The Paris-Nancy Colloquium in Logic and the Philosophy of Mathematics or PANALM is a forum for general expository talks accessible and relevant for all researchers in logic and the philosophy of mathematics. Speakers are invited to describe a whole research line or program that they have been pursuing and present the main results they have obtained in a synoptic and didactic way. PANALM is run jointly by the Institut d’Histoire et de Philosophie des Sciences et des Techniques (IHPST) and the Institut Jean Nicod (IJN) in Paris and the Archives Henri Poincaré (AHP) in Nancy. Each of these institutions will welcome one session of PANALM per semester. PANALM is open to anyone interested, from students to researchers in neighboring disciplines.
Previous speakers in PANALM include Alexander Paseau (Oxford University), Sean Walsh (UCLA), Aybüke Özgün (ILLC, University of Amsterdam), John MacFarlane (UC Berkeley), Carolin Antos (Universität Konstanz), and Paolo Mancosu (UC Berkeley).
Title: Universal Logical Grammar
Abstract: I will present Universal Logical Grammar (ULG), the framework of my ongoing research program, and some results obtained within it. ULG is inspired by Richard Montague’s influential 1970 article “Universal Grammar” (UG) but – unlike Montague’s approach – focuses exclusively on formal-logical languages, thus setting aside, at least for the time being, any ambition to analyze natural languages directly. ULG differs architecturally from UG and its later developments mainly by (a) not requiring interpretations to be compositional and (b) taking syntactic categories to refine, rather than coincide with, the syntactic algebra’s sorts. These architectural innovations make possible substantive new insights regarding the grammatical properties of compositionality and extensionality, and how they are constrained by the consequence relations generated by grammars.
Location: Salle internationale (324, 3rd floor), Archives Henri Poincaré, 91 avenue de la Libération, 54001 Nancy (link google maps)
This session is part of the 2nd Nancy–Irvine FaTiLLaM Workshop on Formalization as Translation in Logic, Language, and Mathematics. The program of the workshop is available here.
Title: Names and Higher-Order Logic
Abstract: A number of central puzzles in philosophy turn on the grammatical category of names. Two important cases are Frege’s puzzle and the puzzle of Empty Names. In this talk, I’ll consider how resources from higher-order logic may be used to provide new treatments of these puzzles. Millians maintain that the semantic value of a name is just an individual, which may be taken as an argument by the semantic value of a predicate. Montagovians, on the other hand, maintain that the semantic value of a name is a higher-order entity that takes the semantic value of a predicate as an argument. Drawing on recent work in higher-order logic, I’ll develop a generalization of the Montagovian account and show how this account may be used to provide attractive resolutions of these two philosophical puzzles.
Location: Salle de réunion de l’Institut Jean Nicod, Rez-de-chaussé, Pavillon Jardin, 29 rue d’Ulm, 75005 Paris (link google maps)
Title: Diagrams in mathematical practice
Abstract: Discussions about diagrams in mathematics most often focus on their role in proofs, reasoning, and the establishment of the validity of arguments. Yet, beyond mathematical reasoning, diagrams play a range of other roles in everyday mathematical practice. They serve as tools for discovery and computation, and they contribute to understanding. In other words, they have multiple heuristic functions. These latter roles of diagrams will be the focus of my talk.
In his influential article On Proof and Progress in Mathematics, the geometer Thurston quickly dismisses the claim that progress in mathematics is achieved by the accumulation of proofs. Instead, he finds it more interesting to discuss how mathematical understanding is attained. As he puts it, ‘what we are doing is finding ways for people to understand and think about mathematics’. I posit that signs, and diagrams in particular, play a central role in facilitating such understanding. This claim rests on the observation that human cognition is limited, and that what we are able to grasp or perceive depends, in part, on how information is presented.
To illustrate this point, I will present cases in which a visual re-presentation of a concept or problem has led to the introduction of new mathematical concepts or proofs. This raises the question of what it is about visual presentations that make this possible. To address this question, I consider in part the notion of a ‘free ride’ and the corresponding theoretical framework developed by Atsushi Shimojima. Shimojima’s framework includes the notions of nomic constraint, over-specification, and, importantly, semantic convention as tools for analysing free rides. I will argue that some mathematical examples conform to this framework. However, mathematical developments can also exceed it, since visual representations may generate entirely new concepts and domains that extend beyond the original target domain.
If time permits, I will briefly display other functions of diagrams, including their use as computational tools, and point to the properties that enable them to serve this function.
Location: Salle de Conférence de l’IHPST, Université Paris 1 Panthéon-Sorbonne, Maison de la Philosophie-Marin Mersenne, 2nd floor, 13 rue du Four, 75006 Paris (link google maps)
Registration
The seminar is free and without registration. Everyone interested is welcome to attend.
For any questions, please send an email to the organizers.
Organizers
Acknowledgement and Support
The workshop is funded by by the Institut d’Histoire et de Philosophie des Sciences et des Techniques (IHPST), the Institut Jean Nicod (IJN) and the Archives Henri Poincaré (AHP).