Philosophy of mathematics ≈ Philosophy of mathematics
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Proofs and Refutations: The Logic of Mathematical Discovery Open
Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the …
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Philosophy of Mathematics Education Open
This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its o…
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The Philosophy of Mathematics Education Open
This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its o…
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An Aristotelian realist philosophy of mathematics: mathematics as the science of quantity and structure Open
Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of math…
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Technology and Mathematics Open
In spite of their practical importance, the connections between technology and mathematics have not received much scholarly attention. This article begins by outlining how the technology–mathematics relationship has developed, from the use…
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Styles of reasoning for mathematics education Open
Although reasoning is a central concept in mathematics education research, the discipline is still in need of a coherent theoretical framework of mathematical reasoning. With respect to epistemological problems in the dominant discourses o…
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PERKEMBANGAN MATEMATIKA DALAM FILSAFAT DAN ALIRAN FORMALISME YANG TERKANDUNG DALAM FILSAFAT MATEMATIKA Open
Philosophy of mathematics does not add a number of new mathematical theorems or theories, so a philosophy of mathematics is not mathematics. The philosophy of mathematics is an area of reflection about mathematics. After studying for a l…
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PERKEMBANGAN MATEMATIKA DALAM FILSAFAT DAN ALIRAN FORMALISME YANG TERKANDUNG DALAM FILSAFAT MATEMATIKA Open
Mathematics and philosophy have a pretty close relationship, compared to other sciences. The reason, philosophy is the base for learning science and mathematics is the mother of all sciences. There are also those who think that philosophy …
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RELATIVE CATEGORICITY AND ABSTRACTION PRINCIPLES Open
Many recent writers in the philosophy of mathematics have put great weight on the relative categoricity of the traditional axiomatizations of our foundational theories of arithmetic and set theory (Parsons, 1990; Parsons, 2008, sec. 49; Mc…
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Purifying applied mathematics and applying pure mathematics: how a late Wittgensteinian perspective sheds light onto the dichotomy Open
In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also s…
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Showing Mathematical Flies the Way Out of Foundational Bottles: The Later Wittgenstein as a Forerunner of Lakatos and the Philosophy of Mathematical Practice Open
This work explores the later Wittgenstein’s philosophy of mathematics in relation to Lakatos’ philosophy of mathematics and the philosophy of mathematical practice. I argue that, while the philosophy of mathematical practice typically iden…
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Mathematics and Ethics Open
In the philosophy of mathematics, ontological and epistemological questions have been discussed for centuries. These two set of questions span out a two-dimensional philosophy of mathematics. I find it important to establish a four dimensi…
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Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do Not Come for Free Open
This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” p…
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Reshaping the metaphor of proof Open
The simplistic view of Mathematics as a logical system of formal truths deduced from a limited set of axioms by a limited set of inference rules immediately shatters when confronted with the history of Mathematics, or current mathematical …
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What is Mathematics - an Overview Open
Mathematics is based on reasoning though man's first experience with mathematics was of an nature. This means that the foundation of mathematics is the study of some logical and philosophical notions. We elaborate in simple terms that th…
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Ontologie et mathématiques : Théorie des Ensembles, théorie des Catégories, et théorie des Infinis, dans L'Être et l'événement, Logiques des mondes et L'Immanence des vérités Open
This paper examines the relationship between philosophy and its conditions. The affirmation “mathematics is ontology”, which I posited thirty years ago, has certain inconveniences. In this article, I present six varying possibilities for o…
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HUBUNGAN FILSAFAT PENDIDIKAN DAN FILSAFAT MATEMATIKA DENGAN PENDIDIKAN Open
Etymologically (meaning according to the word) the term philosophy comes from the Greek philosophia. This word is a compound word philos which means lover or friend of knowledge, and sophia which means wisdom or wisdom. Whereas mathematics…
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Armchair Philosophy Open
The article presents an anti-exceptionalist view of philosophical methodology, on which it is much closer to the methodology of other disciplines than many philosophers like to think. Like mathematics, it is a science, but not a natural sc…
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CONSTRUCTIVISM FROM PHILOSOPHY TO MATHEMATICS LEARNING Open
Constructivism, especially philosophy, understands that knowledge is the result of construction in a personal human being. Develop knowledge through social interaction with other human beings, phenomena, experiences, and environments. Know…
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A Mathematical and Philosophical Dictionary: Containing an Explanation of the Terms, and an Account of the Several Subjects, Comprized under the Heads Mathematics, Astronomy, and Philosophy, Both Natural and Experimental Open
Born into a Newcastle coal mining family, Charles Hutton (1737–1823) displayed mathematical ability from an early age. He rose to become professor of mathematics at the Royal Military Academy and foreign secretary of the Royal Society. Fir…
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The Philosophy of Mathematics Education Open
This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its o…
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Was Wittgenstein a radical conventionalist? Open
This paper defends a reading of Wittgenstein’s philosophy of mathematics in the Lectures on the Foundation of Mathematics as a radical conventionalist one, whereby our agreement about the particular case is constitutive of our mathematical…
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What is Mathematics, Really? Who Wants to Know? Open
Famous physicists, like Einstein and Wigner have been wondering, why mathematical symbolism could play such an effective and decisive role in the development of physics. Since the days of Plato, there have been essentially two different an…
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Ideas and Results in Model Theory: Reference, Realism, Structure and Categoricity Open
The topics of reference, realism, and structure have been discussed extensively in the philosophy of mathematics of the last decades. There have been some parallel discussions in certain parts of philosophy of science and metaphysics. The …
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The Mathematical Universality Theorem Open
I present the Mathematical Universality Theorem, a proposed formal framework suggesting that mathematics is not a descriptive language invented by humans, but the universal structural law that the universe itself is built from. The theorem…
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Mathematical Philosophy Open
Mathematics and philosophy are two words with different meanings and the same thing. With various historical evidence, mathematics as the basis of science is not part of or born from philosophy. In the same position in knowledge, mathemati…
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Rejecting Platonism: Recovering Humanity in Mathematics Education Open
In this paper, I consider a pervasive myth in mathematics education, that of Plato-formalism. I show that this myth is ahistorical, acultural, and harmful, both for mathematics and for society. I argue that, as teachers, we should reject t…
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An essay on Philosophy, Mathematics and Culture Open
The theme of this collection of essays has two elusive concepts, philosophy and mathematics, and the same for the combination of the two, Philosophy of Mathematics. I discussed the evolution of mathematics as an human endeavor, with a holi…
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Poincaré and the Prehistory of Mathematical Structuralism Open
The view that mathematics is about abstract structure is quite deeply rooted in mathematical practice, with further philosophical views about the nature of structures emerging more recently. This essay argues, first, that Poincaré’s views …
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Bringing Together Mathematics and Philosophy with Logic and Poly-Universe Open
In this paper we report on an activity developed in the context of the Erasmus+ PUNTE Project, using the Poly-Universe material, which led to the learning of logic and mathematics among the 10th grade students of a school in the central re…