Goede's theorem and consistent units.
V.Gopal
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.
Neil W Rickert
>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.
Then you failed to find it.
Dirk Bruere
"Neil W Rickert" <ricke...@cs.niu.edu> wrote in message
news:anj2qr$ha1$1...@husk.cso.niu.edu...
> vgop...@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.
>
Dirk
R. Srinivasan
("Inertial frames, special relativity and consistency") available at:
http://philsci-archive.pitt.edu/documents/disk0/00/00/06/66/index.html
See also the relativity papers of Prof. Hajnal Andreka and his group
at:
http://www.math-inst.hu/pub/algebraic-logic/Contents.html#newrelat
Sincerely,
R. Srinivasan srad...@in.ibm.com
David C. Ullrich
>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
Uncle Al
>
> 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!
Dirk Bruere
"R. Srinivasan" <srad...@in.ibm.com> wrote in message
news:f8cdd05c.02100...@posting.google.com...
It really depends on what form a TOE might take, and what type of
mathematics is used.
Dirk
V.Gopal
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.
Neil W Rickert
>Yet.
When Goedel's theorem becomes relevant to physics, physic
will have become irrelevant.
Neil W Rickert
>"Dirk Bruere" <di...@neopax.com> wrote in message news:<anjcq0$el7rh$1...@ID-120108.news.dfncis.de>...
>> "Neil W Rickert" <ricke...@cs.niu.edu> wrote in message
>> news:anj2qr$ha1$1...@husk.cso.niu.edu...
>> > vgop...@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.
Neil W Rickert
>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
No - physics will have become even more interesting.
Dirk
R. Srinivasan
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.
Sincerely,
R. Srinivasan srad...@in.ibm.com
R. Srinivasan
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.
Sincerely,
R. Srinivasan srad...@in.ibm.com
V.Gopal
and what type of mathematics is used. Here everything means,
everything not only in physics but in all areas of enquiry, including
economics.
V.Gopal
Physics will have become Omniscience!