Shows
MCMP – Mathematical Philosophy (Archive 2011/12)The ghosts of departed quantities as the soul of computationSam Sanders (Belgium) gives a talk at the MCMP Colloquium titled "The ghosts of departed quantities as the soul of computation". Abstract: Using techniques from Nonstandard Analysis, we introduce omega-invariance: a new notion of computability based on infinitesimals. We show that omega-invariance can capture two central notions of computability, namely those provided by Recursion Theory and Constructive Analysis. We discuss the philosophical implications of these results.
2019-04-2051 min
MCMPRelating Theories of Intensional Semantics: Established Methods and Surprising ResultsKristina 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...
2018-03-1700 minMCMPThe Unreasonable Effectiveness of Nonstandard AnalysisSam Sanders (MCMP/LMU) gives a talk at the MCMP Colloquium (26 November, 2015) titled "The Unreasonable Effectiveness of Nonstandard Analysis". Abstract: There is a persistent belief, propagated by such luminaries as Errett Bishop and Alain Connes, that infinitesimals (in the sense of Robinson’s Nonstandard Analysis (NSA) ) somehow are fundamentally non-constructive and that NSA is devoid of numerical meaning, as Bishop was wont to say. In this talk, we disprove the Bishop-Connes claim regarding NSA. To this end, we show that theorems of NSA are equivalent to their associated “highly constructive" theorems from numerical analysis (not involving NSA). We shall focus on p...
2018-03-1700 minMCMP – Philosophy of MathematicsOn the Contingency of PredicativismSam Sanders (MCMP) gives a talk at the MCMP Colloquium (16 April, 2015) titled "On the Contingency of Predicativism". Abstract: Following his discovery of the paradoxes present in naive set theory, Russell proposed to ban the vicious circle principle, nowadays called impredicative definition, by which a set may be defined by referring to the totality of sets it belongs to. Russell's proposal was taken up by Weyl and Feferman in their development of the foundational program predicativist mathematics. The fifth `Big Five' system from Reverse Mathematics (resp. arithmetical comprehension, the third Big Five systen) is a textbook example of impredicative (resp. predicative...
2015-05-1100 min