Theorem: For any set P and 2-place function s if there is a number N such that for all x the value of P(x) equals P(s(N,x)) then for any r.e. set Q there is an M such that for all x, Q(x) equals P(s(M,x)).
Define a 2-place relation R as being a Base of Computing if for every r.e. set P there is an N such that P(x) = R(N,x) for all x. For example, let R(x,y) be “Turing Machine x halts on input y.” Then R is a Base of Computing. For each r.e. set P there is a Turing Machine N that halts on just the elements of that set.
When is a given R a Base of Computing, without reference to Turing Machines? The first paragraph above is the answer. R is of the form P (s(a,b)) for some set P and function s. R CONTAINS ITSELF by virtue of a number N that defines P within P: P(s(N,x)) = P(x) for all x.
Godel proved that the relation “Wff x with input y is provable.” contains itself. Turing proved “Turing Machine x halts on input y.” contains itself.
The theorem above generalizes these two observations.
This allows us to construct minimal Bases of Computing by devising P and s that meet the premise of the theorem.
Charlie-Boo <shymath...@gmail.com> writes: > Define a 2-place relation R as being a Base of Computing if for every > r.e. set P there is an N such that P(x) = R(N,x) for all x.
How do you propose to derive the parametrisation theorem from this? In any case, look up "acceptable indexing" and weep.
On Sep 16, 9:51 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> Charlie-Boo <shymath...@gmail.com> writes: > > Define a 2-place relation R as being a Base of Computing if for every > > r.e. set P there is an N such that P(x) = R(N,x) for all x.
> How do you propose to derive the parametrisation theorem from this?
Good question. How about if we add, "There is a recursive function sub such that for all x,y,z R(sub(x,y),z)=R(x,y)."?
[Sorry I just looked at this now - only 1 reply.]
> In any case, look up "acceptable indexing" and weep.
> On Sep 16, 9:51 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> > Charlie-Boo <shymath...@gmail.com> writes: > > > Define a 2-place relation R as being a Base of Computing if for every > > > r.e. set P there is an N such that P(x) = R(N,x) for all x.
> > How do you propose to derive the parametrisation theorem from this?
> Good question. How about if we add, "There is a recursive function > sub such that for all x,y,z R(sub(x,y),z)=R(x,y)."?
> [Sorry I just looked at this now - only 1 reply.]
> > In any case, look up "acceptable indexing" and weep.
> > > Charlie-Boo <shymath...@gmail.com> writes: > > > > Define a 2-place relation R as being a Base of Computing if for every > > > > r.e. set P there is an N such that P(x) = R(N,x) for all x.
> > > How do you propose to derive the parametrisation theorem from this?
> > Good question. How about if we add, "There is a recursive function > > sub such that for all x,y,z R(sub(x,y),z)=R(x,y)."?
> > [Sorry I just looked at this now - only 1 reply.]
> > > In any case, look up "acceptable indexing" and weep.
> > In any case, look up "acceptable indexing" and weep.
> It didn't seem that sad.
It moved me to tears. Did you notice, when you looked up "acceptable indexing", any hint of connection to your notion of a "base of computing", some subtle similarity? Did it perhaps whet your appetite for more, prod you into finding out for yourself what's known about this stuff?
BTW There can be no general proof of s-m-n as it depends on the syntax and semantics of the given system (base), and each is distinct otherwise it would be the same system. That's why Godel and Turing each proved it for their system only.
> > > In any case, look up "acceptable indexing" and weep.
> > It didn't seem that sad.
> It moved me to tears.
Funny you refer to "it" when nothing has been defined. Googling "acceptable indexing" produces nothing but false finds and wikipedia explicitly says there's no such thing (below.)
But you have all the confidence in the world in "it"? How can that be? What is this "it" you are referring to, anyway? Your ego, perhaps?
If you have something intelligent to say, then say it. I won't respond to ill-defined and unfounded statements or silly sarcasm anymore.
> Did you notice, when you looked up "acceptable > indexing", any hint of connection to your notion of a "base of > computing",
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You may create the page ""acceptable indexing"", but consider checking the search results below to see whether it is already cove
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Content pagesMultimediaHelp and Project pagesEverythingAdvancedResults 1 - 20 of 3,781 for acceptable indexing You may create the page "Acceptable indexing", but consider checking the search results below to see whether it is already covered.
