mgr Rafał Dzierwa
The topic of my dissertation is „Formal ontology of properties and the new theory of transcendentals”
My research is mainly at the intersection of ontology and mathematical logic. In my first work I constructed a system of logic that extends of propositional calculus with value operators (good, evil, axiologically neutral) in which i prove a host of theorems about said value operator and questions such as what is a valuation? What is value? What sort of consequence relations hold between descriptive and value judgments?
For my PhD thesis my main subjects are ontology of properties and transcendentals. Some ontological cathegories, such as sets in foundations of mathematics are expressive enough to reconstruct many different cathegories of a given domain. As a result you gain a unified picture of many theoretical domains. My goal is to do something analogous for philosophical ontology with the cathegory of properties as my basis. In chapters devoted to ontology of properties I write about problems of individuality, identity, identity across time, relations, whether objects can differ in virtue of relations only? I also analyse Russell's paradox in propery theory and propose a solution.
Philosophers rutinally talk about transcendental properties or relations. Based on results in ontology of properties I problematize these notions. This justifies the need for a theory of transcendentals not only in the sense of one that enumerates a number of them but also in the sense of a theory of what kind of a thing a transcendental is. Typically in thomistic literature transcendentals are understood to refer to the most fundamental, the most extensive metaphysical principles of everything. In reference to neoplatonic tradition according to which the One is the most fundamental principle, I ask the question whether it is correct to consider Oneness as one of transcendentals or does it need to be considered as a principle even more fundamental that the transcendentals themselves and if so, what kind of consequences for our notion of a trancendental follow.
The method that I use is mostly based on remarks made by Kurt Gödel in his essay The modern development of the foundations of mathematics in the light of philosophy. In order to develop basic concepts I employ phenomenological analysis. As a result, cocnepts become precise enough so that they are fit to use in formulation of axioms, which then allows the use of formal sciences' methods. My work as it fits mostly withing the boundaries of analytic philosophy gives special attention and makes use of results in mathematical logic.