Defences of Kant's foundations of geometry fall short if they are unable to equally ground Euclidean and non-Euclidean geometries. Thus, Kant's account must be separated from geometrical postulates. I argue that characterizing space as the form of outer intuition must be independent of postulates. Geometrical postulates are then expressions of particular spatializing activities made possible by the a priori intuition of space. While Amit Hagar contends that this is to speak of noumena, I argue that a Kantian account of space (...) as the form of outer attention-directing remains seated in the subject. (shrink)

According to Kant, we gain mathematical knowledge by constructing objects in pure intuition. This is true not only of geometry but arithmetic and algebra as well. Construction has prominent place in scholarly accounts of Kant’s views of mathematics. But did Kant have a clear vision of what construction is? The paper argues that Kant employed two different, even conflicting models of construction, depending on the philosophical issue he was dealing with. In the equivalence model, Kant claims that the object constructed (...) in intuition is equivalent to the properties included in the conceptual rule. In the overstepping model of construction, Kant argues that construction goes beyond the concept which is a “mere definition”. What is more, both models of construction can be found in the Doctrine of Method in the first Critique. The paper examines reasons that have led Kant to adopt the two models of construction, and proposes a reading that alleviates the apparent contradiction between the two models. (shrink)

It would seem that some statements like ‘There are exactly four moons of Jupiter’ and ‘The number of moons of Jupiter is four’ have the same truth-conditions and yet differ in ontological commitment. One strategy to resolve this paradoxical phenomenon is to insist that the statements have not only the same truth-conditions but also the same ontological commitments; the other strategy is to reject the presumption that they have the same truth-conditions. This paper critically examines some popular versions of these (...) two strategies, and defends a new solution according to which the statements have the same ontological commitments and yet differ in truth-conditions. (shrink)

This paper considers Kant's understanding of conceptual representation in light of his view of geometry.

El objetivo del presente artículo es ofrecer una interpretación de la doctrina del esquematismo de los conceptos empíricos y matemáticos presentada por Kant en su Crítica de la razón pura. Mostramos que los esquemas de los conceptos empíricos y matemáticos son procedimientos de síntesis gobernados por reglas conceptuales. Aunque no consideramos que esta doctrina kantiana carece de problemas, nuestro trabajo muestra que: 1) esos esquemas pueden distinguirse rigurosamente de sus correspondientes conceptos; 2) esos esquemas no son entidades superfluas. Estas conclusiones (...) se alcanzan mostrando que el contenido de un concepto determina la unidad de elementos sensibles que tiene que ser efectuada por un esquema en tanto procedimiento de síntesis. (shrink)