# Topic Archive: philosophical logic

Computational Logic SeminarTuesday, February 21, 20172:00 pmGraduate Center, rm. 4422

# Generic logical semantics of justifications.

The CUNY Graduate Center

Proofs and justification are gradually making their way from meta-logical notions into the formal logic itself and becoming mathematical logical objects. This makes the logic language (much) more precise and connects the logic apparatus to numerous new areas of interest. In this talk, we describe a generic logical semantics of justifications within the classical truth values logic framework: justifications here appear as sets of formulas with appropriate closure conditions.

University of Nottingham
Mark Jago (Ph.D. 2006, Nottingham University) is a philosopher in Nottingham, UK, interested in philosophical and formal logic, language, metaphysics and the philosophy of mind.
Ruhr University Bochum
Prof. Dr. Wansing (M.A. Phil., Free University of Berlin, 1988; D. Phil., Free University of Berlin, 1992; Habilitation in Logic and Analytical Philosophy, University of Leipzig, 1997) is Professor of Logic and Epistemology at the Ruhr University Bochum, and conducts research in philosophical logic, modal logic, non-classical logic and epistemology.
CUNY Graduate Center, Ph.D. Program in Philosophy
Graham Priest, a Distinguished Professor at CUNY Graduate Center, is the most prominent contemporary champion of dialetheism, the view that some claims can be both true and false. He is known for his in-depth analyses of semantic paradoxes, and his many writings relate to paraconsistent and other non-classical logics. He has taught in Australia at the University of Melbourne since 2001 and has authored numerous books. Over the course of his prominent career, he has published articles in nearly every major journal on philosophy and logic. He has held visiting research positions at many universities, including the Australian National University, the Universities of Cambridge, New York, Pittsburgh, São Paulo, Kyoto, and the Soviet Academy of Sciences. He holds a Ph.D. in mathematics from the London School of Economics.
CUNY Logic WorkshopFriday, November 22, 20132:00 pmGC 6417

# Measure semantics for modal logics

Columbia University

Long before Kripke semantics became standard in modal logic, Tarski showed us that the basic propositional modal language can be interpreted in topological spaces. In Tarski’s semantics for the modal logic $S4$, each propositional variable is evaluated to an arbitrary subset of a fixed topological space. I develop a related, measure theoretic semantics, in which modal formulas are interpreted in the Lebesgue measure algebra, or algebra of Borel subsets of the real interval $[0,1]$, modulo sets of measure zero. This semantics was introduced by Dana Scott in the last several years. I discuss some of my own completeness results, and ways of extending the semantics to more complex modal languages.

CUNY Logic WorkshopFriday, September 27, 20132:00 pmGC 6417

# Satisfaction is not absolute

The City University of New York

I will discuss a number of theorems showing that the satisfaction relation of first-order logic is less absolute than might have been supposed. Two models of set theory $M_1$ and $M_2$, for example, can agree on their natural numbers $langlemathbb{N},{+},{cdot},0,1,{lt}rangle^{M_1}=langlemathbb{N},{+},{cdot},0,1,{lt}rangle^{M_2}$, yet disagree on arithmetic truth: they have a sentence $sigma$ in the language of arithmetic that $M_1$ thinks is true in the natural numbers, yet $M_2$ thinks $negsigma$ there. Two models of set theory can agree on the natural numbers $mathbb{N}$ and on the reals $mathbb{R}$, yet disagree on projective truth. Two models of set theory can have the same natural numbers and have a computable linear order in common, yet disagree about whether this order is well-ordered. Two models of set theory can have a transitive rank initial segment $V_delta$ in common, yet disagree about whether this $V_delta$ is a model of ZFC. The theorems are proved with elementary classical methods.

This is joint work with Ruizhi Yang (Fudan University, Shanghai). We argue, on the basis of these mathematical results, that the definiteness of truth in a structure, such as with arithmetic truth in the standard model of arithmetic, cannot arise solely from the definiteness of the structure itself in which that truth resides; rather, it must be seen as a separate, higher-order ontological commitment.

Kobe University, Visiting Fellow, Grad Center, CUNY
Hitoshi Omori is a visting fellow in the CUNY Graduate Center program in Philosophy, visiting from Kobe University. His main research interests are Logic, Logic And Foundations Of Mathematics, Philosophy of Logic, Philosophical Logic, Modal Logic and Non-Classical Logic.
Columbia University
Professor Gaifman’s first result (obtained when he was a math student) was the equivalence of context-free grammars and categorial grammars. He was Carnap’s research assistant, working on the foundations of probability theory, and got his Ph. D. under Tarski (on infinite Boolean algebras). He worked on a broad spectrum of subjects: in mathematical logic (mostly set theory, where he invented the technique of iterated ultrapowers, and models of Peano’s arithmetic), foundations of probability (where he defined probabilities on first-order and on richer languages), in philosophy of language and philosophy of mathematics, as well as in theoretical computer science.. He held various permanent and visiting positions in mathematics, philosophy and computer science departments. While he was professor of mathematics at the Hebrew University, he taught courses in philosophy and directed the program in History and Philosophy of Science. Gaifman’s recent interests include foundations of probability, rational choice, philosophy of mathematics, logical systems that formalize aspects of natural reasoning, Frege and theories of naming.
The City University of New York
Professor Hamkins (Ph.D. 1994 UC Berkeley) conducts research in mathematical and philosophical logic, particularly set theory, with a focus on the mathematics and philosophy of the infinite.  He has been particularly interested in the interaction of forcing and large cardinals, two central themes of contemporary set-theoretic research.  He has worked in the theory of infinitary computability, introducing (with A. Lewis and J. Kidder) the theory of infinite time Turing machines, as well as in the theory of infinitary utilitarianism and, more recently, infinite chess.  His work on the automorphism tower problem lies at the intersection of group theory and set theory.  Recently, he has been preoccupied with various mathematical and philosophical issues surrounding the set-theoretic multiverse, engaging with the emerging debate on pluralism in the philosophy of set theory, as well as the mathematical questions to which they lead, such as in his work on the modal logic of forcing and set-theoretic geology.