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

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byron

Posts: 865
Registered: 3/3/09
Re: ZFC is inconsistent
Posted: Mar 14, 2013 12:42 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Thursday, March 14, 2013 4:40:18 AM UTC+11, Frederick Williams wrote:
> 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


yes

but
zfc is inconsistent
zfc bans impredicatice statements
but
is impredicative itsels
so
it bans itself
thus
zfc is inconsistent


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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