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'. (shrink)

In his classic 1936 paper Tarski sought to motivate his definition of logical consequence by appeal to the inference form: P(0), P(1), . . ., P(n), . . . therefore ∀nP(n). This is prima facie puzzling because these inferences are seemingly first-order and Tarski knew that Gödel had shown first-order proof methods to be complete, and because ∀nP(n) is not a logical consequence of P(0), P(1), . . ., P(n), . . . by Taski's proposed definition. An attempt to resolve (...) the puzzle due to Etchemendy is considered and rejected. A second attempt due to Gómez-Torrente is accepted as far as it goes, but it is argued that it raises a further puzzle of its own: it takes the plausibility of Tarski's claim that his definition captures our common concept of logical consequence to depend upon our common concept being a reductive conception. A further interpretation of what Tarski had in mind when he offered the example is proposed, using materials well known to Tarski at the time. It is argued that this interpretation makes the motivating example independent of reductive definitions which take natural numbers to be higher-order set theoretic entities, and it also explains why he did not regard the distinction between defined and primitive terms as pressing, as was the distinction between logical and nonlogical terms. (shrink)

Tarski's general conception of logic placed it at the center of all rational thought, and he took its aim to be the creation of a unified conceptual apparatus. In pursuit of this conviction, from his base at the University of California in Berkeley in the post-war years he campaigned vigorously on behalf of logic, locally, nationally and internationally. Though Tarski was ecumenical in his efforts to establish the importance of logic in these various ways, in his own work—even that part (...) of it which is considered to be philosophically significant—he was first and foremost a mathematician, and, even more so, a set-theoretical one. The paper traces this particular conception of logic back to the influence of his teachers in set theory and topology in Warsaw, and then details how it affected his explication of the notions of satisfaction, truth, logical consequence and logical term. (shrink)

Several accounts of logical truth are compared and shown to define distinct concepts. Nevertheless, conditions are given under which they happen to declare exactly the same sentences logically true. These conditions involve the variety of objects in the domain, the richness of the language, and the logical resources available. It is argued that the class of sentences declared logically true by each of the accounts depends on particularities of the actual world.