Goedel's theorems are basd on self-referential consequences of requirement of CONSISTENCY in a CONSISTENT system. Here something remains unprovable. Geodel's theorem has direct impact on physics. If a quantity X is supposed to be compact continuous and consistent then its compactness, continuity and consistency cannot be proved between 0 and 1 or within unit!Then which part of the quantity is compact, continuous and consistent? It means, if acceleration is uniform and continuous between T=0 to T=10 units of time, then uniformity and continuity cannot be proved within unit of time. (Then, when is acceleration uniform and continuous?) Consistency within a consistent system is unprovable. Similarly, during an analysis when we talk of FACTS ABOUT FACTS the analysis cannot begin, proceed and end, exclusively with provable facts. TRUE------>NOT PROVABLE. Provable----->Not true! I am in search of the truth and not the provable.
vgopa...@rediffmail.com (V.Gopal) writes: >Goedel's theorems are basd on self-referential consequences of >requirement of CONSISTENCY in a CONSISTENT system. Here something >remains unprovable. Geodel's theorem has direct impact on physics. If
Goedel's theorem is of no relevance to physics.
> TRUE------>NOT PROVABLE. Provable----->Not true! >I am in search of the truth and not the provable.
> >Goedel's theorems are basd on self-referential consequences of > >requirement of CONSISTENCY in a CONSISTENT system. Here something > >remains unprovable. Geodel's theorem has direct impact on physics. If
> > >Goedel's theorems are basd on self-referential consequences of > > >requirement of CONSISTENCY in a CONSISTENT system. Here something > > >remains unprovable. Geodel's theorem has direct impact on physics. If
> > Goedel's theorem is of no relevance to physics.
> Yet.
Don't agree with this. See my preprint PITT-PHIL-SCI00000666 ("Inertial frames, special relativity and consistency") available at:
On 3 Oct 2002 20:32:17 -0700, vgopa...@rediffmail.com (V.Gopal) wrote:
>Goedel's theorems are basd on self-referential consequences of >requirement of CONSISTENCY in a CONSISTENT system. Here something >remains unprovable. Geodel's theorem has direct impact on physics.
I doubt it.
> If >a quantity X is supposed to be compact continuous and consistent
Talking about a "quantity" being "consistent" is gibberish. Theories are consistent or not, not quantities.
> then >its compactness, continuity and consistency cannot be proved between 0 >and 1 or within unit!Then which part of the quantity is compact, >continuous and consistent? It means, if acceleration is uniform and >continuous between T=0 to T=10 units of time, then uniformity and >continuity cannot be proved within unit of time. (Then, when is >acceleration uniform and continuous?) Consistency within a consistent >system is unprovable. Similarly, during an analysis when we talk of >FACTS ABOUT FACTS the analysis cannot begin, proceed and end, >exclusively with provable facts. > TRUE------>NOT PROVABLE. Provable----->Not true! >I am in search of the truth and not the provable.
> Goedel's theorems are basd on self-referential consequences of > requirement of CONSISTENCY in a CONSISTENT system. Here something > remains unprovable. Geodel's theorem has direct impact on physics.
You are so right. Godel's theorem impacting physics remains unproven. Why did you keep typing?
[snip]
> I am in search of the truth and not the provable.
Good. Go away and join a church. Every one of them has a direct line to the REVEALED truth, and a book to prove it.
-- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) "Quis custodiet ipsos custodes?" The Net!
> > > >Goedel's theorems are basd on self-referential consequences of > > > >requirement of CONSISTENCY in a CONSISTENT system. Here something > > > >remains unprovable. Geodel's theorem has direct impact on physics. If
> > > Goedel's theorem is of no relevance to physics.
> On 3 Oct 2002 20:32:17 -0700, vgopa...@rediffmail.com (V.Gopal) wrote:
> >Goedel's theorems are basd on self-referential consequences of > >requirement of CONSISTENCY in a CONSISTENT system. Here something > >remains unprovable. Geodel's theorem has direct impact on physics.
