Graduate School on Topological Philosophy

International Center for Formal Ontology

6-7 February 2016

Warsaw, Okopowa 55

**School Schedule**

**Saturday, February 6**

10.00-11.30 – *Basic Topology I* (Roland Zarzycki)

11.30-12.00 Coffee

12.00-13.30 *Basic Topology II* (Roland Zarzycki)

13.30-15.00 Dinner

15.00-16.30 *Basic Topology III* (Roland Zarzycki)

16.30-17.00 Coffee

17.00-18.30 *Basic Topology IV* (Roland Zarzycki)

**Sunday, February 7**

10.00-11.30 – *Topological Philosophy I* (Thomas Mormann)

11.30-12.00 Coffee

12.00-13.30 *Topological Philosophy II* (Thomas Mormann)

13.30-15.00 Dinner

15.00-16.30 *Parts and Boundaries * (Achille Varzi)

16.30-17.00 Coffee

17.00-18.30 *On the Logic and Metaphysics of the Concept of Discernibility* (Tomasz Bigaj)

**Basic Topology (8 hours)**

The short introductory course in Topology Basic Topology will provide basic topological vocabulary as well as initial intuitions. Developing the latter is the real aim of the course. Among other topics, the course will definitely undertake the following issues and objects: topology, constructing a topology, topological spaces (examples), homeomorphisms, separation axioms, topological properties, various types of metrics, various types of connectedness, compactness. Any former mathematical background is not required, however, a basic knowledge in set theory and mathematical logic would be an advantage. The course will be based on the extensive study of examples and practical training. After the course, all participants will have acquired the necessary knowledge to take part in Professor Mormann’s Topological Philosophy course.

**Topological Philosophy (4 hours)**

The course consists of the following topics:

- On the Relation between Topology and Philosophy in the 20th Century
- Topology, Set Theory, and Category Theory
- Topological Operators
- Topological Epistemology
- Vagueness in Topological Terms
- Modality and Topology
- The Problem of Gunk

Parts and boundaries (2 hours)

This tutorial will offer a brief introduction to mereotopology, understood as a theory of the interplay between mereological concepts and relations (beginning with parthood and overlap) and topological ones (boundary, contact, and separation). We shall focus mainly on so-called classical mereology, according to which parthood is a partial ordering constrained by extensionality (no two composite wholes have the same proper parts) and closed under composition (any plurality of things compose a whole). On this basis, we shall then look at the topological notion of contact and review various ways in which it can be made interact with parthood. In particular, if mereological overlap amounts to sharing of parts, contact is typically construed as sharing of a common boundary, so we need to be clear about the nature of boundaries, their relationships to extended parts, and the relevant notion of sharing. As it turns out, this may be done in several, non-equivalent ways, and we shall try to sketch a map of the main options, technical and philosophical.

**On the logic and metaphysics of the concept of discernibility (2 hours)**

One of the best-known metaphysical theses of all time is the Leibnizian Principle of the Identity of Indiscernibles, which asserts that no two numerically distinct objects can be qualitatively identical. However, the underlying notion of qualitative identity (or indiscernibility, as it is often called) admits many inequivalent interpretations. In this mini-course we will analyze several logical reconstructions of the concept of (in-)discernibility, and we will explore their mutual logical relations, as well as their connections with the notion of symmetry (or permutation-invariance). The proposed reconstructions will be done within the framework of model theory, with particular emphasis put on the language-dependence of the concept of discernibility. Three basic grades of discernibility will be analyzed: absolute, relative and weak discernibility, as well as two grades based on the notion of the symmetries of models. We will offer an elementary proof of the fact that the considered grades of discernibility form a logical order from the strongest to the weakest one. Some applications of the developed logical tools to the metaphysical discussions on the status of elementary particles in physics will be briefly addressed.

Selected bibliography:

Ladyman, J., Linnebo, O., and Pettigrew, R. (2012), “Identity and discernibility in philosophy and logic”, *The Review of Symbolic Logic*, 5, 162-186

Bigaj, T. (2014), “On discernibility and symmetry”, *Erkenntnis*, DOI 10.1007/s10670-014-9616-y.

