MCMP Summer School Mathematical Philosophy for Female Students
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Francesca Boccuni is currently Associate Professor in Logic at the Faculty of Philosophy at University Vita-Salute San Raffaele. She a member of the promoting committee of the Italian network for the philosophy of mathematics FilMat (www.filmatnetwork.com), of the Cogito research centre in philosophy (www.cogito.lagado.org), and of the scientific committee of the PhD programme in Philosophy at University Vita-Salute San Raffaele. Her research interests concern abstractionism in philosophy of mathematics and Frege’s logicism, second-order logic and plural logic, the issue of reference in mathematics.

Course description: The aim of this series of lectures is to provide a historical and philosophical introduction to Gottlob Frege’s Logicism and Crispin Wright and Bob Hale’s Neologicism in the philosophy of mathematics. Famously, Frege’s foundational programme was doomed to failure due to inconsistency, but the legacy of his inquiry was not lost. Since the mid-1980s, there has been a revived interest in Frege’s philosophy of mathematics, both from a logico-mathematical and a philosophical perspective, which has also given rise to new logicist orientations. The seminal volume Frege’s Conception of Numbers as Objects (1983) by Crispin Wright, Dummett’s Frege. Philosophy of Mathematics (1991), and Crispin Wright and Bob Hale’s The Reason’s Proper Study (2001) have sparked a long-lasting debate on Logicism and Neologicism. In particular, Wright and Hale have carried forward some of Frege’s philosophical insights into the foundations of mathematics. In these lectures, we will first explore the historical and theoretical context in which Frege conducted his investigation, as well as the logical and philosophical aspects of his Logicism. We will then focus on Wright and Hale’s Neologicism and examine its philosophical
underpinnings.

Hilary Greaves is Professor of Philosophy at the University of Oxford. Her research interests range fairly widely across moral philosophy, though with some skew towards more formal ethics and (relatedly) that which intersects more closely with economics. Hilary's existing publications in ethics include work on foundational issues in consequentialism ('global' and 'two-level' forms of consequentialism), "cluelessness", interpersonal comparisons of well-being, interpersonal aggregation (utilitarianism/prioritarianism/egalitarianism/etc.), population ethics (pure and applied), moral uncertainty, healthcare prioritisation, climate change and existential risk.

Course description: These lectures will be an introduction to core topics in formal epistemology, decision theory and formal ethics. In formal epistemology, we will introduce the notion of degrees of belief, and the Bayesian account according to which rational degrees of belief (i) obey the probability calculus at any given time and (ii) are updated by conditionalization when new evidence is acquired. In decision theory, we will introduce the idea that rational decision making under uncertainty is a matter of maximising expected utility, and we will show how this account can be grounded in a representation theorem that begins with preferences over gambles and works “inwards” from there to arrive at probabilities and utilities. In formal ethics, we will show how rival accounts of the good – particularly, utilitarianism, prioritarianism and egalitarianism – can be represented using real-valued functions, and we will see how the utilitarian account can arguably be justified via Harsanyi’s celebrated aggregation theorem.

Alyssa Ney is Professor and Chair of Metaphysics in the Faculty of Philosophy, Philosophy of Science, and Religious Studies at LMU Munich. She received her MA and PhD in Philosophy from Brown University, her MS in Physics from UC Davis, and her BS in Physics and Philosophy from Tulane University. Before coming to LMU, she was Professor of Philosophy at UC Davis and the University of Rochester. Professor Ney's research focuses primarily on questions of fundamentality, the unity of science, and the interpretation of quantum theories.

Evening Lecture "Using Philosophy to Improve Science"

This talk will discuss how the tools we develop as students of mathematical philosophy can contribute to progress outside of philosophy, especially progress on pressing scientific challenges, and how in turn, engagement with science and scientists can serve to improve philosophy, especially at a time when the value of the humanities is being questioned and the discipline is under threat.