在柴廷、维特根斯坦、霍夫施塔特、沃尔珀特、多里亚、达科斯塔、戈德尔、西尔、罗迪赫、贝托、弗洛伊德、贝托、弗洛伊德、莫亚尔-沙罗克和亚诺夫斯基.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    人们普遍认为,不可能性、不完整性、不一致性、不可度、随机性、可预见性、悖论、不确定性和理性极限是完全不同的科学物理或数学问题,在常见。我认为,它们主要是标准的哲学问题(即语言游戏),这些问题大多在80 多年前由维特根斯坦解决。 -/- "在这种情况下,我们'想说'当然不是哲学,而是它的原材料。因此,例如,数学家倾向于对数学事实的客观性和现实性说的,不是数学哲学,而是哲学处理的东西。维特根斯坦 PI 234 -/- "哲学家们经常看到科学的方法,他们不可抗拒地试图以科学的方式提问和回答问题。这种倾向是形而上学的真正源泉,将哲学家带入完全的黑暗之中。 维特根斯坦 -/- 我简要地总结了现代两位最杰出的学生路德维希·维特根斯坦和约翰·西尔关于故意的逻辑结构(思想、语言、行为)的一些主要发现,作为我的起点Wittgenstein 的基本发现——所有真正的"哲学"问题都是相同的——关于在特定上下文中如何使用语言的困惑,因此所有解决方案都是一样的——研究如何在相关上下文中使用语言,使其真实性条件(满意度或 COS 条件)是明确的。基本问题是,人们可以说什么,但一个人不能意味着(状态明确COS)任何任意的话语和意义只有在非常具体的上下文中才可能。 -/- 在两种思想体系的现代视角(被推广为"思维快,思维慢")的框架内,我从维特根斯坦人的角度剖析了一些主要评论员关于这些问题的一些著作,并采用了一个新的表意向性和新的双系统命名法。 我表明,这是一个强大的启发式描述这些假定的科学,物理或数学问题的真实性质,这是真正最好的处理作为标准哲学问题,如何使用语言(语言游戏在维特根斯坦的术语)。 -/- 我的论点是,这里突出特征的意向表(理性、思想、思想、语言、个性等)或多或少地准确地描述了,或者至少作为启发式,我们思考和行为的方式,所以它包含不只是哲学和心理学,但其他一切(历史,文学,数学,政治等) 。特别要注意,我(以及西尔、维特根斯坦和其他人)认为,故意和理性包括有意识的审议语言系统2和无意识的自动预语言系统1行为或反射。 .
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  10. Deleuze and the conceptualizable character of mathematical theories.Simon B. Duffy - 2017 - In Nathalie Sinclair & Alf Coles Elizabeth de Freitas (ed.), What is a Mathematical Concept? Cambridge University Press.
    To make sense of what Gilles Deleuze understands by a mathematical concept requires unpacking what he considers to be the conceptualizable character of a mathematical theory. For Deleuze, the mathematical problems to which theories are solutions retain their relevance to the theories not only as the conditions that govern their development, but also insofar as they can contribute to determining the conceptualizable character of those theories. Deleuze presents two examples of mathematical problems that operate in this way, which he considers (...)
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  11. Counting on Strong Composition as Identity to Settle the Special Composition Question.Joshua Spencer - 2017 - Erkenntnis 82 (4):857-872.
    Strong Composition as Identity is the thesis that necessarily, for any xs and any y, those xs compose y iff those xs are non-distributively identical to y. Some have argued against this view as follows: if some many things are non-distributively identical to one thing, then what’s true of the many must be true of the one. But since the many are many in number whereas the one is not, the many cannot be identical to the one. Hence is mistaken. (...)
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  12. Category Theory and Indefinite Extensibility.Hasen Khudairi - manuscript
    This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility for set-theoretic truths in the category of sets is identifiable with the Grothendieck Universe Axiom and the elementary embeddings in Vopenka's principle. The interaction between the interpretational and objective modalities of indefinite extensibility is defined via the epistemic interpretation of two-dimensional semantics. The semantics can be defined intensionally or hyperintensionally. By characterizing the modal profile of (...)
