Philosophy of Mathematics

Edited by Øystein Linnebo (University of Oslo)
Assistant editor: Sam Roberts (Universität Konstanz)
153 found
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  1. added 2022-06-28
    A Journey Through Computability, Topology and Analysis.Manlio Valenti - 2022 - Bulletin of Symbolic Logic 28 (2):266-267.
    This thesis is devoted to the exploration of the complexity of some mathematical problems using the framework of computable analysis and descriptive set theory. We will especially focus on Weihrauch reducibility as a means to compare the uniform computational strength of problems. After a short introduction of the relevant background notions, we investigate the uniform computational content of problems arising from theorems that lie at the higher levels of the reverse mathematics hierarchy.We first analyze the strength of the open and (...)
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  2. added 2022-06-28
    Two Problems of Number Theory in Islamic Times.J. Sesiano - 1991 - Archive for History of Exact Sciences 41 (3):235-238.
  3. added 2022-06-27
    In Search of Modal Hypodoxes Using Paradox Hypodox Duality.Peter Eldridge-Smith - forthcoming - Philosophia:1-20.
    The concept of hypodox is dual to the concept of paradox. Whereas a paradox is incompatibly overdetermined, a hypodox is underdetermined. Indeed, many particular paradoxes have dual hypodoxes. So, naively the dual of Russell’s Paradox is whether the set of all sets that are members of themselves is self-membered. The dual of the Liar Paradox is the Truth-teller, and a hypodoxical dual of the Heterological paradox is whether ‘autological’ is autological. I provide some analysis of the duality and I search (...)
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  4. added 2022-06-27
    Aristotelova Politika U Horizontu Mjere I odgojaAristotle’s Political Theory in the Horizon of Measure and Education.Željko Senković - 2022 - Metodicki Ogledi 29 (1):11-29.
    U članku se razmatra grčki ideal mjere, najčešće izražen pojmom sredine. To nije samo svegrčki ideal nego drevna i svevremena baština, koja je konvergirala odgoju u ujednosti ‘dobrote i ljepote’. On je življen u polisu, kao što je bio i personalna, unutarduševna težnja. U Aristotelovoj politici počelo mjere prvenstveno je vezano za balansiranje političkih poredaka, ali postoji i druga perspektiva u kojoj je više riječ o vrlini i moralnim kvalitetama aristokracije, gdje se identificira dobrog čovjeka i građanina. Taj pristup srodniji (...)
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  5. added 2022-06-27
    Religious Education and the Limits of Political Liberalism.Eric Farr - 2019 - Philosophy of Education 75:506-518.
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  6. added 2022-06-27
    Political Education in Context: The Promise of More Radical Agonism in 2019.Claudia W. Ruitenberg - 2019 - Philosophy of Education 75:559-564.
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  7. added 2022-06-27
    #NeverAgainMSD Student Activism: A Response to Ruitenberg’s “Educating Political Adversaries”.Kathleen Knight Abowitz & Dan Mamlok - 2019 - Philosophy of Education 75:544-558.
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  8. added 2022-06-27
    More Potent Than Political Power: Beyond Cognitive Dimensions of Democracy.Jane Blanken-Webb & Devon Almond - 2019 - Philosophy of Education 75:424-428.
  9. added 2022-06-27
    Going “to the Limit” of Political Liberalism.Brett Bertucio - 2019 - Philosophy of Education 75:519-523.
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  10. added 2022-06-27
    School Closures as Political Mourning.Terri S. Wilson - 2019 - Philosophy of Education 75:659-665.
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  11. added 2022-06-26
    Salvatore Florio and Øystein Linnebo. The Many and the One. A Philosophical Study of Plural Logic.Francesca Boccuni - forthcoming - Philosophia Mathematica.
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  12. added 2022-06-24
    The Cardinality of the Partitions of a Set in the Absence of the Axiom of Choice.Palagorn Phansamdaeng & Pimpen Vejjajiva - forthcoming - Logic Journal of the IGPL.
