Scientific explanation, unifying mathematics, and indispensability arguments (A new Cicada MES)

摘要

Indispensability arguments occupy a prominent role in discussions of mathematical realism. While different versions of these arguments are discussed in the literature, their general structure remains the same. These arguments contend that insofar as reference to mathematical objects is indispensable to science, we are committed to the existence of these 'objects'. Unsurprisingly, much of the debate concerning indispensability arguments focuses on the crucial contention that mathematical objects are indispensable to science. For these arguments to provide support for mathematical realism, what we require are some compelling examples of mathematics playing an indispensable role in science. Towards this end, Alan Baker has supplied an example in which mathematics appears to be indispensable to a scientific explanation, what has come to be called the "Cicada MES". This example has been the subject of much criticism, most notably that it depends on an unsupported empirical supposition. Recently, Baker proposed a number of revisions to the Cicada MES that aim to address some of these criticisms. In this paper, I argue that while Baker's revisions go some way towards mitigating prominent criticisms of the Cicada MES, the underlying problem with the explanation remains. I argue that his revisions actually go in the wrong direction mathematically and empirically. In contrast, I propose a new Cicada MES. This new version accomplishes Baker's goals and responds to the central objection to the explanation. It invokes a mathematical principle that plays a unifying role in the explanation, which makes providing adequate nominalist surrogates more difficult. And, more importantly, it accommodates an empirically grounded explanation of the phenomenon to be explained. Consequently, this new Cicada MES provides what proponents of indispensability arguments require, a compelling example of mathematics playing an indispensable role in science.