Indiscernibility and Mathematical Structuralism [article]

Teresa Kouri, University Of Calgary, University Of Calgary, Richard Zach
2010
This project describes a solution to a problem in Stewart Shapiro's ante rem structural ism, a theory in the philosophy of mathematics. Shapiro's theory proposes that the nature of mathematical objects is less important than the relations mathematical ob jects have to one another. Thus, mathematical objects are places in patterns and are constituted by the relations they have to the other places. However, Jukka Keränen demonstrated that there are some distinct mathematical objects which bear
more » ... the same relations to every other mathematical object. If Leibniz's Law, the Identity of Indis cernibles, were accepted, this would mean that Shapiro's theory identifies objects which can be mathematically proved to be distinct. This thesis demonstrates that this problem can be avoided by taking identity as a primitive notion, and by using Hilbert's epsilon calculus as a tool for referring to indistinguishable objects. ii Richard Zach. Without his help, advice and encouragement, this project would not have been possible.
doi:10.11575/prism/14329 fatcat:mkzqavkz4bbzzoa3nk7zuknlzu