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  13. A process oriented definition of number.Rolfe David - manuscript
    In this paper Russell’s definition of number is criticized. Russell’s assertion that a number is a particular kind of set implies that number has the properties of a set. It is argued that this would imply that a number contains elements and that this does not conform to our intuitive notion of number. An alternative definition is presented in which number is not seen as an object, but rather as a process and is related to the act of counting and (...)
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  14. The Idea of Infinity in its Physical and Spiritual Meanings.Graham Nicholson - manuscript
    Abstract -/- The concept of infinity is of ancient origins and has puzzled deep thinkers ever since up to the present day. Infinity remains somewhat of a mystery in a physical world in which our comprehension is largely framed around the concept of boundaries. This is partly because we live in a physical world that is governed by certain dimensions or limits – width, breadth, depth, mass, space, age and time. To our ordinary understanding, it is a seemingly finite world (...)
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  15. A Note on Gabriel Uzquiano’s “Varieties of Indefinite Extensibility”.Simon Hewitt - unknown - Notre Dame Journal of Formal Logic 59 (3):455-459.
    It is argued that Gabriel Uzquiano's approach to set-theoretic indefinite extensibility is a version of in rebus structuralism, and therefore suffers from a vacuity problem.
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  16. Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974).John Corcoran - 1979 - MATHEMATICAL REVIEWS 58:3202-3.
    John Corcoran. 1979 Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974). Mathematical Reviews 58 3202 #21388. -/- The “method of analysis” is a technique used by ancient Greek mathematicians (and perhaps by Descartes, Newton, and others) in connection with discovery of proofs of difficult theorems and in connection with discovery of constructions of elusive geometric figures. Although this method was originally applied in geometry, its later application to number played an important role in the early development of (...)
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  17. Hobbes on Natural Philosophy as "True Physics" and Mixed Mathematics.Marcus P. Adams - 2016 - Studies in History and Philosophy of Science Part A 56:43-51.
    I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the ‘that’) with causal principles from geometry (the ‘why’). My argument shows (...)
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  18. Editorial. Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy.Plamen L. Simeonov, Arran Gare, Seven M. Rosen & Denis Noble - 2015 - Progress in Biophysics and Molecular Biology 119 (3):208-218.
    The is the Editorial of the 2015 JPBMB Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy.
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  19. Integral Biomathics Reloaded: 2015.Plamen L. Simeonov & Ron Cottam - forthcoming - Journal Progress in Biophysics and Molecular Biology 119 (2).
    An updated survey of the research scope in Integral Biomathics.
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  20. On the duality between existence and information.David Ellerman - manuscript
    Recent developments in pure mathematics and in mathematical logic have uncovered a fundamental duality between "existence" and "information." In logic, the duality is between the Boolean logic of subsets and the logic of quotient sets, equivalence relations, or partitions. The analogue to an element of a subset is the notion of a distinction of a partition, and that leads to a whole stream of dualities or analogies--including the development of new logical foundations for information theory parallel to Boole's development of (...)
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  21. Groundedness - Its Logic and Metaphysics.Jönne Kriener - 2014 - Dissertation, Birkbeck College, University of London
    In philosophical logic, a certain family of model constructions has received particular attention. Prominent examples are the cumulative hierarchy of well-founded sets, and Kripke's least fixed point models of grounded truth. I develop a general formal theory of groundedness and explain how the well-founded sets, Cantor's extended number-sequence and Kripke's concepts of semantic groundedness are all instances of the general concept, and how the general framework illuminates these cases. Then, I develop a new approach to a grounded theory of proper (...)
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  22. Crunchy Methods in Practical Mathematics.Michael Wood - 2001 - Philosophy of Mathematics Education Journal 14.
