James Q. Morrissey

> > > This statement cannot be proved.
> >
> > which one, and why?
>
> You work it out, you ------- moron. Of course, you'll have to contend with
> self-referential logic, not just notions of basic syntax, so I don't fancy
> your chances of figuring it out.
>
> I would not be surprised if you were ameriKKKan. ameriKKKans have such a
> tenuous grasp on language that the meaning of even the most mildly twisted
> notion escapes them.

this is the point where i stopped reading because it became obvious that not
only were you bigoted (i'm british, actually) but you were ignorant,
arrogant, and instead of having any interest in debate were concerned solely
with dishing out abuse instead of arguing any kind of case. nice try, troll,
but i'm not buying.

feel free to type out whatever slanderous, ill-founded and poorly structured
counter arguments and/or obscenities (are you able to make the distinction?)
you wish but i won't be reading them, as i generally killfile the people who
post your sort of drivel.

JQM

Kadaitcha Man

"James Q. Morrissey" <mellon_collie2003@btopenworld.com> wrote in message
news:c98n6r$clp$1@sparta.btinternet.com...
> > > > This statement cannot be proved.
> > >
> > > which one, and why?
> >
> > You work it out, you ------- moron. Of course, you'll have to contend
with
> > self-referential logic, not just notions of basic syntax, so I don't
fancy
> > your chances of figuring it out.
> >
> > I would not be surprised if you were ameriKKKan. ameriKKKans have such a
> > tenuous grasp on language that the meaning of even the most mildly
twisted
> > notion escapes them.
>
> this is the point where i stopped reading

You are a liar.

> because it became obvious that not
> only were you bigoted (i'm british, actually)

Shame on you, eh.

> but you were ignorant,
> arrogant,

And that's a revelation to you, is it?

> and instead of having any interest in debate

Actually, the statement "this statement cannot be proved" is very
interesting. It leads into major discussions about truth outrunning
provability. In fact, entire bodies of human and mathematical philosphies
are founded upon it. More shame on you, eh.

> were concerned solely
> with dishing out abuse instead of arguing any kind of case.

Here, choke on this, ----tard... focus the single, beady, close-set eye that
sits in the middle of your steeply sloping forehead on the words 'Part 1
demonstrably shows that the self is the notional equivalent of "this
sentence is unprovable".'

PART 1: You cannot prove that you are you
+=======================================+

If you cannot prove that you are you, how can you logically
expect anyone to prove that God exists?

This is a two part proof. Part 1 is an argument. Part 2 is
a logical proof of the conclusion of Part 1.

1) You cannot prove that you are you.
Corollary 1 of 1): Only you know that you are you.
Corollary 2 of 1): Truth outruns provability.

Proof by argument:
Assume you are requested to prove your identity
to someone or some government agency.

Assume you provide bank statements, photo drivers'
license, birth certificate and passport.

Those things are erroneously labelled as proof.

They are actually only reasonable evidence of who
you are, and the assumption of proof is ascribed to
the documents. That is to say, the documents are
not proof, but are assumed to be reasonable as proof.
This can be further illustrated by the fact that
false documentation is often accepted as "proof" of
identity.

The corollary of that argument is that if these
documents were indeed proof of identity, then false
documentation would not be accepted as proof at all,
in any scenario. That is to say, lies cannot prove
truth.

In other words, the documents are not proof, but
reasonably assumed to be proof.

Now, let's assume you decide that you can actually
prove that you are you by taking a DNA test. One
could reasonably infer that the final proof would
lie there. However that is a wholly fallacious
position, and this is why:

I have here a report from an actual DNA test. It
states, and I quote verbatim:

There are two figures given in the Report:

(i) A Paternity Index - a number which is
the ratio of the likelihood of the
putative father being the true father,
as compared to a male chosen at random
from the population.

(ii) A Relative Chance of Paternity - a
percentage probability based on the
Paternity Index.

1) In this case, the Paternity Index of
137,649 means that X is about 137,649
times more likely to be the father of
Y than is another male chosen at
random from the Australian population.

2) In this case, the probability of X
being the father of Y is 99.9993%.

So, there you have it. 99.9993% is still not 100% proof.
Now, to further complicate matters, even if we grant that
99.9993% is so close to 100% that it doesn't actually
matter, all that has been proven is that you are the
child of parents W and X. You still have not established
that you are you. Only you know that you are you.

