COPERNICAN APPROACHES
TO CLASSES
SPEAKERS
ABOUT
In “Class and Membership” (2003) Kit Fine proposed a “Copernican Revolution” in the theory of classes. In the iterative conception of set one takes the set-membership relation for granted and one iteratively expands the ontology of sets. In the Copernican approach to classes one takes the ontology of classes for granted and one iteratively expands the class-membership relation. A striking feature of this theory is that it allows a universal (and thus a self-membered) class while retaining classical logic. Related theories have been explored by Button, Church, Forster, Linnebo, and Roberts, amongst others.
The goal of this workshop is to bring together leading specialists to assess the current state of the Copernican Revolution.
TOPICS
Topics may include:
- Logical classes as opposed to combinatorial sets;
- Liberalizing predicativity beyond the vicious circle principle;
- Church-Oswald set theory;
- Developing strong (and/or) useful theories of classes;
- Further applications: mereology, properties, propositions, etc.;
- The justifiability of using classical logic in developing such theories;
- Copernican approaches to arbitrary objects;
- The metaphysical interpretation of these theories (using essence, real definition etc).
SCHEDULE
Friday 30th (GMH 652)
11.00 – 12.00: Sam Roberts (University of Konstanz), How to be a Copernican about properties
Abstract
The Copernican approach was first proposed by Kit Fine—who applied the framework to classes—and independently by Øystein Linnebo—who applied it to properties. In this talk, I’ll explore its application to properties. I’ll begin by extracting a minimal Copernican theory and then raise what I take to be the most pressing unresolved questions. I’ll examine several answers to these questions that have been put forward and argue that they lead to importantly different views.
12.20 – 14.00: Lunch
14.20 – 15.20: Jon Erling Litland (University of Texas Austin), Copernican Ground
Abstract
Many grounding theorists tacitly assume structured propositions holding that the proposition Pa is identical to the proposition Qb iff P=Q and a=b. But this is couter-cantorian: it allows us to construct an injection from the properties of propositions into the propositions. Grounding theorists are on the hook for counter-cantorianism anway: standard principles about immediate ground allow us to construct an injection from properties of propositions to propositions. This paper proposes that we should accept the counter-cantorian consequences and it develops a systematic counter-cantorian theory. The idea is that properties are defined by specifying their grounding profiles, the contribution they make to how propositions formed by applying them are grounded. Properties are generated in a hierarchy of orders. To avoid paradox we take the “Copernican Turn” and impose a restriction on the use of the grounding relation in defining grounding profiles: in defining grounding profiles at some order o we are restricted to using the grounding-relation as it has been defined up through order o. We then use the theory to throw new light on some of the following issues: absolutely general quantification; the puzzles of ground; the Russell-Myhill Paradox; the Kaplan-Prior paradox.
15.20 – 15.40: Break
15.40 – 17.00: Øystein Linnebo (University of Oslo), Constructing untyped properties
Abstract
Orthodox “Copernicanism” faces various challenges. To overcome these, I explore a constructional approach to untyped properties, starting with the Vicious Circle Principle and gradually liberalizing. The exploration identifies three constructional routes to (a version of) the allegedly “Copernican” theory.
Saturday 31st (GMH 652)
10.00 – 11.20: Tim Button (University College London), Levels make a Fine Church
Abstract
I will discuss three theories of sets, which provide us with a Boolean algebra of sets whilst containing ZFC. The first theory is Fine’s (2005); the second is Church’s (1974); the third is a slight refinement of Church’s theory (which I presented in 2024). I will explain how these refinements can help further the cause of Copernican revolutionaries.
11.20 – 11.40: Break
11.40 – 13.00: Gabriel Uzquiano (University of Southern California), Iterative Divisibility
Abstract
The Copernican approach to classes takes the ontology of classes for granted and embarks in a journey of ideological expansion, whereby one iteratively generates successive reinterpretations of the class-theoretic vocabulary which acknowledge as classes some of what prior interpretations had treated as urelements.
We will explore the prospects of a Copernican approach to the part to whole relation. We take the universe of all objects for granted and ask how to decompose it into parts. Given a minimal expansion of the mereological framework, we deploy a variant of Russell’s paradox to suggest that there is no maximal decomposition of the universe into parts. No matter what a putative interpretation of the mereological vocabulary may be, we may iteratively generate successive reinterpretations of the vocabulary which come to acknowledge as complex parts some of what prior interpretations had treated as mereological atoms. The iteration supports an open-ended series of ever more fine-grained decompositions of the universe into parts in which successive members of the series come to draw mereological distinctions to which prior members had been blind.
One application of the framework is the articulation of a mereological view of classes on which they are conceived as parts of the set-theoretic universe. There is, however, no maximal decomposition of the domain of set theory into classes but rather an open-ended series of decompositions that support a variety of ever more powerful class comprehension principles in line with the original Copernican approach to classes.
13.00 – 14.00: Lunch
14.00 – 15.20: Kit Fine (New York University), Classes and A-objects
Abstract
I explain the intimate connection between Copernican class theory and the theory of A-objects and how the construction of Copernican classes might be extended to A-objects.
15.20 – 15.40: Break
15.40 – 16.40: Roundtable
VENUE
The conference takes place at the University of Oslo, Department of Philosophy, Classics, History of Art and Ideas, situated in Blindern Campus, building: Geor Morgenstiernes hus.
The conference room is GMH 652. This is the conference room situated at the 6th floor of the department, at the end of the corridor.
How to get to Blindern (Link 1/Link 2)
- Tram: line 17 and 18 towards Rikshospitalet, Stop at Universitetet Blindern (or John Colletts Plass in case of road works).
- Metro (T Bane): line 4 (Vestli via Storo), 5 (Ringen via Storo) 5 (Sognsvann), Stop at Blindern.