Inconsistent boundaries

Research on this paper was supported by a grant from the Marsden Fund, Royal Society of New Zealand.Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected (Varzi in Noûs 31:26–58, 1997). In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of empty parts, in delivering a balanced and bounded metaphysics of naive space.PostprintPeer reviewe

Stanislaw Lesniewski: rethinking the philosophy of mathematics

Near the end of the nineteenth century, a part of mathematical research was focused on unification: the goal was to find 'one sort of thing' that mathematics is (or could be taken to be) about. Quite quickly sets became the main candidate for this position. While the enterprise hit a rough patch with Frege's failure and set-theoretic paradoxes, by the 1920s mathematicians (roughly speaking) settled on a promising axiomatization of set theory and considered it foundational. In parallel to this development was the work of Stanislaw Lesniewski (1886-1939), a Polish logician who did not accept the existence of abstract (aspatial, atemporal and acausal) objects such as sets. Lesniewski attempted to find a nominalistically acceptable replacement for set theory in the foundations of mathematics. His candidate was Mereology - a theory which, instead of sets and elements, spoke of wholes and parts. The goal of this paper will be to present Mereology in this context, to evaluate the feasibility of Lesniewski's project and to briefly comment on its contemporary relevance

Intuitionistic Mereology

Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import

Mereology then and now

This paper offers a critical reconstruction of the motivations that led to the development of mereology as we know it today, along with a brief description of some questions that define current research in the field

RECENZIJA KNJIGE Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk, and Dominik Traczykowski (ur.) FORMAL AND INFORMAL METHODS IN PHILOSOPHY, Brill | Rodopi, 2020

BOOK REVIEW: Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk, and Dominik Traczykowski (Eds.), FORMAL AND INFORMAL METHODS IN PHILOSOPHY, Brill | Rodopi, 2020, pp. vii + 320, ISBN-10: 9004420495, ISBN-13: 978-90-04-42050-2, Hardback, €149.00 / $179.00RECENZIJA KNJIGE: Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk, and Dominik Traczykowski (Eds.) FORMAL AND INFORMAL METHODS IN PHILOSOPHY, Brill | Rodopi, 2020, str. vii + 320, ISBN-10: 9004420495, ISBN-13: 978-90-04-42050-2, Tvrdi uvez, €149.00 /$179.0

RECENZIJA KNJIGE Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk, and Dominik Traczykowski (ur.) FORMAL AND INFORMAL METHODS IN PHILOSOPHY, Brill | Rodopi, 2020

BOOK REVIEW: Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk, and Dominik Traczykowski (Eds.), FORMAL AND INFORMAL METHODS IN PHILOSOPHY, Brill | Rodopi, 2020, pp. vii + 320, ISBN-10: 9004420495, ISBN-13: 978-90-04-42050-2, Hardback, €149.00 / $179.00RECENZIJA KNJIGE: Marcin Będkowski, Anna Brożek, Alicja Chybińska, Stepan Ivanyk, and Dominik Traczykowski (Eds.) FORMAL AND INFORMAL METHODS IN PHILOSOPHY, Brill | Rodopi, 2020, str. vii + 320, ISBN-10: 9004420495, ISBN-13: 978-90-04-42050-2, Tvrdi uvez, €149.00 /$179.0

Intuitionistic Mereology

Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import

Events, Topology, and Temporal Relations

We are used to regarding actions and other events, such as Brutus’ stabbing of Caesar or the sinking of the Titanic, as occupying intervals of some underlying linearly ordered temporal dimension. We talk about ‘now’ and ‘then’ in an effort to put some order in our description of what goes on. And since different events seem to overlap in so many different ways, a full account of their temporal relations seems to run afoul of a reductionist strategy. This raises two philosophical questions. The first is whether we can actually go beyond time, as it were, i.e., whether we can take events as bona fide entities and deal with them directly, just as we can deal with spatial entities such as physical bodies or masses without confining ourselves to their spatial representations. This is a controversial issue (though probably not as controversial as it used to be), and ties in with a number of unsettled problems concerning, e.g., the structure of causality or the definition of adequate identity and individuation criteria for events. The second question is whether we can perhaps do without time, i.e., whether we can dispense with time points or intervals as an independent ontological category and focus only on actual or potential happenings, in opposition to the form of reductionism mentioned above—in short, whether we can account for the temporal dimension in terms of suitable relations among events. This is also a highly controversial issue, and relates to the classical dispute concerning relational vs. absolutist conceptions of (space and) time. Time need not be posited as an independent notion—be it as a primary ontological category (intervals or instants) or in the form of some primitive, irreducible relation of temporal precedence. Rather, time can simply be viewed as a by-product of the possibility of orienting the domain of all happenings. If one will, this can then be read as evidence in favor of a (somewhat moderate) form of relationalism