Of course, you could always argue that you're an only
child, but again, how do you PROVE that to be true?
Statutory declarations from your parents and other
relatives? Again, they are documents that are not
proof, but can be assumed to be reasonable as proof
for different purposes.

Conclusion: Truth outruns provability.

PART 2: You cannot prove that you are you
+=======================================+

The logical proof for the conclusion of Part 1 is Gödel's First
Incompleteness Theorem. The following section deals with the
applicability of this proof.

Applicability of the logical proof:
+=================================+

The formal proof applies directly to the conclusion of Part 1, viz
truth outruns provability. I have argued at other times that Gödel's
First Incompleteness Theorem applies to the self but this has been
disputed a number of times. However the arguments against it have
been outright assertions based on a fixed notion that the proof only
applies to formal mathematical systems. For the sake of illustration,
I will go into that argument in more detail. When the proof is
presented, it will be in support of the conclusion of Part 1, not in
support of my claim that the theorem does indeed apply to the self.

Other objections have been based entirely on the meaning of two words,
computable and provable. These objections are petty but have been dealt
with below.

Part 1 shows that the self is an incontrovertible instance of truth, and
that all forms of proof are inadequate to prove the self. Furthermore
Part 1 demonstrably shows that the self is the notional equivalent of
"this sentence is unprovable".

Only the knowledge that the self has of itself is adequate. This
knowledge that the self has of itself constitutes a clear self-reference.
"I know that I am I." In this instance, the conclusion is that the truth
of the self is beyond proof.

Since the self is self-referential, it has the fundamental
trait required of a formal system for it to be a Gödelian
self-referential system. The self has been shown by argument
in Part 1 as being equivalent to the statement "this sentence
is unprovable".. The argument in Part 1 should be sufficient
to convince the most hardened opponent that the self is a
Gödelian self-referential system, however additional support
for the position is provided below.

"The proof, published by Kurt Gödel in 1931, of the existence
of formally undecidable propositions in any formal system of
arithmetic. More precisely, his first incompleteness theorem…
states that in any formal system S of arithmetic, there will be
a sentence P of the language of S such that if S is consistent,
neither P nor its negation can be proved in S. …This makes it
possible to show that there must be a sentence P of S which can
be interpreted (very roughly) as saying 'I am not provable'.

A Dictionary Of Philosophy. Second edition. (Pan Books 1984). Page 133.
Source: http://www.faragher.freeserve.co.uk/godeldef2.htm

Part 1 clearly shows that the self is equivalent to the statement
'I am not provable'. That is so despite "formally undecidable
propositions in any formal system of arithmetic".

The next question to be decided is if the self is actually
a formal system that constitutes an adequately axiomatisable
system.

I will define a part of the human mind that directly deals with
encoding and decoding syntactic notions of things like "formula",
"sentence" and "proof"', that also applies axioms, evaluates
assumptions for validity and so on, as being a system - Sf.

In order to demonstrate the existence of Sf, one should only need
point to what is going on inside your own head...

Answer this question:

"Ten plus five minus two equals what?"

If you get 13, there is direct evidence that Sf decoded the
syntactic notions of a formula from an encoded sentence, also
applied axioms (add and subtract rules) and possibly performed
a verification process before it accepted the output as correct,
then encoded it back to a formula, which Sf expressed as the
number 13.

A) The human mind Sf can encode and decode syntactic notions
of things like "formula", "sentence" and "proof"', can apply
axioms (rules), evaluate assumptions for validity and so on
to arrive at a rational output.

To apply the logical proof to the self, the following assumption
is required:

ASSUMPTION: The human mind Sf can encode sequences of numbers
and can computably generate axioms. Consequently it can encode
the syntactic notions of "formula", "sentence" and "proof".

Logical Proof - Truth Outruns Provability
+=======================================+

Purpose: To prove that truth outruns provability

Definitions:

Computable: Capable of being computed, numbered, or reckoned.
Note: The definition of computable does not imply machine
computation. The mind is capable of performing
such computations and can apply rules (axioms)
to those computations independently of a machine.

Provable: Capable of being proved; Capable of being established as
truth.