> I doubt it.
> > If > >a quantity X is supposed to be compact continuous and consistent
> Talking about a "quantity" being "consistent" is gibberish. Theories > are consistent or not, not quantities.
> > then > >its compactness, continuity and consistency cannot be proved between 0 > >and 1 or within unit!Then which part of the quantity is compact, > >continuous and consistent? It means, if acceleration is uniform and > >continuous between T=0 to T=10 units of time, then uniformity and > >continuity cannot be proved within unit of time. (Then, when is > >acceleration uniform and continuous?) Consistency within a consistent > >system is unprovable. Similarly, during an analysis when we talk of > >FACTS ABOUT FACTS the analysis cannot begin, proceed and end, > >exclusively with provable facts. > > TRUE------>NOT PROVABLE. Provable----->Not true! > >I am in search of the truth and not the provable.
> David C. Ullrich
In physics even before you start correlating verious physical quantities, say, mass, length, force or energy etc., the first thing you have to do is to assume that unit of each and everything (and unit of every size) is homogeneous, continuous and consistent. Without this assumption no calculation is logically correct.
"Dirk Bruere" <d...@neopax.com> writes: >"Neil W Rickert" <rickert...@cs.niu.edu> wrote in message >news:anj2qr$ha1$1@husk.cso.niu.edu... >> vgopa...@rediffmail.com (V.Gopal) writes: >> >Goedel's theorems are basd on self-referential consequences of >> >requirement of CONSISTENCY in a CONSISTENT system. Here something >> >remains unprovable. Geodel's theorem has direct impact on physics. If >> Goedel's theorem is of no relevance to physics. >Yet.
When Goedel's theorem becomes relevant to physics, physic will have become irrelevant.
sradh...@in.ibm.com (R. Srinivasan) writes: >"Dirk Bruere" <d...@neopax.com> wrote in message <news:anjcq0$el7rh$1@ID-120108.news.dfncis.de>... >> "Neil W Rickert" <rickert...@cs.niu.edu> wrote in message >> news:anj2qr$ha1$1@husk.cso.niu.edu... >> > vgopa...@rediffmail.com (V.Gopal) writes: >> > >Goedel's theorems are basd on self-referential consequences of >> > >requirement of CONSISTENCY in a CONSISTENT system. Here something >> > >remains unprovable. Geodel's theorem has direct impact on physics. If >> > Goedel's theorem is of no relevance to physics. >> Yet. >Don't agree with this. See my preprint PITT-PHIL-SCI00000666 >("Inertial frames, special relativity and consistency") available at: >http://philsci-archive.pitt.edu/documents/disk0/00/00/06/66/index.html
The question that is stated to be undecidable is not a physics question. That it is expressed using the terminology of physics does not make it a question of physics.
vgopa...@rediffmail.com (V.Gopal) writes: >In physics even before you start correlating verious physical >quantities, say, mass, length, force or energy etc., the first thing >you have to do is to assume that unit of each and everything (and unit >of every size) is homogeneous, continuous and consistent. Without this >assumption no calculation is logically correct.
The last time I checked, physicists were still involved in developing their own systems of units. They were not taking something for granted and making assumptions about it.
> "Dirk Bruere" <d...@neopax.com> writes: > >"Neil W Rickert" <rickert...@cs.niu.edu> wrote in message > >news:anj2qr$ha1$1@husk.cso.niu.edu... > >> vgopa...@rediffmail.com (V.Gopal) writes:
> >> >Goedel's theorems are basd on self-referential consequences of > >> >requirement of CONSISTENCY in a CONSISTENT system. Here something > >> >remains unprovable. Geodel's theorem has direct impact on physics. If
> >> Goedel's theorem is of no relevance to physics.
> >Yet.
> When Goedel's theorem becomes relevant to physics, physic > will have become irrelevant.