    In the Zermelo–Fraenkel set theory, $|\textrm {fin}|<2^{|A|}\leq |\textrm {Part}|$ for any infinite set $A$, where $\textrm {fin}$ is the set of finite subsets of $A$, $2^{|A|}$ is the cardinality of the power set of $A$ and $\textrm {Part}$ is the set of partitions of $A$. In this paper, we show in ZF that $|\textrm {fin}|<|\textrm {Part}_{\textrm {fin}}|$ for any set $A$ with $|A|\geq 5$, where $\textrm {Part}_{\textrm {fin}}$ is the set of partitions of $A$ whose members are finite. We also (...)
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  13. added 2022-06-21
    Origins and Varieties of Logicism. A Foundational Journey in the Philosophy of Mathematics.Andrea Sereni & Francesca Boccuni (eds.) - 2021
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  14. added 2022-06-19
    Simultaneously Vanishing Higher Derived Limits Without Large Cardinals.Jeffrey Bergfalk, Michael Hrusak & Chris Lambie-Hanson - forthcoming - Journal of Mathematical Logic.
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  15. added 2022-06-18
    Fermat’s Last Theorem Proved in Hilbert Arithmetic. III. The Quantum-Information Unification of Fermat’s Last Theorem and Gleason’s Theorem.Vasil Penchev - forthcoming - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN):1-30.
    The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace (...)
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  16. added 2022-06-18
    Turin, 1916, G. Fubini : Une Expérience de Patrimonialisation En Théorie des nombresTurin, 1916, G. Fubini: An Experiment in the Patrimonialisation of Number Theory. [REVIEW]Erika Luciano - 2022 - Philosophia Scientae 26:123-144.
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  17. added 2022-06-18
    The Justificatory Force of Experiences: From a Phenomenological Epistemology to the Foundations of Mathematics and Physics.Philipp Berghofer - 2022 - Springer (Synthese Library).
  18. added 2022-06-17
    Reverse Mathematics.John Stillwell - 2021 - In Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer.
    Reverse mathematics is a new take on an old idea: asking which axioms are necessary to prove a given theorem. This question was first asked about the parallel axiom in Euclid’s geometry and later about the axiom of choice in set theory. Obviously, such questions can be asked in many fields of mathematics, but in recent decades, it has proved fruitful to focus on subsystems of second-order arithmetic, where much of mainstream mathematics resides. It has been found that many basic (...)
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  19. added 2022-06-15
    The Nature of Correlation Perception in Scatterplots.Ronald A. Rensink - 2017 - Psychonomic Bulletin & Review 24 (3):776-797.
    For scatterplots with gaussian distributions of dots, the perception of Pearson correlation r can be described by two simple laws: a linear one for discrimination, and a logarithmic one for perceived magnitude (Rensink & Baldridge, 2010). The underlying perceptual mechanisms, however, remain poorly understood. To cast light on these, four different distributions of datapoints were examined. The first had 100 points with equal variance in both dimensions. Consistent with earlier results, just noticeable difference (JND) was a linear function of the (...)
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  20. added 2022-06-15
    The Intended Model of Arithmetic.Paula Quinon - 2010 - Dissertation, University of Paris 1 Sorbonne-Pantheon
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  21. added 2022-06-14
    The Making of Mathematics. Heuristic Philosophy of Mathematics.Carlo Cellucci - 2022 - Cham, Switzerland: Springer.
    Mainstream philosophy of mathematics, namely the philosophy of mathematics that has prevailed for the past century, claims that the philosophy of mathematics cannot concern itself with the making of mathematics, in particular discovery, but only with finished mathematics, namely mathematics presented in finished form. On this basis, mainstream philosophy of mathematics argues that mathematics is theorem proving by the axiomatic method. This, however, is untenable because it is incompatible with Gödel’s incompleteness theorems, and cannot account for many features of mathematics. (...)
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  22. added 2022-06-13
    Does Anti-Exceptionalism About Logic Entail That Logic is a Posteriori?Jessica M. Wilson & Stephen Biggs - 2022 - Synthese 200 (3):1-17.
