We may take probability as a measure of our certainty about the
occurrence of some event or as a measure of the frequency of occurrence
of the event (these originally listed by herbzet). But isn't there a
more fundamental issue to be considered? -

- What counts as an 'outcome'? If I throw a die up onto a glass ceiling
and the outcome is a one for the floor-below dweller, it will be a six
for the floor-above dweller. For the dwellers who floor-slide there will
be no single outcome. Again, 'thrown' in space a die appears to have no
outcomes at all.

We might then conclude that an event carries its possible outcomes with
it, fully formed and 'ready to go', like the die with 6 faces. But
doesn't outcome here mean simply 'property'? No. 'Ready to go' in this
case would mean an apparant, perspectival, restriction being placed on
the dies outcomes that arises by by hooking up the thrown die to another
event, an event such as the limited view granted by the perspective of a
glass ceiling dweller. Importantly then, 'outcome' is 'property' in
relationship.

What do you get if you swap the second order induction axiom from full
second order arithmetic for the induction schema from Peano
Arithmetic? How much weaker is the resulting theory?

A Curious Question
~v~~

Is there anything which is not predicated of "not"?

~v~~

Law enforcement is now intercepting text messages,
as proven by Operation Sudden Fall in San Diego.

http://www.usdoj.gov/dea/pubs/states/newsrel/sd050608.html
http://www.signonsandiego.com/news/education/20080506-1338-bn06sdsu2.html

Don't let your personal SMS/text messages fall into
the wrong hands. Encrypt your messages with one
of these:

http://www.CryptoSMS.org
http://www.CryptoSMS.com
http://www.FortressMail.net/fortress_sms.htm
http://www.Cop2p.com/encrypted_sms.html

Be Safe, Be Encrypted, Fuck the Police!!

I am reposting this from google because, for some reason, this seems
not to be getting through mail notifications, and I believe there is
some significant argument here.

I apologise in case you are receiving this twice.

-LV

On 9 May, 18:05, Julio Di Egidio diegidio.name> wrote:

As part of an abduction procedure,
see http://code.google.com/p/biohacker/source/browse/trunk/BPS/ltms/abduction.lisp
if interested,
I need to efficiently solve the following problem:

Given an or-set of and-sets, for example,
(:OR (:AND A B C) (:AND D E A))
and given a dictionary, where each element of an and-set is listed,
with another or-set of and-sets as value, for example,
A -> (:OR (:AND 1 2) (:AND 3 4))
B -> (:OR (:AND 2 3) (:AND 4))
C -> (:OR (:AND 1) (:AND 3))
D -> (:OR (:AND 1) (:AND 3 4))
E -> (:OR (:AND 1 2) (:AND 3))
find a new minimal or-set of and-set consistent, containing all
combinations of possibilities for the elements, but omitting
supersets, for example:
(:OR (:AND 1 2) (:AND 3 4))

the australian philospher colin dean points out that godel makes 2
deceitful moves in his imcompleteness theorem proof

http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf

godels incompleteness theorem reads- note it says to every ω-consistent
recursive class c of formulae

http://www.mrob.com/pub/math/goedel.html

Proposition VI: To every ω-consistent recursive class c of formulae there
correspond recursive class-signs r, such that neither v Gen r nor Neg (v
Gen r) belongs to Flg(c) (where v is the free variable of r).

now
1) he derives his incompleteness theorem from system P which is made up of
peano and PM but decietfully says it applyies to other system

quote

In the proof of Proposition VI the only properties of the system P
employed were the following:

1. The class of axioms and the rules of inference (i.e. the relation
"immediate consequence of") are recursively definable (as soon as the
basic signs are replaced in any fashion by natural numbers).

the australian philosopher colin leslie dean points out that Godel use
peano axioms which is impredicative-thus his theorem is invalid

http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf

godel constructs his system P from which he proves his incompleteness
theorem

quote

http://www.mrob.com/pub/math/goedel.html

In the proof of Proposition VI the only properties of the system P
employed were the following:

1. The class of axioms and the rules of inference (i.e. the relation
"immediate consequence of") are recursively definable (as soon as the
basic signs are replaced in any fashion by natural numbers).

2. Every recursive relation is definable in the system P (in the sense of
Proposition V).

Hence in every formal system that satisfies assumptions 1 and 2 and is
ω-consistent, undecidable propositions exist of the form (x) F(x), where
F is a recursively defined property of natural numbers, and so too in
every extension of such

Mortal man -- Truth or belief??

Is every man ever born or yet to be born proveably mortal?? Has such a
proof been been produced. Conclusive proof.

When a man X is to "proved" mortal, a typical "logic" is:

1. X is mortal
2. Because X is a man [grounds of inference. That X is a man can be
proved]
3. Every man is mortal. For example every man like Plato has died
4. X too is a man
5. Therefore X is mortal.
Notice that 5 relies on the truth of 3. But if ONE single man is found
to be immortal, 3 is refuted. Truth of 3 is dependent on truth of 5.

Questions arise.
Have all the men so far born have been observed to have died?? It is a
impossible task for anyone or even a large number of investigators. It
it beyond reason to think that maybe ONE man IS immortal??

Even if true that all men so far born have been mortal, is it fair to
extrapolate this observation to future??

Mortal man -- Truth or belief??

Is every man ever born or yet to be born proveably mortal?? Has such a
proof been been produced. Conclusive proof.

When a man X is to "proved" mortal, a typical "logic" is:

1. X is mortal
2. Because X is a man [grounds of inference. That X is a man can be
proved]
3. Every man is mortal. For example every man like Plato has died
4. X too is a man
5. Therefore X is mortal.
Notice that 5 relies on the truth of 3. But if ONE single man is found
to be immortal, 3 is refuted. Truth of 3 is dependent on truth of 5.

Questions arise.
Have all the men so far born have been observed to have died?? It is a
impossible task for anyone or even a large number of investigators. It
it beyond reason to think that maybe ONE man IS immortal??

Even if true that all men so far born have been mortal, is it fair to
extrapolate this observation to future??