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ANR Gödel

Kurt Gödel philosopher : from logic to cosmology

ANR Research Project 2009-2013
Director : Gabriella Crocco

Overview

Kurt Gödel is specifically known for his work in logic and set theory. But he published little during his lifetime and from the 1940s on he dedicated most of working hours to philosophy. A great number of his thoughts and reflections are documented in the Max-Phil notebooks in the Gödel archive of the Institute for Advanced Studies in Princeton. The aim of the ANR project was to make these notes available to a larger public. His unpublished writings show a deep intertwining of scientific topics with philosophical ideas and problems. On the one hand one observes that all of his great scientific results are deliberately developed in order to shed light or sort out philosophical problems. On the other hand one notices that Gödel was rather focused on metaphysical matters such the relations between concepts and objects, but also the analysis of the nature of space, time, matter and life. The ideas that he developed in these analyses are in turn active in his scientific work. The analysis of the relations between the ideas of concepts and objects is effective in Gödel’s work on the foundations of mathematics, and the analysis of the nature of space, time and matter is effective in his stationary solution for the gravitational field equations.
Gödel’s notebooks are written in Gabelsberger, a shorthand system for the German language that is no longer taught. This circumstance has led to an undeniable and considerable obstacle for the research on Gödel’s thinking. Therefore several international specialists have been brought together to work on this difficult material : specialists of Gabelsberger, specialists in logic, set theory, cosmology, theory of relativity and quantum mechanics as well as specialists in several domains of philosophy such as ancient philosophy, medieval philosophy, Leibniz, Kant, German idealism, Husserl, Frege, Russell and Carnap. After having assorted the unpublished material the group has started to work on a first critical edition for the time being of the most interesting parts, namely the (Max-Phil 1938-1955). Afterwards the group has set out to resolve two eminent important but unresolved questions for the research on Gödel : his ideas on concepts and his ideas on physics.

Main objectives

Preliminary technical objectives
1. Make the content of Gödel’s archives easily accessible to the group
2. Engage Gabelsberger specialists to transcribe the manuscripts
3. Choose the most interesting manuscripts among the huge number of documents in the archives.
These preliminary tasks have been accomplished, 1) converting the microfilms into Jpeg images, (for internal use only) 2) working with Robin Rollinger (transcriber of Husserl) and training Eva-Maria Engelen in Gabelsberger, to permit her to achieve a fluent reading of the texts and 3) choosing together with the group of international specialists on Gödel that are members of the project (Mark van Atten, Göran Sundholm, Akihiro Kanamori, Cheryl et John Dawson, Richard Tieszen) to concentrate on the Max-Phil dated 1938-1955.

Scientific objectives : support the two following claims, suggested by Wang’s books on Gödel.
1) The keystone of Gödel’s scientific work is a metaphysics that was put in place gradually over his career. This metaphysics is inspired by Leibniz. Its main tenet is an original theory of concepts, a Logica magna. Set theory depends on this theory of concepts, as well as the possibility of deciding the continuum hypothesis.
2) Physics, and cosmology, are, according to Gödel, a branch of logic, that is, of the theory of concepts. This thesis restore to cosmology the meaning it had during the golden age of physics : it is not an outgrowth of astronomy or astrophysics, but rather a vision of the cosmos that can be rigorously derived from ontological assumptions.

Results

The most important theoretical result of the work consists in the confirmation that a complete understanding of Gödel’s work in logic and physics is not possible without taking his philosophical ideas into consideration, and, vice versa, that Gödel as a philosopher is not fully understood without bearing in mind his scientific views. This global approach emerges from intensive studies on a period in Gödel’s thinking in which he was steeped in Leibniz’s philosophy. This period ended with several drafts of a paper on Carnap, and preceded his study on Husserl. Several specialists from Europe and USA have leant over transcriptions during the course of three international conferences and succeeded in opening up new perspectives and interpretations of Gödel’s philosophy and his scientific work.

