What is Propositional Logic a Theory of, if Anything?

  • Oswaldo ChateaubriandEmail author
Part of the Trends in Logic book series (TREN, volume 39)


In this chapter I discuss some traditional philosophical questions relating to propositional logic, among which are the following: (1) Must the objects of propositional logic (propositions, sentences, thoughts, judgments, etc.) have structure? (2) What is the nature of quantification in propositional logic? (3) What is the connection between material implication and the material conditional? (4) What is the role of the material conditional in propositional logic? (5) What is the role of truth-values?


Propositional Logic Object Language Truth Relation Propositional Variable Logical Implication 
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  1. 1.
    Bochenski, I. (1961). A history of formal logic. Notre Dame, IN: University of Notre Dame Press.Google Scholar
  2. 2.
    Boole, G. (1854). An investigation of the laws of thought. London (Reprinted, New York): Dover.Google Scholar
  3. 3.
    Chateaubriand, O. (1999). Proof and logical deduction. In H. H. Hauesler & L. C. Pereira (Eds.), Pratica: Proofs, types and categories. Rio de Janeiro: Editora PUC.Google Scholar
  4. 4.
    Chateaubriand, O. (2001). Logical forms. Part I: Truth and description. Campinas: Unicamp.Google Scholar
  5. 5.
    Church, A. (1956). Introduction to mathematical logic (Vol. 1). Princeton, NJ: Princeton University Press.Google Scholar
  6. 6.
    Enderton, H. B. (1972). A mathematical introduction to logic. New York: Academic Press.Google Scholar
  7. 7.
    Frege, G. (1960). On sense and reference. In P. Geach & M. Black (Eds.), Translations from the philosophical writings of Gottlob Frege. Oxford: Blackwell.Google Scholar
  8. 8.
    Frege, G. (1964). The basic laws of arithmetic: Exposition of the system (M. Furth, Trans.). Los Angeles, Berkeley: University of California.Google Scholar
  9. 9.
    Frege, G. (1967). Begriffsschrift, a formula language, modelled upon that of arithmetic, for pure thought. In J. van Heijenoort (Ed.), From Frege to Gödel. Cambridge, MA: Harvard University Press.Google Scholar
  10. 10.
    Goodman, N. (1947). The problem of counterfactual conditionals. The Journal of Philosophy, 44, 113–128.CrossRefGoogle Scholar
  11. 11.
    Kleene, S. C. (1952). Introduction to Metamathematics. New York: Van Nostrand.Google Scholar
  12. 12.
    Lukasiewicz, J., & Tarski, A. (1956). Investigations into the sentential calculus. In A. Tarski (Ed.), Logic, semantics, metamathematics. Oxford: Clarendon Press.Google Scholar
  13. 13.
    Mates, B. (1972). Elementary logic (2nd ed.). New York: Oxford University Press.Google Scholar
  14. 14.
    Monk, J. D. (1976). Mathematical logic. New York: Springer.CrossRefGoogle Scholar
  15. 15.
    Quine, W. V. (1951). Mathematical logic (revised edition). Cambridge, MA: Harvard University Press.Google Scholar
  16. 16.
    Quine, W. V. (1970). Philosophy of logic. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  17. 17.
    Quine, W. V. (1972). Methods of logic (3rd ed.). New York: Holt, Rinehart and Winston.Google Scholar
  18. 18.
    Quine, W. V. (1976a). Carnap on logical truth. In W. V Quine (Ed.), The ways of paradox and other essays (revised edition). Cambridge, MA: Harvard University Press.Google Scholar
  19. 19.
    Quine, W. V. (1976b). Ontological remarks on the propositional calculus. In W. V. Quine (Ed.), The ways of paradox and other essays (revised edition). Cambridge, MA: Harvard University Press.Google Scholar
  20. 20.
    Rasiowa, H., & Sikorski, R. (1963). The mathematics of metamathematics. Warzawa: Panstwowe Wydawnictwo Naukowe.Google Scholar
  21. 21.
    Russell, B. (1903). The principles of mathematics. Cambridge: Cambridge University Press.Google Scholar
  22. 22.
    Russell, B. (1906). The theory of implication. American Journal of Mathematics, 28, 159–202.CrossRefGoogle Scholar
  23. 23.
    Whitehead, A. N., & Russell, B. (1925). Principia Mathematica (Vol. 1, 2nd ed.). Cambridge: Cambridge University Press.Google Scholar

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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.PUC-Rio/CNPqRio de JaneiroBrazil

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