    This paper focuses on the distinction between methods which are mathematically "clever", and those which are simply crude, typically repetitive and computer intensive, approaches for "crunching" out answers to problems. Examples of the latter include simulated probability distributions and resampling methods in statistics, and iterative methods for solving equations or optimisation problems. Most of these methods require software support, but this is easily provided by a PC. The paper argues that the crunchier methods often have substantial advantages from the perspectives (...)
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  23. A Cognitive Approach to Benacerraf's Dilemma.Luke Jerzykiewicz - 2009 - Dissertation, University of Western Ontario
    One of the important challenges in the philosophy of mathematics is to account for the semantics of sentences that express mathematical propositions while simultaneously explaining our access to their contents. This is Benacerraf’s Dilemma. In this dissertation, I argue that cognitive science furnishes new tools by means of which we can make progress on this problem. The foundation of the solution, I argue, must be an ontologically realist, albeit non-platonist, conception of mathematical reality. The semantic portion of the problem can (...)
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  24. The philosophy of mathematics and the independent 'other'.Penelope Rush - unknown
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  25. Completions, Constructions, and Corollaries.Thomas Mormann - 2009 - In H. Pulte, G. Hanna & H.-J. Jahnke (eds.), Explanation and Proof in Mathematics: Philosophical and Educational Perspectives. Springer.
    According to Kant, pure intuition is an indispensable ingredient of mathematical proofs. Kant‘s thesis has been considered as obsolete since the advent of modern relational logic at the end of 19th century. Against this logicist orthodoxy Cassirer’s “critical idealism” insisted that formal logic alone could not make sense of the conceptual co-evolution of mathematical and scientific concepts. For Cassirer, idealizations, or, more precisely, idealizing completions, played a fundamental role in the formation of the mathematical and empirical concepts. The aim of (...)
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  26. The gödel paradox and Wittgenstein's reasons.Francesco Berto - 2009 - Philosophia Mathematica 17 (2):208-219.
    An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match (...)
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  27. Sources for the Philosophy of Archytas.Monte Ransome Johnson - 2008 - Ancient Philosophy 28 (1):173-199.
    A review of Carl Huffman's new edition of the fragments of Archytas of Tarentum. Praises the extensive commentary on four fragments, but argues that at least two dubious works not included in the edition ("On Law and Justice" and "On Wisdom") deserve further consideration and contain important information for the interpretation of Archytas. Provides a complete translation for the fragments of those works.
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Explanation in Mathematics
  1. Unrealistic Models in Mathematics.William D'Alessandro - 2022 - Philosophers’ Imprint.
    Models are indispensable tools of scientific inquiry, and one of their main uses is to improve our understanding of the phenomena they represent. How do models accomplish this? And what does this tell us about the nature of understanding? While much recent work has aimed at answering these questions, philosophers' focus has been squarely on models in empirical science. I aim to show that pure mathematics also deserves a seat at the table. I begin by presenting two cases: Cramér’s random (...)
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  2. Naive cubical type theory.Bruno Bentzen - 2022 - Mathematical Structures in Computer Science:1-27.
    This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the homotopy type theory book for dependent type theory augmented with axioms for univalence and higher inductive types. We adopt a cartesian cubical type theory proposed by Angiuli, Brunerie, Coquand, Favonia, Harper, and Licata as the implicit foundation, confining our presentation (...)
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  3. Mathematical and Non-causal Explanations: an Introduction.Daniel Kostić - 2019 - Perspectives on Science 1 (27):1-6.
    In the last couple of years, a few seemingly independent debates on scientific explanation have emerged, with several key questions that take different forms in different areas. For example, the questions what makes an explanation distinctly mathematical and are there any non-causal explanations in sciences (i.e., explanations that don’t cite causes in the explanans) sometimes take a form of the question of what makes mathematical models explanatory, especially whether highly idealized models in science can be explanatory and in virtue of (...)
