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We are continuing our discussion about Higher-Order Logic (HOL), this time focusing specifically on arguments against adopting Higher-Order logics for various purposes. These arguments range from (HOL) being set theory in disguise, the (lack of) applicability of (HOL) for its intended purposes, and the serious metalogical issues the logic faces.
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.
For this special Christmas meeting, Rodrigo will be introducing Kurt Gödel’s argument about the existence of God, a classic medieval argument formalized in modal logic.
No reading preparation is required.
During the session, Rodrigo will present the argument, followed by a discussion.
Slides used during the presentation are available here. See also a handout with the proof.
Our third reading will be Richard Tieszen’s Richard’s Mathematics and Transcendental Phenomenology.
For this session we expect attendants to have read in advance the full second chapter from the book containing the essay; that is:
The text can be accessed freely by University of Amsterdam students through this link to the library catalogue. (Recently there have been problems when accessing online collections, so it might be necessary to open the link on an incognito tab).
What are numeral words, and how do they work in different languages? Can we extract meaningful insights on the nature of numbers by inspecting the linguistics of the words that denote them?
During the session, Bobby will present an overview of the topic and the different research approaches to date, followed by a discussion.
Slides used in the presentation are available here