Alejandro Di Rienzo

I develop an axiomatic system of mereology that accounts for the ways in which musical works can be said to have parts. I distinguish two fundamental modes of composition that musical works exhibit: successive composition, whereby sound events are concatenated in time, and simultaneous composition, whereby sound events occur at the same time. I define various relations of parthood in terms of these operations and study the general principles governing them. I prove that they share some basic properties with the relation of parthood of classical mereology but depart from classical mereology in important respects concerning decomposition and composition principles.

I examine five principles about the metaphysics of properties, each of which has been defended in the literature: (1) the sum of properties is their corresponding conjunctive property, (2) the mereology of properties is classical, (3) properties are individuated by necessary co-instantiation, (4) sums of objects belonging to different categories do not belong to the category of any of their parts, and (5) there is at least a property necessarily instantiated by every individual. I prove that this package of views entails that there is exactly one property. Since this conclusion is highly implausible, I will discuss some ways of modifying the package in order to avoid it.

According to a widespread opinion in the philosophy of mathematics, the objects of mathematics (numbers, sets, topological spaces, categories, etc.) are non-spatiotemporal and causally inert. In the case of sets, this standard opinion has been challenged by various philosophers who claim that some sets do have spatiotemporal location. In this paper I want to examine the thesis that sets are spatiotemporal and explore its implications. First, I will offer precise formulations of the thesis that impure sets are spatiotemporal in the framework of formal theories of location. It turns out that there are logically non-equivalent ways of doing this, and I will explore their differences and logical connections. I will discuss some puzzles that those formulations of the thesis give rise to in the presence of certain assumptions about mereology and location.

En este artículo discutiré algunos problemas lógicos de la omnipotencia que van más allá de las clásicas paradojas ligadas a esta noción. Presentaré una versión refinada de la paradoja de Fitch sobre la omnipotencia que tiene en cuenta la distinción entre acciones básicas y derivadas, así como la distinción entre la capacidad de hacer algo y la mera posibilidad metafísica de hacerlo. También explico cómo esta paradoja puede reformularse para obtener una versión afín a la paradoja del mentiroso que afecta a la consistencia de ciertas nociones de omnipotencia. Por último, evalúo algunas posibles respuestas disponibles para el teísta y un intento de usar la paradoja de Fitch como argumento a favor de la existencia de Dios.