Daru-Journal of Faculty of Pharmacy (section Indexing) Indexing : Daru is indexed and abstracted in the following bibliographical database s: Chemical Abstracts Service (CAS), http://library. ... 4 KB (514 words) - 16:52, 10 May 2009 Scrabble (section Acceptable words) unless they also appear as acceptable entries: "Jack" is a proper noun, but the ... External links - : com/en/adults/index. html Scrabble website ... 54 KB (8,420 words) - 02:40, 21 October 2009 Depth of field (section Acceptable sharpness) of field (DOF) is the portion of a scene that appears acceptably sharp in the image. ... large white index mark, the focus is set to that distance. ... 75 KB (11,649 words) - 13:43, 29 October 2009 Overfishing (section Acceptable levels) Overfishing occurs when fishing activities reduce fish stocks below an acceptable ... External links: org/sof/sofia/index_en. htm SOFIA report ... 33 KB (4,804 words) - 02:49, 21 October 2009 Placebo-controlled study (section Indexing) Indexing ... a significant level of placebo response can also prove to be an index of how much the treatment has been directed at a wrong target. ... 30 KB (4,498 words) - 20:34, 14 October 2009 Grid (spatial index) (section Grid-based spatial indexing) be assigned unique identifiers and used for spatial indexing purposes. ... may be considered a perfectly acceptable example of a spatial index ... 6 KB (878 words) - 11:12, 21 July 2009 Entity-attribute-value model system designer may consider it an acceptable alternative to creating ... with the standard indexing by class ID/attribute ID, DBMS optimizers ... 51 KB (7,994 words) - 03:36, 21 October 2009 Spark plug (section Indexing spark plugs) specified acceptable range, to ensure longer life between plug changes. ... A matter of some debate is the "indexing" of plugs upon ... 32 KB (5,174 words) - 01:23, 29 October 2009 Dave Strickler (section Compilation and indexing) 1924–1995: The Complete Index, regarded as a major reference work by researchers ... Compilation and indexing: Strickler's main source of ... 4 KB (623 words) - 23:59, 1 July 2009 IUPAC nomenclature of inorganic chemistry 2005 (section List of acceptable names) Bridging index: Where there are more than two centres that are bridged a bridging index is added as a subscript. ... List of acceptable names ... 37 KB (4,821 words) - 10:04, 8 October 2009 Enterprise content management (section Components for subject indexing of captured information) Components for subject indexing of captured information ... acceptability with unchangeable storage, protection against manipulation and erasure, etc. ... 57 KB (7,504 words) - 17:17, 28 October 2009 Acceptable.TV Acceptable. TV was a television program from the makers of Channel 101 that first aired on VH1 on March 23, 2007. ... com/news/index. ... 6 KB (786 words) - 02:37, 25 October 2009 Acceptable use policy An acceptable use policy (AUP; also sometimes acceptable usage policy or Fair Use ... uk/aup/index statement of the philosophy of the sponsor ... 12 KB (1,927 words) - 20:08, 25 October 2009 Geo targeting continue to debate about when cloaking might be acceptable and when it is not" ... References : com/help/us/ysearch/indexing/indexing-14. ... 7 KB (997 words) - 22:47, 15 August 2009 Tourism carrying capacity (section Limits of Acceptable Change) Fundamentally, acceptable conditions are a matter of human judgment ... local tolerance for tourism as described by Doxey’s Index of irritation. ... 8 KB (1,221 words) - 14:34, 28 October 2009 Drilling fluid (section Control corrosion (in acceptable level)) Control corrosion (in acceptable level): Drill-string and casing in continuous contact with drilling fluid may ... Further Reading : com/ index. php? ... 23 KB (3,576 words) - 19:43, 6 October 2009 Die Kassierer Shortly after the indexing the cover was changed, so that the LP was acceptable for sale in Germany again. Further attempts to label other ... 5 KB (695 words) - 13:10, 18 October 2009 Motorola 68020 a 68020/25 with a 68882/33 was perfectly acceptable and quite common. ... The new addressing modes added scaled indexing and another level of ... 6 KB (854 words) - 10:32, 17 September 2009 Web crawler This does not seem acceptable. ... The crawler was integrated with the indexing process, because text parsing was done for full-text indexing ... 41 KB (6,138 words) - 18:04, 29 October 2009 Branch table the input data to ensure it is acceptable; transform ing the data into ... htm Example code generated for array indexing if structure size is ... 12 KB (1,713 words) - 17:57, 28 October 2009
> some subtle similarity?
Yes, Wikipedia doesn't say anything about either.
