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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.Themes and summary (AI-generated based on podcaster-provided show and episode descriptions):
➤ mathematical philosophy, formal logic and metaphysics • semantics and philosophy of language: compositionality, opacity, quotation, conditionals • realism/structuralism, model-theoretic arguments • modality, laws of nature, measurement • truth relativism • existence debates (God, nonexistents)This podcast presents research talks and discussions in mathematical philosophy, using tools from logic, formal semantics, and related mathematical methods to make traditional philosophical questions more precise. Across the episodes, speakers develop and assess formal frameworks for thinking about meaning, truth, inference, and ontology, often with an eye to how philosophical commitments show up in (or can be avoided by) particular logical or semantic theories.
A recurring focus is the philosophy of language and formal semantics: how compositionality should work, how to model intensionality and opacity in possible-worlds frameworks, and whether phenomena like quotation—often treated as resistant to substitution and existential generalization—can nonetheless be given a systematic, compositional semantic analysis. Relatedly, several discussions probe the interaction between natural-language interpretation and logical validity, including debates about conditionals and alleged counterexamples to standard inference patterns such as modus ponens and modus tollens, where improved semantic analysis can change what follows from what.
Another major theme is metaphysics informed by formal methods. Topics include the nature of abstract structures and their dependence on concrete realizations in debates over mathematical structuralism; questions about existence and quantification, including linguistic analyses of apparent talk about “nonexistent” entities; and dispositional approaches to modality, especially whether the logical behavior of possibility and necessity can be grounded in dispositions of concrete objects. Issues in the metaphysics and philosophy of science also appear, including structural realism and the problem of relating or “bridging” different theories, as well as debates about laws of nature and the explanatory status of variational principles like the principle of least action.
The podcast also engages with epistemology and meta-philosophical questions about formal systems themselves, such as whether logic carries metaphysical presuppositions or can be insulated from ontological commitment to abstracta. In addition, it extends formal and metaphysical analysis into applied domains, including realism about measurement and magnitudes and the metaphysical individuation and classification of diseases, where causal and dispositional accounts are brought to bear. Some content addresses philosophical theology in German-language debates about whether God exists, emphasizing rational argumentation and the structure of pro and con arguments.