MathematicsAnalogies SIGNED

Project "MathematicsAnalogies" data sheet

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 Project objective

This project investigates how mathematics analogies impact metaphysical realism-antirealism. The overarching goal is to develop a systematic account of the potentials and limits of using mathematics as a model for other a priori domains, thus responding to the rapidly increasing literature exploiting structural parallels between mathematics and other a priori domains. In current ontological, semantic, and epistemic debates, mathematics frequently functions as a model for other a priori domains. Metaethicists in particular have started to use local structural parallels between mathematics and morality in order to corroborate particular metaethical views, but mathematics has also been argued to share relevant features with the domains of logic, modality, and religion. The 'mathematics analogies' employed in those arguments share a common form: a local analogy between mathematics and another domain is identified, based on which a global conclusion is drawn about one or both of the domains. What is completely missing in these debates, however, is a discussion of (a) the plausibility of the analogies in light of their mathematical background assumptions, (b) an adequate methodology for analogical reasoning about a priori domains, and (c) the prospects of developing a unified framework for all a priori domains. This is the gap this project is going to fill. Conducting this project as a Marie Sklodowska Curie Fellow at the best European institution for mathematical philosophy, the MCMP in Munich, will establish me firmly as an independent scholar in my field and thus, help me reach my goal of attaining a permanent academic position.