GCAS Forms and Formalization Studies Group
The Forms and Formalization Studies Group of the GCAS includes faculty who specialize in the development of, reflection on, and employment of mathematical, logical and diagrammatic models and methods within various areas of philosophy and critical theory. We are committed to researching, communicating and teaching rigorous formal approaches as a way to think clearly, powerfully and creatively and to open new avenues in contemporary thought.
Core members and relevant research areas:
Rocco Gangle: diagrammatic reasoning- category theory - Peirce’s existential graphs- formal models of abductive inference - epistemic game theory
Paul Livingston (acting director): incompleteness/undecidability - computational theory - set theory - (philosophical) foundations of logic and mathematics.
Tzuchien Tho: philosophical and historical questions in integral and differential calculus, functions, sets history of the mathematization of natural science (especially mechanics) - “structuralism” in mathematics (ie. Bourbaki, Grothendieck) - category theory.
John Bova: metalogic/metamathematics - philosophical interpretations of diagonalization - Platonic dialectic and its contemporary potentials - reflection, reflexivity, and self-reference - negation, duality, reversibility, and relations - concepts of complexity – Peircean semiotic - algebraic structures for formal ontology & mereology - extensionality, intensions, and theories of truth.