Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes

Replies: 53   Last Post: Feb 13, 2013 3:53 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Charlie-Boo

Posts: 1,582
Registered: 2/27/06
Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes

Posted: Feb 11, 2013 1:59 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Feb 9, 8:09 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Feb 10, 10:19 am, Charlie-Boo <shymath...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>

> > On Feb 7, 1:51 am, fom <fomJ...@nyms.net> wrote:
>
> > > On 2/5/2013 9:32 AM, Charlie-Boo wrote:
>
> > > > On Feb 4, 4:26 pm, fom <fomJ...@nyms.net> wrote:
> > > >> On 2/4/2013 8:46 AM, Charlie-Boo wrote:
>
> > > >>> On Feb 4, 12:25 am, fom <fomJ...@nyms.net> wrote:
> > > >>>> On 2/3/2013 10:19 PM, Charlie-Boo wrote:
> > > >>>> <snip>

>
> > > >>>>>>>> In PROLOG we use lowercase words for TERMS
> > > >>>>>>>> and uppercase words for VARIABLES

>
> > > >>>>>>>> ATOMIC PREDICATE
>
> > > >>>>>>> ATOMIC PREDICATE meaning relation?
>
> > > >>>>>>> C-B
>
> > > >>>>>> RELATION
> > > >>>>>> p(a, b, e)

>
> > > >>>>> If wffs are built on relations then { x | x ~e x } is not a wff
> > > >>>>> because ~e is not a relation.

>
> > > >>>> Well-formed formulas are built from the alphabet
> > > >>>> of a formal language.  If the language contains
> > > >>>> a symbol of negation, then NOT(xex) will be a
> > > >>>> well-formed formula.

>
> > > >>> You have to define what value a symbol may have - how it is
> > > >>> interpreted in your definition of a wff.  You need to complete B
> > > >>> below to see there is no paradox if you are consistent about what a
> > > >>> wff may contain and what values it may equal after substitution
> > > >>> (interpretation) if it contains variables for functions.

>
> > > >> First, I was not in a good mood when I posted.  So, I may
> > > >> have been too dogmatic.

>
> > > >> What you seem to be objecting to is the historical development
> > > >> of a logical calculus along the lines of Brentano and DeMorgan.

>
> > > I meant Bolzano here.
>
> > > > The only objecting in my Set Theory proposal is perhaps objecting to
> > > > the fact that ZF has a dozen messy axioms, a dozen competing
> > > > axiomatizations, a dozen interpretations of the most popular
> > > > Axiomatization, and (Wikipedia), The precise meanings of the terms
> > > > associated with the separation axioms has varied over time.  The
> > > > separation axioms have had a convoluted history, with many competing
> > > > meanings for the same term, and many competing terms for the same
> > > > concept.

>
> > > > (DeMorgan is an example of why Logic and Set Theory are the same thing
> > > > and should be combined - same as Math and Computer Science etc.)

>
> > > How do you see Logic and Set Theory as being the same?
>
> > Both are concerned with mappings to {true,false}.  A propositional
> > calculus proposition is 0-place.  A set is 1-place.  A relation is any
> > number of places.  (A relation is a set - of tuples.)

>
> > So you have the same rules of inference: Double Negative, DeMorgan
> > etc. apply to propositions and sets.

>
> > To prove incompleteness, Godel had to generalize wffs as expressing
> > propositions to expressing sets when the wff has a free variable.

>
> > C-B
>
> Yes but you change the rules of the game depending what you want to
> prove.
>
> Let:
>
> LANGUAGE 1     LANGUAGE 2
>
> seta(x)        <->       x e seta
>
> proof(x)       <->       x e proof
>
> proveby(x,y)  <->    (x,y) e proveby
>
> russell(x)      <->    not( x e x)
>
> -------------------
>
> In ZFC you "UNSTRATIFY" Russel's set
> but in all theories > PA you necessitate Godel's Statment!
>
> Sheer blindness!
>
> TOM: Jerry can't say  this sentence is true!
> JERRY:  Tom can't say this sentence is true!
>
> TOM AND JERRY ARE *INCOMPLETE* !!


There are a lot of premises there.

TOM can express "unprovable by JERRY".
TOM can express truth in JERRY. (Uh-oh, Tarski)
JERRY can express "unprovable by TOM".
JERRY can express truth in TOM. (Uh-oh, Tarski)

But I use CBL where this is all easily formalized.

C-B

> must be unrelated to logic!
>
> Herc
> --www.BLoCKPROLOG.com




Date Subject Author
2/1/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/3/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/3/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/3/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/3/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/3/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/3/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/3/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/3/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/3/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
camgirls@hush.com
2/4/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/4/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
billh04
2/4/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/4/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle to Resolve Several Paradoxes
William Hale
2/4/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle to Resolve Several Paradoxes
Lord Androcles, Zeroth Earl of Medway
2/9/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/5/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/4/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/5/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/5/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/5/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Brian Q. Hutchings
2/6/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/6/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/4/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
fom
2/4/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/4/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
fom
2/5/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/7/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
fom
2/9/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/9/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/11/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/10/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
fom
2/10/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/10/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
fom
2/10/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/11/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/11/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/11/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/11/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/13/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/11/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/11/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
fom
2/5/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/5/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
fom
2/6/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
fom
2/11/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/11/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
fom
2/13/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/13/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
fom
2/4/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Graham Cooper
2/4/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo
2/5/13
Read Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Charlie-Boo

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.