    The debate between exceptionalists and anti-exceptionalists about logic is often framed as concerning whether the justification of logical theories is a priori or a posteriori (for short: whether logic is a priori or a posteriori). As we substantiate (S1), this framing more deeply encodes the usual anti-exceptionalist thesis that logical theories, like scientific theories, are abductively justified, coupled with the common supposition that abduction is an a posteriori mode of inference, in the sense that the epistemic value of abduction is (...)
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  23. added 2022-06-11
    Safety First: Making Property Talk Safe for Nominalists.Jack Himelright - 2022 - Synthese 200 (3):1-26.
    Nominalists are confronted with a grave difficulty: if abstract objects do not exist, what explains the success of theories that invoke them? In this paper, I make headway on this problem. I develop a formal language in which certain platonistic claims about properties and certain nominalistic claims can be expressed, develop a formal language in which only certain nominalistic claims can be expressed, describe a function mapping sentences of the first language to sentences of the second language, and prove some (...)
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  24. added 2022-06-10
    Some Paradoxes of Infinity Revisited.Yaroslav Sergeyev - 2022 - Mediterranian Journal of Mathematics 19:143.
    In this article, some classical paradoxes of infinity such as Galileo’s paradox, Hilbert’s paradox of the Grand Hotel, Thomson’s lamp paradox, and the rectangle paradox of Torricelli are considered. In addition, three paradoxes regarding divergent series and a new paradox dealing with multiplication of elements of an infinite set are also described. It is shown that the surprising counting system of an Amazonian tribe, Pirah ̃a, working with only three numerals (one, two, many) can help us to change our perception (...)
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  25. added 2022-06-08
    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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  26. added 2022-06-03
    Topology Optimization of Computer Communication Network Based on Improved Genetic Algorithm.Kayhan Zrar Ghafoor, Jilei Zhang, Yuhong Fan & Hua Ai - 2022 - Journal of Intelligent Systems 31 (1):651-659.
    The topology optimization of computer communication network is studied based on improved genetic algorithm, a network optimization design model based on the establishment of network reliability maximization under given cost constraints, and the corresponding improved GA is proposed. In this method, the corresponding computer communication network cost model and computer communication network reliability model are established through a specific project, and the genetic intelligence algorithm is used to solve the cost model and computer communication network reliability model, respectively. It has (...)
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  27. added 2022-06-03
    Álgebras booleanas, órdenes parciales y axioma de elección.Franklin Galindo - 2017 - Divulgaciones Matematicas 18 ( 1):34-54.
    El objetivo de este artículo es presentar una demostración de un teorema clásico sobre álgebras booleanas y ordenes parciales de relevancia actual en teoría de conjuntos, como por ejemplo, para aplicaciones del método de construcción de modelos llamado “forcing” (con álgebras booleanas completas o con órdenes parciales). El teorema que se prueba es el siguiente: “Todo orden parcial se puede extender a una única álgebra booleana completa (salvo isomorfismo)”. Donde extender significa “sumergir densamente”. Tal demostración se realiza utilizando cortaduras de (...)
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  28. added 2022-06-03
    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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  29. added 2022-06-02
    El Teorema de Completitud de Gödel, el Teorema del Colapso Transitivo de Mostowski y el Principio de Reflexión.Franklin Galindo -
    Es conocido que el Teorema de Completitud de Gödel, el Teorema del Colapso Transitivo de Mostowski y el Principio de Reflexión son resultados muy útiles en las investigaciones de Lógica matemática y/o los Fundamentos de la matemática. El objetivo de este trabajo es presentar algunas demostraciones clásicas de tales resultados: Dos del Teorema de Completitud de Gödel, una del Teorema del Colapso Transitivo de Mostowski y una del Principio de Reflexión. Se aspira que estas notas sean de utilidad para estudiar (...)
