Church’s Thesis: Logic, Mind and Nature (2011)
The main goals of the conference included the discussion over the major results concerning the CT, as well as the presentation of contemporary approaches to the problems connected with the CT.
Conference goals
In 1935 Alonzo Church formulated a thesis called, after Kleene, the Church’s Thesis (CT). The acceptance of the CT led to a negative answer to Hilbert’s Entscheindungsproblem. Since then, many important logicians and philosophers have ventured to solve the numerous problems connected to the CT. The problems include attempts at a proof of the CT, analysis of its status and its logical value, etc. These various lines of research have shown that the CT has many incarnations and constitutes an interdisciplinary problem. The research concerning the CT, as well as an analogical thesis developed by Alan Turing, has resulted in important insights regarding the concept of computability. Georg Kreisel formulated three versions of the CT, pertaining to machine, human, and physical computability. With respect to this, the conference’s focus was on three areas connected to the CT: logic, mind and nature.
Organizers
Studia Logica
Copernicus Center for Interdisciplinary Studies
Pontifical University of John Paul II, Faculty of Philosophy
Committees
Honorary Chairman of the Conference
Michał Heller (Copernicus Center for Interdisciplinary Studies)
Programme Committee
- Chairman: Jacek Malinowski (Institute of Philosophy and Sociology of the Polish Academy of Sciences)
- Heinrich Wansig (Ruhr University Bochum)
- Hannes Leitgeb (University of Bristol)
- Leon Horsten (University of Bristol)
- Adam Olszewski (Pontifical University of John Paul II in Cracow)
Organizing Committee
- Chairman: Adam Olszewski
- Bartosz Brożek
- Jacek Malinowski
- Małgorzata Dróżdż
- Łukasz Kurek
Office
- Piotr Urbańczyk
- Tomasz Strzeboński
Invited speakers
- Jack Copeland (University of Canterbury)
- Marie Duží (VSB-Technical University of Ostrava)
- Yuri Gurevich (Microsoft)
- Petr Hájek (Academy of Sciences of the Czech Republic)
- Pavel Materna (Academy of Sciences of the Czech Republic)
- David McCarty (Indiana University)
- Wilfried Sieg (Carnegie Mellon University)
- Oron Shagrir (Hebrew University of Jerusalem)
- Stewart Shapiro (Ohio State University)
- Jan Woleński (Jagiellonian University)
- Ryszard Wójcicki (Institute of Philosophy and Sociology of the Polish Academy of Sciences)
- Konrad Zdanowski (Istitute of Mathematics of the Polish Academy of Sciences)
Programme
Friday, June 3 |
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| Opening session Aula of the Polish Academy of Arts and Sciences, Sławkowska St. 17, Kraków |
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| 9:30 | Opening addresses: Jacek Malinowski, Studia Logica Editor-in-Chief Michał Heller, Director of the Copernicus Center Władysław Zuziak, Rector of the Pontifical Unversity of John Paul II Adam Olszewski, Chairman of the Organizing Committee |
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| Plenary session: invited lectures Chairman: Michał Heller Aula of the Polish Academy of Arts and Sciences, Sławkowska St. 17, Kraków |
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| 10:00 | Stewart Shapiro, Open-texture, computability, and Church’s Thesis | |
| 11:00 | Coffee break | |
| 11:20 | Marie Duží and Pavel Materna, Concepts and Church-Turing Thesis | |
| 12:20 | Jack Copeland, The Mathematical Objection: Turing, Gödel, and Penrose on the Mind | |
| 13:20 | Lunch break | |
| Afternoon sessions: contributed papers Pontifical University of John Paul II, Franciszkańska St. 1, Kraków |
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| Section A Chairman: Wilfried Sieg Room: 120 |
Section B Chairman: Oron Shagrir Room: 111 |
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| 15:00 | Arnon Avron, A Logical Generalization of Church Thesis | Masaharu Mizumoto, Wittgenstein and Turing vs. Cantor |
| 15:45 | Benjamin Wells, Pseudorecursiveness and the Church-Turing Thesis | Jonathan Yaari, Justifying the Church-Turing Thesis: A Scientific Approach |
