Abstract
The core idea of social constructivism in mathematics is that mathematical entities are social constructs that exist in virtue of social practices, similar to more familiar social entities like institutions and money. Julian C. Cole has presented an institutional version of social constructivism about mathematics based on John Searle’s theory of the construction of the social reality. In this paper, I consider what merits social constructivism has and examine how well Cole’s institutional account meets the challenge of accounting for the characteristic features of mathematics, especially objectivity and applicability. I propose that in general social constructivism shows promise as an ontology of mathematics, because the view can agree with mathematical practice and it offers a way of understanding how mathematical entities can be real without conflicting with a scientific picture of reality. However, I argue that Cole’s specific theory does not provide an adequate social constructivist account of mathematics. His institutional account fails to sufficiently explain the objectivity and applicability of mathematics, because the explanations are weakened and limited by the three-level theoretical model underlying Cole’s account of the construction of mathematical reality and by the use of the Searlean institutional framework. The shortcomings of Cole’s theory give reason to suspect that the Searlean framework is not an optimal way to defend the view that mathematical reality is socially constructed.
Highlights
One central question in the philosophy of mathematics is the question of the nature of mathematical objects and their existence
I examine one form of social constructivism in detail: Cole’s (2013, 2015) institutional theory of the social construction of mathematical reality.2. Cole bases his account on John Searle’s theory of social construction and defends the view that mathematical reality is a product of imposing function onto reality and that its existence depends on collective recognition
I have proposed that a view that sees mathematical entities as socially constructed has some promise as an ontology of mathematics
Summary
One central question in the philosophy of mathematics is the question of the nature of mathematical objects and their existence. As anyone familiar with ordinary mathematics may tell you, there is a clear difference between these two numbers: n exists, but m does not. I examine one form of social constructivism in detail: Cole’s (2013, 2015) institutional theory of the social construction of mathematical reality.. My aim in this paper is to consider what merits social constructivism has and to examine how well the institutional account meets the challenges facing social constructivist accounts of mathematics. I explore how mathematical practice motivates a social constructivist view of mathematics and describe the details of Cole’s institutional theory. I suggest that the institutional social ontology Cole uses is not an optimal way to defend the view that mathematical reality is socially constructed
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