A fair estimation of the ways in which mathematics helps with science should also consider the ways in which mathematics hurts science. This chapter argues that each of the positive contributions isolated in the first six chapters can also become a negative contribution if certain mistakes are made. In these cases the mathematics contributes to an illusion of success even though a scientist is making a serious mistake in representing a target system. Case studies are developed for each of these illusions. Ultimately, the double-edged character of mathematics forces a re-evaluation of some traditional forms of scientific realism. Pincock suggests that the viable scope of a representation is a more urgent issue for the realist than the existence of unobservable entities.
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