No - physics will have become even more interesting.
> >> > >Goedel's theorems are basd on self-referential consequences of > >> > >requirement of CONSISTENCY in a CONSISTENT system. Here something > >> > >remains unprovable. Geodel's theorem has direct impact on physics. If
> >> > Goedel's theorem is of no relevance to physics.
> >> Yet.
> >Don't agree with this. See my preprint PITT-PHIL-SCI00000666 > >("Inertial frames, special relativity and consistency") available at:
> The question that is stated to be undecidable is not a physics > question. That it is expressed using the terminology of physics > does not make it a question of physics.
The question referred to is the proposition P, defined as "F is an inertial frame in U(IBC)", where U is a universe of material objects (point masses) and IBC are appropriate initial-boundary conditions. My preprint establishes that if the theory SR (as defined in my preprint) is consistent, then P is undecidable in SR.
It is true that my paper is written in informal terms, and it may appear at first sight that P is not a physics question. But it is easy to state P, in equivalent terms, as the proposition R defined as: "Particle A in U(IBC) has zero acceleration for all times". It is clear that A must be attached to a frame of reference F which must be inertial, by the above formulation. So R and P are equivalent and R is clearly a physics question. One could also specify (in the proposition R) any time-dependent acceleration for particle A, and one could still deduce from this that R is equivalent to assuming a certain frame F as inertial.
As I have stated in my preprint, I need to formalize my argument. I am trying to understand the formidable amount of work done by Prof. Andreka and his group in order to accomplish this task.
Of course, you can question my (and Prof. Andreka's) assumption that classical first order logic (in which Goedel's theorems are formulated) is the appropriate logic in which SR should be formalized. Prof. Andreka and co-workers do offer some justification for this assumption in their papers.
> > > > >Goedel's theorems are basd on self-referential consequences of > > > > >requirement of CONSISTENCY in a CONSISTENT system. Here something > > > > >remains unprovable. Geodel's theorem has direct impact on physics. If
> > > > Goedel's theorem is of no relevance to physics.
> > > Yet.
> > Don't agree with this. See my preprint PITT-PHIL-SCI00000666 > > ("Inertial frames, special relativity and consistency") available at:
> It really depends on what form a TOE might take, and what type of > mathematics is used.
> Dirk
You are right. An assumption in the above papers is that special relativity theory can be formalized in classical first-order logic (in which Goedel's theorems are formulated). Not being an expert on Goedel, I don't know much about whether Goedel's theorems can be (or have been) extended to other logics.
> > > > > >Goedel's theorems are basd on self-referential consequences of > > > > > >requirement of CONSISTENCY in a CONSISTENT system. Here something > > > > > >remains unprovable. Geodel's theorem has direct impact on physics. If
> > > > > Goedel's theorem is of no relevance to physics.
> > > > Yet.
> > > Don't agree with this. See my preprint PITT-PHIL-SCI00000666 > > > ("Inertial frames, special relativity and consistency") available at:
> > It really depends on what form a TOE might take, and what type of > > mathematics is used.
> > Dirk
> You are right. An assumption in the above papers is that special > relativity theory can be formalized in classical first-order logic (in > which Goedel's theorems are formulated). Not being an expert on > Goedel, I don't know much about whether Goedel's theorems can be (or > have been) extended to other logics.
I fully agree that everything depends on what form a TOE MIGHT take and what type of mathematics is used. Here everything means, everything not only in physics but in all areas of enquiry, including economics.
> > >> >Goedel's theorems are basd on self-referential consequences of > > >> >requirement of CONSISTENCY in a CONSISTENT system. Here something > > >> >remains unprovable. Geodel's theorem has direct impact on physics. If
> > >> Goedel's theorem is of no relevance to physics.
> > >Yet.
> > When Goedel's theorem becomes relevant to physics, physic > > will have become irrelevant.
> No - physics will have become even more interesting.
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