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Space and time live in you, not the world
💡 Space and time are the mind's own forms of intuition, which is why geometry and arithmetic can be both necessary and informative.
In the section he called the Transcendental Aesthetic, Kant makes a startling claim: space and time are not things out there, nor relations among independent objects. They are the two pure forms of intuition — the mind's built-in framework for receiving any sensory input at all.
His argument: you can imagine empty space or empty time, but you cannot imagine any object without placing it somewhere and somewhen. Space and time can't be learned from experience, because they're the precondition for having ordered experience in the first place. That's exactly why geometry (the science of space) and arithmetic (tied to time's succession) can be synthetic a priori — they describe the unavoidable form our sensibility imposes.
The consequence is radical. Space and time are 'empirically real' — perfectly valid for everything we can experience — but 'transcendentally ideal': they belong to the structure of our perceiving, not to reality as it is in itself. Remove the perceiver, and it makes no sense to ask what's 'really' spatial or temporal.
Source: Critique of Pure Reason — Immanuel Kant