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  4. Astronomy, Geometry, and Logic, Rev. 1c: An ontological proof of the natural principles that enable and sustain reality and mathematics.Michael Lucas Monterey & Michael Lucas-Monterey - manuscript
    The latest draft (posted 05/14/22) of this short, concise work of proof, theory, and metatheory provides summary meta-proofs and verification of the work and results presented in the Theory and Metatheory of Atemporal Primacy and Riemann, Metatheory, and Proof. In this version, several new and revised definitions of terms were added to subsection SS.1; and many corrected equations, theorems, metatheorems, proofs, and explanations are included in the main text. The body of the text is approximately 18 pages, with 3 sections; (...)
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  5. Not So Distinctively Mathematical Explanations.Aditya Jha, Clemency Montelle, Douglas I. Campbell & Phillip Wilson - manuscript
    (Longer version - work in progress) Various accounts of distinctively mathematical explanations (DMEs) of complex systems have been proposed recently which bypass the contingent causal laws and appeal primarily to mathematical necessities constraining the system. These necessities are considered to be modally exalted in that they obtain with a greater necessity than the ordinary laws of nature (Lange 2016). This paper focuses on DMEs of the number of equilibrium positions of n-tuple pendulum systems and considers several different DMEs of these (...)
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  6. Unification and mathematical explanation in science.Sam Baron - 2021 - Synthese 199 (3-4):7339-7363.
    Mathematics clearly plays an important role in scientific explanation. Debate continues, however, over the kind of role that mathematics plays. I argue that if pure mathematical explananda and physical explananda are unified under a common explanation within science, then we have good reason to believe that mathematics is explanatory in its own right. The argument motivates the search for a new kind of scientific case study, a case in which pure mathematical facts and physical facts are explanatorily unified. I argue (...)
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  7. In Education We Trust.Venkata Rayudu Posina -
    Beginning with an examination of the deep history of making things and thinking about making things made-up in our minds, I argue that the resultant declarative understanding of the procedural knowledge of abstracting theories and building models—the essence(s) of the practice of science—embodied in Conceptual Mathematics is worth learning beginning with high school, along with grammar and calculus. One of the many profound scientific insights introduced—in a manner accessible to total beginners—in Lawvere and Schanuel's Conceptual Mathematics textbook is: the way (...)
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  8. Proof, Explanation, and Justification in Mathematical Practice.Moti Mizrahi - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (4):551-568.
    In this paper, I propose that applying the methods of data science to “the problem of whether mathematical explanations occur within mathematics itself” (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of (...)
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  9. Notes on how-possible reasoning.Besim Karakadılar - manuscript
    A brief outline for some alternative lines of thought on the general structure of how-possible reasoning and its implications for formally and informally conceivable things, and the concept of mathematical truth.
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  10. How can necessary facts call for explanation.Dan Baras - 2020 - Synthese 198 (12):11607-11624.
    While there has been much discussion about what makes some mathematical proofs more explanatory than others, and what are mathematical coincidences, in this article I explore the distinct phenomenon of mathematical facts that call for explanation. The existence of mathematical facts that call for explanation stands in tension with virtually all existing accounts of “calling for explanation”, which imply that necessary facts cannot call for explanation. In this paper I explore what theoretical revisions are needed in order to accommodate this (...)
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  11. Using corpus linguistics to investigate mathematical explanation.Juan Pablo Mejía Ramos, Lara Alcock, Kristen Lew, Paolo Rago, Chris Sangwin & Matthew Inglis - 2019 - In Eugen Fischer & Mark Curtis (eds.), Methodological Advances in Experimental Philosophy. London: Bloomsbury Academic. pp. 239–263.
    In this chapter we use methods of corpus linguistics to investigate the ways in which mathematicians describe their work as explanatory in their research papers. We analyse use of the words explain/explanation (and various related words and expressions) in a large corpus of texts containing research papers in mathematics and in physical sciences, comparing this with their use in corpora of general, day-to-day English. We find that although mathematicians do use this family of words, such use is considerably less prevalent (...)
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  12. Avis sur « Je suis une Boucle Etrange » (I Am a Strange Loop) de Douglas Hofstadter (2007) (examen révisé 2019).Michael Richard Starks - 2020 - In Bienvenue en Enfer sur Terre : Bébés, Changement climatique, Bitcoin, Cartels, Chine, Démocratie, Diversité, Dysgénique, Égalité, Pirates informatiques, Droits de l'homme, Islam, Libéralisme, Prospérité, Le Web, Chaos, Famine, Maladie, Violence, Intellige. Las Vegas, NV USA: Reality Press. pp. 110-127.