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  30. added 2022-06-02
    El Método de Forcing: Algunas aplicaciones y una aproximación a sus fundamentos metamatemáticos.Franklin Galindo - manuscript
    Es conocido que el método de forcing es una de las técnicas de construcción de modelos más importantes de la Teoría de conjuntos en la actualidad, siendo el mismo muy útil para investigar problemas de matemática y/o de fundamentos de la matemática. El destacado matemático Joan Bagaria afirma lo siguiente sobre el método de forcing en su artículo "Paul Cohen y la técnica del forcing" (Gaceta de la Real Sociedad Matemática Española, Vol. 2, Nº 3, 1999, págs 543-553) : "Aunque (...)
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  31. added 2022-06-02
    TRES TEOREMAS SOBRE CARDINALES MEDIBLES.Franklin Galindo - 2021 - Mixba'al. Revista Metropolitana de Matemáticas 12 (1):15-31.
    El estudio de los "cardinales grandes" es uno de los principales temas de investigación de la teoría de conjuntos y de la teoría de modelos que ha contribuido con el desarrollo de dichas disciplinas. Existe una gran variedad de tales cardinales, por ejemplo cardinales inaccesibles, débilmente compactos, Ramsey, medibles, supercompactos, etc. Tres valiosos teoremas clásicos sobre cardinales medibles son los siguientes: (i) compacidad débil, (ii) Si κ es un cardinal medible, entonces κ es un cardinal inaccesible y existen κ cardinales (...)
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  32. added 2022-06-02
    Algunas notas introductorias sobre la Teoría de Conjuntos.Franklin Galindo - 2019 - Apuntes Filosóficos: Revista Semestral de la Escuela de Filosofía 18 (55):201-232.
    The objective of this document is to present three introductory notes on set theory: The first note presents an overview of this discipline from its origins to the present, in the second note some considerations are made about the evaluation of reasoning applying the first-order Logic and Löwenheim's theorems, Church Indecidibility, Completeness and Incompleteness of Gödel, it is known that the axiomatic theories of most commonly used sets are written in a specific first-order language, that is, they are developed within (...)
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  33. added 2022-06-01
    The Axiom of Choice is False Intuitionistically.Charles Mccarty, Stewart Shapiro & Ansten Klev - forthcoming - Bulletin of Symbolic Logic:1-26.
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  34. added 2022-06-01
    Hacia una interpretación semiótica de los signos matemáticos.Miguel Ariza - 2007 - Mathesis 2 (2):227-251.
    El análisis de las propiedades geométricas de las configuraciones finitas ha sido uno de los objetivos fundamentales del estudio de las diversas geometrías discretas y de la geometría combinatoria. Este artículo propone plantear la posibilidad de una elucidación de lo matemático desde una perspectiva derivada de las ‘matemáticas en acción’ y no desde una concepción ‘analítico gramatical’ de sus fundamentos, y establecer, al menos, un mínimo umbral de validez, que articule una interpretación semiótica de los signos matemáticos, a través del (...)
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  35. added 2022-05-30
    Noesis, semiosis y matemáticas.Miguel Ariza - 2009 - Mathesis 4 (2):203-220.
    El presupuesto según el cual el contenido de una manifestación compleja está en función de los contenidos de sus partes componentes, expresa claramente una intuición que solemos tener sobre lo múltiple; implica una reflexión sobre la relación entre el todo y las partes que lo componen; involucra una teoría de las multiplicidades que entraña atributos de naturaleza matemática; presenta el problema de cómo los seres humanos nos relacionamos con los entornos del mundo para generar unidad de sentido. La significación es (...)
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  36. added 2022-05-29
    Un problema abierto de independencia en la teoría de conjuntos relacionado con ultrafiltros no principales sobre el conjunto de los números naturales N, y con Propiedades Ramsey.Franklin Galindo - manuscript
    En el ámbito de la lógica matemática existe un problema sobre la relación lógica entre dos versiones débiles del Axioma de elección (AE) que no se ha podido resolver desde el año 2000 (aproximadamente). Tales versiones están relacionadas con ultrafiltros no principales y con Propiedades Ramsey (Bernstein, Polarizada, Subretículo, Ramsey, Ordinales flotantes, etc). La primera versión débil del AE es la siguiente (A): “Existen ultrafiltros no principales sobre el conjunto de los números naturales (ℕ)”. Y la segunda versión débil del (...)
