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It seems undeniable that we can create new fictions by analogy and combination, which are merely inspired by what we take the basic structure of reality.

For example, we do not (directly) experience a quantity that could be described by a complex number, we do not experience tesseracts in our space, or loops in time. But can we not understand all this, at least to some degree?

How did Kant resolve the contradiction that we are bound by the categories yet obviously can move beyond them through fictions created by analogy and combination?

It seems that Kant in his framework would’ve needed to insist that e. g. complex numbers must be unthinkable or self-contradictory.

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  • Kant's productive imagination is operative in pure intuition, and is capable of producing all sorts of combinations beyond those in reality. We can then map them to it abstractly. For example, he could accommodate complex numbers by a geometric model, as Argand and Gauss did in his spirit. Kitcher sketches how this could be done for mathematics up to roughly mid-19th century in Kant and the Foundations of Mathematics, and argues why it would still be insufficient for modern mathematics.
    – Conifold
    Commented Jan 4, 2022 at 23:01
  • How are you sure what you experienced through sense perceptions are not same in kind and only differ in degree with fiction and analogy? According to representationalism of philosophy of mind, all we perceived are mere reflexive fictions from the universe per the reflection principle. From the perennial Shurangama sutra: With your own mind, you grasp at your own mind. What is not illusory turns into illusion. If you don’t grasp, there is no non-illusion... n this Samapatti that is likened to illusion. Transcend all study instantly... Commented Jan 5, 2022 at 2:24
  • @Conifold but you leave out “analogy”. Combination is obviously much less problematic since those concepts can be deconstructed to simple elements. Analogy would be moving from areas bound by smooth loops (that we can imagine and for which “obvious” statements, like that non-self-intersecting loops divide the plane into exterior and interior areas, are “obviously” true) to fractals.
    – viuser
    Commented Jan 5, 2022 at 5:27
  • Analogy is beside the point because we do not base reasoning on it. We can surely psychologically associate what we observe empirically to what productive imagination conjures up, or even stimulate it to conjure up something similar, but Kant is not interested in psychological motivations for this or that construction.
    – Conifold
    Commented Jan 5, 2022 at 5:32

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