Truth: Conformity to fact or reality; exact accordance with
that which is, or has been; or shall be. Conformity to
rule; exactness.

Proof. Given a computably generated set of axioms, let PROVABLE be the set
of numbers which encode sentences which are provable from the given axioms.

Thus for any sentence s,

(1) < s > is in PROVABLE iff s is provable.

Since the set of axioms is computably generable,
so is the set of proofs which use these axioms and
so is the set of provable theorems and hence
so is PROVABLE, the set of encodings of provable theorems.
Since computable implies definable in adequate theories, PROVABLE
is definable.
Let s be the sentence "This sentence is unprovable".
By Tarski, s exists since it is the solution of:
(2) s iff < s > is not in PROVABLE.
Thus
(3) s iff < s > is not in PROVABLE iff s is not
provable.
Now (excluded middle again) s is either true or false.
If s is false, then by (3), s is provable.
This is impossible since provable sentences are true.
Thus s is true.
Thus by (3), s is not provable.
Hence s is true but unprovable.

Source:
http://www.math.hawaii.edu/~dale/god...Incompleteness
For Tarski, see same page.

Conclusion: There are statements that are true but cannot be proved.
Corollary: Truth outruns provability.


> nice try, troll,

Me? A troll?

<aside>
WEIL


--
Kadaitcha Man: Registered Linux User #344402
Akhenaten: Registered Linux Machine #235500
gentoo Linux kernel 2.6.5 <-- rolled my own

Kadaitcha Man

"James Q. Morrissey" <mellon_collie2003@btopenworld.com> wrote in message
news:c98n6r$clp$1@sparta.btinternet.com...
> > > > This statement cannot be proved.
> > >
> > > which one, and why?
> >
> > You work it out, you ------- moron. Of course, you'll have to contend
with
> > self-referential logic, not just notions of basic syntax, so I don't
fancy
> > your chances of figuring it out.
> >
> > I would not be surprised if you were ameriKKKan. ameriKKKans have such a
> > tenuous grasp on language that the meaning of even the most mildly
twisted
> > notion escapes them.
>
> this is the point where i stopped reading

You are a liar.

> because it became obvious that not
> only were you bigoted (i'm british, actually)

Shame on you, eh.

> but you were ignorant,
> arrogant,

And that's a revelation to you, is it?

> and instead of having any interest in debate

Actually, the statement "this statement cannot be proved" is very
interesting. It leads into major discussions about truth outrunning
provability. In fact, entire bodies of human and mathematical philosphies
are founded upon it. More shame on you, eh.

> were concerned solely
> with dishing out abuse instead of arguing any kind of case.

Here, choke on this, ----tard... focus the single, beady, close-set eye that
sits in the middle of your steeply sloping forehead on the words 'Part 1
demonstrably shows that the self is the notional equivalent of "this
sentence is unprovable".'

PART 1: You cannot prove that you are you
+=======================================+

If you cannot prove that you are you, how can you logically
expect anyone to prove that God exists?

This is a two part proof. Part 1 is an argument. Part 2 is
a logical proof of the conclusion of Part 1.

1) You cannot prove that you are you.
Corollary 1 of 1): Only you know that you are you.
Corollary 2 of 1): Truth outruns provability.

Proof by argument:
Assume you are requested to prove your identity
to someone or some government agency.

Assume you provide bank statements, photo drivers'
license, birth certificate and passport.

Those things are erroneously labelled as proof.

They are actually only reasonable evidence of who
you are, and the assumption of proof is ascribed to
the documents. That is to say, the documents are
not proof, but are assumed to be reasonable as proof.
This can be further illustrated by the fact that
false documentation is often accepted as "proof" of
identity.

The corollary of that argument is that if these
documents were indeed proof of identity, then false
documentation would not be accepted as proof at all,
in any scenario. That is to say, lies cannot prove
truth.

In other words, the documents are not proof, but
reasonably assumed to be proof.

Now, let's assume you decide that you can actually
prove that you are you by taking a DNA test. One
could reasonably infer that the final proof would
lie there. However that is a wholly fallacious
position, and this is why:

I have here a report from an actual DNA test. It
states, and I quote verbatim:

There are two figures given in the Report:

(i) A Paternity Index - a number which is
the ratio of the likelihood of the
putative father being the true father,
as compared to a male chosen at random
from the population.