> Did it perhaps whet your appetite > for more, prod you into finding out for yourself what's known about > this stuff?
Well, none of my 300 books on Logic, Theory of Computation, Recursion Theory, Incompleteness in Logic and Theoretical Computer Science contains my theorem, so I guess they are lagging a little behind.
Charlie-Boo <shymath...@gmail.com> writes: > On Nov 1, 1:05 pm, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
>> Did it perhaps whet your appetite for more, prod you into finding out >> for yourself what's known about this stuff?
> Well, none of my 300 books on Logic, Theory of Computation, Recursion > Theory, Incompleteness in Logic and Theoretical Computer Science > contains my theorem, so I guess they are lagging a little behind.
None of these 300 books have anything to say about acceptable indexings either? If you don't have one already, get a copy of Rogers's _Theory of Recursive Functions and Effective Computability_ and look up "acceptable indexing" in the index. The role of the parametrisation theorem will emerge from a general theorem about indexings you'll find.
On Nov 1, 1:40 pm, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> Charlie-Boo <shymath...@gmail.com> writes: > > On Nov 1, 1:05 pm, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> >> Did it perhaps whet your appetite for more, prod you into finding out > >> for yourself what's known about this stuff?
> > Well, none of my 300 books on Logic, Theory of Computation, Recursion > > Theory, Incompleteness in Logic and Theoretical Computer Science > > contains my theorem, so I guess they are lagging a little behind.
> None of these 300 books have anything to say about acceptable indexings > either? If you don't have one already, get a copy of Rogers's _Theory of > Recursive Functions and Effective Computability_ and look up "acceptable > indexing" in the index. The role of the parametrisation theorem will > emerge from a general theorem about indexings you'll find.
I'm looking at it now. What page is my theorem on?
On Nov 1, 1:40 pm, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> Charlie-Boo <shymath...@gmail.com> writes: > > On Nov 1, 1:05 pm, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> >> Did it perhaps whet your appetite for more, prod you into finding out > >> for yourself what's known about this stuff?
> > Well, none of my 300 books on Logic, Theory of Computation, Recursion > > Theory, Incompleteness in Logic and Theoretical Computer Science > > contains my theorem, so I guess they are lagging a little behind.
> None of these 300 books have anything to say about acceptable indexings > either? If you don't have one already, get a copy of Rogers's _Theory of > Recursive Functions and Effective Computability_ and look up "acceptable > indexing" in the index. The role of the parametrisation theorem will > emerge from a general theorem about indexings you'll find.
I asked, “When is a given R a Base of Computing, without reference to Turing Machines?” and point out that my definition of P does not.
The definition of acceptable indexing given by Rogers is (pg 41, 2-10), “There exists a recursive function f . . .”, which does make reference to the Turing Machines.
The point is to define a Base of Computing (Roger calls an Acceptable Indexing) self-contained (no reference to another Base of Computing) in as simple a manner as possible, as I describe in the last paragraph. Rogers does not.
Charlie-Boo <shymath...@gmail.com> writes: > The point is to define a Base of Computing (Roger calls an Acceptable > Indexing) self-contained (no reference to another Base of Computing) > in as simple a manner as possible, as I describe in the last > paragraph. Rogers does not.
Did you by any chance notice a little result relating acceptable indexings to the enumeration and parametrisation theorems? Did you ever actually /read/ (in the ordinary sense of the word) any of the 300 books you say you have?
On Nov 1, 3:10 pm, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> Charlie-Boo <shymath...@gmail.com> writes: > > The point is to define a Base of Computing (Roger calls an Acceptable > > Indexing) self-contained (no reference to another Base of Computing) > > in as simple a manner as possible, as I describe in the last > > paragraph. Rogers does not.
> Did you by any chance notice a little result relating acceptable > indexings to the enumeration and parametrisation theorems? Did you ever > actually /read/ (in the ordinary sense of the word) any of the 300 books > you say you have?
Yeah, we already went through that. So what?
BTW Rogers' Condition 1 implies condition 2. The inverse of a recursive map is recursive. (Return the smallest number that maps to it.)
> On Nov 1, 3:10 pm, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> > Charlie-Boo <shymath...@gmail.com> writes: > > > The point is to define a Base of Computing (Roger calls an Acceptable > > > Indexing) self-contained (no reference to another Base of Computing) > > > in as simple a manner as possible, as I describe in the last > > > paragraph. Rogers does not.