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  37. added 2022-05-29
    Nota: ¿CUÁL ES EL CARDINAL DEL CONJUNTO DE LOS NÚMEROS REALES?Franklin Galindo - manuscript
    Qué ha pasado con el problema del cardinal del continuo después de Gödel (1938) y Cohen (1964)? Intentos de responder esta pregunta pueden encontrarse en los artículos de José Alfredo Amor (1946-2011), "El Problema del continuo después de Cohen (1964-2004)", de Carlos Di Prisco , "Are we closer to a solution of the continuum problem", y de Joan Bagaria, "Natural axioms of set and the continuum problem" , que se pueden encontrar en la biblioteca digital de mi blog de Lógica (...)
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  38. added 2022-05-29
    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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  39. added 2022-05-28
    Tópicos de Ultrafiltros.Franklin Galindo - 2020 - Divulgaciones Matematicas 21 (1-2):54-77.
    Ultrafilters are very important mathematical objects in mathematical research [6, 22, 23]. There are a wide variety of classical theorems in various branches of mathematics where ultrafilters are applied in their proof, and other classical theorems that deal directly with ultrafilters. The objective of this article is to contribute (in a divulgative way) to ultrafilter research by describing the demonstrations of some such theorems related (uniquely or in combination) to topology, Measure Theory, algebra, combinatorial infinite, set theory and first-order logic, (...)
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  40. added 2022-05-28
    Un teorema sobre el Modelo de Solovay.Franklin Galindo - 2020 - Divulgaciones Matematicas 21 (1-2): 42–46.
    The objective of this article is to present an original proof of the following theorem: Thereis a generic extension of the Solovay’s model L(R) where there is a linear order of P(N)/fin that extends to the partial order (P(N)/f in), ≤*). Linear orders of P(N)/fin are important because, among other reasons, they allow constructing non-measurable sets, moreover they are applied in Ramsey's Theory .
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  41. added 2022-05-28
    ¿Cómo utilizar el Teorema de Herbrand para decidir la validez de razonamientos en lenguaje de primer orden, en conformidad con el Teorema de Indecidibilidad de Church?Franklin Galindo & María Alejandra Morgado - 2019 - Apuntes Filosóficos: Revista Semestral de la Escuela de Filosofía 18 (55):67-86.
    This article’s objetive is to present four application examples of Herbrand’s theorem to decide the validity of reasoning on first order language, in accordance whit Church’s Undecidability’s theorem. Also, to tell which is the principal problem around it. The logical resolution calculus will be worked on this article, which is a method used in artificial intelligence.
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  42. added 2022-05-28
    Dos Tópicos de Lógica Matemática y sus Fundamentos.Franklin Galindo - 2014 - Episteme NS: Revista Del Instituto de Filosofía de la Universidad Central de Venezuela 34 (1):41-66..
    El objetivo de este artículo es presentar dos tópicos de Lógica matemática y sus fundamentos: El primer tópico es una actualización de la demostración de Alonzo Church del Teorema de completitud de Gödel para la Lógica de primer orden, la cual aparece en su texto "Introduction to Mathematical Logic" (1956) y usa el procedimientos efectivos de Forma normal prenexa y Forma normal de Skolem; y el segundo tópico es una demostración de que la propiedad de partición (tipo Ramsey) del espacio (...)
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  43. added 2022-05-28
    Constructibilidad relativizada y el Axioma de elección.Franklin Galindo & Carlos Di Prisco - 2010 - Mixba'al. Revista Metropolitana de Matemáticas 1 (1):23-40.
