Logic and Philosophy of Mathematics
At the heart of human reasoning itself, the Department of Philosophy's research in logic and the foundations of mathematics leverages conceptual analysis techniques from philosophy, mathematics, linguistics and computer science.
Our integrative investigations tackle foundational problems with symbolic logic modeling knowledge representation and inferential mechanisms.
Categorical Logic
Applications of category theory to logic link mathematical syntax and semantics. This includes developing new logical systems like homotopy type theory suited to computerized formal verification of proofs.
Computability and Automated Proof Search
Research analyzes key logical systems and advances methods for automated reasoning to formally verify mathematical proofs and ensure software correctness.
Homotopy Type Theory
HTT refers to a new interpretation of Martin-Löf’s constructive type theory into abstract homotopy theory, which was pioneered at CMU by Awodey and his students. Logical constructions in type theory correspond to homotopy-invariant constructions on spaces, while theorems and even proofs in the logical system inherit a homotopical meaning.
Philosophy and History of Mathematics
Influenced by major 19th century conceptual revolutions, research links modern issues to the dramatic evolution of mathematical thought using perspectives like reductive structuralism. Case studies provide context on pivotal proofs.
Philosophy of Language and Linguistics
Leveraging philosophy of language with linguistics techniques, research investigates phenomena spanning communicative intention identification, discourse interpretation, modality, and developing structured language acquisition methodologies.
Philosophical Logic
Modeling modal notions like knowledge, conditionals and necessity, projects creatively apply interdisciplinary techniques from computer science and linguistics to long-standing conceptual issues in philosophy.
Proof Theory
Building on Hilbert's program, research uses proof analysis to address consistency and foundations questions in mathematics. Additional projects develop new methods for constructing proofs and extracting computational meaning from classical reasoning.