Johannes Korbmacher

The topic of this dissertation are essential properties. The aim is to give an explication of the concept of essential properties in terms of the concept of metaphysical grounding. Along the way, the author proves several new results about formal theories of metaphysical grounding and develops a new hyperintensional theory of properties. Chapter 1 is the introduction of the thesis in which the author motivates the problem of explicating the concept of essential properties and gives adequacy criteria for a successful explication tracing back to Carnap. The author discusses the orthodox explication of essential properties in terms of metaphysical necessity and Fine's objections to it. He goes on to develop a new ground-theoretic explication of essential properties in an informal way, where the basic idea is that a property is essential to an object if and only if the property is metaphysically grounded in the identity or haecceity of the object. The author argues informally that the new explication provides natural solutions to the problems raised by Fine and make it the goal for the rest of the dissertation to make the account formally precise. Chapter 2 focuses on a axiomatic theories of metaphysical grounding. In particular, the author develops a new formal approach to the relation of partial ground, i.e. the relation of one truth holding partially in virtue of another. The main novelty of the chapter is the use of a grounding predicate rather than an operator to formalize statements of (partial) ground. The author develops the new theory in formal detail as a first-order theory, proves its consistency, and shows that it's a conservative extension of the well-known theory of positive truth. Moreover, the author constructs a concrete model of the theory. Then, the author extends the framework with typed truth predicates, which allow us to make statements about the grounds and truth of statements about the truth of other sentences. Also this theory the author proves consistent and a conservative extension of the ramified theory of positive truth. A model construction extending the construction of the base theory is also given. Ultimately, the author discards the theory for the purpose of the dissertation, because of technical problems that arise when we try to develop a satisfactory explication of essential properties in the framework. The author leaves further development of the framework for future work and argues that further investigating could lead to interesting and fruitful discussion between formal theorists of truth and metaphysical theorists of grounding. Chapter 3 develops a logic of iterated ground, i.e. relations of ground between statements of ground, using the operator approach. The author first discusses certain conceptual distinctions in the context of metaphysical ground in general and iterated ground in particular. The author argues that different conceptions of iterated ground lead to different logics of iterated ground. He goes on to develop the logic of iterated ground based on the idea that if one truth is grounded in others, then it's these grounds that ground the statement of ground itself. This view traces back to remarks by de Rosset and Litland. The logic is developed in formal detail, both syntactically and semantically, and its formal properties are investigated. To conclude the chapter, the author discusses certain problems that arise when we're trying to prove a completeness result for the logic and sketches a way around them. In chapter 4, the author develops a new hyperintensional theory of properties, which can distinguish in natural, semantic terms between necessarily co-extensional but intuitively distinct properties. The theory is based on the idea that we can individuate properties by means of what the author calls "exemplification criteria" of an object for a property, roughly the states of affairs that if they obtain explain why the object has the property. The author develops this theory both formally and informally and discusses in detail how it achieves a natural distinction between necessarily co-extensional but intuitively distinct properties. Chapter 5 is the conclusion, where the author brings the results of chapter 3 and 4 to bear on the informal explication of essential properties in terms of metaphysical ground from the introduction. The author argues that together the iterated logic of ground from chapter 3 and the hyperintensional property theory of chapter 4 allow us to make the explication formally precise in a way that satisfies the adequacy criteria for a successful explication laid out by Carnap. The author concludes with a brief discussion of possible ways of extending the results of the dissertation in various ways.

This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our theory is a proof-theoretically conservative extension of the ramified theory of positive truth up to

Informally, structural properties of mathematical objects are usually characterized in one of two ways: either as properties expressible purely in terms of the primitive relations of mathematical theories, or as the properties that hold of all structurally similar mathematical objects. We present two formal explications corresponding to these two informal characterizations of structural properties. Based on this, we discuss the relation between the two explications. As will be shown, the two characterizations do not determine the same class of mathematical properties. From this observation we draw some philosophical conclusions about the possibility of a ‘correct’ analysis of structural properties.

We develop an exact truthmaker semantics for permission and obligation. The idea is that with every singular act, we associate a sphere of permissions and a sphere of requirements: the acts that are rendered permissible and the acts that are rendered required by the act. We propose the following clauses for permissions and obligations: - a singular act is an exact truthmaker of Pφ iff every exact truthmaker of φ is in the sphere of permissibility of the act, and - a singular act is an exact truthmaker of Oφ iff some exact truthmaker of φ is in the sphere of requirements of the act. We show that this semantics is hyperintensional, and that it can deal with some of the so-called paradoxes of deontic logic in a natural way. Finally, we give a sound and complete axiomatization of the semantics.

This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that the theory is a proof-theoretically conservative extension of the theory PT of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground.