最終更新日：2022/12/24
Kurt Gödel is reported to have remarked ‘‘There never were any set-theoretic paradoxes, but the property-theoretic paradoxes are still unresolved.’’ The idea behind the first part of his remark is presumably that the notion of set was hierarchical from the start, so that it should have been obvious all along that there was no Russell set (in the mathematical sense of ‘set’). The idea behind the second part is that this obvious resolution of Russell’s ‘‘paradox’’ for sets simply doesn’t carry over to the paradox for properties.
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元となった例文
Kurt
Gödel
is
reported
to
have
remarked
‘‘There
never
were
any
set-theoretic
paradoxes,
but
the
property-theoretic
paradoxes
are
still
unresolved.’’
The
idea
behind
the
first
part
of
his
remark
is
presumably
that
the
notion
of
set
was
hierarchical
from
the
start,
so
that
it
should
have
been
obvious
all
along
that
there
was
no
Russell
set
(in
the
mathematical
sense
of
‘set’).
The
idea
behind
the
second
part
is
that
this
obvious
resolution
of
Russell’s
‘‘paradox’’
for
sets
simply
doesn’t
carry
over
to
the
paradox
for
properties.
