Applying Mathematics in the Natural Sciences An Unreasonably Effective Method

In this thesis the unreasonable effectiveness of mathematics in the natural sciences is discussed. I will show that this is a deep philosophical problem for which no easy solution is available. A historical analysis of the role of mathematics in science shows that basic mathematics, an abstraction from empirical observation, evolved into complex mathematics, a human invention completely detached from its empirical roots. The conclusion of this analysis is that the applicability of mathematics cannot be explained by adhering to the empirical roots of mathematics. This poses a philosophical problem: how can something that is anthropocentric describe and predict the intricate workings of natural phenomena so accurately? This question is my main research question and is also thoroughly discussed by Mark Steiner (1998). He places emphasis on the predictive power of mathematics in the natural sciences and I will show that Steiner’s main argument, that anthropocentric elements in mathematics play a crucial, and unreasonable effective, role in the discovery of new physical theories is a valid observation in need of an explanation. The mapping accounts of Pincock (2004) and Bueno and Colyvan (2011) are discussed, who attempt to render the anthropocentric elements in mathematics intelligible. They both turn out to be incomplete and therefore, I have provided an improved inferential mapping account that is able to render parts of the anthropocentric influences in mathematics intelligible. However the successful use of tractability assumptions cannot be explained by this mapping account. This leads to the conclusion that the world looks ’user-friendly’, because our anthropocentric assumptions result in correct knowledge about the natural world. Therefore, one cannot refrain from a metaphysical discussion about the relation between mathematics, mind and world. I discuss several metaphysical accounts, of which the most reasonable is the simple explanation that we just ’see what we look for’. A price needs to be paid however; complete knowledge about the world around us will never be possible. Moreover, it remains mysterious that we are able to control natural phenomena in such a detailed way, whilst only having knowledge of a small part of it. The final chapter mentions the changing role of mathematics in science in the last 30 years, where advancements in theoretical physics increased the importance of mathematical methods, whereas advancements in computer science decreased this role. I conclude that now more than ever, it is important to reflect on the role of mathematics in the