On Wed, 27 Nov 2002, Ken Hirsch wrote:
Jim Choate writes:
It's not I who is doing the misreading. I sent this along because I don't
know -your- level, which considering your understanding of
'completeness'...
Peter Fairbrother has said nothing inaccurate about completeness, whereas
Jim Choate wrote:
Para-consistent logic is the study of logical schemas or
systems in which the fundamental paradigms are paradoxes. It's a way of
dealing with logical situations in which true/false can't be determined
even axiomatically.
Most paraconsistent logics deal with paradoxes, but I
On Wed, 20 Nov 2002, Peter Fairbrother wrote:
Completeness has nothing to do with whether statements can or cannot be
expressed within a system.
A system is complete if every sentence that is valid within the system can
be proved within that system.
Introduction to Languages, Machines and
Jim Choate wrote:
On Wed, 13 Nov 2002, Tyler Durden wrote:
Damn what a pack of geeks! (Looks like I might end up liking this list!)
When we say complete, are we talking about completeness in the Godelian
sense? According to Godel, and formal system (except for the possibility of
the
On Wed, 13 Nov 2002, Tyler Durden wrote:
used for useful computation will suffer from incompletenenss, so I would
assume para-consistent logic would fall under that category (is that
similar to fuzzy logic?).
Not really. Para-consistent logic is the study of logical schemas or
systems in
On Wed, 13 Nov 2002, Tyler Durden wrote:
Damn what a pack of geeks! (Looks like I might end up liking this list!)
When we say complete, are we talking about completeness in the Godelian
sense? According to Godel, and formal system (except for the possibility of
the oddballs mentioned
On Wed, 13 Nov 2002, Ben Laurie wrote:
Jim Choate wrote:
What I'd like to know is does Godel's apply to all forms of
para-consistent logic as well
It applies to any sufficiently complex axiomatic system. Allegedly.
Actually it doesn't, it applied to 'complete' systems. There is -no-
Fernandes Esteves [EMAIL PROTECTED], Mike Rosing
[EMAIL PROTECTED]
CC: Cypherpunks [EMAIL PROTECTED]
Subject: Re: The End of the Golden Age of Crypto
Date: Thu, 14 Nov 2002 19:41:40 -0500
From: Andri Isidoro Fernandes Esteves [EMAIL PROTECTED]
Date: Thu, 14 Nov 2002 14:31:41 +
To: Mike Rosing
On Friday 15 November 2002 01:43, Sam Ritchie wrote:
Actually, hehe, I've made this comparison before, of religion to a disease.
(first off, let me clarify that I have nothing against anyone's religion!
I'm looking at this from an outsider's perspective, and harbor no biases.)
The torah, for
From: Andri Isidoro Fernandes Esteves [EMAIL PROTECTED]
Date: Thu, 14 Nov 2002 14:31:41 +
To: Mike Rosing [EMAIL PROTECTED]
Cc: [EMAIL PROTECTED]
Subject: Re: The End of the Golden Age of Crypto
On Thursday 14 November 2002 03:50, you wrote:
On Wed, 13 Nov 2002, Sam Ritchie wrote
From: Andri Esteves [EMAIL PROTECTED]
Date: Fri, 15 Nov 2002 01:29:26 +
To: [EMAIL PROTECTED]
Subject: Re: The End of the Golden Age of Crypto
On Friday 15 November 2002 00:41, you wrote:
Indeed, I've heard the same. One could argue that for someone to believe in
something (religion
Jim Choate wrote:
On Wed, 13 Nov 2002, Peter Fairbrother wrote:
Jim Choate wrote:
What I'd like to know is does Godel's apply to all forms of
para-consistent logic as well
However you can have eg arithmetics without Peano counting, and so on, and
there are (trivial according
Tim May wrote:
There are a lot of Godel anecdotes to tell. I never met him.
Two things about his theory:
1. There's a more powerful (IMNSHO) formulation of it in terms of
algorithmic information theory, usually associated with Greg Chaitin
but also drawing on the AIT work of Kolmogorov
On Thu, 14 Nov 2002, [iso-8859-1] Andri Isidoro Fernandes Esteves wrote:
The religious person is always battling against reality wich with a minimum
of inteligence from the observer always bring doubts on the truth of his
faith.
It's a state of mind wich can only be compared with mental
On Friday 15 November 2002 00:41, you wrote:
Indeed, I've heard the same. One could argue that for someone to believe in
something (religion) so intensely as to shun all moral explanation against
this hypothesis and to persist in those beliefs without any proof is akin
to schizophrenia. But
I would however, reverse your two definitions, I think the word belief suggests the
more rational, evidence based mental model, faith is a subset belief that requires no
evidence.
