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Showing 1 to 19 of 19 for “"Philosophy of Mathematics"”.
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Avicenna's Philosophy of Mathematics
I discuss four different aspects of Avicenna’s philosophical views on mathematics, as scattered across his various works. I first explore the negative aspect of his ontology of mathematics, which concerns the question of what mathematical objects (i.e., numbers and geometrical shapes) are not. …
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Paul Ernest's Social Constructivist Philosophy of Mathematics Education
The main focus of this project is to critically analyze Ernest's philosophy of mathematics education and his conceptions of mathematical knowledge and democratic education. Specifically, I use textual analysis to interpret what he intends for each group of students and to critically analyze the …
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A defence of predicativism as a philosophy of mathematics
A specification of a mathematical object is impredicative if it essentially involves quantification over a domain which includes the object being specified (or sets which contain that object, or similar). The basic worry is that we have no non-circular way of understanding such a specification. …
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Leaving mathematics as it is: Wittgenstein’s later philosophy of mathematics
Wittgenstein’s later philosophy of mathematics has been widely interpreted to involve Wittgenstein’s making dogmatic requirements of what can and cannot be mathematics, as well as involving Wittgenstein dismissing whole areas (e.g. set theory) as not legitimate mathematics. Given that Wittgenstein …
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Aristotle and Frege on Method in the Philosophy of Mathematics
Aristotle discusses the philosophy of mathematics in the final books of the Metaphysics and approaches questions and problems in this subject from a metaphysical perspective. This way of undertaking the philosophy of mathematics is informed by his understanding of the nature and ends of science, …
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Investigations linking the philosophy and psychology of mathematics
Recent progress in the field of cognitive science, specifically with respect to mathematical cognition, along with the turn in the philosophy of mathematics to a focus on mathematical practice, make for a great opportunity for interdisciplinary work that brings together the cognitive science of …
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Carnap and the Ontology of Mathematics
In this thesis I investigate Rudolf Carnap's philosophy of mathematics. Most philosophers assume that the nature of mathematics raises deep philosophical questions, which call for theories about how we manage to know about and interact with abstract objects. Carnap's position, in contrast, is …
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Valued Kinds of Knowledge and Ways of Knowing in Mathematics and the Teaching and Learning of Mathematics: A Worldview Analysis
This dissertation is a theoretical investigation of the kinds of knowledge and ways of knowing that are valued within mathematics and the teaching and learning of mathematics. Central to this research is a theoretical framework based upon the Traditional Western Worldview and an Indigenous …
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Plural predication
My thesis consists of three self-contained but interconnected papers. In the first one, 'Word and Objects', I assume that it is possible to quantify over absolutely everything, and show that certain English sentences containing collective predicates resist paraphrase in first-order languages and …
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Nominalism In Mathematics - Modality And Naturalism
<p>I defend modal nominalism in philosophy of mathematics - under which quantification over mathematical ontology is replaced with various modal assertions - against two sources of resistance: that modal nominalists face difficulties justifying the modal assertions that figure in their theories, …
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A comparative philosophical analysis of primary mathematics curricula between the mainland of China and England in the United Kingdom
… undertakes a comparative philosophical analysis of ongoing primary mathematics curricula in the mainland of China and England, while acknowledging the profound impact that the philosophy of mathematics education has on shaping these curricula, as evidenced by the works of Hersh (1979), Lerman …
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A Handbook For Secondary Teachers of Remedial Mathematics in Georgia
<p>Several changes affecting the context of mathematics education were identified in Reshaping School Mathematics (Mathematical Sciences Education Board National Research Council [MSEB], 1990). The need for mathematics has changed to demand a higher level of quantitative literacy. New mathematics …
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Ontological Pragmatism
Ontology is the study of what exists. Metaontology is the study of ontology. This dissertation is a work in metaontology. In particular, its goal is to develop, motivate, defend, and explore a distinctively pragmatist metaontology --- a pragmatist account of how to answer existence questions. To do …
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Aristotle on the metaphysical status of mathematical entities
The purpose of this dissertation is to provide an account of the metaphysical status of mathematical entities in Aristotle. Aristotle endorses a form of realism about mathematical entities: for him as well as for Platonists, anti–realism, the view that mathematical objects do not exist, is not a …
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Finding meaning in mathematics through its philosophy: An empirical study with 17-year-old Greek students
… this thesis investigates the question: What mathematics can mean to students philosophically and psychologically? It is reasonable to assume that students may touch upon philosophical issues in trying to make sense of mathematics, since, in a sense, all individuals philosophise while …
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Axiomatization and Incompleteness in Arithmetic and Set Theory
… I argue that are (at least) two distinct kinds of mathematical incompleteness. Part A of the thesis discusses Gödelian incompleteness, while Part B is concerned with set-theoretic incompleteness. Both parts are concerned with the philosophical justification of reflection principles and other …
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Metaphor and mathematics
Traditionally, mathematics and metaphor have been thought of as disparate: the former rigorous, objective, universal, eternal, and fundamental; the latter imprecise, derivative, nearly - if not patently - false, and therefore of merely aesthetic value, at best. A growing amount of contemporary …
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The Look of Math
… is injected by a given observer. “The look of math” is a part of ethnomathematics, or the culture of mathematics, which necessarily and anti-Platonically (i.e., taking math to be purely a human endeavor) contains mathematics per se. Formal elements in math-as-art can be categorized as …
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Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis
… we also attempt to clarify and evaluate a set of comparisons of NSA and SIA, namely John L. Bell’s 5 mathematico-philosophical contentions and Bell’s historical contention.