The unifying theme of my research is a concern with notions of meaning. I investigate mechanisms of emergence, transmission, modification and manipulation of meaning(s) in formalized scientific and mathematical theories, as well as in everyday linguistic exchanges. In doing so, I make use of a variety of mathematical, linguistic and philosophical tools. To better assess the scope and robustness of answers given in terms of these instruments I examine their historical roots and conceptual foundations.

In the philosophy of logic I have been concerned with a foundational issue underlying the model-theoretic notion of logical consequence. In the philosophy of mathematics I am attempting to provide a well-motivated realist foundation for important mathematical theories . In the philosophy of language I am pursuing questions about the malleability of meaning and the way meanings oftentimes escape our control.

Philosophy of Logic. At the foundation of Tarski’s celebrated model-theoretic definition of logical consequence lies a distinction of the expressions of a language into two importantly different categories: the logical and the non-logical. While the former are held fixed, the latter are varied in a determination of ‘what follows from what’, i.e., which arguments are valid. To determine the precise limits of the class of logical constants is thus of crucial importance for generating an adequate relation of logical consequence. Counting too many expressions as belonging to the logical lexicon risks misclassifying arguments, providing them with more ‘logical credibility’ than they actually possess. Counting too few as logical results in a notion of logical consequence too weak to fulfil its purpose of effectively structuring deductive dependencies between information.

This is the so-called demarcation problem of the logical constants: the search for philosophically informative and mathematically precise constraints adequately delineating the class of logical constants of a given language. In my research on the demarcation problem, I defend a richer conception of the nature of logical meaning, including as irreducible components both semantic/model-theoretic and inferential/proof-theoretic features of an expression. A criterion of logicality based on this broader view of how logical expressions mean what they mean consequently takes into account both types of meaning-relevant aspects.

I give an overview of different types of criteria of logicality as devised in response to the demarcation problem in Logical Constants. In The Ways of Logicality: Invariance and Categoricity, co-authored with D. Bonnay, we propose and explore a combined criterion of logicality that takes into account both semantic and inferential considerations in the determination of logicality. Logical Constants and Arithmetical Forms further explores the significance of the bounds of logic set by this criterion (a more comprehensive investigation of the limits of such a criterion for expressions from the category of (generalized) quantifiers can also be found in my dissertation Logical Constants between Inference and Reference).

Philosophy of Mathematics. Mathematical realism holds that the statements of mathematics are determinately true or false and that they are so because of the mathematical entities and structures referred to in these statements. Moderate mathematical realists additionally demand that reference to the objects and structures responsible for the truth or falsity of mathematical statements be achieved through naturalistically acceptable, non-mysterious means. Moderate realists face an epistemological challenge: to explain how, given the abstract nature of mathematics, successful reference to mathematical structures and entities is possible without invoking scientifically unacceptable means. What is it, in other words, that enables the determinate reference to mathematical entities and structures the moderate mathematical realist claims possible?

The skeptical challenge advanced against the moderate realist often relies on expressive weaknesses of the formalisms used by her to articulate the mathematical theories of interest. Enriching these formalisms with more expressive devices, however, is ruled out on the basis of the indeterminate nature of these devices themselves. Based on results and insights from the debate concerning what it takes for an expression to be logical I argue that the sceptical challenge can, in many instances, be successfully met and determinate reference to a wide array of mathematically significant structures be achieved.

In Logical Constants and Arithmetical Forms I explore the connection between the debate concerning logicality and determinate mathematical reference. In Securing Arithmetical Determinacy I demonstrate how determinate reference to the natural number structure can be achieved in a naturalistically acceptable fashion. My habilitation project, New Foundations for Mathematical Realism, builds on these ideas to show how a wide variety of mathematically significant structures falls into the purview of the moderate mathematical realist and re-assesses the basis for such a position.