Phenomena and noumena

What do you all think of the possibility that the empty set is the
"noumenon" of Kantian philosophy? The word "noumenon" is used to refer to
the "thing in itself," which, unlike phenomena, cannot be directly known.
The argument is this:

Everything collectively reminds us of ourselves and each other, so there
must be an external world. However, consciousness is subject to brain
activity, so there is a sense in which everything we see is fundamentally
internal. Thus, as Kant would say, there is an "objective side" and a
"subjective side" of reality.

It is easy to see that nonempty sets exist as unified aggregates of objects
of perception, but there is no object of perception corresponding to the
empty set. The most fundamental use of the empty set in mathematics is to
represent negation as an object. It is the set of all objects satisfying the
negative property; e.g., "x is both odd and even." But what is the negative
property? All objects satisfy some property -- e.g., the property of
existence -- so the negative property can only exist as an abstract
construction; for example, as the conjunction of a property and its
negation. Such properties do not apply to objects of perception and
therefore must relate in some way to the noumenon (the thing in itself).

What do you think?


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Relevant Pages

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