Notas sobre quantificação irrestrita e semântica clássica
DOI :
https://doi.org/10.61378/enun.v4i2.77Mots-clés :
quantificação irrestrita, generalidade absoluta, lógica clássicaRésumé
Meu objetivo no presente artigo é apresentar o que penso ser as principais objeções à legitimidade de quantificações irrestrita no âmbito de uma lógica e uma semântica clássicas. Minha conclusão aponta para um dilema entre a lógica clássica e a possibilidade de um discurso formal sobre a generalidade absoluta. Da forma como penso, esse dilema impõe importantes consequências para algumas agendas filosóficas.
Références
BAYS, T. Skolem’ s paradox. In: ZALTA, E. N. (Ed.). The Stanford encyclopedia of philosophy. [s.n.], 2014. Último acesso em: 13/06/2019. Disponível em: <http://plato.stanford.edu/entries/paradox-skolem/>.
BENACERRAF, P.; PUTNAM, H. Philosophy of mathematics. 2a. ed. Cambridge: Cambridge University Press, 1983.
BRADLEY, F. H. Appearance and reality. London: S. Sonnenschein, 1897. BURGESS, J. E pluribus unum: plural logic and set theory. Philosophia Mathematica, v. 3, n. 22, p. 193–221, 2004.
CANTOR, G. Letter to dedekind. In: HEIJENOORT, J. v. (Ed.). From Frege to Gödel. Cambridge, Mass.: Harvard University Press, 1967. p. 113–117.
CARNAP, R. Empiricism, semantics, and ontology. Analysis, v. 4, p. 20–40, 1950.
CARTWRIGHT, R. Speaking of everything. Noûs, v. 28, p. 1–20, 1994.
COHEN, P. Set theory and the continuum hypothesis. New York: Dover Publications, 1966.
DUMMETT, M. The philosophical significance of Gödel’s theorem. In:DUMMETT, M. (Ed.). Truth and others enigmas. Cambridge: Harvard University Press, 1978. p. 186–201.
DUMMETT, M. Frege: philosophy of language. Cambridge, Mass.: Harvard University Press, 1981.
DUMMETT, M. Frege: philosophy of mathematics. Cambridge, Mass.: Harvard University Press, 1991.
DUMMETT, M. The seas of language. Oxford: Oxford University Press, 1993.
FEFERMAN, S. Predicativity. In: SHAPIRO, S. (Ed.). The oxford handbook of philosophy of mathematics and logic. Oxford: Oxford University Press, 2005. p.590–624.
GOODMAN, N. Fact, fiction, and forecast. Cambridge, Mass.: Harvard University Press, 1983.
GRIM, P. There is no set of all truths. Analysis, v. 44, p. 206–208, 1984.
GRIM, P. The incomplete universe. Cambridge, Mass.: MIT Press, 1991.
HEIJENOORT, J. v. (Ed.). From Frege to Gödel. Cambridge, Mass.: Harvard University Press, 1967.
INWAGEN, P. v. Ontology, identity, and modality: essays in metaphysics. Cambridge: Cambridge University Press, 2001.
INWAGEN, P. v. Carnap and the polish logician. Acta Analytica, v. 17, n. 28, p.7–17, 2002.
LEWIS, D. Counterfactuals. Oxford: Blackwell, 1973.
LEWIS, D. On the plurality of worlds. Oxford: Blackwell, 1984a.
LEWIS, D. Putnam’s paradox. The Australasian Journal of Philosophy, v. 62, p.221–36, 1984b.
LEWIS, D. Parts of classes. Oxford: Blackwell, 1991.
LOWE, E. J. A survey of metaphysics. Oxford, UK: Oxford University Press, 2002.
MCGEE, V. There’s a rule for everything. In: RAYO, A.; UZQUIANO, G. (Ed.). Absolute generality. Oxford: Oxford University Press, 2006. p. 180–202.
PARSONS, C. The problem of absolute universality. In: RAYO, A.; UZQUIANO, G. (Ed.). Absolute generality. Oxford: Oxford University Press, 2006. p. 203–219.
PONTES, A. e. Quantificação. In: Compêndio em linha de problemas de filosofia analítica. Lisboa: Centro de Filosofia da Universidade de Lisboa, 2019. p. 1–44.
POTTER, M. Set theory and its philosophy. Oxford: Oxford University Press, 2004.
PRIEST, G. Beyond the limits of thought. 2a. ed. Oxford: Oxford University Press, 2002.
PUTNAM, H. Models and reality. In: BENACERRAF, P.; PUTNAM, H. (Ed.). Philosophy of mathematics. 2a. ed. Cambridge: Cambridge University Press, 1983. p. 421–44.
PUTNAM, H. The Many faces of realism. La Sale, IL: Open Court Publishing Company, 1987.
QUINE, W. v. O. From a logical point of view. Cambridge, Mass.: Harvard University Press, 1953.
QUINE, W. v. O. Mathematical logic. 2a edição revisada. New York: Harper & Row, 1962.
QUINE, W. v. O. Ontological relativity and others essays. New York: Columbia University Press, 1969.
RAYO, A.; UZQUIANO, G. Absolute generality. Oxford: Oxford University Press, 2006.
RESCHER, N.; GRIM, P. Plenum theory. Noûs, v. 42, n. 3, p. 422–439, 2008. RUSSELL, B. The principles of mathematics. Cambridge: Cambridge University Press, 1903.
RUSSELL, B. On some difficulties in the theory of the transfinite numbers and order types. Proceedings of the London Mathematical Society, v. 4, p. 29–53, 1907.
RUSSELL, B. Mathematical logic as based on the theory of types. American Journal of Mathematics, v. 30, p. 222–62, 1908.
RUSSELL, B. Introduction to mathematical philosophy. London: Allen & Unwin, 1919.
RUSSELL, B. Letter to frege. In: HEIJENOORT, J. v. (Ed.). From Frege to Gödel. Cambridge, Mass.: Harvard University Press, 1967. p. 124–5.
SHAPIRO, S. Foundations witthout foundationalism. Oxford: Oxford University Press, 1991.
SHAPIRO, S. Thinking about mathematics. Oxford: Oxford University Press, 2000.
SHAPIRO, S. (Ed.). The oxford handbook of philosophy of mathematics and logic. Oxford: Oxford University Press, 2005.
SKOLEM, T. Some remarks on axiomatized set theory. In: HEIJENOORT, J. v. (Ed.). From Frege to Gödel. Cambridge, Mass.: Harvard University Press, 1967. p. 291–301.
SMULLYAN, R.; FITTING, M. Set theory and the continuum problem. New York: Dover Publications, 1966.
STALNAKER, R. C. Ways a world might be: metaphysical and anti-metaphysical essays. Oxford: Clarendon Press, 2003.
TARSKI, A. O conceito de verdade nas linguagens formalizadas. In: MORTARI, C. A.; DUTRA, L. H. de A. (Ed.). A concepção semântica da verdade: textos clássicos de Tarski. São Paulo: Editora Unesp, 2006. p. 19–148.
WHITEHEAD, A. N. Process and reality. New York/London: The Free Press, 1978.
WILLIAMSON, T. Everything. Philosophical Perspectives, v. 17, p. 415–65, 2003.
YABLO, S. Paradox without self-reference. Analysis, v. 53, n. 4, p. 251–3, 1993.