Further results are expected from a new Research Project directed by Eva-Maria Engelen in collaboration with Gabriella Crocco and funded by the Berlin-Brandeburgische Akademie der Wissenschaften. (http://www.bbaw.de/forschung/goedel )


Supporting Agencies, Institutions & Departments :

  • Agence Nationale de la recherche (Project ID : ANR-09-BLAN-0313. ANR Program : Programme Blanc 2009. Project Director : Université Aix-Marseille (ex Université de Provence) et CNRS (CEPERC UMR7304) - Gabriella CROCCO. Project Partner : University Paris-1Panthéon Sorbonne et CNRS (IHPST UMR 8590) – Pierre Kerszberg. ANR grant : 270 000,00 euros)
  • Aix-Marseille Université (ex Université de Provence)
  • CNRS - Institut des sciences humaines et sociales

Total funding : 458.000 €
Beginning and duration : 1st September 2009, 48 months

Members :

  • Mark van Atten (SND, Université Paris 4 / CNRS).
  • Eric Audureau (CEPERC, Université Aix-Marseille / CNRS)
  • Gabriella Crocco (CEPERC, Université Aix-Marseille, France),
  • John Dawson (Pennsylvania State University, USA),
  • Cheril Dawson (Independent Researcher, USA)
  • Akihiro Kanamori (Boston University, USA),
  • Pierre Kerszberg (IHPST, Université Paris 1 /CNRS),
  • Eberhard Knobloch (Technische Universität Berlin, Germany),
  • Göran Sundholm (Universiteit Leiden, Netherlands),
  • Richard Tieszen (California State University, San José, USA),

Participants (ANR, AMU, CNRS funded research) :

Researchers

  • Robin Rollinger (Institute of Philosophy of the Czech Academy of Sciences) : funded by the ANR for the transcription of the manuscripts from Gabelsberger ; Research project “Brentano, Bolzano, Husserl and the Austrian debate on the philosophy of knowledge”,
  • Eva-Maria Engelen (Universität Konstanz), funded by the ANR project for a special training in Gabelsberger and by CNRS as transcriber of the manuscripts from Gabelsberger

Post-doctoral fellows

  • Paola Cantù (Université Aix-Marseille, CNRS and CEPERC), Research project : “Bolzano, Peano and Gödel’s on the algebra of concepts : a Leibnizian inheritance.”
  • Shinji Ikeda (Université de Toyama), Research project : “Leibniz and Gödel”

Doctoral fellows

  • Julien Bernard (Université Aix-Marseille, CEPERC), Research Project : “Gödel, Weyl and the criticism of relativity theory”
  • Amélie Mertens (Université Aix-Marseille, CEPERC), Translation into French

Graduate students

  • Bertrand Granier (Université Aix-Marseille), Translation into French

Conferences and workshops :

1) ANR - Workshop “Kurt Gödel philosopher : from logic to metaphysics”, 1st-3rd December 2010, Paris, ENSTA

PDF - 108.1 ko
Program 1st-3rd december 2010

2) Journées d’études de présentation de projet ANR Gödel, Université Aix-Marseille, Aix-en-Provence, Maison des Astronomes, IMéRA, 27th-28th September 2012

Invited Speakers
Gabriella Crocco, Göran SUNDHOLM, Eva-Maria ENGELEN, Paola Cantu, Eric Audureau, Amélie Mertens

Organizing Committee
Paola CANTU (Université Aix-Marseille, CNRS)

PDF - 109.3 ko
Program 27th-28th september 2012

3) International conference “Kurt Gödel philosopher : from logic to cosmology “ Université Aix-Marseille, Aix-en-Provence, July 11-13, 2013.

Overview
Gödel’s writings published during his lifetime show his dual interest in scientific questions and in fundamental philosophical questions. The posthumous publication of certain manuscripts and talks enables one better to understand this double interest in science and in philosophy. On the one hand, Gödel developed most of his scientific results in order to solve or clarify certain philosophical questions. On the other hand, his scientific work in the foundations of mathematics and in cosmology enriched his philosophical thought on, for example, the a priori classification of philosophical systems, and on the relations between the notions of concept and object. Hence, not only did Gödel, as is well known, believe that philosophy might become an exact theory, provided that one does for metaphysics what Newton did for physics ; he should moreover be aligned with Descartes, Leibniz, and other early modern philosophers who believed that science and philosophy are inseparable.
The conference will explore several features of Gödel’s philosophy that emerge from the unpublished manuscripts Max-Phil, which have been partly transcribed by the research group directed by Gabriella Crocco at CEPERC (Université Aix-Marseille).
The presentation of the state of the art of the transcriptions of Max-Phil IX-XV will be accompanied by an exploration of Gödel’s philosophy of logic, mathematics, and physics by international specialists and young Gödel scholars.

