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The Forum is open to everyone, including students, visitors, and faculty members from all departments and institutes!

The 60 minute lecture is followed by a 10 minute break and a 30-60 minute discussion. The language of presentation is English or Hungarian.

The scope of the Forum includes all aspects of theoretical philosophy, including:

  • logic and philosophy of formal sciences
  • philosophy of science
  • modern metaphysics
  • epistemology
  • philosophy of language
  • problems in history of philosophy and history of science, relevant to the above topics
  • particular issues in natural and social sciences, important for the discourses in the main scope of the Forum.


7 December (Wednesday) 5:00 PM  Room 226
Gábor Etesi
Department of Geometry, Mathematical Institute
Budapest University of Technology and Economics

Feynman integrals and the current status of the Continuum Hypothesis
It is well-known that in infinite dimensions there is no analogue of the Lebesgue measure. Mainly this is the reason why Feynman integration, a central concept in quantum field theory, lacks any rigorous mathematical basis. On the other hand recent advances of set theory indicate that the usual ZFC axioms of mathematics should be extended by further natural ones such that within this improved axiom system the cardinality of the continuum could be fixed. In the talk we will speculate if these new axioms could help to define a meaningful measure theory in infinite dimensions. These speculations will end without any definitive conclusion.

Finally, if time allows we will also review two further candidates for a meaningful integration theory in infinite dimensions: (i) A. Connes' non-commutative integration, (ii) an integration based on zeta-function regularization.

14 December (Wednesday) 5:00 PM  Room 226
Institute for Philosophical Research, HAS, Budapest
Dynamic Models of the Growth of Reflexive  Knowledge

If you have an idea and I have an idea and we exchange these ideas,
then will each of us have two ideas…?”
(After G.B. Show.)

1. Introduction

The ‘growth of knowledge’ was a common assumption lurking behind the debates of the 60ies and is still considered as evidence for and against epistemic views in contemporary philosophy of science, let alone in scientists’ opinions themselves. In the intersection of the various approaches one finds the thesis that knowledge does grow as a result of collaboration and information exchange. The willingness of researchers, learners and institutions to exchange information is usually remarkable, but in certain cases the benefits of such exchanges or the evidence for the growth of knowledge as their result may not be obvious. Simple counterexamples to the thesis and empirical studies of research networks underline the need for more exact definitions of ‘growth’ and logic models of the dynamics of information exchange.

2. Conceptions of ‘growth’ and reflexive knowledge

Several different uses of the term of ‘growth’ can be identified with respect to knowledge, including individual level as well as collective level notions. The main alternatives are critically reviewed to assess their strengths and weaknesses with respect to the description of the dynamics of information exchange. Leaving behind various conceptions of individual and “objective” knowledge I point to the importance not only of shared views (mutual knowledge), but reflection on, and awareness of what the others know. Various conceptions of social and group knowledge can be defined and the interpretation of growth in these contexts is a challenging precondition of exact models of the growth of knowledge.

3. Dynamic logic models of information exchange

The models discussed introduce conditions for common knowledge in the spirit of Logics of Communication and Change (van Benthem et al. 2006). This framework is capable of a compositional analysis of complex communication scenarios such as announcements to subgroups, or private and secret massaging. Making such models an integral part of the assessment of the growth of knowledge in science or research networks may provide new assessment paradigms for empirical research. Based on dynamic-models one can analyze multi-agent scenarios, such as revealing individuals’ answers to a group in order to promote discussion, peer assessment, forming (sub)groups of differing levels of ability, or giving particular roles to different performers in a group.

4. Models of distributed knowledge in groups and networks

The process of seeking and interpreting assessment of evidence where researchers are to tell how they need to go further, naturally introduced exchange of information between peers about their knowledge. In these situations distribution of knowledge may depend on rationality conditions that guarantee the existence of a “wise man” who represents the cumulative knowledge of the group. I present some recent logic results on the preconditions of no-wise-man distributions. Crucial issues depend on the underlying protocols that govern information exchange in social groups and networks. As a result, the current demand for social software raise the problem of the comparison of the efficiency of networking scenarios based on sharing and representing information about knowledge states.

5. In conclusion

Analysis of conceptions of growth in a composite framework of dynamic epistemic logic and knowledge networks can provide new models and insights for the development of knowledge based communication protocols and social software. Making the protocols dependent on the assessment of the knowledge states of the members can be shown to have tremendous effects to the performance of the group that is sharing information according to different models of information exchange scenarios. A networking scenario may determine not only the efficiency of information exchange but the very nature of group knowledge that it produces.


van Benthem J., van Eijck, J, and Kooi, B. (2006): “Logics of Communication and Change” Information and Computation, 204(11): 1620-1662.

Bird, A. (2007): ‘What is Scientific Progress?’, Noûs 41: 64-89.

Bird, A. (2008): ‘Scientific Progress as Accumulation of Knowledge—A Reply to Rowbottom’, Studies in History and Philosophy of Science 39, 279–281.

Fahrbach, L. (2011): How the Growth of Science Ended Theory Change. Synthese, 180(2):139-155.

J.Y. Halpern and Y.O. Moses. (1990): Knowledge and common knowledge in a distributed environment. Journal of the ACM, 37(3):549-587.

W. van der Hoek and J.-J. Ch Meyer. (1992): Making some issues of implicit knowledge explicit. International Journal on Foundations of Computer Science, 3(2):193-224,

Pacuit. E. and Simon, S. (2011): Reasoning with Protocols under Imperfect Information. The Review of Symbolic Logic, 4: 412-444.

Rowbottom, D. P. (2011): ‘Kuhn vs. Popper on Criticism and Dogmatism in Science: A Resolution at the Group Level’, Studies in History and Philosophy of Science 42 (1):117-124.