[FOM] Who was the first to accept undefinable individuals in mathematics?
W. Mueckenheim
mueckenh at rz.fh-augsburg.de
Tue Mar 10 08:38:37 EDT 2009
Until the end of the nineteenth century mathematicans dealt with
definable numbers only. This was the most natural thing in the world.
An example can be found in a letter from Cantor to Hilbert, dated
August 6, 1906: "Infinite definitions (that do not happen in finite
time) are non-things. If Koenigs theorem was correct, according to
which all finitely definable numbers form a set of cardinality
aleph_0, this would imply that the whole continuum was countable, and
that is certainly false." Today we know that Cantor was wrong and
that an uncountable continuum implies the existence of undefinable numbers.
Who was the first mathematician to deliberately accept undefinable
individuals like real numbers in mathematics?
Regards, WM
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