Besides being a logician and philosopher, I am a logical atomist. On my novel reading of that view, the philosophical practice of logical atomists is term busting, which is defining claims containing apparent terms using claims that do not contain them.
The theory of descriptions is the most familiar example of term busting: one defines claims like “Pegasus is a winged horse” and “The present king of France is bald” using claims in which apparent terms like “Pegasus” and “the present king of France” no longer occur. There are many other examples of term busting in Principia Mathematica: throughout that work, claims in which apparent terms for mathematical objects occur, like number-terms and class-terms, are replaced by claims that involve no number-talk and no class-talk, but only talk of properties.
What is striking is that Russell took the varied examples of term busting in Principia as suggestive of a quite general and fruitful philosophical research program. The term busting philosophical method can be applied to other problematic philosophical notions, like cause, the universe, and ontological priority, thereby eliminating problematic ontological posits and undercutting arguments that make such posits seem necessary.
The upshot of term busting, then, is the dissolution of some outstanding philosophical problems and the logical clarification of those that remain. Bringing that logical atomist research program to life and revamping it using the tools of modern logic, then applying it to today’s philosophical concepts, is a central part of my research agenda.
Another crucial piece of my agenda is to consider what sort of logic one must embrace for the logical atomist program to be viable. The advantage of logical atomism lies in its translation program: anything its dialectical opponents can say with class-talk, for example, a logical atomist is able to say just as well, and without class-talk. One needs a rather strong logic to make this translation program feasible, which raises substantial philosophical questions about the logic underlying logical atomism.
So naturally enough, much of my current research centers on the nature of logic. This program engages with the history of analytic philosophy, a tradition in which logical innovations were influential and part of its vitality. It also branches out into the philosophy of computing and computer-assisted proofs, and the extent to which computation serves as a paradigm of reasoning and proving. It also engages with the nature of logic through questions like What are the grounds of logic? How do we know logical truths? This in turn leads to metaphilosophical questions like How does logic relate to philosophy? How can computers help us leverage logical tools in doing philosophy or (inclusive) history of philosophy?
In short, my agenda is a logic-first, logic-last research program centered on the Socratic question, What is logic? and the meta-Socratic question What is philosophy as the search for logical forms, especially in the digital age?