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)

This article addresses Kant's distinction between a synthetic and an analytic method in philosophy. I will first consider how some commentators have accounted for Kant's distinction and analyze some passages in which Kant defined the analytic and the synthetic method. I will suggest that confusion about Kant's distinction arises because he uses it in at least two different senses. I will then identify a specific way in which Kant accounts for this distinction when he is differentiating between mathematical and philosophical (...) syntheses. I will examine Kant's arguments in the Critique of Pure Reason with the latter sense of the distinction in mind. I will evaluate if he uses the analytic or the synthetic method and if the synthetic method is able to identify, without a previous consideration of some sort of given knowledge, sufficient conditions for deriving some aspects of our knowledge. (shrink)

In his 1763 Prize Essay, Kant is thought to endorse a version of formalism on which mathematical concepts need not apply to extramental objects. Against this reading, I argue that the Prize Essay has sufficient resources to explain how the objective reference of mathematical concepts is secured. This account of mathematical concepts’ objective reference employs material from Wolffian philosophy. On my reading, Kant's 1763 view still falls short of his Critical view in that it does not explain the universal, unconditional (...) applicability of mathematical concepts. (shrink)