    Dernier Sermon de l’Église du naturalisme fondamentaliste par le pasteur Hofstadter. Comme son travail beaucoup plus célèbre (ou infâme pour ses erreurs philosophiques implacables) Godel, Escher, Bach, il a une plausibilité superficielle, mais si l’on comprend que c’est le scientisme rampant qui mélange les vrais problèmes scientifiques avec les questions philosophiques (c’est-à-dire, les seules vraies questions sont ce que les jeux linguistiques que nous devrions jouer), alors presque tout son intérêt disparaît. Je fournis un cadre d’analyse basé sur la psychologie (...)
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  13. Modality and constitution in distinctively mathematical explanations.Mark Povich - 2020 - European Journal for Philosophy of Science 10 (3):1-10.
    Lange argues that some natural phenomena can be explained by appeal to mathematical, rather than natural, facts. In these “distinctively mathematical” explanations, the core explanatory facts are either modally stronger than facts about ordinary causal law or understood to be constitutive of the physical task or arrangement at issue. Craver and Povich argue that Lange’s account of DME fails to exclude certain “reversals”. Lange has replied that his account can avoid these directionality charges. Specifically, Lange argues that in legitimate DMEs, (...)
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  14. Revisão de ‘Eu sou um Loop Estranho’ (I am a Strange Loop) por Douglas Hofstadter (2007) (revisão revisada 2019).Michael Richard Starks - 2020 - In Entendendo as Conexões entre Ciência, Filosofia, Psicologia, Religião, Política, Economia, História e Literatura - Artigos e Avaliações 2006-2019. Las Vegas, NV USA: Reality Press. pp. 251-268.
    Último sermão da Igreja do naturalismo fundamentalista pelo pastor Hofstadter. Como o seu muito mais famoso (ou infame por seus erros filosóficos implacáveis) Godel, Escher, Bach, ele tem uma plausibilidade superficial, mas se se compreende que este é um cientificismo desenfreado que mistura questões científicas reais com os filosóficos (ou seja, o somente as edições reais são que jogos da língua nós devemos jogar) então quase todo seu interesse desaparece. Eu forneci um quadro para análise baseada na psicologia evolutiva e (...)
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  15. Proving Quadratic Reciprocity: Explanation, Disagreement, Transparency and Depth.William D’Alessandro - 2020 - Synthese (9):1-44.
    Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...)
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  16. Viewing-as explanations and ontic dependence.William D’Alessandro - 2020 - Philosophical Studies 177 (3):769-792.
    According to a widespread view in metaphysics and philosophy of science, all explanations involve relations of ontic dependence between the items appearing in the explanandum and the items appearing in the explanans. I argue that a family of mathematical cases, which I call “viewing-as explanations”, are incompatible with the Dependence Thesis. These cases, I claim, feature genuine explanations that aren’t supported by ontic dependence relations. Hence the thesis isn’t true in general. The first part of the paper defends this claim (...)
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  17. Revisão de ' Os Limites Exteriores da Razão ' (The Outer Limits of Reason)por Noson Yanofsky 403p (2013) (revisão revisada 2019).Michael Richard Starks - 2019 - In Delírios Utópicos Suicidas no Século XXI Filosofia, Natureza Humana e o Colapso da Civilization- Artigos e Comentários 2006-2019 5ª edição. Las Vegas, NV USA: Reality Press. pp. 188-202.
    Eu dou uma revisão detalhada de "os limites exteriores da razão" por Noson Yanofsky de uma perspectiva unificada de Wittgenstein e psicologia evolutiva. Eu indico que a dificuldade com tais questões como paradoxo na linguagem e matemática, incompletude, undecidabilidade, computabilidade, o cérebro eo universo como computadores, etc., todos surgem a partir da falta de olhar atentamente para o nosso uso da linguagem no apropriado contexto e, consequentemente, a falta de separar questões de fato científico a partir de questões de como (...)