> > Did you by any chance notice a little result relating acceptable > > indexings to the enumeration and parametrisation theorems? Did you ever > > actually /read/ (in the ordinary sense of the word) any of the 300 books > > you say you have?
> Yeah, we already went through that. So what?
> BTW Rogers' Condition 1 implies condition 2. The inverse of a > recursive map is recursive. (Return the smallest number that maps to > it.)
> C-B
For the record, Rogers is saying essentially nothing about bases of computing in general. He defines (pg. 41), "The standard Godel numbers of 1.8 provide such a numbering [note: no s-m-n guaranteed in the definition of "numbering"]; call it pi0." Then he says IF there are recursive functions that map between the representations of the same set using pi0 and your numbering, then your numbering meets s-m- n.
But that works simply by definition of s-m-n being a recursive substitution function and the fact that composition is closed under recursive functions: the composition of recursive functions is recursive. s-m-n is really saying that "substitution is recursive" - the map from wff number A and number B to wff number C of A with B substituted for its free variables is recursive". So if you add another layer by changing the "syntax" used to represent the same set via the same "algorithm", and saying that change is recursive (map between representations), then the new substitution function is also recursive.
That would work regardless of the nature of the functions being enumerated (represented.) It is just saying that the composition of any recursive substitution function and a recursive map between a known Base of Computing (Godel's wffs of Logic) is recursive but that is true just by the statement that they are both recursive functions. Make the rest of the words anything that makes mathematical sense and it is still a true statement.
The argument is so trivial that it does not relate to the notion of defining a Base of Computing.
It is only begging the question. A recursive function over Godel's system satisfies s-m-n if/since Godel's system does.
The problem (as I stated) is to define the simplest possible conditions for a Base of Computing (self contained.)
Charlie-Boo <shymath...@gmail.com> writes: > The argument is so trivial that it does not relate to the notion of > defining a Base of Computing.
The sad fact is that you clearly don't understand the result alluded to, characterising acceptable indexings. In another message you suggested it's pointless to debate "psychopaths and abusive people". Taking this kind advice to heart, I now beat a hasty retreat, once again leaving you to your unperturbed, free to carry on with your lofty undertaking of axiomatising all of computability theory and churning out an endless stream of exciting theorems of CBL. Good luck!
On Nov 2, 8:32 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> Charlie-Boo <shymath...@gmail.com> writes: > > The argument is so trivial that it does not relate to the notion of > > defining a Base of Computing.
> The sad fact is that you clearly don't understand the result alluded to
I gave a detailed explanation. You gave none.
None of what you have said indicates or requires any understanding of Rogers' material. You only say to look at it. Well, I did. And I wrote my analysis - in detail and repeatedly explaining with different words. You only erased it and made unsubstantiated claims. If it is wrong, then refute it. Show how I am wrong when I say that his argument applies to ANY numbering of ANY functions, not just an acceptable numbering of recursive functions.
What is your "solid basis" for stating that I don't understand it? You say "clearly" - so what is the basis? If you have no basis, you meet the psychological definition of being psychotic.
It IS truly sad, Atta. You once actually posted technical points that contributed to discussions. What went wrong? How did you get so lost?
You have stooped to bogus references that you yourself cannot defend other than by being cavalier and sarcastic.
> characterising acceptable indexings. In another message you suggested > it's pointless to debate "psychopaths and abusive people". Taking this > kind advice to heart, I now beat a hasty retreat, once again leaving you > to your unperturbed, free to carry on with your lofty undertaking of > axiomatising all of computability theory and churning out an endless > stream of exciting theorems of CBL. Good luck!
Charlie-Boo <shymath...@gmail.com> writes: > Show how I am wrong when I say that his argument applies to ANY > numbering of ANY functions, not just an acceptable numbering of > recursive functions.
Well, you could just try to understand the result at issue. It doesn't merely establish that the enumeration theorem and the parametrisation theorems hold for acceptable indexings.
> It IS truly sad, Atta. You once actually posted technical points that > contributed to discussions. What went wrong? How did you get so > lost?
Who knows? I agree it's very sad when people in news debates stoop to the level of comparing others to terrorists.
On Nov 2, 10:29 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> Charlie-Boo <shymath...@gmail.com> writes: > > Show how I am wrong when I say that his argument applies to ANY > > numbering of ANY functions, not just an acceptable numbering of > > recursive functions.
> Well, you could just try to understand the result at issue. It doesn't > merely establish that the enumeration theorem and the parametrisation > theorems hold for acceptable indexings.
