Palavras-chave
Referência
Epistemologia aritmética
Números
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Resumo
Is the debate over the existence of numbers unsolvable? Mario Gómez-Torrente presents a novel proposal to unclog the old discussion between the realist and the anti-realist about numbers. In this paper, the strategy is outlined, highlighting its results and showing how they determine the desiderata for a satisfactory theory of the reference of Arabic numerals, which should lead to a satisfactory explanation about numbers. It is argued here that the theory almost achieves its goals, yet it does not capture the relevant association between how a number can be split up and the morphological property of Arabic numerals to be positional. This property seems to play a substantial role in providing a complete theory of Arabic numerals and numbers.
Referências
ACKERMAN, D. “De Re Propositional Attitudes Toward Integers". In: Southwestern Journal of Philosophy, IX, pp. 145–153, 1978.
BALAGUER, M. Platonism and Anti-Platonism in Mathematics. Oxford: Oxford University Press, 1998.
BUENO, O. “Modal Epistemology and Mathematical Epistemology". In FISCHER, R. and LEÓN, F. (Eds.). Modal Epistemology After Rationalism, pp. 67–83. Dordrecht: Springer, 2016.
BURGESS, J. and ROSEN, G. A Subject With No Object. Oxford: Oxford University Press,1997.
FIELD, H. Realism, Mathematics, and Modality. Oxford: Blackwell, 1989.
FREGE, G.Foundations of Arithmetic. Halle: L. Nebert, 1884.
GÓMEZ-TORRENTE, M. “On the Essence and Identity of Numbers". In: Theoria, XXX, pp. 317– 329, 2015.
GÓMEZ-TORRENTE, M. Roads to Reference: An Essay on Reference Fixing in Natural Language. Oxford: Oxford University Press, 2019.
GROENENDIJK, J. and STOKHOF, M. “Questions". In vAN BENTHEM, J. and TER MEULEN, A. (Eds). Handbook ofLogic and Language, pp. 1055–1124. Amsterdam: Elsevier Science, 1997.
HALE, B. and WRIGHT, C. “The Metaontology of Abstraction". In CHALMERS, D. J., MANLEY, D. and WASSERMAN, R. (Eds.). Metametaphysics, pp. 178–212. Nueva York: Oxford University Press, 2009.
KRIFKA, M. “Questions". In MAIENBORN, C. vON HEUSINGER, K. and PorTNER, P. (eds). Semantics: An International Handbook of Natural Language Meaning, Vol. 2, pp. 1742–1785. Germany: De Gruyter Moton, 2011.
KRIPKE, S. “Logicism, Wittgenstein, and De Re Beliefs About Numbers". Unpublished transcript of the Whitehead Lectures delivered at Harvard University in May of 1992.
ROSEN, G. “Nominalism, Naturalism, Epistemic Relativism". In: Philosophical Perspectives, XV, pp. 69–91, 2001.
WRIGHT, C. Frege’s Conception of Numbers as Objects. Aberdeen: Aberdeen UniversityPress, 1983.
YABLO, S. “Go Figure: A Path Through Fictionalism". Midwest Studies in Philosophy, XXV, pp. 72– 102, 2010.
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