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.
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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.
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.
Relating Theories of Intensional Semantics: Established Methods and Surprising Results
MCMP
19 minutes 3 seconds
7 years ago
Relating Theories of Intensional Semantics: Established Methods and Surprising Results
Kristina Liefke (LMU/MCMP) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "Relating Theories of Intensional Semantics: Established Methods and Surprising Results". Abstract: Formal semantics comprises a plethora of ‘intensional’ theories which model propositional attitudes through the use of different ontological primitives (e.g. possible/impossible worlds, partial situations, unanalyzable propositions). The ontological relations between these theories are, today, still largely unexplored. In particular, it remains unclear whether the basic objects of some of these theories can be reduced to objects from other theories (s.t. phenomena which are modeled by one theory can also be modeled by the other theories), or whether some of these theories can even be reduced to ontologically ‘poor’ theories (e.g. extensional semantics) which do not contain intensional objects like possible worlds.
This talk surveys my recent work on ontological reduction relations between the above theories. This work has shown that – more than preserving the modeling success of the reduced theory – some reductions even improve upon the theory’s modeling adequacy or widen the theory’s modeling scope. Our talk illustrates this observation by two examples: (i) the relation between Montague-/possible world-style intensional semantics and extensional semantics, and (ii) the relation between intensional semantics and situation-based single-type semantics. The relations between these theories are established through the use of associates from higher-order recursion theory (cf. (i)) and of type-coercion from programming language theory (cf. (ii)).
Part of this work is joined with Markus Werning (RUB Bochum) and Sam Sanders (LMU Munich/MCMP).
MCMP
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.