Invited speakers
John Dawson (Pennsylvania State University, USA), Akihiro Kanamori (Boston University, USA), Eberhard Knobloch (Technische Universität Berlin, Germany), Massimo Mugnai (Scuola Normale Superiore, Pisa, Italy), Göran Sundholm (Universiteit Leiden, Netherlands), Richard Tieszen (California State University, San Jose, USA)

Scientific Committee
John Dawson (Pennsylvania State University, USA), Akihiro Kanamori (Boston University, USA), Eberhard Knobloch (Technische Universität Berlin, Germany), Göran Sundholm (Universiteit Leiden, Netherlands), Richard Tieszen (California State University, San José, USA), Gabriella Crocco (CEPERC, Université Aix-Marseille), Pierre Kerszberg (IHPST, Université Paris 1 /CNRS), Mark Van Atten (SND, Université Paris 4 / CNRS), Eric Audureau (CEPERC, Université Aix-Marseille / CNRS), Paola Cantù (CEPERC, Université Aix-Marseille /CNRS), Eva-Maria Engelen (CEPERC, Université Aix-Marseille / Universität Konstanz, Germany).

Organizing Committee
Gabriella Crocco (CEPERC, Université Aix-Marseille), Pierre Kerszberg (IHPST, Université Paris 1 / CNRS), Mark Van Atten (SND, Université Paris 4 / CNRS), Eric Audureau (CEPERC, Université Aix-Marseille / CNRS), Paola Cantù, (CEPERC, Université Aix-Marseille / CNRS), Eva-Maria Engelen (CEPERC, Université Aix-Marseille / Universität Konstanz, Germany).

PDF - 126.7 ko
Program July 11-13, 2013


Publications

  • Gödel’s Manuscripts

1. Gödel, Kurt, Max Phil X, eds. Crocco, Gabriella et al., transcription Engelen, Eva-Maria, and Rollinger, Robin, based on an earlier work by Dawson, Cheryl in collaboration with van Atten, Mark, Crocco, Gabriella, Cantù, Paola. Introduction and annotations by G. Crocco, Aix-en-Provence : PUP, forthcoming.
2. Gödel, Kurt, Max Phil X, French translation by Crocco, Gabriella, Mertens, Amélie, ed. by G. Crocco, Aix-en-Provence : PUP, forthcoming.
3. Gödel, Kurt, Max Phil X, Italian translation by G. Crocco and Paola Cantù, ed. by G. Crocco, in preparation.
4. Gödel, Kurt, Max Phil IX-XV, eds. by Crocco, Gabriella et al., transcription by Engelen, Eva-Maria, based on earlier work by Dawson, Cheryl and Rollinger, Robin, electronic version, in preparation. Voir transcriptions

  • Books

• Bernard, Julien, L’idéalisme dans l’infinitésimal, Weyl et l’espace à l’époque de la relativité , monographie base sur la thèse de doctorat, lauréat du prix Paul Ricoeur 2012, Presses Universitaires de Paris-Ouest, 2013.
• Crocco, Gabriella and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, forthcoming.
• Dybjer P., Lindström S., Palmgren E. & Sundholm G. (eds.) (2012), “Epistemology versus Ontology Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf Logic”, Epistemology and the Unity of Science, vol. 27. Dordrecht : Springer Netherlands.
• Tieszen, Richard After Gödel : Platonism and Rationalism in Mathematics and Logic. Oxford : Oxford University Press, 2011.
• Van Atten, Mark (2015). Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Dordrecht : Springer.

