Revista Latinoamericana de Filosofia 40 (2):129-143 (2014)

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En este artículo, analizo las principales respuestas que se han dado al argumento finitista de Etchemendy, y muestro que ninguna de ellas es exitosa. Primero, describo y critico las propuestas que intentan resolverlo apelando a consideraciones modales. Estas soluciones fallan porque presuponen un finitismo demasiado débil, donde se acepta la existencia de infinitos conjuntos o de mundos posibles con infinitos objetos. Pero hay versiones más fuertes del finitismo que reintroducen el problema. Luego considero las soluciones que apelan a categorías semánticas. Una de ellas categoriza incorrectamente este problema como un desacuerdo sobre el significado de los cuantificadores. La otra solución falla porque, si fuera tomada en serio, tendría efectos muy nocivos para la lógica en general. Finalmente argumento que la mejor solución es morder la bala y aceptar que la lógica no debería ser fuertemente independiente de algunos asuntos que tradicionalmente fueron considerados como 'extralógicos'. In this paper, I analyze the main replies that have been given to Etchemendy's finitist argument, and I show that none of them is successful. First, I describe and criticize the proposals that try to solve the problem by appealing to modal considerations. These solutions fail because they presuppose a very weak finitism, where the existence of infinitely many sets, or possible words with infinitely many objects, is accepted. But there are stronger versions of finitism that reintroduce the problem. Then I consider the solutions which appeal to semantical categories. One of them incorrectly categorizes the problem as a disagreement in the meaning of the quantifiers. The other fails because, if taken seriously, it would have harmful effects on logic in general. Finally I argue that the best solution is to bite the bullet and accept that logic shouldn't be strongly independent from some issues which were traditionally considered as 'extra-logical'.
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References found in this work BETA

Philosophy of Logic.W. V. Quine - 1970 - Harvard University Press.
Does Conceivability Entail Possibility.David J. Chalmers - 2002 - In Tamar Szabo Gendler & John Hawthorne (eds.), Conceivability and Possibility. Oxford University Press. pp. 145--200.
The Concept of Truth in Formalized Languages.Alfred Tarski - 1936 - In A. Tarski (ed.), Logic, Semantics, Metamathematics. Oxford University Press. pp. 152--278.
The Concept of Logical Consequence.John Etchemendy - 1990 - Harvard University Press.
What is Mathematical Truth?Hilary Putnam - 1975 - In Mathematics, Matter and Method. Cambridge University Press. pp. 60--78.

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