A Christian Perspective On Mathematical Philosophies

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A Christian Perspective on Mathematical Philosophies Mathematics is a foundational element of our daily lives It is taught in school from a very young age, and yet, it is seldom that we question why we know what we know, or where this structure came from. Over millennia of mathematical development, philosophers and mathematicians alike have developed numerous philosophies of mathematics describing this world of mathematics, where that structure comes from and how we know what is true. In a discussion about the modern developments of mathematics Jeremy Avigrad describes the modern interpretations of Quinean view by Penelope Maddy known as Mathematical Naturalism: "[Maddy proposes that] Once one accepts that mathematics, as a whole, is useful to the sciences, she argues, one should evaluate mathematical developments by the internal standards of the community. For example, one may appeal to internal measures of simplicity and generality that may not always line up exactly with broader scientific values, but have proved to be useful for the development of mathematical practice. Thus, in a sense, mathematicians can enjoy a collective bargaining agreement with respect to the broader scientific community.(emphasis added)" I strongly don’t agree with this statement.…show more content…
While much of the understanding of the philosophy of mathematics has been a journey away from Platonism towards Structuralism and even more abstract or arbitrary theories like Fictionalism, when actively working in mathematics, mathematicians default to being Platonists. It is almost impossible to work with a theory, a structure or even just a number while questioning its existence or validity. While one can philosophically establish that all mathematical properties are arbitrary, when a mathematician is actually using math, the relationship with the mathematical concepts is

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