**Roland Zarzycki** got his PhD in mathematics at the University of Wroclaw, successfully defending his thesis Limit groups with respect to Thompson’s group *F* and some other finitely generated groups in 2010. He is also a PhD candidate in the department of social sciences at the University of Wrocław. He is an academic teacher, researcher, author, and coordinator of scientific projects. As a specialist in algebraic topology, during his time working at the Univerity of Wrocław he conducted research in the field of geometric group theory, implementing a research project Limitis of Thompson’s group F. On the other hand, he was also actively developing his investigations into political philosophy (The politics of small things as the discourse of the common day ethics in the globalized world), at the New York’s New School among other places, where he stayed on a research grant. He is a frequent conference speaker, including conferences in Hoboken, NJ and Lincoln, NE. Thanks to his dual background, he is able to present advanced material from the field of mathematics in an intelligible way for students of social sciences.

**Thomas Mormann** is Professor of Philosophy at the University of the Basque Country in Donostia-San Sebastian, Spain. He obtained his PhD in Mathematics from the University of Dortmund (1978) and his *Habilitationschrift* in Philosophy, Logic and Philosophy of Science from the University of Munich (1995). He is the author of numerous papers in topological philosophy and related areas. The following ones may be mentioned: *Set Theory, Topology, and the Possibility of Junky Worlds*, Notre Dame Journal of Formal Logic 55(1), 79–90, 2014; *Topological Representations of Mereological Systems*, Poznan Studies In The Philosophy Of Science And The Humanities 76(2001), 467–490; *Topological Aspects of Combinatorial Possibility*, Logic And Logical Philosophy 5, 75-92, 1997; *Trope Sheaves, A Topological Ontology of Tropes*, Logic And Logical Philosophy 3, 1-22, 1996; *Natural Predicates and Topological Structures of Conceptual Spaces*, Synthese 95, 219-240, 1993, *Topology as an Issue for Philosophy of Science*, in H. Andersen, D. Dieks, W.J. Gonzalez, T. Uebel and G. Wheeler (eds.) New Challenges to Philosophy of Science, Springer, 423–434, 2013. A maxim that guides his work is Marshall Stone’s famous dictum ‘**One Must Always Topologize’**. In his research Mormann intends to make evident that topology could be a useful means for dealing with a variety of philosophical problems in new and fruitful ways.

**Achille Varzi** is Professor of Philosophy at Columbia University, New York (USA). A graduate of the University of Trento (Italy), he received his Ph.D. in philosophy from the University of Toronto (Canada). His main research interests are in logic and metaphysics. He is an editor of The Journal of Philosophy, a subject editor of the Stanford Encyclopedia of Philosophy, and an associate or advisory editor of The Monist, Synthese, Dialectica, The Review of Symbolic Logic, and other journals. He also writes for the general public and contributes regularly to several Italian newspapers.Website: http://www.columbia.edu/~av72/.

**Tomasz Bigaj **(PhD in philosophy in 1996, University of Warsaw) is an associate professor at the Institute of Philosophy, University of Warsaw, Poland, and a Marie Curie visiting fellow at the University of Bristol. His recent research focuses on selected topics in the metaphysics of quantum mechanics, including the counterfactual analysis of quantum non-locality and causality, the dispositional interpretation of quantum properties, and the problem of identity and indiscernibility in philosophy and physics. He was a visiting Fulbright fellow at the University of Michigan, Ann Arbor, USA. Among his publications are: the book Non-locality and Possible Worlds. A Counterfactual Perspective on Quantum Entanglement (Ontos Verlag 2006) and over forty articles in Polish and international journals and collections of essays (including Journal of Philosophical Logic, Synthese, Erkenntnis, Ontology of Spacetime II, Studies in History and Philosophy of Modern Physics, Philosophy of Science, Poznań Studies in the Philosophy of the Sciences and the Humanities, and Foundations of Science).

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