Michele Lubrano

We contribute to the ongoing discussion on mathematical structuralism by focusing on a question that has so far been neglected: when is a structure part of another structure? This paper is a first step towards answering the question. We will show that a certain conception of structures, abstractionism about structures, yields a natural definition of the parthood relation between structures. This answer has many interesting consequences; however, it conflicts with some standard mereological principles. We argue that the tension between abstractionism about structure and classical mereology is an interesting result and conclude that the mereology of abstract structures is a subject that deserves further exploration. We also point out some connections between our discussion of the mereology of structures and recent work on non-well-founded mereologies.

In the present contribution I would like to examine some theories of the ontology of abstract entities that take inspiration from the deep insights of Gottlob Frege. These theories develop in full details some ideas explicitly or implicitly articulated in Frege’s works and try to defend a sophisticated version of Platonism about abstract entities. The review of such theories should allow us to cast light on their merits and their possible flaws and, moreover, to determine which of them is the more promising justification of such Platonism.

In this contribution I will examine Cotnoir’s (2013) solution to the problems that alethic pluralism faces when it comes to logical paradoxes. I will argue that his proposal fails to be a viable option and I will put forward an alternative approach, more Tarskian in spirit, but with the same “pluralist” trait of Cotnoir’s solution. Such an alternative approach is based on the idea that each truth predicate can be associated with an index that fully describes its relation with other truth predicates.I will show how such indexes must be constrained in order to avoid logical paradoxes