Re: Why? [was Re: Cantor`s powerset theorem is false?]

david petry wrote:
MoeBlee wrote:
david petry wrote:
Patricia Shanahan wrote:

I've become curious about why so many people seem to want to disprove
Cantor's Theorem. It's a recurring theme in this newsgroup.

It's been going on for many years. Few people are really articulate
about why they want to disprove the theorem, but I believe it's because
Cantor's theorem appears to imply the existence of a world beyond what
common sense would suggest really exists.

Cantor's theorem is implied by the axioms of set theory, so whatever
world beyond common sense is implied, it is implied by the axioms.

Boring.

You made a comment that is better understand in the context I provided.
Entertaining you is not my purpose.

For
finite sets, Cantor's theorem is EXACTLY what common sense tells us.

Boring.

You're the one who mentioned "common sense".

And for infinite sets, Cantor's theorem tells us that infinite sets are
just like finite sets as regards the particular feature that there is
no bijection between a set and its power set.

But that's a matter of faith.

No, it's a matter of deduction from axioms. How one regards the axioms
beyond formal syntax and formal semantics is a matter of one's
mathematical philosophy.

For finite sets, we can observe that
property. Not so with infinite sets.

And it's boring.

We deduce the property for infinite sets. And we even deduce that
property for ALL finite sets as opposed to just observing it for
certain finite sets.

And your grunts of "boring" are boring.

MoeBlee

.

Relevant Pages

  • Re: Why? [was Re: Cantor`s powerset theorem is false?]
    ... Few people are really articulate ... Cantor's theorem is implied by the axioms of set theory, ... world beyond common sense is implied, it is implied by the axioms. ... finite sets, Cantor's theorem is EXACTLY what common sense tells us. ...
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  • Re: Why? [was Re: Cantor`s powerset theorem is false?]
    ... Cantor's theorem is implied by the axioms of set theory, ... world beyond common sense is implied, it is implied by the axioms. ... finite sets, Cantor's theorem is EXACTLY what common sense tells us. ... And for infinite sets, Cantor's theorem tells us that infinite sets are ...
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