  • Research Articles

2009
1. Van Atten, Mark “Monads and sets. On Gödel, Leibniz, and the reflection principle”. In Judgement and knowledge. Papers in honour of B.G. Sundholm. G. Primiero and S. Rahman (eds). College Publications, 3-33, (2009).

2010
1. Cantù, Paola, “Sul concetto di eguaglianza. Peano e la sua scuola” [On the concept of equality. Peano and his school] (Italian) in C. S. Roero (ed.) Peano e la sua scuola fra matematica, logica e interlingua. Atti del Congresso Internazionale di Studi (Torino, 6-7 Ottobre 2008), Torino : Università di Torino, 2010, pp. 545-561.
2. Engelen, Eva-Maria, “Husserl and the History of Consciousness”, in : Science and the Life-World. Essays on Husserl’s Crisis of the European Sciences, ed. by D. Hyder et H.-J. Rheinberger, Stanford (Stanford University Press) 2010, p. 136-149.
3. Van Atten, Mark, “Construction and constitution in mathematics”. The new yearbook for phenomenology and phenomenological philosophy 10, 43-90, (2010).

2011
1. Crocco, Gabriella, “Gödel Leibniz and Russell’s Mathematical logic”. In : Ralf Krömer and Yannick Chin-Drian (eds.), New essays on Leibniz reception in philosophy of science 1800-2000, Basel : Birkhäuser 2011
2. Kanamori, Akihiro“Historical Remarks on Suslin’s Problem”, in Juliette Kennedy and Roman Kossak (editors), Set Theory, Arithmetic and Foundations of Mathematics : Theorems, Philosophies, Lecture Notes in Logic vol. 36, Association of Symbolic Logic, 2011, 1-12.
3. Tieszen, Richard, "Gödel’s Path from Hilbert and Carnap to Husserl", in Edmund Husserl 1859 - 2009. Neue Abhandlungen der Akademie der Wissenschaften zu Göttingen, K. Cramer and C. Beyer (eds.), Berlin : de Gruyter 2011.
4. Tieszen, Richard, “Intentionality, Intuition and Proof in Mathematics”, in Foundational Theories of Classical and Constructive Mathematics, G. Sommaruga (ed.), Springer 2011, 245-263.
5. Van Atten, Mark, “A note on Leibniz’ argument against infinite wholes”, British journal for the history of philosophy 19(1), 2011, 121-129.

2012
1. Engelen, Eva-Maria and B. Röttger-Rössler “Current Disciplinary and Interdisciplinary Debates on Empathy” Emotion Review 2012, 4 (1), p. 3-8.
2. Engelen, Eva-Maria, „Das Gefühl des Lebendigseins als einfache Form phänomenalen Bewusstseins. Ein Aristotelischer Theorieansatz “, in : The Feeling of Being Alive, hrsg. v. S. Marienberg and J. Fingerhut, Berlin (De Gruyter) 2012, p. 239-256.
3. Engelen, Eva-Maria, “Meaning and Emotion”, in : Dynamicity in Emotion Concepts, ed. by P. A. Wilson, Lodz Studies in Language, Volume 27, Frankfurt a. Main (Peter Lang) 2012, p. 61-72.
4. Kanamori, Akihiro“The Mathematical Infinite as a Matter of Method”, Annals of the Japan Association for Philosophy of Science 20(2012), 3-15.
5. Kanamori, Akihiro“In Praise of Replacement”, The Bulletin of Symbolic Logic 18(2012), 45-90.
6. Kanamori, Akihiro“Set Theory from Cantor to Cohen”, chapter in : Dov Gabbay, Akihiro Kanamori, and John Woods (editors), Sets and Extensions in the Twentieth Century, volume 6 of the Handbook for the History of Logic, Cambridge University Press, 2012, 1-71.
7. Kanamori, Akihiro“Sets and Extensions in the Twentieth Century”, with Dov Gabbay and John Woods, volume 6 of the Handbook for the History of Logic, Cambridge University Press, Cambridge, 2012.
8. Sundholm, B.G. (2012), “Inference versus consequence” revisited : inference, consequence, conditional, implication, Synthese 187(3) : 943-956.
9. Sundholm, B.G. (2012), Error, Topoi : An International Review of Philosophy 31(1) : 87-92.Tieszen, Richard, "Logic", in Routledge Companion to Phenomenology, S. Luft and S. Overgaard (eds.), London : Routledge 2012.
10. Tieszen, Richard, “Monads and Mathematics : Gödel and Husserl”, Axiomathes 2012, 22, 31-52.