All of us have beliefs (under my schema above) that are evidence based (we believe in
the atomic model). Often our
On Wed, 13 Nov 2002, Tyler Durden wrote:
Damn what a pack of geeks! (Looks like I might end up liking this list!)
It's full of nut cases too :-)
I have not, however, heretofore considered that there could exist systems
that had some form of completeness built in. My intuition (which is
passed around a
proof of the existence of God! (But towards the end of his life he also
started wearing a surgical mask everywhere and became intensely
germaphobic...)
From: Mike Rosing [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Subject: Re: The End of the Golden Age of Crypto
Date: Wed, 13 Nov
Jim Choate wrote:
What I'd like to know is does Godel's apply to all forms of
para-consistent logic as well
And I replied:
No. There are consistent systems, and complete systems, that do not admit
Godel's theorem, but apparently not a system that is both (although even the
last is
On Wednesday, November 13, 2002, at 09:12 AM, Tyler Durden wrote:
All religions are complete systems. Some people consider them useful,
but I'm not sure it classifies as the real world.
:-)
I've wondered about that...I suspect that if God exists, then He is
true but unprovable in any useful
: The End of the Golden Age of Crypto
Date: Wed, 13 Nov 2002 07:27:44 -0600 (CST)
On Wed, 13 Nov 2002, Peter Fairbrother wrote:
Jim Choate wrote:
What I'd like to know is does Godel's apply to all forms of
para-consistent logic as well
And I replied:
No. There are consistent
Jim Choate wrote:
What I'd like to know is does Godel's apply to all forms of
para-consistent logic as well
It applies to any sufficiently complex axiomatic system. Allegedly.
Cheers,
Ben.
--
http://www.apache-ssl.org/ben.html http://www.thebunker.net/
There is no limit to what a
On Wed, 13 Nov 2002, Peter Fairbrother wrote:
Jim Choate wrote:
What I'd like to know is does Godel's apply to all forms of
para-consistent logic as well
And I replied:
No. There are consistent systems, and complete systems, that do not admit
Godel's theorem, but apparently not
From: Tyler Durden [EMAIL PROTECTED]
Date: Wed, 13 Nov 2002 12:12:34 -0500
To: [EMAIL PROTECTED], [EMAIL PROTECTED]
Subject: Re: The End of the Golden Age of Crypto
All religions are complete systems. Some people consider them useful,
but I'm not sure it classifies as the real world
On Wed, 13 Nov 2002, Sam Ritchie wrote:
That's the whole deal with the bible, and its various internal
contradictions. If anything can be proven true in the bible, then there's no
room for faith anymore, which nullifies religious beliefs; and if anything
can be proven false, then there's no
Tim wrote:
It would be nice to have crypto
systems based on at least problems which have been shown to be
NP-complete.
Even here, one has to be careful. The knapsack cryptosystem, based on the
NP-Complete problem Subset Sum, crashed and burned spectacularly a number
of years back.
The
Tyler Durden wrote:
(I believe that the non-existence of the last prime number is also
unprovable.)
Could you give some details/ a ref please?
The usual proof by contradiction is easy and well-known. Suppose there is a
last prime. Generate a list of all the primes sooner than or equal to the
a little chatty and clumsy at this point.
From: Tim May [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Subject: Re: The End of the Golden Age of Crypto
Date: Tue, 12 Nov 2002 11:04:32 -0800
On Tuesday, November 12, 2002, at 10:22 AM, Tyler Durden wrote:
Well, my main point was that the fact that we
On Tuesday, November 12, 2002, at 11:04 AM, Tim May wrote:
(There are famous examples of using Hamiltonian cycles for giving zero
knowledge proofs. I wrote one up here for the list about 10 years
ago...it may be findable by searching on the right keywords. But using
one of the NP-complete
, folks. It's the End of the Golden Age of Crypto. Time to move on to
the Golden Age of something else.
--
Mike Duvos $PGP 2.6 Public Key available $
[EMAIL PROTECTED]$via Finger $
,
Har.
Yes, folks. It's the End of the Golden Age of Crypto.
Well, I'm not quite ready to run out and close the patent office yet.
We still have quantum cryptography and one-time pads, which, if our
current understanding is correct, are intrinsically unbreakable.
If one-way functions turn out
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