system
Given the following post, respond as if you're commenting on Reddit:
human
What does synthetic a priori knowledge have to do with the thing-in-itself?

In other words … how do they relate to each other? These are two separate, but related, theories, right? According to Kant, the thing-in-itself is impossible to know, but any possibility of metaphysical knowledge will be that of the synthetic a priori variety. Thanks. I'll hang up and listen.
gpt
Synthetic a priori knowledge, for Kant, is possible because of our a priori intuition of space and time. These are intuitions, and have to do with both our experience of objects and the possibility of experience in general. In the schematism, Kant explains how we can use these a priori intuitions of space and time to apply the categories according to "schemata," which are something in the imagination that provides something like a "rule" or a "blueprint" for an object. For example, Kant says, the schema for a plate would be "circle."

So how does this apply to examples like mathematics? The idea of number would fall under the category of quantity, and its schema is based off sequence in time (a priori intuition). The schema isn't a picture in your head, because you can picture five things in your head, but not a thousand, yet five and a thousand can both be imaginatively constructed using the same number schema. This schema serves as a kind of "middle term" that brings together your a priori intuition of space/time (say, the time it would take to count to ten, the temporal sequence) with the category of the understanding (quantity) and applies it as a rule for sensations (numbers are constructed in sequence according to a rule). This is also, for Kant, how we construct ideas like "dog" as a rule that classifies a diverse amount of sensations as a "dog." The schema "dog" is a certain rule that organizes our sensations into the experience of a dog.

Yet because we need both the intuitions and the concepts, that is, both the *a priori* conditions of space and time **and** the categories, neither pure intuition alone nor the pure application of categories can supply us with a priori knowledge.

Since the *a priori* conditions of space and time are conditions of receptivity (the sensations we receive), not spontaneity (the categories we think), there's something "outside" of the manifold that we're experiencing (the thing in-itself), yet we cannot apply concepts to it, because there's no schema to allow this.

Thus, Kant famously writes:

>Thoughts without content are empty, intuitions without content are blind.

We can *think* the thing in-itself, and we know it must exist, but because our intuition of space and time is what makes *a priori synthesis* and the application of the categories possible, we can't know what things are like prior to our spatio-temporal intuition.

Edit: Only a being with **intellectual intuition** (like God, for example) could ask about, say, the idea of "things in general" (not just spatio-temporal things), and then ask if "every thing has its cause." Because we can only apply the concept of cause based on the schema, and this involves the spatio-temporal intuition of an irreversible ordered sequence. Likewise, we cannot ask whether the thing in-itself is a "cause," because this would require us to know how to apply the causality to non-temporal, non-spatial things, again requiring intellectual intuition.