Re: Should we worry about contradictions?


aatu.koskensilta@xxxxxxxxx kirjoitti:

Chip Eastham wrote:
Russell's paradox is the quintessence of Cantor's paradox,
applying the diagonal argument to the universal set to show
that it cannot be in one-to-one correspondence with its
power set.

Russell indeed was led to his paradox by reflecting on Cantor's proof.

So I think it reasonable to say "destroyed 'naive' set theory"
as it was practiced by Cantor, Dedekind, et al.

In what sense did Cantor, Dedekind and other actual set theorists
practice "'naive' set theory" that was "destroyed" by Russell's
paradox? What result of Cantor, Dedekind or any other set theorist was
invalidated by Russell's paradox?

In Peter G. Hinman`s book of logic (2005), it is said that Cantor based
his deveploment on to principles: Extensionality and Global
compherension. Well, we all know that Global compherension leads to
Russell paradox. I don`t know what is the truth about Cantor`s work and
I have read also that opinions like Hinman`s
are wrong.

.

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