Skip to main content

Is There a Logic of Society?

  • Chapter
  • First Online:
Proof, Computation and Agency

Part of the book series: Synthese Library ((SYLI,volume 352))

  • 920 Accesses

Abstract

Continuing the discussion above, we came to identify “valid proof” with “proof in first order logic,” proved complete by Gödel. And we came to identify effective procedures with procedures which could be carried out (or somehow simulated) by Turing machines.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Indeed it is sufficient if β, applied once, yields B under the precondition that both A and B hold.

  2. 2.

    Akbar was the grandfather of Shah Jehan who built the Taj Mahal in memory of his wife Mumtaz.

References

  1. Adams E. Probability and the logic of conditionals. In P. Suppes and J. Hintikka, editors, Aspects of Inductive Logic, Pages 265–316. North Holland, Amsterdam, The Netherlands, 1968.

    Google Scholar 

  2. Sarin A. Akbar and Birbal, Penguin India, Panchseel Park, New Delhi, 2005.

    Google Scholar 

  3. Bacharach M. In N. Gold and R. Sugden, editors, Beyond Individual Choice: Teams and Frames in Game Theory. Princeton University Press, Princeton, NJ, 2006.

    Google Scholar 

  4. Benthem J., van Eijck J., and Kooi B. Common knowledge in update logics. In R. der Meyden, editor, Theoretical Aspects of Rationality and Knowledge, pages 253–261, Proceedings of the Tenth Conference, National University of Singapore, 2005.

    Google Scholar 

  5. Gödel K., Die Vollständigkeit der Axiome des logischen Funktionen-kalküls, Monatshefte für Mathematik und Physik, 37: 349–360, 1930.

    Article  Google Scholar 

  6. Grice P. Studies in the Way of Words. Harvard University Press, Cambridge, MA, 1989.

    Google Scholar 

  7. Hardin G. The tragedy of the commons, Science, 162: 1243–1248, 1968.

    Article  Google Scholar 

  8. Kozen D., and Tiuryn J. Logics of programs. In J. V. Leeuwen, editor, Handbook of Theoretical Computer Science, vol. B, pages 789–840. North Holland, Amsterdam, 1990.

    Google Scholar 

  9. Lewis D. Convention: A Philosophical Study. Harvard University Press, Cambridge, MA, 1969.

    Google Scholar 

  10. Nash J. Equilibrium points in N-person games, Proc Natl Acad Sci USA, 36: 48–49, 1950.

    Article  Google Scholar 

  11. Pacuit E. Topics in Social Software: Information in Strategic Situations Doctoral dissertaion, City University of New York, 2005.

    Google Scholar 

  12. Pacuit E., and Parikh R. Social interaction, knowledge, and social software. In D. Goldin, S. Smolka, and P. Wegner, editors, Interactive Computation: The New Paradigm. Springer, Berlin, Germany, 2006.

    Google Scholar 

  13. Pacuit E., Parikh R., and Cogan E. The logic of knowledge based obligation, presented at Society of Exact Philosophy meeting in Maryland, and at DALT 2004, Synthese, 149: 311–341, 2006. Also in in Knowledge, Rationality & Action, 57–87, 2006.

    Article  Google Scholar 

  14. Parikh R. The Logic of games and its applications, Ann. Discrete Math., 24: 111–140, 1985.

    Google Scholar 

  15. Parikh R. Knowledge based computation (Extended abstract). In Proc. AMAST-95 Montreal, July 1995, Edited by Alagar and Nivat, Springer Lecture Notes in CS no. 936, pages 127–142.

    Google Scholar 

  16. Parikh R. Social software, Synthese, 132: 187–211, September 2002.

    Article  Google Scholar 

  17. Parikh R., and Ramanujam R. A knowledge based semantics of messages, J. Logic, Language and Information, 12: 453–467, 2003.

    Article  Google Scholar 

  18. Parikh R. WHAT do we know and what do WE know? the proceedings of Theoretical Aspects of Rationality and Knowledge, R. van der Meyden, editor, University of Singapore, June 2005.

    Google Scholar 

  19. Pauly M. Logic for Social Software, Ph.D. Thesis, University of Amsterdam. ILLC Dissertation Series 2001–10, ISBN: 90-6196-510-1.

    Google Scholar 

  20. Edgington D. ‘Conditionals’, http://plato.stanford.edu/entries/conditionals

  21. Ramsey F.P. Truth and probability. In The Foundations of Mathematics, pages 156–198. Routledge and Kegan Paul, London, 1931.

    Google Scholar 

  22. Savage L.J. The Foundations of Statistics. Wiley, New York, NY, 1954.

    Google Scholar 

  23. Schelling T. The Strategy of Confict. Harvard University press, Cambridge, MA, 1960.

    Google Scholar 

  24. Sen A. Commodities and Capabilities. Elsevier Science, Amsterdam, 1985.

    Google Scholar 

  25. Turing A.M. On computable numbers, with an application to the Entscheidungsproblem, Proc. London Maths. Soc., ser. 2, 42: 230–265, 1936–1937.

    Google Scholar 

  26. von Neumann J., and Morgenstern O. Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ, 1944.

    Google Scholar 

Download references

Acknowledgments

Thanks to Johan van Benthem, Jongjin Kim and Eric Pacuit for comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rohit Parikh .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Parikh, R. (2011). Is There a Logic of Society?. In: van Benthem, J., Gupta, A., Parikh, R. (eds) Proof, Computation and Agency. Synthese Library, vol 352. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0080-2_2

Download citation

Publish with us

Policies and ethics