References in:
Add references
You must login to add references.


Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problemrealismis examined and rejected in favor of another approachnaturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines. 



James Franklin has argued that the formal, mathematical sciences of complexity — network theory, information theory, game theory, control theory, etc. — have a methodology that is different from the methodology of the natural sciences, and which can result in a knowledge of physical systems that has the epistemic character of deductive mathematical knowledge. I evaluate Franklin’s arguments in light of realistic examples of mathematical modelling and conclude that, in general, the formal sciences are no more able to guarantee certainty (...) 

The formal sciences  mathematical as opposed to natural sciences, such as operations research, statistics, theoretical computer science, systems engineering  appear to have achieved mathematically provable knowledge directly about the real world. It is argued that this appearance is correct. 