2013
1. Sundholm, B.G. (2013), “Containment and Variation ; Two Strands in the Development of Analyticity from Aristotle to Martin-Löf”. In : Schaar M. van der (Ed.) Judgement and the Epistemic Foundation of Logic Logic, Epistemology, and the Unity of Science no. 31. Dordrecht : Springer Netherlands. 23-35.
2. Sundholm B.G. (2013), “Demonstrations versus Proofs, Being an Afterword to Constructions, Proofs and the Meaning of the Logical Constants.” In : M. van der Schaar (Ed.) Judgement and the Epistemic Foundation of Logic Logic, Epistemology, and the Unity of Science no. 31. Dordrecht : Springer Netherlands. 15-22.
3. Cantù, Paola, “An argumentative approach to ideal elements in mathematics”. In Aberdein, A. and Dove, I. J., editors, The Argument of Mathematics, pages 79–99. Springer, Dordrecht, 2013.

2014
1. Cantù, Paola, “The Right Order of Concepts : Grassmann, Peano, Gödel and the Inheritance of Leibniz’s Universal Characteristic”, Philosophia Scientiae - Studies in History and Philosophy of Science, 18-1 (2014), pp. 157—182, ISSN 1281-2463.
2. van Atten, Mark. “Gödel and intuitionism.” In Dubucs, Jacques, and Michel Bourdeau, eds. Constructivity and Computability in Historical and Philosophical Perspective. Dordrecht : Springer, 2014, ch 7, pp. 169-210.

2015
1. Bernard, Julien and Gabriella Crocco, “The Paradox of Concept in Max-Phil IX and X”. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
2. Bernard, Julien, “From the Physical Existence of Tuples to Quantum Materia Prima, Gödel revives some Leibnizian ideas on physics within the frame of contemporary physics of matter” . In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
3. Cantù Paola, “Peano and Gödel”. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
4. Crocco, Gabriella and Eva-Maria Engelen, “Kurt Gödel’s Philosophical Remarks (Max-Phil)”. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
5. Crocco, Gabriella, “Kurt Gödel’s Philosophical Remarks (Max-Phil)”. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
6. Dawson, John W., “What have we learned from the Gödel Nachlaß, and what more may it have to offer ?”. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
7. Engelen, Eva-Maria, “About the Pleasure and the Difficulties of Interpreting Kurt Gödel’s Philosophical Remarks”. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
8. Kanamori, Akihiro, “Gödel vis-à-vis Russell : From Logic and Set Theory to Philosophy”, with Juliet Floyd. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
9. Knobloch, Eberhard, “Leibniz’s Conception of a General Characteristic Art or Combinatorial Art : Leibnizian Examples”. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
10. Kovač, Srećko, “Causality as a Central Concept of Gödel’s Philosophy”. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
11. Mertens, Amélie, “Gödel’s distinction between objective and subjective concepts”. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
12. Mugnai, Massimo, “Leibniz and Gödel”. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
13. Ternullo, Claudio, “Intensional and extensional formal theories : Gödel and Bernays on the relationship between mathematics and logic” . In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
14. Tieszen, Richard, “Leibniz, Husserl and Gödelian Monadology”. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
15. van Atten, Mark. “Gödel’s Dialectica Interpretation and Leibniz” . In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.
16. Weingartner, Paul and Silvia Haring, “On the Compatibility of Evil and Freedom”. In G. Crocco and E-M. Engelen (eds.), Kurt Gödel : Philosopher- Scientist, Presses Universitaires de Provence, Aix en Provence, 2015.

In preparation
17. Gabriella Crocco « Mathematics, logic and time in Gödel’s thought around the fifties ».