Date: Jan 2, 2013 4:19 PM
Subject: Distinguishability argument x Cantor's arguments?
At the following post
I have presented the "distinguishability" argument. Which is an
argument of intuition, it is not formalizable so far. The impression
this argument imparts is that there are countably many reals?
On the other hand Cantor have presented many arguments all of which
are rigorously formalized in second order logic under full semantics,
and those arguments PROVED that there are uncountably many reals!
So which one we to believe?
The answer is Cantor's of course!
Because Cantor's arguments are very clear, and are formalizable in an
exact manner, so they are quite understandable and obvious. While the
distinguishability argument of mine is actually ambiguous and shredded
in mystery.The Consideration step in that argument and the analogy of
that with the Generalization step in that argument is really just an
intuitive leap nothing more nothing less.
This only demonstrates how common intuition fail at absolute infinity.