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Topic: mathematical infinite as a matter of method
Replies: 25   Last Post: May 4, 2013 11:24 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: mathematical infinite as a matter of method
Posted: May 4, 2013 8:30 PM

On May 4, 11:59 pm, fom <fomJ...@nyms.net> wrote:
> On 5/4/2013 1:21 AM, Graham Cooper wrote:
>
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>

> > On May 4, 2:17 pm, fom <fomJ...@nyms.net> wrote:
> >> On 5/3/2013 8:20 PM, Graham Cooper wrote:
>
> >>> You don't just 'choose' a foundational theory, none of ZFC holds up
> >>> to Induction, when it's derived proofs are more closely examined
> >>> there is a lot of convoluted circular reasoning...

>
> >> of the late nineteenth and twentieth century went to great pains
> >> to reject epistemology.  They are simply rediscovering it within
> >> their formalisms while continuing along that path of rejection.

>
> > Nonsense, Plato wouldn't be so unkind...
>
> > the incompleteness theorem is just a note from mum that they couldn't
> > do their homework...

>
> > ...the homework told them so...
>
> > Q1 You can't solve this!
>
> >> There are not many choices...
>
> >>http://en.wikipedia.org/wiki/M%C3%BCnchhausen_Trilemma
>
> >> At least I know why I make the choices I make.
>
> >> AxAy(xcy <-> (Az(ycz -> xcz) /\ Ez(xcz /\ -ycz)))
>
> >> AxAy(xey <-> (Az(ycz -> xez) /\ Ez(xez /\ -ycz)))
>
> >> Unfortunately, they would do you no good either.
>
> > Well with ordinary subset
>
> > xcy <-> Aa aex->aey
>
> > is sufficient to eliminate quantifiers.
>
> > Aa ...
> > and
> > { a | ... }

>
> > both mean " ALL A such that ... "
>
> > When you see a 'C'
> > in your equations there is a hidden ALL()
> > ranging over all the elements

>
> There is nothing "hidden" about it.
>
> When a mathematician begins a proof, the statement
> of the premises are to be considered as true.  Thus,
> proofs do not begin with statements containing free
> variables.
>
> Meanings are hidden when one confuses the
> product of logical analysis -- namely a language
> signature of undefined symbols -- with the
> stipulation that a theory is foundational.  In
> the latter case, the theory ought to indicate
> some means by which the primitive relations are
> recognized independent of stipulation.
>
> There is little difference between purport and
> authorial intention.  But, mathematical logic is
> supposed to frown upon intention.  Rather, the
> goal of logical analysis is to discern an
> objectively recognizable underlying logical form.
>
>
>

> > Quantified Logic and Set Theory are equivalent theories, you don't
> > need the syntax of both.

>
> When one actually uses pencil and paper,
> one knows what constitutes transformation
> rules in a proof and what constitutes
> statements to which those transformation
> rules are applied.
>
>
> And, for the record, your statement only
> holds in the sense of "set theory" obtained
> relative to the Russellian view. Cantor
> rejected the "extension of a concept"
> interpretation and attributed Russell's
>
>
>
>
>
>
>
>
>
>
>

> > ------------
>
> > AxAy(xcy <-> (Az(ycz -> xcz) /\ Ez(xcz /\ -ycz)))
>
> > RE:  ~ycz
>
> > which just means x is PROPER subset of y
>
> > I use  not(ss(..,..))
>
> > in a different way, to remove an ALL() quantifier.
>
> > ~An  p(n)    <->   En ~p(n)
>
> > Proof By Counter-Example
>
> > ----------------
>
> > e.g   p(n) <->  x MOD 2 = 0
>
> > ~An p(n)  == not all numbers are even
>
> > .........
>
> > PROOFBYCOUNTEREXAMPLE.PRO
>
> > nat(0).
> > nat(s(X)) :- nat(X).
> > even(0).
> > even(s(s(X))) :- even(X).
> > odd(s(0)).
> > odd(s(s(X))) :- odd(X).

>
> > e(A,nats) :- nat(A).
> > e(A,evens) :- even(A).
> > e(A,odds) :- odd(A).

>
> > e(A, not(evens)) :- e(A, odds).
> > e(A, not(odds)) :- e(A, evens).

>
> > intersects(S1,S2) :- e(A,S1),e(A,S2).
> > not(ss( S1 , S2 )) :- intersects( S1, not(S2) ).
> > ********************

>
> > This tiny program will work out that
>
> > ?- not(ss(nats,evens)) .
> >> YES
>
> > i.e   ~nats c evens
>
> > by actually testing 0, finding it's both nat & even,
> > testing s(0), and finding not s(0) e evens

>
> > Are all natural numbers even -> NO!
>
> > (this is early work since I didn't have to program ALL() yet!)
>
> > -------------
>
> > This kind of CATEGORICAL NEGATION
>
> > if it's ODD its not EVEN
> > if it's BLUE it's not RED

>
> > is used in human logic every day!
>
> > e(A, not(evens)) :- e(A, odds).
> > e(A, not(odds)) :- e(A, evens).

>
> > -------------
>
> > PROLOG SET THEORY is the paradigm that early logicians could only
> > glimpse a small part of the program.

>
> Some, perhaps.  Frege changed his mind.
>
> "The more I have thought the matter
> over, the more convinced I have become
> that arithmetic and geometry have
> developed on the same basis -- a
> geometrical one in fact -- so that
> mathematics in its entirety is
> really geometry"
>
>
> Negation is eliminable.

You're comparing a

T-ACCOUNTS double journal paper accounting method lecture

to M.Y.O.B. and ORACLE ACCOUNTING PACKAGES.

----

What you call LOGIC doesn't work, and doesn't do anything.

Your CONCLUSIONS of X > INF

and IF HALT(S) GOTO S

are mutually supportable piffle!

----

X e PS(N)
<->
TM_N(X) halts

...

has the SAME CONSTRUCTION METHOD as Chaitans Omega

but its a COMPUTABLE POWERSET OF N.

-----

2 birds with 1 stone!

----------------

Your EXTRA REAL is only valid with

AN INFINITE SEQUENCE OF INFERENCES.

That Paradigm is not even used with a valid set theory

(Depth First Limited)

Herc
--
www.BLoCKPROLOG.com

Date Subject Author
4/21/13 fom
4/21/13 Virgil
5/2/13 Hercules ofZeus
5/2/13 fom
5/2/13 Virgil
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Brian Q. Hutchings
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 fom
5/4/13 Graham Cooper
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
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