How are a priori synthetic judgements possible?

Lecture 8/8. Reason, properly disciplined, draws permissible inferences from the resulting concepts of the understanding. The outcome is knowledge. When rightly employed, the perceptual and cognitive powers match up the right way with the real world and ground the knowledge-claims of the developed sciences. However, there is a strong tendency to stretch these processes beyond the permissible boundaries and seek what Kant refers to as "transcendental ideas" that go beyond the realm of actual or possible experience.

Lecture 7/8. Kant argues that: "The synthetic unity of consciousness is... an objective condition of all knowledge. It is not merely a condition that I myself require in knowing an object, but is a condition under which every intuition must stand in order to become an object for me".

Lecture 6/8. Empiricists have no explanation for how we move from "mere forms of thought" to objective concepts. The conditions necessary for the knowledge of an object require a priori categories as the enabling conditions of all human understanding.

Lecture 5/8. The very possibility of self-awareness (an "inner sense" with content) requires an awareness of an external world by way of "outer sense". Only through awareness of stable elements in the external world is self-consciousness possible.

Lecture 4/8. Kant claims that, "our sense representation is not a representation of things in themselves, but of the way in which they appear to us. Hence it follows that the propositions of geometry... cannot be referred with the assurance to actual objects; but rather that they are necessarily valid of space... [and] space is nothing else than the form of all external appearances". [Prolegomena 286-287]

Lecture 3/8. Kant's so-called "Copernican" revolution in metaphysics begins with the recognition of the observer's contribution to the observation. Thus, to the extent that Hume's empiricism restricts knowledge to experience, empiricism succeeds only by accepting the a priori grounding of experience itself.

Lecture 2/8. The significant advances in physics in the 17th century stood in vivid contrast to the stagnation of traditional metaphysics, but why should metaphysics be conceived as a "science" in the first place?

Lecture 1/8. Both sense and reason are limited. Kant must identify the proper mission and domain of each, as well as the manner in which their separate functions come to be integrated in what is finally the inter-subjectively settled knowledge of science.