This chapter explores Wittgenstein’s two references to the arts in 4.014. The first is his musical example of the unity of language and the world; the second his allusion to the fairytale The Gold-Children by Brothers Grimm. The chapter argues, first, that Wittgenstein’s early notion of logic incorporates forms that for Kant belong to transcendental aesthetic, namely, space and time. Second, it spells out how this commitment motivates Wittgenstein’s musical example and why it is crucial to draw a distinction between transcendental form and empirical structures made possible by that form. Finally, the chapter argues, pace Peter Sullivan, that the unity of language and the world is guaranteed by the metaphysical subject as their common origin. If the fairytale is read as a condensed illustration of Wittgenstein’s position, then this common origin is signified by a golden fish.

I reconstruct the preliminary arguments of the Transcendental Aesthetic, which provide the criteria of on which Kant’s central arguments will turn. Kant characterizes intuition as (i) object-giving, (ii) immediate, (iii) affection-dependent representation containing (iv) a matter of sensation that can be distinguished from (v) an a priori form. I explain Kant’s curiously teleological claim that all thought “aims at” intuition in terms of his “baseline conception” of intuition as providing nonintellectual grounds of truth: This is what it means for intuition to be object-giving. I then argue that Kant’s theory of discursive marks entails that object-giving representations must be immediate. Further, the intuition paired with a discursive intellect must be receptive (i.e. affection dependent). These claims can be justified via pure apperception. What cannot be is Kant’s characterization of intuition as sensible. But I show that Kant’s form/matter distinction and his subsequent arguments require only the receptivity of intuition, not its sensory embodiment. The chief doctrines of the Aesthetic can be justified via pure apperception, as part of a top-down approach to intuition.

Chapter 2 explains the place of mathematics in Kant’s Critique of Pure Reason. The Transcendental Aesthetic and the Axioms of intuition both make claims about mathematics that overlap and also appear inconsistent concerning the possibility and the applicability of mathematics. This has baffled prior commentators, leading them either to claim that Kant was inconsistent or to introduce distinctions to render him consistent. Two of those distinctions are between pure and applied mathematics and between general “topological” mathematics and a mathematics that includes a metric. Both these interpretations are supported by the fact that the Axioms of Intuition makes important claims about the applicability of mathematics, but the interpretations cannot be sustained. A consideration of the treatment of space and time in the Transcendental Aesthetic and the Axioms of Intuition faces parallel tensions. Examining the latter tensions points to a distinction between indeterminate space and time and determinate spaces and times as a solution, which also solves the tension concerning mathematics. This resolution allows us to see that the Axioms of Intuition concerns not just applied mathematics and not just the introduction of a metric, but all mathematics, topological or otherwise, and both pure and applied.