(ii) A Relative Chance of Paternity - a
percentage probability based on the
Paternity Index.

1) In this case, the Paternity Index of
137,649 means that X is about 137,649
times more likely to be the father of
Y than is another male chosen at
random from the Australian population.

2) In this case, the probability of X
being the father of Y is 99.9993%.

So, there you have it. 99.9993% is still not 100% proof.
Now, to further complicate matters, even if we grant that
99.9993% is so close to 100% that it doesn't actually
matter, all that has been proven is that you are the
child of parents W and X. You still have not established
that you are you. Only you know that you are you.

Of course, you could always argue that you're an only
child, but again, how do you PROVE that to be true?
Statutory declarations from your parents and other
relatives? Again, they are documents that are not
proof, but can be assumed to be reasonable as proof
for different purposes.

Conclusion: Truth outruns provability.

PART 2: You cannot prove that you are you
+=======================================+

The logical proof for the conclusion of Part 1 is Gödel's First
Incompleteness Theorem. The following section deals with the
applicability of this proof.

Applicability of the logical proof:
+=================================+

The formal proof applies directly to the conclusion of Part 1, viz
truth outruns provability. I have argued at other times that Gödel's
First Incompleteness Theorem applies to the self but this has been
disputed a number of times. However the arguments against it have
been outright assertions based on a fixed notion that the proof only
applies to formal mathematical systems. For the sake of illustration,
I will go into that argument in more detail. When the proof is
presented, it will be in support of the conclusion of Part 1, not in
support of my claim that the theorem does indeed apply to the self.

Other objections have been based entirely on the meaning of two words,
computable and provable. These objections are petty but have been dealt
with below.

Part 1 shows that the self is an incontrovertible instance of truth, and
that all forms of proof are inadequate to prove the self. Furthermore
Part 1 demonstrably shows that the self is the notional equivalent of
"this sentence is unprovable".

Only the knowledge that the self has of itself is adequate. This
knowledge that the self has of itself constitutes a clear self-reference.
"I know that I am I." In this instance, the conclusion is that the truth
of the self is beyond proof.

Since the self is self-referential, it has the fundamental
trait required of a formal system for it to be a Gödelian
self-referential system. The self has been shown by argument
in Part 1 as being equivalent to the statement "this sentence
is unprovable".. The argument in Part 1 should be sufficient
to convince the most hardened opponent that the self is a
Gödelian self-referential system, however additional support
for the position is provided below.

"The proof, published by Kurt Gödel in 1931, of the existence
of formally undecidable propositions in any formal system of
arithmetic. More precisely, his first incompleteness theorem…
states that in any formal system S of arithmetic, there will be
a sentence P of the language of S such that if S is consistent,
neither P nor its negation can be proved in S. …This makes it
possible to show that there must be a sentence P of S which can
be interpreted (very roughly) as saying 'I am not provable'.

A Dictionary Of Philosophy. Second edition. (Pan Books 1984). Page 133.
Source: http://www.faragher.freeserve.co.uk/godeldef2.htm

Part 1 clearly shows that the self is equivalent to the statement
'I am not provable'. That is so despite "formally undecidable
propositions in any formal system of arithmetic".

The next question to be decided is if the self is actually
a formal system that constitutes an adequately axiomatisable
system.

I will define a part of the human mind that directly deals with
encoding and decoding syntactic notions of things like "formula",
"sentence" and "proof"', that also applies axioms, evaluates
assumptions for validity and so on, as being a system - Sf.

In order to demonstrate the existence of Sf, one should only need
point to what is going on inside your own head...

Answer this question:

"Ten plus five minus two equals what?"

If you get 13, there is direct evidence that Sf decoded the
syntactic notions of a formula from an encoded sentence, also
applied axioms (add and subtract rules) and possibly performed
a verification process before it accepted the output as correct,
then encoded it back to a formula, which Sf expressed as the
number 13.

A) The human mind Sf can encode and decode syntactic notions
of things like "formula", "sentence" and "proof"', can apply
axioms (rules), evaluate assumptions for validity and so on
to arrive at a rational output.

To apply the logical proof to the self, the following assumption
is required:

ASSUMPTION: The human mind Sf can encode sequences of numbers
and can computably generate axioms. Consequently it can encode
the syntactic notions of "formula", "sentence" and "proof".

