The syntactical approach to knowledge, the predicate approach to knowledge, and quantification.

My research project focuses on questions such as: When we are modeling knowledge, can we steer be-tween representing epistemic agents as logically omniscient (i.e., knowing all logical truths and all logical consequences of what one knows already) on the one hand and logically incompetent (i.e., not being able to make any logical inference or knowing any logical truth) on the other hand? Can we make model situations in which someone knows that there exists a prime larger than the largest known prime, but does not know what that number is? Can we develop a theory in which one quantifies over the objects of knowledge? These questions are related. One option that goes a long way to answering the above questions is to conceive of knowledge as a predicate that combines with names of sentences. But this answer is confronted with self-referential paradoxes (e.g., this sentence is not known). My research goal is to find a solution. The inter-play between actual knowledge and possible knowledge may provide a key to the solution. What is at stake is the expressive power of our formal theories of knowledge, and their philosophical relevance depends part-ly on their expressive power.

Keywords:Omniscience, Competence, Expressive power, Quantification, Predicate, Paradox, Knowledge

Disciplines:Theory and methodology of philosophy, Philosophy, Other philosophy, ethics and religious studies not elsewhere classified