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Alternative Ontology For Ante Rem Structuralism Based On Huayan Buddhist Metaphysics, Chul Soon Hwang

CMC Senior Theses

Ante rem structuralism is a version of mathematical structuralism presented by Shapiro (1997) that asserts the existence of mathematical objects. It stands out amongst other structuralist views in that it secures a face value semantics for mathematical statements. In this paper, I propose an alternative ontology where structures are fully explained by relations. I argue that this alternative ontology avoids arguments against ante rem structuralism’s endorsement of indiscernible entities while retaining the convenience of a face value semantics for mathematical expressions.

This ontology is based on mereological nihilism and the Huayan Buddhist argument that an object can be fully described …

Maths Living In Social Arenas, From Practice To Foundations, Nigel Vinckier

Journal of Humanistic Mathematics

Maths comes to life in human interaction. This has consequences for the mathematics itself. This paper discusses how this ``coming to life'' of mathematics in different social arenas influences the foundations of maths. We will argue that this influence is profound, to the extent that it is hard to upkeep the idea that there is or should be one foundation on which all mathematics can be built.

The Philosophy Of Mathematics: A Study Of Indispensability And Inconsistency, Hannah C. Thornhill

Scripps Senior Theses

This thesis examines possible philosophies to account for the practice of mathematics, exploring the metaphysical, ontological, and epistemological outcomes of each possible theory. Through a study of the two most probable ideas, mathematical platonism and fictionalism, I focus on the compelling argument for platonism given by an appeal to the sciences. The Indispensability Argument establishes the power of explanation seen in the relationship between mathematics and empirical science. Cases of this explanatory power illustrate how we might have reason to believe in the existence of mathematical entities present within our best scientific theories. The second half of this discussion surveys …

Prove It!, Kenny W. Moran

Journal of Humanistic Mathematics

A dialogue between a mathematics professor, Frank, and his daughter, Sarah, a mathematical savant with a powerful mathematical intuition. Sarah's intuition allows her to stumble into some famous theorems from number theory, but her lack of academic mathematical background makes it difficult for her to understand Frank's insistence on the value of proof and formality.

Pedagogy On The Ethnomathematics--Epistemology Nexus: A Manifesto, Ilhan M. Izmirli

Journal of Humanistic Mathematics

In this paper, we will elaborate on a pronouncement that should be at the onset of any study in epistemology and ethnomathematics, namely, we will argue that learners do think mathematically and it is our responsibility as educators to recognize and appreciate their modes of mathematical reasoning.

We will conduct our study in five parts. Following a brief introduction, in the second part, we will briefly discuss some of the critical tenets of epistemology especially as it applies to mathematics. The third part will be devoted to elucidating the basic nomenclature and hypotheses associated with ethnomathematics. In the fourth part …