The workshop is funded by the National Science Foundation (SES-1921688) and is aimed at bringing together academics who study the notion of mathematical explanation from philosophical and from educational/psychological perspectives. The idea is to bring together philosophers of mathematics, epistemologists, psychologists, and mathematics educators, to discuss how developments in their own fields could meaningfully contribute to the work on mathematical explanation where their fields intersect. In particular, we want to explore the ways in which mathematical explanation engenders understanding, by focusing on (1) the relationship between different types of philosophical accounts of mathematical explanation, (2) educational approaches to the characterization of effective explanations in the mathematics classroom, and (3) work at the intersection of these two perspectives.
All speakers:
Mark Colyvan
University of Sydney
Matthew Inglis
Loughborough University
Marc Lange
University of North Carolina, Chapel Hill
Tania Lombrozo
Princeton University
Alexander Renkl
University of Freiburg
Keith Weber
Rutgers University – New Brunswick
Orit Zaslavsky
New York University
Professor Williamson will give 3 lectures: September 19, 21, and 23. All will take place in AB-2400 [East Wing] from 4:30-6:30pm.
The lectures will discuss problems in the methodology of contemporary philosophy. Although philosophy without use of counterexamples would be a disaster, the way they are currently handled is naïve. In particular, it is too vulnerable to fake counterexamples generated by more or less universal human heuristics.
Lecture One: Heuristics [9/19]
Human cognition, from sense perception to abstract reflection, frequently employs heuristics, quick, easy, efficient, and imperfectly reliable ways of solving problems. To a neglected extent, philosophical problems and paradoxes from reliance on the outputs of fallible heuristics. This will be illustrated with examples involving vagueness, conditionals, belief ascription, truth and falsity, and reasons aggregation. Potential lessons for philosophical method will be discussed.
Lecture Two: Overfitting [9/21]
Overfitting is a well-recognized methodological problem in natural science, where use of models with too many degrees of freedom leads to unstable theorizing and failure to detect errors in the data. Overfitting is also a major but ill-recognized methodological problem in philosophy, exacerbated by its reliance on heuristics. General intellectual tendencies conducive to overfitting in philosophy will be discussed.
Lecture Three: Hyperintensionality [9/23]
The ‘hyperintensional revolution’ proclaims that central metaphysical distinctions cannot be captured in modal terms since they are sensitive to differences between necessary equivalents. Such hyperintensionalism fits the profile of overfitting. It is motivated by case judgments that are explicable as results of a fallible heuristic and it leads to models with too many degrees of freedom.
Professor Williamson will give 3 lectures: September 19, 21, and 23. All will take place in AB-2400 [East Wing] from 4:30-6:30pm.
The lectures will discuss problems in the methodology of contemporary philosophy. Although philosophy without use of counterexamples would be a disaster, the way they are currently handled is naïve. In particular, it is too vulnerable to fake counterexamples generated by more or less universal human heuristics.
Lecture One: Heuristics [9/19]
Human cognition, from sense perception to abstract reflection, frequently employs heuristics, quick, easy, efficient, and imperfectly reliable ways of solving problems. To a neglected extent, philosophical problems and paradoxes from reliance on the outputs of fallible heuristics. This will be illustrated with examples involving vagueness, conditionals, belief ascription, truth and falsity, and reasons aggregation. Potential lessons for philosophical method will be discussed.
Lecture Two: Overfitting [9/21]
Overfitting is a well-recognized methodological problem in natural science, where use of models with too many degrees of freedom leads to unstable theorizing and failure to detect errors in the data. Overfitting is also a major but ill-recognized methodological problem in philosophy, exacerbated by its reliance on heuristics. General intellectual tendencies conducive to overfitting in philosophy will be discussed.
Lecture Three: Hyperintensionality [9/23]
The ‘hyperintensional revolution’ proclaims that central metaphysical distinctions cannot be captured in modal terms since they are sensitive to differences between necessary equivalents. Such hyperintensionalism fits the profile of overfitting. It is motivated by case judgments that are explicable as results of a fallible heuristic and it leads to models with too many degrees of freedom.
Professor Williamson will give 3 lectures: September 19, 21, and 23. All will take place in AB-2400 [East Wing] from 4:30-6:30pm.
The lectures will discuss problems in the methodology of contemporary philosophy. Although philosophy without use of counterexamples would be a disaster, the way they are currently handled is naïve. In particular, it is too vulnerable to fake counterexamples generated by more or less universal human heuristics.
Lecture One: Heuristics [9/19]
Human cognition, from sense perception to abstract reflection, frequently employs heuristics, quick, easy, efficient, and imperfectly reliable ways of solving problems. To a neglected extent, philosophical problems and paradoxes from reliance on the outputs of fallible heuristics. This will be illustrated with examples involving vagueness, conditionals, belief ascription, truth and falsity, and reasons aggregation. Potential lessons for philosophical method will be discussed.
Lecture Two: Overfitting [9/21]
Overfitting is a well-recognized methodological problem in natural science, where use of models with too many degrees of freedom leads to unstable theorizing and failure to detect errors in the data. Overfitting is also a major but ill-recognized methodological problem in philosophy, exacerbated by its reliance on heuristics. General intellectual tendencies conducive to overfitting in philosophy will be discussed.
Lecture Three: Hyperintensionality [9/23]
The ‘hyperintensional revolution’ proclaims that central metaphysical distinctions cannot be captured in modal terms since they are sensitive to differences between necessary equivalents. Such hyperintensionalism fits the profile of overfitting. It is motivated by case judgments that are explicable as results of a fallible heuristic and it leads to models with too many degrees of freedom.