andrei rodin Andrei Rodin's blog about History and Philosophy of Mathematics

7-es Rencontres Français de Philosophie des Mathematiques, Paris 5-7 Nov (program)

New Spaces in Mathematics and Physics: Formal and Philosophical Reflections , Paris, 28 Sent – 2 Oct 2015 (program)

UPDATES:

- Book of abstracts (pdf)

-  Youtube stream records are now available (see separate links for the first and the second day in the Program below)

-  Materials of the talks (slides and in once case a paper) are available (also in the below Program).

Where: Institute of Philosophy, Russian Academy of Sciences. Moscow, Volkhonka 14, build. 5

When: 21-23 September 2015

Title: New mathematical methods in today’s physics: logical, epistemological and computational aspects

Where: Institute of Philosophy, Russian Academy of Sciences. Moscow, Volkhonka 14, build. 5

When: 21-23 September 2015

Aim and Scope

Over the last few decades there were a number of important attempts to apply the new 20-th century mathematics in physics. Mathematics in its turn borrowed from physics many important ideas and motivations. During the planned Conference these developments will be discussed and scrutinized from various viewpoints including logical, epistemological and historical ones.
The Conference will bring together physicists, mathematicians and philosophers working on mathematical foundations of physics. We aim, in partiular, at developing a new theoretical and pragmatic perspective on the famous problem of “unreasonable effectiveness of mathematics in the natural sciences” stressed by E. Wigner back in 1960. We hope that this event will help to strengthen conceptual ties between mathematics and logic, on the one hand, and physics and other natural sciences, on the other hand. The Conference is designed as the concluding event of 3-year long research project “Epistemological strategies of application of mathematics in natural sciences” funded by RFBR (grant N 13-06-00515), which will allow the participants of this project to share their results and exchange their ideas with an international scientific community and establish a new horizon for their further researches. Proceedings of the Conference will be published in 2016 (through “Proceedings of Science” or another similar tool).

Program:

Monday 21st September ( stream record)

09:00 – 09:15 : Opening words

09:15 – 10:45 :  Vladislav Terechovich (SPB)  Explanatory Potential of Mathematics in Quantum Physics (abstract)(slides)
10:45 – 11:15 : Coffee Break

11:15 – 12:30  : Mark Lachieze-Rey (University Paris-Diderot)  Which mathematics for quantum gravity ? (abstract)(slides)

12:30 – 14:00 : Lunch

14:00 – 15:30 : A.D. Panov (Skobeltsyn Institute of Nuclear Physics). Bell’s theorem, computability of quantum theory, and relativity of the ‘local realism’ (abstract)(slides)

15:30 – 16:00 : Coffee Break

16:00 – 17:30 :  Andrei Rodin (Institute of Philosophy RAS)

Constructive Axiomatic Method and Modern Physics (abstract)(slides)

Tuesday 22nd September (stream record)

09:15 – 10:45 : Sergei Kovalyov (Institute of Control Science RAS) Computational Fracture Mechanics: Towards Multi-* Analysis (abstract)(slides)

10:45 – 11:15 : Coffee Break

11:15 – 12:30: Jairo da Silva (University of São Paulo) Structuralism and the Applicability of Mathematics in Physics (abstract)(paper)

12:30 – 14:00 : Lunch

14:00 – 15:30 : Alexander Pechenkin (MSU) Foundations of Physics and Phenomenological Reduction (abstract)(slides)

15:30 – 16:00 : Coffee Break

16:00 – 18:00 : Round Table discussion

Upcoming Talk at the 15th Congress on Logic, Methodology, and Philosophy of Science (Helsinki, 3-8 August 2015)

Title: Constructive Axiomatic Method in Euclid, Hilbert and Voevodsky

Slides   (NEW!)

Abstract:
The standard version of formal axiomatic method stemming from Hilbert [Hilbert (1899)] and recently defended by Hintikka [Hintikka (2011)] is not fully adequate to the recent successful practice of axiomatizing mathematical theories. In particular, the axiomatic architecture of Homotopy Type theory (HoTT) [Voevodsky et. al. 2013] does not quite fit the standard Hilbertian pattern of axiomatic theory.  At the same time HoTT and some other recent theories fall under a more general and in some respects more traditional notion of axiomatic theory, which I call after Hilbert and Bernays [Hilbert&Bernays (1934-1939)] “genetic” or “constructive” (interchangeably) and demonstrate it using the Classical example of the First Book of Euclid’s  “Elements”. On the basis of these modern and ancient examples I claim that Hintikka’s semantic-oriented formal axiomatic method is not self-sustained but requires a support of some more basic constructive method. I provide an independent epistemological grounding for this claim by showing the need to complement Hintikka’s account of axiomatic method with a constructive notion of formal semantics.

