Reading meetings are the most common event hosted by our group. We read together/present a text, and freely discuss together.
This time we take a recourse to mereology! In his talk, Elias Bronner will introduce the philosophical motivations for the field, Leśniewski’s nominalistic position. Further, we will discuss basic mereology and its relation to Boolean Algebras. Elias will conclude with touching upon a recent interpretation of mereology within set theory by J.D. Hamkins which suggests that mereology is too weak of a system to serve as a foundation for mathematics.
This time we continued Derek So’s discussion of phenomenology, its recent developments and relations to linear logic and embodied cognition.
Main Readings:
Additional Readings:
Zahavi, D. Husserl’s Phenomenology, Stanford Univ. Press, pp. 14-26.
A fragment on categorial intuition by Jan Gronwald.
In relation to the first chapter of “Mathematical Intuition” by Richard Tiszen, we discussed some notions of Husserl’s phenomenology that pertain to the categorial intuition.
Derek So introduced us to some basic concepts of Husserl’s phenomenology. We focused on intentionality, synthetic and eidetic intuition. Then briefly discussed the different conceptions of intuition in more contemporary phenomenology.
Main Readings:
Tieszen, R. Mathematical Intuition: Phenomenology and Mathematical Knowledge. Dodrecht-Boston-London: Kluwer Academic Publishers. SUBCHAPTER 2. OF CH. 2, “INTENTIONALITY AND INTUITION”, pp. 21-25.
We partially discussed the 1st chapter from “Mathematical Intuition” by Richard Tiszen.
Main Readings
We discussed some popular misinterpretations of Gödel’s Theorem.
These were (1) Lucas/Penrose style of arguments against mechanism, (2) GIT as a confirmation of Platonism, (3) The “postmodern” interpretation.
The talk was given by Jan Gronwald.
Main Readings:
(Benacerraf, 1967) God, the Devil and Gödel. in: The Monist 51(1): pp. 9-32.
(Copeland and Shagrir, 2013), Turing versus Gödel on Computability and the Mind, in: B. Copeland, C. Posy, O. Shagrir (ed.), „Computability: Turing, Gödel, Church, and Beyond”. Cambridge, Mass.: MIT Press.
Tomasz will introduce us to Michael Dummet’s famous argument against strict finitism in the philosophy of mathematics. Dummet observed that every strict finitist is committed to the paradox arising with the use of vague expressions – the Sorites paradox – and concluded that “strict finitism is, therefore, an untenable position”. Or is it?
Slides used in the presentation are available here.
Main reading:
Additional Bibliography
Next reading will be Solomon Feferman’s Conceptions of the Continuum, available here.
Marta will present the paper, followed by a discussion.
Slides used in the presentation are available here.
Our next reading meeting will revolve around Solomon Feferman’s article Gödel’s Incompleteness Theorems, Free Will and Mathematical Thought.
The paper can be freely accessed from the Mathematics Department site at the University of Stanford.
During the meeting, Ezra will present the paper, followed by a discussion.
Slides used in the presentation are available here.
Next reading meeting will touch on theoretical computer science. We will be seeing how computational complexity can potentially offer new insights into philosophy of mathematics. We will be reading Scott Aaronson’s survey paper Why Philosophers Should Care about Computational Complexity.
For the meeting, we expect attendants to read in advance sections 1-5, 8-9 and 12 of the paper, available here.
The meeting will have a presentation by Andrea and Noel, followed, as usual, by a discussion.
We will be reading Iannis Xenakis’ Formalized Music: Thought and Mathematics in Composition, where mathematics and music come together.
During the session, Paul Maurice will present the paper, followed by a discussion.