Kant's solution of the problem, based mainly on the reality of
Mathematics, and especially of Geometry, is the direct opposite of
Hume's.
It will be most easy to give a clear account of Kant's solution by using
a very familiar illustration. There is a well-known common toy called a
Kaleidoscope, in which bits of coloured glass placed at one end are seen
through a small round hole at the other. The bits of glass are not
arranged in any order whatever, and by shaking the instrument may be
rearranged again and again indefinitely and still without any order
whatever. But however they may be arranged in themselves they always
form, as seen from the other end, a symmetrical pattern. The pattern
indeed varies with every shake of the instrument and consequent
re-arrangement of the bits of glass, but it is invariably symmetrical.
Now the symmetry in this case is not in the bits of glass; the colours
are there no doubt, but the symmetrical arrangement of them is not. The
symmetry is entirely due to the instrument. And if a competent enquirer
looks into the instrument and examines its construction, he will be able
to lay down with absolute certainty the laws of that symmetry which
every pattern as seen through the instrument must obey.
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