11 episodes

Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.
The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.
Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

MCMP – Ethics and Value Theory Ludwig-Maximilians-Universität München

    • Society & Culture

Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.
The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.
Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

    • video
    Being a woman in (mathematical) philosophy

    Being a woman in (mathematical) philosophy

    Catarina Dutilh Novaes (Groningen) gives a talk at the MCMP Colloquium (15 May, 2013) titled "Being a woman in (mathematical) philosophy". Abstract: Why are there so few women in philosophy, and in technical areas such as mathematical philosophy in particular? Philosophy has the worst gender balance of all fields in the humanities, at around 16%-25% worldwide. The presence of women in philosophy is comparable to engineering and physics; it is worse than in mathematics. Is this a problem? And if it is, what can be done about it? What is it like, being a woman in (mathematical) philosophy? In my talk, I discuss some unconscious psychological phenomena that are now thought to greatly contribute to the phenomenon of poor gender balance in several professional spheres, academia in particular. I will focus especially on implicit biases and stereotype threat, two phenomena widely documented by the literature in social psychology, and how they impact the position of women and other under-represented groups in academia, in philosophy in particular. Many points can be generalized to other dimensions of exclusion such as race/ethnicity, class, sexual orientation etc., but in this talk I will focus predominantly on the issue of gender imbalance. I will also discuss reasons why everyone should be concerned by this situation (i.e. not only the members of the under-represented groups themselves), as well as practical measures that may help improve the position of women in philosophy and elsewhere in academia.

    • 1 hr 28 min
    • video
    Duality, Logic and Judgment Aggregation

    Duality, Logic and Judgment Aggregation

    Alessandra Palmigiano (ILLC) gives a talk at the MCMP Colloquium (10 January, 2013) titled "Duality, Logic and Judgment Aggregation". Abstract: In the last decades, logic has facilitated the build-up of a critical mass of results and insights generalizing the original Arrovian problem in Social Choice, and culminating in the formation of judgment aggregation theory. Within this framework, the Arrovian-type impossibility results are obtained as consequences of characterization theorems, which provide necessary and su_cient conditions for agendas to have aggregator functions on them satisfying given axiomatic conditions. Methodologically, there are two tools, both derived from logic, underlying these generalizations: one is the ultra_lter argument, occurring both in a model-theoretic and in an algebraic setting; the other tool, providing a unifying framework for the agenda-based characterization theorems, is the notion of property space. Duality theory can provide insights into, and connections between, these two tools. In the present talk, Stone-type duality theory will be illustrated, as well as its main logical signi_cance: namely, providing a systematic, triangular connection between logical languages, their model-theoretic semantics and their algebraic semantics. Then, applications of duality theory will be discussed to the ultrafilter argument and property spaces.

    • 1 hr 3 min
    • video
    Normativity in reasoning

    Normativity in reasoning

    John Broome (Oxford) gives a talk at the MCMP Colloquium (2 May, 2013) titled "Normativity in reasoning". Abstract: Reasoning is a mental process in the course of which some premise-attitudes of yours give rise to a conclusion-attitude. Some reasoning is active: it is something you do rather than something that happens in you. It is often assumed that active reasoning has to involve beliefs with a normative content. I shall argue that this is not so.

    • 50 min
    • video
    Refutation of Putnam's Collapse of the Fact/Value Dichotomy

    Refutation of Putnam's Collapse of the Fact/Value Dichotomy

    Eckehart Köhler (Vienna) gives a talk at the MCMP Colloquium (22 May, 2013) titled "Refutation of Putnam's Collapse of the Fact/Value Dichotomy". Abstract: In 2002, Hilary Putnam shocked philosophers with the story that value terms have “thick” meanings, where facts and values are “entangled”. (“Crime” and “cruel” are especially “thick”.) This phenomenon is easy to explain, since many professionals treat norms factually, e.g. currently “valid” price quotations, whereas a document leaves the deontic modality ambiguous. Those same professionals certainly are able to distinguish the modalities of propositions they use in their professional work for themselves! (E.g., an active legislator can distinguish those bills which he wants passed from bad bills, etc., and similarly in all professions, at least where procedures for norming exist.) Putnam entirely ignores this. Putnam even ignores Decision Theory, where he has done work. This is crucial: standard Bayesian Decision Theory absolutely requires independence of facts and values, since probability and utility must be independent — if they were not, then no one could empirically predict behavior, nor could anyone recommend optimal policy to a client. Putnam got his collapse from Quine’s collapse of the analytic/synthetic dichotomy, and (correctly!) concluded that if the latter fails, so does the former. But since probabili-ties are “orthogonal” to utilities (which we know from their measurement), “Hume’s Law” is valid; and so is the analytic/synthetic dichotomy. I discuss Morton White’s attempt to subsume analyticity under ethical value. Finally, I claim that (Dewey’s and Quine’s) Naturalism collapses once this (empirically real) sensorium for observing normative validity is acknowledged which is separate from sensory perception.

    • 44 min
    • video
    What's the Problem with the Boundary Problem?

    What's the Problem with the Boundary Problem?

    David Kinkead (Queensland) gives a talk at the MCMP Colloquium (23 April, 2014) titled "What's the Problem with the Boundary Problem?". Abstract: Democracy begins with the people; democratic theory simply presupposes them. But democratic theory is silent on who ought be included amongst the people. It can’t, because any democratic process first requires the identification of some determinate group of agents - the demos - in order to act democratically. So how should the demos be defined? It can’t be done democratically because that would require the identification of some prior demos to decide this question, and an infinite regress of who should vote on who should vote ensues. The question of who is logically and temporally prior to the question of how and what. Yet who the people are is also a fundamental driver of what they decide. Drawing borders in one location will lead to different political outcomes had those borders been drawn somewhere else. Denying a voice to outsiders affected by some policy, intentionally or otherwise, violates a key principle of justice. For accounts of democracy that rely on the quality of decisions or outcomes to justify the authority of the state, this presents a major challenge. This problem has become known as the Boundary Problem of democratic theory. First raised by Robert Dahl in 1970, the Boundary Problem has increasingly been recognised to pose an intractable challenge to justifications of democracy, one that cannot be addressed from within democratic theory itself. Yet despite the growing awareness of the Boundary Problem and it’s implications, literature on the specific conditions under which it arises, or which accounts of democratic legitimacy it challenges the most, is largely non-existent. A key factor contributing to the paucity of research on the problem is its counter-factual nature and associated lack of empiric data from which to make observations. In this paper, I attempt to overcome these methodological obstacles by taking a generative approach to political philosophy. Using mathematical modelling and computer simulation, I demonstrate that the Boundary Problem primarily affects certain types of democratic accounts that rely on difference making claims, and show how the clustering of agents and beliefs across and within polities plays a critical role in its manifestation.

    • 33 min
    • video
    The Logic of Love

    The Logic of Love

    Aviv Keren (Jerusalem) gives a talk at the MCMP Colloquium (15 January, 2015) titled "The Logic of Love". Abstract: This philosophical work sets the ground for a game-theoretic account of (romantic) love, substantiating the folk-psychological conception of love as 'a unification of souls'. It does so by setting up a universal conceptual framework of cognitive agency, which makes this possible. Building on existing theories, this framework extends the gene's eye view of evolution towards the evolution of cognition, that is unified with a distributed theory of selfhood. In this framework, an application of a general principle of cooperation, in particular, produces love as a theoretical evolutionary prediction (unveiling its rationality).

    • 51 min

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