Logic, Methodology and Philosophy of Science
This volume contains the abstracts of the talks given at the 2015 European Summer Meeting of the Association for Symbolic Logic—Logic Colloquium ’15—taking place on August 3 - 8, 2015, in Helsinki, Finland. The Colloquium is co-located with the 15th International Congress of Logic, Methodology and Philosophy of Science, CLMPS, and the SLS Summer School in Logic.
As usual, the talks at the Logic Colloquium consist of invited plenary lectures, invited talks in the various special sessions, tutorials, and, last but not least, contributed papers. Abstracts of all of these presentations are given here. The book of abstracts is an important part of the Logic Colloquium, since it not only gives the authors the opportunity to present their topic and main results, but also helps the Colloquium participants choose which of the many parallel sessions to attend at any given time.
I would like to thank my colleagues in the Program Committee for a very constructive and pleasant period of collaborative effort, which has resulted in, we think, an excellent program of invited speakers, representing current frontline research in the main areas of logic. We are also particularly happy that there are so many contributed papers at this year’s Logic Colloquium. Finally, I want to thank all the members of the Organizing Committee, and in particular its chair Jouko Väänänen, for their expert and smooth organization of this important event.
The version of 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 formal 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.