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Formal Systems as Physical Objects: A Physicalist Account of Mathematical Truth
mathematical truth physicalism formal systems deduction
2008/4/22
This paper is a brief formulation of a radical thesis. We start with the formalist doctrine that mathematical objects have no meanings; we have marks and rules governing how these marks can be combine...
On Optimism and Opportunism in Applied Mathematics (Mark Wilson Meets John von Neumann on Mathematical Ontology)
Applied mathematics axiomatic method
2008/4/22
Applied mathematics often operates by way of shakily rationalized expedients that can neither be understood in a deductive-nomological nor in an anti-realist setting. Rather do these complexities, so ...
The Ontological Commitments of Mathematical Models
Mathematical realism Indispensability argument Mathematical models
2008/4/21
Some philosophers of mathematics argue that the role of mathematical models in science is merely representational: when scientists use mathematical models they only believe that they are adequate repr...
Toward a Hermeneutic Categorical Mathematicsorwhy Category theory does not support mathematical structuralism
Category theory Hermeneutics Mathematics
2008/4/21
In this paper I argue that Category theory provides an alternative to Hilbert’s Formal Axiomatic method and doesn't support Mathematical Structuralism.
Mathematical Rigor in Physics: Putting Exact Results in Their Place
rigorous results mathematical rigor condensed matter physics
2008/4/15
The present paper examines the role of exact results in the theory of many-body physics, and specifically the example of the Mermin-Wagner theorem, a rigorous result concerning the absence of phase tr...
MATHEMATICAL MODELS IN SCIENCE: A DEBATE ABOUT ONTOLOGY
Mathematical realism Indispensability argument
2008/4/15
Some philosophers of mathematics argue that the role of mathematical models in science is merely representational: when scientists use mathematical models they only believe that they are adequate repr...
Mathematical Kinds, or Being Kind to Mathematics
natural kinds mathematics laws projectability
2008/4/15
In 1908, Henri Poincaré claimed that:
...the mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a mathematica...
Many arguments found in the physics literature involve concepts that are not well-defined by the usual standards of mathematics. I argue that physicists are entitled to employ such concepts without ri...
This survey article describes Frege's celebrated foundational work against the context of other late nineteenth century approaches to introducing mathematically novel "extension elements" within both ...
We approach the philosophy of mathematics via an analysis of
mathematics as it is practised. This leads us to a classification in terms of four concepts, which we define and illustrate with a variety...
ETHNOMATHEMATICS AND MATHEMATICAL DIVERSITY: A RADICAL CONSTRUCTIVIST PERSPECTIVE
ETHNOMATHEMATICS MATHEMATICAL DIVERSITY
2008/4/8
Borba's use of ethnomathematics as a way of seeing diversity in our ways of doing mathematics complements the work of others in that area and forms the framework for understanding the important role o...
CONSTRUCTING MATHEMATICAL KNOWLEDGE: EPISTEMOLOGY AND MATHEMATICS EDUCATION
CONSTRUCTING MATHEMATICAL KNOWLEDGE
2008/4/8
This book provides a panorama of complementary and forward looking perspectives on the learning of mathematics and epistemology. It explores constructivist and social theories of learning, and discuss...
RATIONALES, PURPOSES AND METACONCEPTS IN MATHEMATICAL ACTIVITY
RATIONALES PURPOSES METACONCEPTS
2008/4/8
Careful observation of students' activity in a year 10 mathematics class clearly demonstrates the necessity of distinguishing between task objectives, learning objectives and management (or organisati...
THE MYTHIC QUEST OF THE HERO: STEPS TOWARDS A SEMIOTIC ANALYSIS OF MATHEMATICAL PROOF
MATHEMATICAL THE MYTHIC QUEST OF THE HERO
2008/4/8
This is a speculative exploration of the semiotics of mathematical text which draws upon diverse sources from philosophy, mythology and literary criticism. It represents an incomplete opening of a lin...
MAKING SENSE OF MATHEMATICAL MEANING-MAKING:THE POETIC FUNCTION OF LANGUAGE
MAKING SENSE MATHEMATICAL MEANING-MAKING
2008/4/8
In trying to make sense of mathematical meaning-making, sections of the mathematics education community have increasingly turned to linguistics as a basis for theorising mathematical discourse. In thi...