Unit 2 Quiz — How Is Pure Mathematics Possible? (§§1–13)
Question 1 of 9
In Kant's terms, what makes a judgment ANALYTIC rather than synthetic?
Why does Kant hold that '7 + 5 = 12' is a synthetic judgment?
What are the two defining marks of a priori knowledge for Kant?
Which best states the guiding question of the Prolegomena and the method Kant uses to pose it?
Why must the intuition that grounds pure mathematics be a PURE intuition?
On Kant's account, what are space and time?
How does Kant's transcendental idealism differ from Berkeley's idealism?
Which pairing correctly matches transcendental idealism with its companion thesis?
✍️ Open answer · AI-graded
Reconstruct Kant's argument in Part I of the Prolegomena for how pure mathematics is possible, showing how it leads from the claim that mathematical judgments are synthetic a priori all the way to transcendental idealism. Then explain, with care, why Kant insists his idealism is not Berkeley's.
What to cover: Trace the chain: mathematics is synthetic a priori, therefore it needs pure intuition, therefore space and time are our forms of sensibility, therefore its objects are appearances. Then distinguish transcendental (formal) idealism, with its empirical realism, from Berkeley's reduction of bodies to ideas.
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