Munich-Nancy Workshop (26 May 2019)
Idea & Motivation
This workshop brings together philosophers and logicians from the University of Lorraine, IHPST (Paris), and MCMP working issues related to formalisation and understanding in mathematics and logic.
- Máté Szabo (University of Lorraine)
- Alberto Naibo
- Gerhard Heinzmann (University of Lorraine)
- Matteo De Benedetto (MCMP/LMU Munich)
|10:00 - 11:30||Máté Szabo (University of Lorraine): Gödel's and Post's Proofs of Incompleteness|
|11:30 - 11:45||Coffee Break|
|11:45 - 13:15||Alberto Naibo: Formalization and Axiomatization: An Intuitionistic Approach to Preference Relations|
|13:15 - 14:45||Lunch Break|
|14:45 - 16:15||Gerhard Heinzmann (University of Lorraine): Mathematical Understanding by Thought experiments.|
|16:15 - 16:30||Coffee Break|
|16:30 - 18:00||Matteo De Benedetto: Explicating ‘Explication’ via Conceptual Spaces|
Recent years have witnessed a revival of interest in the method of explication as a procedure for conceptual engineering in philosophy and in science. In the philosophical literature, there has been a lively debate about the different desiderata that a good explicatum has to satisfy. In comparison, the goal of explicating the concept of explication itself has not been central to the philosophical debate. The main aim of this talk is to suggest a way of filling this gap by explicating ‘explication’ within conceptual spaces theory. Specifically, I show how different, strictly-conceptual readings of explication desiderata can be precisely framed as geometrical or topological constraints over the conceptual spaces related to the explicandum and the explicatum. Moreover, I show also how the richness of the geometrical representation of concepts in conceptual spaces theory allows us to achieve more fine-grained readings of explication desiderata, thereby overcoming some alleged limitations of explication as a procedure of conceptual engineering.top
In the 1920s, Emil Post worked on the questions of mathematical logic that would come to dominate the discussions in the 1930s: incompleteness and undecidability. To a remarkable degree, Post anticipated Gödel’s incompleteness theorem, but did not attempt to publish his work at the time for various reasons. Instead, he submitted it for publication in 1941, adding an introduction and footnotes discussing how his results relate to the ones of Gödel, Turing and Church. In the Introduction, written in 1941, Post emphasized that “with the 'Principia Mathematica' as a common starting point, the roads followed towards our common conclusions are so different that much may be gained from a comparison of these parallel evolutions.”
Although there is a diagonal argument in the center of both Gödel’s and Post’s proofs, the proofs are presented in strikingly different formal frameworks. Examining the proofs in detail, we distill and emphasize two key dissimilarities. The first considers the scope and generality of their proofs. Gödel was dissatisfied with the specificity of his (1931), i.e. being tied to 'Principia Mathematica' and related systems. On the other hand Post took a purely syntactic approach which allowed him to characterize a much more general notion of formal systems which are shown to be affected by the incompleteness phenomena. The second dissimilarity arises from the fact that Post was first and foremost interested in the decidability of symbolic logics and of 'Principia Mathematica' in particular. As a consequence he arrived at incompleteness as a corollary to undecidability. This “detour,” compared to Gödel’s more direct proof of incompleteness, convinced Post that his characterization of formal systems is not only very general, but gives the correct characterization.top
For information about practical matters and registration, please contact Marianna Antonutti Marfori at Marianna.AntonuttiMarfori@lrz.uni-muenchen.de.
- Regular fee: 50 EUR;
- reduced fee (for graduate students): 30 EUR;
- Members of the MCMP and LMU: registration free of charge.
To register please send a message to Marianna Antonutti Marfori at Marianna.AntonuttiMarfori@lrz.uni-muenchen.de.
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This workshop is funded by the Deutsche Forschungsgemeinschaft (DFG).