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Topic: ZFC is inconsistent
Replies: 54   Last Post: Mar 23, 2013 9:02 PM

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Frederick Williams

Posts: 2,164
Registered: 10/4/10
Re: ZFC is inconsistent
Posted: Mar 13, 2013 1:40 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

spermatozon@yahoo.com wrote:
>

> Now we have paradoxes like
> Russells paradox
> Banach-Tarskin paradox


Though Russell's paradox and the Banach-Tarski paradox (note the
spelling in each case) are reasonably called paradoxes, they are
paradoxes in two very different senses.

In the Russell case, a contradiction arises from a few very reasonable
(or at least reasonable-seeming) assumptions. Therefore one or more of
those assumptions must be rejected.

In the Banach-Tarski case, assuming the axiom of choice leads not to a
contradiction, but to something unexpected. If you find that unexpected
thing actually repugnant, then reject the axiom of choice. Otherwise
accept that the unexpected happens. Some mathematicians do reject the
axiom of choice, but I do not know if any have done so because of
Banach-Tarski.

I suspect that a good many, on first hearing of the Banach-Tarski
paradox, thought 'Wow! How about that! Isn't mathematics fun?' And
perhaps: 'So what happens if Choice is false? Do any loopy things happen
in that case?' Meanwhile, note that if set theory is consistent, one
may safely assume either Choice or its negation.

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting


Date Subject Author
3/13/13
Read ZFC is inconsistent
byron
3/13/13
Read Re: ZFC is inconsistent
Inverse 18 Mathematics
3/13/13
Read Re: ZFC is inconsistent
byron
3/13/13
Read Re: ZFC is inconsistent
YBM
3/23/13
Read Re: ZFC is inconsistent
Jesse F. Hughes
3/13/13
Read Re: ZFC is inconsistent
Frederick Williams
3/14/13
Read Re: ZFC is inconsistent
byron
3/15/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/15/13
Read Re: ZFC is inconsistent
YBM
3/15/13
Read Re: ZFC is inconsistent
Virgil
3/15/13
Read Re: ZFC is inconsistent
fom
3/16/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: ZFC is inconsistent
fom
3/16/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: ZFC is inconsistent
Virgil
3/17/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/17/13
Read Re: ZFC is inconsistent
Virgil
3/18/13
Read Re: ZFC is inconsistent
fom
3/18/13
Read Re: ZFC is inconsistent
fom
3/17/13
Read Re: ZFC is inconsistent
fom
3/17/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/17/13
Read Re: ZFC is inconsistent
Virgil
3/17/13
Read Re: ZFC is inconsistent
fom
3/18/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/18/13
Read Re: ZFC is inconsistent
Virgil
3/17/13
Read Re: ZFC is inconsistent
Virgil
3/18/13
Read Re: ZFC is inconsistent
fom
3/16/13
Read Re: ZFC is inconsistent
Virgil
3/16/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: ZFC is inconsistent
fom
3/16/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: ZFC is inconsistent
Virgil
3/17/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/17/13
Read Re: ZFC is inconsistent
Virgil
3/17/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/17/13
Read Re: ZFC is inconsistent
Virgil
3/17/13
Read Re: ZFC is inconsistent
fom
3/17/13
Read Re: ZFC is inconsistent
fom
3/17/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/17/13
Read Re: ZFC is inconsistent
fom
3/17/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/17/13
Read Re: ZFC is inconsistent
Virgil
3/18/13
Read Re: ZFC is inconsistent
fom
3/18/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/18/13
Read Re: ZFC is inconsistent
Virgil
3/18/13
Read Re: ZFC is inconsistent
mueckenh@rz.fh-augsburg.de
3/18/13
Read Re: ZFC is inconsistent
fom
3/18/13
Read Re: ZFC is inconsistent
Virgil
3/18/13
Read Re: ZFC is inconsistent
Virgil
3/18/13
Read Re: ZFC is inconsistent
fom
3/18/13
Read Re: ZFC is inconsistent
Virgil
3/18/13
Read Re: ZFC is inconsistent
fom
3/18/13
Read Re: ZFC is inconsistent
fom
3/17/13
Read Re: ZFC is inconsistent
Virgil
3/16/13
Read Re: WM is inconsistent
Virgil

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