Church’s Thesis: Logic, Mind and Nature (2011) – Centrum Kopernika Badań Interdyscyplinarnych UJ

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

Opening session
Aula of the Polish Academy of Arts and Sciences, Sławkowska St. 17, Kraków
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
Plenary session: invited lectures
Chairman: Michał Heller
Aula of the Polish Academy of Arts and Sciences, Sławkowska St. 17, Kraków
10:00 Stewart ShapiroOpen-texture, computability, and Church’s Thesis
11:00 Coffee break
11:20 Marie Duží and Pavel MaternaConcepts and Church-Turing Thesis
12:20 Jack CopelandThe 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
Section A
Chairman: Wilfried Sieg
Room: 120
Section B
Chairman: Oron Shagrir
Room: 111
15:00 Arnon AvronA Logical Generalization of Church Thesis Masaharu MizumotoWittgenstein and Turing vs. Cantor
15:45 Benjamin WellsPseudorecursiveness and the Church-Turing Thesis Jonathan YaariJustifying the Church-Turing Thesis: A Scientific Approach
16:30 Anatolij DvurecenskijState BL-Algebras and State-Morphism Algebras Stanisław KrajewskiIs Church’s Thesis unique?
17:15 Coffee break
17:30 Wolfgang DegenChurch’s Thesis and Other Principles of Reducibility Roberto ArpaiaGödel’s ideas on the limits of the Church-Turing’s Thesis in philosophy of mind: some possible applications
18:15 Csaba HenkComputability in terms of finitary witnesses Bartosz Brożek and Adam OlszewskiMathematical Subject and Church’s Thesis

Saturday, June 4

Plenary session: invited lectures
Chairman: David McCarty
Aula of the Polish Academy of Arts and Sciences, Sławkowska St. 17, Kraków
9:00 Ryszard WójcickiAccessibility of Truth; an Essay on Problems of Knowledge Formation
10:00 Yuri GurevichWhat’s an algorithm?
11:00 Coffee break
11:20 Wilfried SiegGödel’s philosophical challenge (to Turing): “The human mind infinitely surpasses any finite machine.”
12:20 Jan WoleńskiOn the Status of Church’s Thesis
13:20 Lunch break
Afternoon sessions: contributed papers
Pontifical University of John Paul II, Franciszkańska St. 1, Kraków
Section A
Chairman: Stewart Shapiro
Room: 120
Section B
Chairman: Jan Woleński
Room: 111
15:30 Nachum Dershowitz and Evgenia FalkovichA Formalization and Proof of the Extended Church-Turing Thesis Darren AbramsonComputation 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 MiłkowskiHow could we tell that the mind is a Turing machine?
17:00 Coffee break
17:15 Paula QuinonComputability on Strings Marcin SchroederMind, Meaning, and Computation: The Missing Link of Information Integration
18:00 Szymon SzymczakIs the Church-Turing Thesis mathematically provable? Paweł GrabarczykThe Cognitive Criterion

Sunday, June 5

Plenary session: invited lectures
Chairman: Jack Copeland
Aula of the Polish Academy of Arts and Sciences, Sławkowska St. 17, Kraków
9:00 David McCartyMathematical Realism and Church’s Thesis
10:00 Petr HájekComputational complexity, arithmetical hierarchy and mathematical fuzzy logic
11:00 Coffee break
11:20 Oron ShagrirWho is the “human computer” in Turing’s analysis of computability?
12:20 Konrad ZdanowskiOn 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
Section A
Chairman: Yuri Gurevich
Room: 120
Section B
Chairman: Pavel Materna
Room: 111
15:00 Paolo GentiliniDiscussing Church’s Thesis through evolutionary effective learning machines based on Constructive Paraconsistent Logic and Informational Logic Rafal UrbaniakHow Not To Use the Church-Turing Thesis Against Platonism
15:45 Krzysztof WójtowiczHypercomputation and Philosophy of Mathematics Paolo CotognoChurch’s Thesis: There Is No ‘Easy Half’
16:30 Andrew PolonskyChurch’s Thesis and Computable Processes Kim SolinAre 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

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 Website

Conference Photos (by Professor Adam Walanus)
Day 1 | Day 2 | Day 3

Proceedings

Plenary lectures delivered during the conference are available at our YouTube channel.