| 16:30 | Anatolij Dvurecenskij, State BL-Algebras and State-Morphism Algebras | Stanisław Krajewski, Is Church’s Thesis unique? |
| 17:15 | Coffee break | |
| 17:30 | Wolfgang Degen, Church’s Thesis and Other Principles of Reducibility | Roberto Arpaia, Gödel’s ideas on the limits of the Church-Turing’s Thesis in philosophy of mind: some possible applications |
| 18:15 | Csaba Henk, Computability in terms of finitary witnesses | Bartosz Brożek and Adam Olszewski, Mathematical Subject and Church’s Thesis |
Saturday, June 4 |
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| Plenary session: invited lectures Chairman: David McCarty Aula of the Polish Academy of Arts and Sciences, Sławkowska St. 17, Kraków |
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| 9:00 | Ryszard Wójcicki, Accessibility of Truth; an Essay on Problems of Knowledge Formation | |
| 10:00 | Yuri Gurevich, What’s an algorithm? | |
| 11:00 | Coffee break | |
| 11:20 | Wilfried Sieg, Gödel’s philosophical challenge (to Turing): “The human mind infinitely surpasses any finite machine.” | |
| 12:20 | Jan Woleński, On the Status of Church’s Thesis | |
| 13:20 | Lunch break | |
| Afternoon sessions: contributed papers Pontifical University of John Paul II, Franciszkańska St. 1, Kraków |
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| Section A Chairman: Stewart Shapiro Room: 120 |
Section B Chairman: Jan Woleński Room: 111 |
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| 15:30 | Nachum Dershowitz and Evgenia Falkovich, A Formalization and Proof of the Extended Church-Turing Thesis | Darren Abramson, Computation and the Mental: Church’s Thesis. ‘Right-to-left’ |
| 16:15 | Selmer Bringsjord and Naveen Sundar G., In Further Defense of the Unprovability of Church’s Thesis | Marcin Miłkowski, How could we tell that the mind is a Turing machine? |
| 17:00 | Coffee break | |
| 17:15 | Paula Quinon, Computability on Strings | Marcin Schroeder, Mind, Meaning, and Computation: The Missing Link of Information Integration |
| 18:00 | Szymon Szymczak, Is the Church-Turing Thesis mathematically provable? | Paweł Grabarczyk, The Cognitive Criterion |
Sunday, June 5 |
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| Plenary session: invited lectures Chairman: Jack Copeland Aula of the Polish Academy of Arts and Sciences, Sławkowska St. 17, Kraków |
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| 9:00 | David McCarty, Mathematical Realism and Church’s Thesis | |
| 10:00 | Petr Hájek, Computational complexity, arithmetical hierarchy and mathematical fuzzy logic | |
| 11:00 | Coffee break | |
| 11:20 | Oron Shagrir, Who is the “human computer” in Turing’s analysis of computability? | |
| 12:20 | Konrad Zdanowski, On intended models for arithmetic and intended notations | |
| 13:20 | Lunch break | |
| Afternoon sessions: contributed papers Pontifical University of John Paul II, Franciszkańska St. 1, Kraków |
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| Section A Chairman: Yuri Gurevich Room: 120 |
Section B Chairman: Pavel Materna Room: 111 |
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| 15:00 | Paolo Gentilini, Discussing Church’s Thesis through evolutionary effective learning machines based on Constructive Paraconsistent Logic and Informational Logic | Rafal Urbaniak, How Not To Use the Church-Turing Thesis Against Platonism |
| 15:45 | Krzysztof Wójtowicz, Hypercomputation and Philosophy of Mathematics | Paolo Cotogno, Church’s Thesis: There Is No ‘Easy Half’ |
| 16:30 | Andrew Polonsky, Church’s Thesis and Computable Processes | Kim Solin, Are epistemological aspects of computability theory paid enough attention to? |
| 17:15 | Coffee break | |
| 17:40 | Closing session The conclusion of the conference, Ryszard Wójcicki Room: 120 |
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Patronages
Honorary patronage: Marek Sowa – Marshal of the Assembly of the Province of Małopolska
Business patronage:
Dryvit Systems
Miejskie Przedsiębiorstwo Wodociągów i Kanalizacji S.A. w Krakowie
Media patronage: Wortal Filozofia
Links
Conference Photos (by Professor Adam Walanus)
Day 1 | Day 2 | Day 3
Plenary lectures delivered during the conference are available at our YouTube channel.