    El objetivo de este trabajo es presentar en un solo cuerpo tres maneras de relativizar (o generalizar) el concepto de conjunto constructible de Gödel que no suelen aparecer juntas en la literatura especializada y que son importantes en la Teoría de Conjuntos, por ejemplo para resolver problemas de consistencia o independencia. Presentamos algunos modelos resultantes de las diferentes formas de relativizar el concepto de constructibilidad, sus propiedades básicas y algunas formas débiles del Axioma de Elección válidas o no válidas en (...)
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  44. added 2022-05-28
    Perfect Set Properties in Models of ZF.Franklin Galindo & Carlos Di Prisco - 2010 - Fundamenta Mathematicae 208 (208):249-262.
    We study several perfect set properties of the Baire space which follow from the Ramsey property ω→(ω) ω . In particular we present some independence results which complete the picture of how these perfect set properties relate to each other.
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  45. added 2022-05-27
    A Note on Consistency and Platonism.Alfredo Roque Freire & V. Alexis Peluce - forthcoming - In 43rd International Wittgenstein Symposium proceedings.
    Is consistency the sort of thing that could provide a guide to mathematical ontology? If so, which notion of consistency suits this purpose? Mark Balaguer holds such a view in the context of platonism, the view that mathematical objects are non-causal, non-spatiotemporal, and non-mental. For the purposes of this paper, we will examine several notions of consistency with respect to how they can provide a platon-ist epistemology of mathematics. Only a Gödelian notion, we suggest, can provide a satisfactory guide to (...)
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  46. added 2022-05-24
    The Infinite: Third Edition.A. W. Moore - 2018 - Routledge.
    This third edition of The Infinite includes a new part 'Infinity Superseded' which contains two new chapters refining Moore's ideas through a re-examination of the ideas of Spinoza, Hegel, and Nietzsche. Much of this is heavily influenced by the work of Deleuze. There is also a new technical appendix on still unresolved issues about different infinite sizes.
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  47. added 2022-05-20
    How Does Hands-On Making Attitude Predict Epistemic Curiosity and Science, Technology, Engineering, and Mathematics Career Interests? Evidence From an International Exhibition of Young Inventors.Yuting Cui, Jon-Chao Hong, Chi-Ruei Tsai & Jian-Hong Ye - 2022 - Frontiers in Psychology 13:859179.
    Whether the hands-on experience of creating inventions can promote Students’ interest in pursuing a science, technology, engineering, and mathematics (STEM) career has not been extensively studied. In a quantitative study, we drew on the attitude-behavior-outcome framework to explore the correlates between hands-on making attitude, epistemic curiosities, and career interest. This study targeted students who joined the selection competition for participating in the International Exhibition of Young Inventors (IEYI) in Taiwan. The objective of the invention exhibition is to encourage young students (...)
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  48. added 2022-05-19
    Zeno Paradox, Unexpected Hanging Paradox (Modeling of Reality & Physical Reality, A Historical-Philosophical View).Farzad Didehvar - manuscript
    . In our research about Fuzzy Time and modeling time, "Unexpected Hanging Paradox" plays a major role. Here, we compare this paradox to the Zeno Paradox and the relations of them with our standard models of continuum and Fuzzy numbers. To do this, we review the project "Fuzzy Time and Possible Impacts of It on Science" and introduce a new way in order to approach the solutions for these paradoxes. Additionally, we have a more general discussion about paradoxes, as Philosophical (...)
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  49. added 2022-05-15
    Mathematics is Ontology? A Critique of Badiou's Ontological Framing of Set Theory.Roland Bolz - 2020 - Filozofski Vestnik 2 (41):119-142.
    This article develops a criticism of Alain Badiou’s assertion that “mathematics is ontology.” I argue that despite appearances to the contrary, Badiou’s case for bringing set theory and ontology together is problematic. To arrive at this judgment, I explore how a case for the identification of mathematics and ontology could work. In short, ontology would have to be characterised to make it evident that set theory can contribute to it fundamentally. This is indeed how Badiou proceeds in Being and Event. (...)
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  50. added 2022-05-14
    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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