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

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)

Title: Geometry, Logic and Axiomatic Method in the 21st Century: Back to Euclid?

When: December 11, 12:15 P.M.

Where: University of Turku (Finland), Department of Social Sciences, Filosofian seminaarihuone 169.

For more info click here

e-book is now also available

The conference Philosophy, Mathematics, Linguistics: Aspects of Interaction
2014 (PhML-2014) will be held on April 21–25, 2014 at the Euler
International Mathematical Institute (EIMI), which is a research unit of the
St. Petersburg Department of Steklov Institute of Mathematics (PDMI) of the
Russian Academy of Sciences (RAS).

The conference PhML-2014 is a sequel in the series of conferences intended
to provide a forum for philosophers, mathematicians, linguists, logicians,
and computer scientists who share an interest in cross-disciplinary research.

For more info see http://www.pdmi.ras.ru/EIMI/2014/PhML/index.html

Important Dates

Submission deadline for contributed papers: February 1st, 2014
Notification of acceptance: March 1st, 2014
Conference starts: April 21st, 2014

The Book finally got published!

http://www.springer.com/philosophy/book/978-3-319-00403-7

Tout objet est une flèche, toute flèche est un objet. (abstract in English). Séminaire itinérant de categories Paris, Université Paris-Diderot, le 16 Novembre 2013