One of the key passages is from Prolegomena to Any Future Metaphysics (1783). According to Kant pure intution is the means to obtain mathematical theorems as synthetic a priori propositions. This possibility
must be grounded in some pure intuition or other, in which it can present, or, as one calls it, construct all of its concepts in concreto yet a priori. (§7)
I do not see what the content of this type of intuition can be. Because Kants excludes the presence of any object as content of pure intuition. Instead he says:
There is therefore only one way possible for my intuition to precede the actuality of the object and occur as an a priori cognition, namely if it contains nothing else except the form of sensibility, which in me as subject precedes all actual impressions through which I am affected by objects. For I can know a priori that the objects of the senses can be intuited only in accordance with this form of sensibility. From this it follows: that propositions which relate merely to this form of sensory intuition will be possible and valid for objects of the senses; also, conversely, that intuitions which are possible a priori can never relate to things other than objects of our senses. (§8)
How is intuition possible without the presence of any object of intution? Of course I can make a mathematical construction only in my mind. But even then I imagine and remember some objects in question.
How can mathematical propositions be verifed by the means of pure intution?
Which mathematical propositions are obtained by pure intuition, do we have some examples?
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