CSS colloquium: Jacob Busch, Aarhus University
The fertility based argument for mathematical realism: a barren effort
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Koll. G (1532-214)
It has been argued that mathematics plays a fertile role in science. Bangu (2012) argues that mathematics is involved in a general discovery patterns, documented by Steiner in a series of papers (1989, 1995, 1998, 2005). Furthermore, Baker has suggested, that this crucial role that mathematics plays in science, may in turn be used to argue that there is good reason for believing that mathematical entities exist, through a new kind of indispensability argument – that takes mathematics to be indispensable to the advancement of new theory. I trace fertility considered as a theoretical virtue through the writings of McMullin, and discuss how it has to be interpreted in order to play the role sought out for it in current debate. I argue that although there may be a place for fertility considered as a post hoc established virtue of scientific theories, we should not expect for fertility to be a property of theories that they exhibit prior to realising their potential for fertility, and it thus becomes difficult to understand how fertility is to play the role suggested by Bangu.