Bibliography:

[Euclides(1883-1886)] Euclides (1883-1886) Heiberg (ed.) Euclidis Opera Omnia, Lipsiae, v. 1.

[Hilbert(1899)]: Hilbert D. (1899), Grundlagen der Geometrie, Leipzig.

[Hilbert&Bernays(1934-1939)]: Hilbert D. and Bernays P. (1934-1939), Grundlagen der Mathematik (in two volumes), Springer.

[Hintikka(2011)]:  Hintikka J (2011) What is axiomatic method?, Synthese 183(1):69–85.

[Voevodsky et al. (2013)] Voevodsky V. et al. (2013), Homotopy Type Theory: Univalent Foundations of Mathematics, Institute for Advanced Study (Princeton).

Публичная лекция в рамках проекта “Анатомия философии: как работает текст”. 22 января 2015, Библиотека им. Ф.М. Достоевского (Москва, Чистопрудный бульвар, 23) (слайды) (видeо на youtube)

в разделе my events выложены слайды и аудио докладов

Summary: Knowledge Representation is a rapidly developing area of Artificial Intelligence, which brings together computer scientists and philosophers. The purpose of this workshop is to explore some applications of Category theory and Ontologies in Knowledge Representation.

When: Wednesday September 17 from 10 A.M. to 7 P.M.
Where: Institute of Philosophy of Russian Academy of Sciences (14/5 Volkhonka st., Moscow) Room 525.
Venue: Metro station Kropotkinskaya

Languages: Morning Session will be in Russian, Afternoon Session will be in English

Web:  iph.ras.ru/science_events.htm

Schedule:
10:00 – 10:50
Sergei Kavalyaov (ICS RAS)
Category-theoretic models and methods for development of information systems
Coffee Break 15 mins
11:05 – 12:55
Alex Shkotin (SGM RAS)
Ontologies for Petrology
Coffee Break 15 mins
12:10 – 13:00
Andrei Rodin (IP RAS)
Categorical approaches in Knowledge Representation
LUNCH 2h
15:00 – 15:50
Irina Starikova (Sao Paulo U)
Cognitive Representations in Mathematical Reasoning
Coffee Break 15 mins
16:05 – 16:55
Vitaly Khudovakshev (SPBU) (Skype)
Probabilistic Programming and the Generic Aprroach in Knowledge Representation
Coffee Break 15 mins
17:10 – 18:00
Henson Graves (Lockheed Martin) (Skype)
A Mathematical Framework for Engineering and Science Applications
(TBC)
18:00 – 19:00
General Discussion

The formal axiomatic method popularized by Hilbert and recently defended by Hintikka is not fully adequate to the recent practice of axiomatizing mathematical theories. The axiomatic architecture of Topos theory and Homotopy type theory do not fit the pattern of the formal axiomatic theory in the standard sense of the word.  However these theories fall under a more general and in some respects more traditional notion of axiomatic theory, which I call after Hilbert constructive. I show that the formal axiomatic method always requires a support of some more basic constructive method.

Longer version (PDF)  , the same on arXiv

Shorter journal version (PDF)

Дорогие Коллеги,

в рамках регулярного семинара “Актуальные проблемы философии науки и техники” под руководством В.И Аршинова и А.В. Родина

в ЧЕТВЕРГ 27го февраля в 11 часов утра в аудитории 525 ИФРАНа (Москва, Волхонка 14)

состоится доклад Андрея Родина “Аксиоматический метод как средство научного познания” и презентация новой книги Родина “Аксиоматический метод и теория категорий” (Andrei Rodin, Axiomatic Method and Category Theory, Springer, Synthese Library vol. 364, 2014). http://www.springer.com/philosophy/book/978-3-319-00403-7

С содержанием книги можно ознакомиться здесь: http://arxiv.org/abs/1210.1478

Семинар открыт для всех желающих,

с уважением,
АР

http://www.maa.org/publications/maa-reviews/axiomatic-method-and-category-theory

(pdf)

Черновик новой статьи (русский) (pdf). Критика и комментарии приветствуются.

Objectivity, Objecthood and Genetic Axiomatic Methods in Modern Categorical Mathematics 

talk at the conference Philosophy, Mathematics, Linguistics: Aspects of Interaction 2014 (PhML-2014) , April 21–25, 2014,  in the Euler International Mathematical Institute (EIMI)

abstract (pdf)