Social Construction in the Philosophy of Mathematics: A Critical Evaluation of Julian Cole’s Theory†

摘要

Julian Cole argues that mathematical domains are the products of social construction. This view has an initial appeal in that it seems to salvage much that is good about traditional platonistic realism without taking on the ontological baggage. However, it also has problems. After a brief sketch of social constructivist theories and Cole’s philosophy of mathematics, I evaluate the arguments in favor of social constructivism. I also discuss two substantial problems with the theory. I argue that unless and until social constructivists can address the two concerns, we have reason to be skeptical about social constructivism in the philosophy of mathematics.