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  18. Reseña de 'The Outer Limits of Reason' por Noson Yanofsky 403p (2013).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 71-90.
    Doy una revisión detallada de ' los límites externos de la razón ' por Noson Yanofsky desde una perspectiva unificada de Wittgenstein y la psicología evolutiva. Yo indiqué que la dificultad con cuestiones como la paradoja en el lenguaje y las matemáticas, la incompletitud, la indeterminación, la computabilidad, el cerebro y el universo como ordenadores, etc., surgen de la falta de mirada cuidadosa a nuestro uso del lenguaje en el adecuado contexto y, por tanto, el Error al separar los problemas (...)
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  19. Reseña de ‘Soy un Bucle Extraño’ ( I am a Strange Loop) de Douglas Hofstadter.Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 21-43.
    Último sermón de la iglesia del naturalismo fundamentalista por el pastor Hofstadter. Al igual que su mucho más famoso (o infame por sus incesantemente errores filosóficos) trabajo Godel, Escher, Bach, tiene una plausibilidad superficial, pero si se entiende que se trata de un científico rampante que mezcla problemas científicos reales con los filosóficos (es decir, el sólo los problemas reales son los juegos de idiomas que debemos jugar) entonces casi todo su interés desaparece. Proporciono un marco para el análisis basado (...)
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  20. Teaching and Learning Guide for: Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11):e12629.
    This is a teaching and learning guide to accompany "Explanation in Mathematics: Proofs and Practice".
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  21. Explanation in mathematics: Proofs and practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11):e12629.
    Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do (...)
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  22. ملاحظات على استحالة, عدم اكتمال, بارااتساق,عدم تحديد, عشوائية, الحوسبة, مفارقة, وعدم اليقين في Chaitin, Wittgenstein, Hofstadter, Wolpert, دوريا, دا كوستا, جوديل, سيرل, روديش, بيرتو, فلويد, مويال شاروك ويانوفسكي.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    ويعتقد عادة أن الاستحالة، وعدم اكتمال، وParaconsistency، وعدم تحديد، العشوائية، والحوسبة، والمفارقة، وعدم اليقين وحدود العقل هي قضايا علمية مادية أو رياضية متباينة وجود القليل أو لا شيء في المشتركه. أقترح أنها مشاكل فلسفية قياسية إلى حد كبير (أي ألعاب اللغة) التي تم حلها في الغالب من قبل فيتغنشتاين أكثر من 80years منذ. -/- "إن ما نميل إلى قوله في مثل هذه الحالة هو، بطبيعة الحال، ليس فلسفة، ولكنه مادة خام. وهكذا، على سبيل المثال، ما يميل عالم الرياضيات إلى قوله (...)
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  23. असंभव, अपूर्णता, अनिर्णय, अनिर्णय, यादृच्छिकता, गणना, विरोधाभास, और चैटिन, विटगेनस्टीन, Hofstadter, Wolpert, डोरिया, दा कोस्टा, गोडेल, सीरले, Rodych, Berto, Floyd में अनिश्चितता पर टिप्पणी मोयाल-शररॉक और यानोफ्स्की.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    यह आमतौर पर सोचा जाता है कि असंभवता, अपूर्णता, Paraconsistency, अनिर्णितता, Randomness, Computability, विरोधाभास, अनिश्चितता और कारण की सीमा अलग वैज्ञानिक शारीरिक या गणितीय मुद्दों में कम या कुछ भी नहीं कर रहे हैं आम. मेरा सुझाव है कि वे काफी हद तक मानक दार्शनिक समस्याओं (यानी, भाषा का खेल) जो ज्यादातर 80years पहले Wittgenstein द्वारा हल किए गए थे. -/- "क्या हम 'इस तरह के एक मामले में कहने के लिए' कर रहे हैं, ज़ाहिर है, दर्शन नहीं है, लेकिन (...)
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