Abstract
Our understanding of mathematics arguably increases with an examination of its growth, that is with a study of how mathematical theories are articulated and developed in time. This study, however, cannot proceed by considering particular mathematical statements in isolation, but should examine them in a broader context. As is well known, the outcome of the debates in the philosophy of science in the last few decades is that the development of science cannot be properly understood if we focus on isolated theories (let alone isolated statements). On the contrary, we ought to consider broader epistemic units, which may include paradigms (Kuhn 1962), research programmes (Lakatos 1978a), or research traditions (Laudan 1977). Similarly, the first step to be taken by any adequate account of mathematical change is to spell out what is the appropriate epistemic unit in terms of which the evaluation of scientific change is to be made. If we can draw on the considerations that led philosophers of science to expand the epistemic unities they use, and adopt a similar approach in the philosophy of mathematics, we shall also conclude that mathematical change is evaluated in terms of a‘broader’ epistemic unit than the one that is often used, such as, statements or theories.
Many thanks to Newton da Costa, Steven French, Joke Meheus, and Sarah Kattau for helpful discussions on the issues examined here.
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Bueno, O. (2002). Mathematical Change and Inconsistency. In: Meheus, J. (eds) Inconsistency in Science. Origins, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0085-6_4
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