But "acceptable indexing" is his term, not existing and with no established significance. What is the point or value of referring to something that someone just made up with no justification?
So you say "There exist things that it does other than these quasi- theorems." but again give no basis, a continuation of your psychosis.
And you offer no refutation of my results, no matter how detailed and eplicit I make them.
> > It IS truly sad, Atta. You once actually posted technical points that > > contributed to discussions. What went wrong? How did you get so > > lost?
> Who knows? I agree it's very sad when people in news debates stoop to > the level of comparing others to terrorists.
On Nov 2, 10:29 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> Charlie-Boo <shymath...@gmail.com> writes: > > Show how I am wrong when I say that his argument applies to ANY > > numbering of ANY functions, not just an acceptable numbering of > > recursive functions.
> Well, you could just try to understand the result at issue. It doesn't > merely establish that the enumeration theorem and the parametrisation > theorems hold for acceptable indexings.
> > It IS truly sad, Atta. You once actually posted technical points that > > contributed to discussions. What went wrong? How did you get so > > lost?
> Who knows? I agree it's very sad when people in news debates stoop to > the level of comparing others to terrorists.
I appreciate the reference to Rogers, but beyond that, you speak of only silly things.
And the truth is, Rogers does not provide a self-contained (ergo simple) definition of a Base of Computing. He refers to (relies on) Godel's (huge) definition of using Logic to define the r.e. sets (a wff with a free variable represents the set of numbers that when substituted for the free variable form a provable wff.)
My definitions do not refer to any Base of Computing - it is self- contained and simple.
If you want to refer to the literature, then find very simple bases - not ones that include (by reference in the definition) big messy formalizations like Godel's. (Godel's intent was to formalize observations about Logic, not to develop the simplest possible base. He uses Logic - which is not simple - because his interest is in Logic.)
For example, Combinatory Logic is one of the simplest known bases. Also, Wolfram is said to have a simple base in his book.
But then note that their bases are still procedural - and I am attempting to use (am using) only "descriptive" definition - you have a relation that has certain properties, and infer that it is a base.
<shymath...@gmail.com> wrote: >On Nov 2, 10:29 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: >> Charlie-Boo <shymath...@gmail.com> writes: >> > Show how I am wrong when I say that his argument applies to ANY >> > numbering of ANY functions, not just an acceptable numbering of >> > recursive functions.
>> Well, you could just try to understand the result at issue. It doesn't >> merely establish that the enumeration theorem and the parametrisation >> theorems hold for acceptable indexings.
>But "acceptable indexing" is his term, not existing and with no >established significance. What is the point or value of referring to >something that someone just made up with no justification?
>So you say "There exist things that it does other than these quasi- >theorems." but again give no basis, a continuation of your psychosis.
>And you offer no refutation of my results, no matter how detailed and >eplicit I make them.
>> > It IS truly sad, Atta. You once actually posted technical points that >> > contributed to discussions. What went wrong? How did you get so >> > lost?
>> Who knows? I agree it's very sad when people in news debates stoop to >> the level of comparing others to terrorists.
>Because you are both psychotic?
Wow - you got him there, Charlie!
Very impressive, making the transition from dumb as a brick, in a "no, if something is not spelled out in words of one syllable then it doesn't exist" sort of way, to simply pathetic is just five words.
>> "Wovon mann nicht sprechen kann, darüber muss man schweigen" >> - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
David C. Ullrich
"Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to." (John Jones, "My talk about Godel to the post-grads." in sci.logic.)
> On Mon, 2 Nov 2009 10:00:33 -0800 (PST), Charlie-Boo
> <shymath...@gmail.com> wrote: > >On Nov 2, 10:29 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > >> Charlie-Boo <shymath...@gmail.com> writes: > >> > Show how I am wrong when I say that his argument applies to ANY > >> > numbering of ANY functions, not just an acceptable numbering of > >> > recursive functions.
> >> Well, you could just try to understand the result at issue. It doesn't > >> merely establish that the enumeration theorem and the parametrisation > >> theorems hold for acceptable indexings.
> >But "acceptable indexing" is his term, not existing and with no > >established significance. What is the point or value of referring to > >something that someone just made up with no justification?
> >So you say "There exist things that it does other than these quasi- > >theorems." but again give no basis, a continuation of your psychosis.
> >And you offer no refutation of my results, no matter how detailed and > >eplicit I make them.
