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Replies: 92   Last Post: Mar 15, 2008 12:59 AM

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 Marshall Posts: 1,936 Registered: 8/9/06
Posted: Mar 10, 2008 1:46 PM

On Mar 9, 7:00 pm, magi...@math.berkeley.edu (Arturo Magidin) wrote:
>
> >> Proof by contradiction can be formalized as
>
> >> (P -> (A and not(A))) -> not(P).
[...]
> The proof in question, in fact, does not even use proof by
> contradiction. It has the form
>
> (P -> not(P)) -> not(P).
>
> This is not a proof by contradiction.

Does the second one have a name?

Superficially, the two formulas appear similar. Certainly they
evoke a similar sense. Is there any sense in which we might
consider an antecedent as being in-scope in the consequent,
which would allow us to connect the two? Or is the relationship
a superficial structural similarity merely?

Does anything interesting happen if we transform them somewhat?

(P -> (A and not(A))) -> not(P)
(P -> false) -> not(P).
(not(P) or false) -> not(P)
not(P) -> not(P)

Well, I seem to have destroyed the formula's essential nature
by these manipulations. How did THAT happen? Apparently
truth-value-preserving transformations don't preserve some things
that aren't truth values.

Marshall

Date Subject Author
3/9/08 goodchild.trevor@gmail.com
3/9/08 magidin@math.berkeley.edu
3/10/08 LudovicoVan
3/10/08 Aatu Koskensilta
3/10/08 LudovicoVan
3/10/08 Aatu Koskensilta
3/10/08 LudovicoVan
3/10/08 Aatu Koskensilta
3/10/08 LudovicoVan
3/10/08 LudovicoVan
3/10/08 G. Frege
3/10/08 LudovicoVan
3/9/08 fishfry
3/10/08 LudovicoVan
3/9/08 goodchild.trevor@gmail.com
3/9/08 Aatu Koskensilta
3/9/08 goodchild.trevor@gmail.com
3/9/08 donstockbauer@hotmail.com
3/10/08 LudovicoVan
3/9/08 Aatu Koskensilta
3/9/08 magidin@math.berkeley.edu
3/9/08 Aatu Koskensilta
3/10/08 magidin@math.berkeley.edu
3/10/08 Aatu Koskensilta
3/10/08 magidin@math.berkeley.edu
3/10/08 Herman Jurjus
3/10/08 Aatu Koskensilta
3/10/08 Herman Jurjus
3/10/08 Aatu Koskensilta
3/10/08 LudovicoVan
3/10/08 goodchild.trevor@gmail.com
3/10/08 goodchild.trevor@gmail.com
3/10/08 LudovicoVan
3/10/08 magidin@math.berkeley.edu
3/10/08 Marshall
3/10/08 G. Frege
3/10/08 G. Frege
3/10/08 LudovicoVan
3/11/08 Marshall
3/11/08 magidin@math.berkeley.edu
3/11/08 G. Frege
3/11/08 magidin@math.berkeley.edu
3/12/08 G. Frege
3/13/08 magidin@math.berkeley.edu
3/12/08 magidin@math.berkeley.edu
3/12/08 pn4039@albany.edu
3/12/08 Jack Markan
3/12/08 G. Frege
3/13/08 pn4039@albany.edu
3/13/08 magidin@math.berkeley.edu
3/13/08 G. Frege
3/14/08 pn4039@albany.edu
3/14/08 G. Frege
3/14/08 magidin@math.berkeley.edu
3/14/08 G. Frege
3/14/08 Michael Press
3/13/08 Timothy Murphy
3/13/08 Marshall
3/13/08 Timothy Murphy
3/13/08 quasi
3/13/08 quasi
3/13/08 quasi
3/13/08 quasi
3/14/08 Timothy Murphy
3/12/08 G. Frege
3/13/08 LudovicoVan
3/13/08 LudovicoVan
3/13/08 LudovicoVan
3/13/08 G. Frege
3/13/08 LudovicoVan
3/11/08 G. Frege
3/15/08 Tim Little
3/9/08 goodchild.trevor@gmail.com
3/10/08 G. Frege
3/10/08 LudovicoVan
3/10/08 G. Frege
3/10/08 G. Frege
3/10/08 LudovicoVan
3/10/08 Aatu Koskensilta
3/10/08 LudovicoVan
3/12/08 pn4039@albany.edu
3/12/08 G. Frege
3/13/08 LudovicoVan
3/13/08 Marshall
3/13/08 LudovicoVan
3/12/08 Jack Markan
3/10/08 G. Frege
3/10/08 G. Frege
3/10/08 Jesse F. Hughes
3/10/08 G. Frege
3/10/08 G. Frege
3/10/08 LudovicoVan
3/10/08 G. Frege