Kant's first critique, Videos 32-36

This document will cover comments and notes on a series of videos on the critique by Victor Gijsberts.
here is an excerpt taken for the description of video 32:

Wait, where are videos 29, 30 and 31? Due to illness, holiday and the pressure to continue my course, I've had to leave a gap for three videos finishing up the B Deduction. I'll fill that gap sooner or later, but first we continue on with the Analytic of Principles!

Video 32, Introduction to the Analytic of Principles

To repeat from earlier in the book,
We have concepts defined by the categories. Concepts can be combined by the understanding into judgements. Judgements in reason are become inferences.
The analytic of principles speaks of the possibility for synthetic a priori judgements.

Humans have the fundamental capacity to follow rules. This ability is crucial to the functioning of our understanding. This capacity is discussed twofold in the analytic of principles.

Video 33, The Schematism

The schematism discusses how we can apply the understanding to intuition. More specifically, we have general categories as defined in the transcendental Deduction, which are separate form our spacio-temporal sensibility. The transcendental schema is what connects the categories to human cognition.

The schema of an object is the rule for generating that object. In this sense, it is a compromise between the general concept and particular object. The Schemata therefore closely mirror the categories.

Video 34, System of all Principles

The supreme principle of analytic cognition is that of non-contradiction. This principle allows us to make truth claims in pure logic. The formulation of this principle should not contain time for this is a synthetic concept.
The supreme principle of synthetic cognition does contain time as it includes the possibility of experience. It is therefore formulated as; “every object stands under the necessary condition of the synthetic unity of the manifold of intuition”. Thus, what makes experience possible, also makes the object of experience possible.

Video 35, Axioms of Intuition

The axioms of intuition are based on the fact that all intuitions are extensive magnitudes. They are then filled in by mathematics. All appearances are in space and time and therefore only graspable through the synthesis of the manifold. Spacio-Temporal objects are only graspable through the same process that we group space and time themselves. When we do this, we homogenize atomic-time-magnitudes into an extended magnitude. Because of this, mathematics are applicable to spacio-temporal objects.

Video 36, Anticipations of Perception

In this part, Kant speaks of what happens when something appears to us. An appearance can have an intensive magnitude or an extensive magnitude. An intensive magnitude is not a manifold such as pain or brightness, which cannot be separated by number. Intensive magnitudes can only vary in intensity.
An extensive magnitude occurs when we perceive a manifold such as the perception of a house which can be separated into its constituent parts. Mathematics can be applied to both of these appearances.