Rohit Jivanlal Parikh

Rohit Jivanlal Parikh (born November 20, 1936 in Palanpur, Gujarat, India), is a mathematician, logician, and philosopher who has worked in many areas in traditional logic, including recursion theory and proof theory. His catholic attitude towards logic has led to work on topics like vagueness, ultrafinitism, belief revision, logic of knowledge, game theory and social software (social procedure). This last area seeks to combine techniques from logic, computer science (especially logic of programs) and game theory to understand the structure of social algorithms. Examples of such are elections, transport systems, lectures, conferences, and monetary systems, all of which have properties of interest to those who are logically inclined.

Rohit Parikh was married to Carol Parikh (nee Geris) from 1968 to 1994. Carol is best known for her prize winning stories and for her influential biography of Oscar Zariski, The Unreal Life of Oscar Zariski. They have two children, Vikram (born 1969) and Uma (born 1974).

Vision statement

I think it is a scandal that Russell’s paradox is still effectively unsolved after a hundred years. We do not need to worry about large cardinals, but need instead to worry about the fact that our notion of set is conceptually deficient. Apart from this I believe that both logic and philosophy are in a state of cowardly subservience to science, which is true as far as it goes, but whose language is severely limited, unable to analyze propositional attitudes, or the game theoretic notion of agent. This subservience leaves us in a state of smug satisfaction, but leaves fundamental problems unaddressed. I would suggest that people pay more attention to Zeno’s paradoxes, to McTaggart's paper on Time, and perhaps also to the writings of the thirteenth-century Zen teacher Dogen Zenji in his Genjokoan.

Posts

• Editor, International Journal of the Foundations of Computer Science, 1990-1995
• Editor, Journal of Philosophical Logic, 2000-2003

Awards and recognition

• William Lowell Putnam Mathematical Competition Prize Winner, 1955, 1956, 1957
• Gibbs Prize, Bombay University, 1954

Academic and research appointments

• Distinguished Professor, City University of New York, (Brooklyn College and CUNY Graduate Center), 1982–Present
• Professor, Mathematics, Boston University, 1972-1982
• Visiting Professor, Mathematics, Courant Institute, 1981
• Associate Professor,Mathematics, Boston University, 1967-1972
• Visiting Associate Professor, Mathematics, SUNY at Buffalo, 1971-1972
• Lecturer, Bristol University, 1965-1967
• Reader, Panjab University, 1964-1965
• Instructor, Stanford University 1961-1963
• Visiting Appointments at Stanford, TIFR Bombay, ETH Zurich, and Caltech

Main publications

• On Context Free Languages, Journal of the Assoc. Comp. Mach. 13 (1966) 570-81. Originally published in 1961 as a research report at RLE, MIT.
• Existence and Feasibility in Arithmetic, Jour. Symbolic Logic 36 (1971) 494-508.
• On the Length of Proofs, Transactions of the Amer. Math. Soc. 177 (1973) 29-36.
• (With M. Parnes) Conditional Probability can be Defined for Arbitrary Pairs of Sets of Reals, Advances in Math 9 (1972) 520- 522.
• (With D.H.J. de Jongh) Well Partial Orderings and Hierarchies, Proc. Kon. Ned. Akad. Sci Series A 80 (1977) 195- 207.
• (With D. Kozen) An Elementary Completeness Proof for PDL Theoretical Computer Science 14 (1981) 113-118.
• The Problem of Vague Predicates, in Logic, Language and Method Ed. Cohen and Wartofsky, Reidel (1982) 241-261.
• The Logic of Games and its Applications, Annals of Discrete Math., 24 (1985) 111-140.
• (With R. Ramanujam) Distributed Processing and the Logic of Knowledge, in Logics of Programs, Springer Lecture Notes in Computer Science, 193 pp. 256-268.
• Communication, Consensus and Knowledge, (with P. Krasucki), Jour. Economic Theory 52 (1990) pp. 178-189.
• Knowledge and the Problem of Logical Omniscience ISMIS- 87 (International Symp. on Methodology for Intelligent Systems), North Holland (1987) pp. 432-439.
• Finite and Infinite Dialogues, in the Proceedings of a Workshop on Logic from Computer Science, Ed. Moschovakis, MSRI publications, Springer 1991 pp. 481-498.
• Vagueness and Utility: the Semantics of Common Nouns in Linguistics and Philosophy 17 1994, 521-35.
• Topological Reasoning and The Logic of Knowledge (with Dabrowski and Moss) Annals of Pure and Applied Logic 78 (1996) 73-110.
• Belief revision and language splitting, in Proc. Logic, Language and Computation, Ed. Moss, Ginzburg and de Rijke, CSLI 1999, pp. 266-278 (earlier version appeared in 1996 in the preliminary proceedings).
• (with Samir Chopra), Relevance Sensitive Belief Structures, Annals of Mathematics and Artificial Intelligence, 28(1-4): 259-285 (2000).
• Social Software, Synthese, 132, Sep 2002, 187-211.
• (with Jouko Vaananen), Finite information logic, Annals of Pure and Applied Logic, 134 (2005) 83-93.
• (With R. Ramanujam), A Knowledge based Semantics of Messages, Jour. Logic, Language and Information, 12 2003, 453-467.
• Levels of Knowledge, Games, and Group Action, Research in Economics, 57 2003, 267-281.
• (with Eric Pacuit and Eva Cogan) The logic of knowledge based obligation, in Knowledge, Rationality and Action, 2006. Work in Progress.
• Currently working on books in reasoning about knowledge as well as on social software. Also, working on the issue of logical omniscience.

References

• Rohit Parikh's Curriculum Vitae
• Brooklyn College home page
• Philosophy Dept. CUNY home page
• An Interview with Rohit Parikh
• Wikipedia page on social software
• http://web.cs.gc.cuny.edu/~kgb/socsoft/
• http://www.illc.uva.nl/ADMW05/
• http://www.philog.ruc.dk/phiconf4.html
• http://www.lorentzcenter.nl/lc/web/2006/235/info.php3?wsid=235
• Knowledge, Games and Belief Group, Graduate Center City University of New York