> >> > It IS truly sad, Atta. You once actually posted technical points that > >> > contributed to discussions. What went wrong? How did you get so > >> > lost?
> >> Who knows? I agree it's very sad when people in news debates stoop to > >> the level of comparing others to terrorists.
> >Because you are both psychotic?
> Wow - you got him there, Charlie!
> Very impressive, making the transition from dumb > as a brick, in a "no, if something is not spelled out > in words of one syllable then it doesn't exist" sort > of way, to simply pathetic is just five words.
> On Mon, 2 Nov 2009 10:00:33 -0800 (PST), Charlie-Boo
> <shymath...@gmail.com> wrote: > >On Nov 2, 10:29 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > >> Charlie-Boo <shymath...@gmail.com> writes: > >> > Show how I am wrong when I say that his argument applies to ANY > >> > numbering of ANY functions, not just an acceptable numbering of > >> > recursive functions.
> >> Well, you could just try to understand the result at issue. It doesn't > >> merely establish that the enumeration theorem and the parametrisation > >> theorems hold for acceptable indexings.
> >But "acceptable indexing" is his term, not existing and with no > >established significance. What is the point or value of referring to > >something that someone just made up with no justification?
> >So you say "There exist things that it does other than these quasi- > >theorems." but again give no basis, a continuation of your psychosis.
> >And you offer no refutation of my results, no matter how detailed and > >eplicit I make them.
> >> > It IS truly sad, Atta. You once actually posted technical points that > >> > contributed to discussions. What went wrong? How did you get so > >> > lost?
> >> Who knows? I agree it's very sad when people in news debates stoop to > >> the level of comparing others to terrorists.
> >Because you are both psychotic?
> Wow - you got him there, Charlie!
> Very impressive, making the transition from dumb > as a brick, in a "no, if something is not spelled out > in words of one syllable then it doesn't exist" sort > of way, to simply pathetic is just five words.
> >> "Wovon mann nicht sprechen kann, darüber muss man schweigen" > >> - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
> David C. Ullrich
> "Understanding Godel isn't about following his formal proof. > That would make a mockery of everything Godel was up to." > (John Jones, "My talk about Godel to the post-grads." > in sci.logic.)- Hide quoted text -
<shymath...@gmail.com> wrote: >On Nov 3, 6:31 am, David C. Ullrich <dullr...@sprynet.com> wrote: >> On Mon, 2 Nov 2009 10:00:33 -0800 (PST), Charlie-Boo
>> <shymath...@gmail.com> wrote: >> >On Nov 2, 10:29 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: >> >> Charlie-Boo <shymath...@gmail.com> writes: >> >> > Show how I am wrong when I say that his argument applies to ANY >> >> > numbering of ANY functions, not just an acceptable numbering of >> >> > recursive functions.
>> >> Well, you could just try to understand the result at issue. It doesn't >> >> merely establish that the enumeration theorem and the parametrisation >> >> theorems hold for acceptable indexings.
>> >But "acceptable indexing" is his term, not existing and with no >> >established significance. What is the point or value of referring to >> >something that someone just made up with no justification?
>> >So you say "There exist things that it does other than these quasi- >> >theorems." but again give no basis, a continuation of your psychosis.
>> >And you offer no refutation of my results, no matter how detailed and >> >eplicit I make them.
>> >> > It IS truly sad, Atta. You once actually posted technical points that >> >> > contributed to discussions. What went wrong? How did you get so >> >> > lost?
>> >> Who knows? I agree it's very sad when people in news debates stoop to >> >> the level of comparing others to terrorists.
>> >Because you are both psychotic?
>> Wow - you got him there, Charlie!
>> Very impressive, making the transition from dumb >> as a brick, in a "no, if something is not spelled out >> in words of one syllable then it doesn't exist" sort >> of way, to simply pathetic is just five words.
>> >> "Wovon mann nicht sprechen kann, darüber muss man schweigen" >> >> - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
>> David C. Ullrich
>> "Understanding Godel isn't about following his formal proof. >> That would make a mockery of everything Godel was up to."
>What is the purpose of providing any proof if not for people to read >it and follow through the logic? Speaking of stupid.
Once again, this is very impressive. See, that's not something I said, it's something someone else said. Yes, it's stupid. I mean duh, look at the attribution:
>> (John Jones, "My talk about Godel to the post-grads." >> in sci.logic.)- Hide quoted text -
>> - Show quoted text -
David C. Ullrich
"Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to." (John Jones, "My talk about Godel to the post-grads." in sci.logic.)
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