Logical Proof - Truth Outruns Provability
+=======================================+

Purpose: To prove that truth outruns provability

Definitions:

Computable: Capable of being computed, numbered, or reckoned.
Note: The definition of computable does not imply machine
computation. The mind is capable of performing
such computations and can apply rules (axioms)
to those computations independently of a machine.

Provable: Capable of being proved; Capable of being established as
truth.

Truth: Conformity to fact or reality; exact accordance with
that which is, or has been; or shall be. Conformity to
rule; exactness.

Proof. Given a computably generated set of axioms, let PROVABLE be the set
of numbers which encode sentences which are provable from the given axioms.

Thus for any sentence s,

(1) < s > is in PROVABLE iff s is provable.

Since the set of axioms is computably generable,
so is the set of proofs which use these axioms and
so is the set of provable theorems and hence
so is PROVABLE, the set of encodings of provable theorems.
Since computable implies definable in adequate theories, PROVABLE
is definable.
Let s be the sentence "This sentence is unprovable".
By Tarski, s exists since it is the solution of:
(2) s iff < s > is not in PROVABLE.
Thus
(3) s iff < s > is not in PROVABLE iff s is not
provable.
Now (excluded middle again) s is either true or false.
If s is false, then by (3), s is provable.
This is impossible since provable sentences are true.
Thus s is true.
Thus by (3), s is not provable.
Hence s is true but unprovable.

Source:
http://www.math.hawaii.edu/~dale/god...Incompleteness
For Tarski, see same page.

Conclusion: There are statements that are true but cannot be proved.
Corollary: Truth outruns provability.


> nice try, troll,

Me? A troll?

<aside>
WEIL


--
Kadaitcha Man: Registered Linux User #344402
Akhenaten: Registered Linux Machine #235500
gentoo Linux kernel 2.6.5 <-- rolled my own

Kadaitcha Man

"James Q. Morrissey" <mellon_collie2003@btopenworld.com> wrote in message
news:c98n6r$clp$1@sparta.btinternet.com...
> > > > This statement cannot be proved.
> > >
> > > which one, and why?
> >
> > You work it out, you ------- moron. Of course, you'll have to contend
with
> > self-referential logic, not just notions of basic syntax, so I don't
fancy
> > your chances of figuring it out.
> >
> > I would not be surprised if you were ameriKKKan. ameriKKKans have such a
> > tenuous grasp on language that the meaning of even the most mildly
twisted
> > notion escapes them.
>
> this is the point where i stopped reading

You are a liar.

> because it became obvious that not
> only were you bigoted (i'm british, actually)

Shame on you, eh.

> but you were ignorant,
> arrogant,

And that's a revelation to you, is it?

> and instead of having any interest in debate

Actually, the statement "this statement cannot be proved" is very
interesting. It leads into major discussions about truth outrunning
provability. In fact, entire bodies of human and mathematical philosphies
are founded upon it. More shame on you, eh.

> were concerned solely
> with dishing out abuse instead of arguing any kind of case.

Here, choke on this, ----tard... focus the single, beady, close-set eye that
sits in the middle of your steeply sloping forehead on the words 'Part 1
demonstrably shows that the self is the notional equivalent of "this
sentence is unprovable".'

PART 1: You cannot prove that you are you
+=======================================+

If you cannot prove that you are you, how can you logically
expect anyone to prove that God exists?

This is a two part proof. Part 1 is an argument. Part 2 is
a logical proof of the conclusion of Part 1.

1) You cannot prove that you are you.
Corollary 1 of 1): Only you know that you are you.
Corollary 2 of 1): Truth outruns provability.

Proof by argument:
Assume you are requested to prove your identity
to someone or some government agency.

Assume you provide bank statements, photo drivers'
license, birth certificate and passport.

Those things are erroneously labelled as proof.

They are actually only reasonable evidence of who
you are, and the assumption of proof is ascribed to
the documents. That is to say, the documents are
not proof, but are assumed to be reasonable as proof.
This can be further illustrated by the fact that
false documentation is often accepted as "proof" of
identity.

The corollary of that argument is that if these
documents were indeed proof of identity, then false
documentation would not be accepted as proof at all,
in any scenario. That is to say, lies cannot prove
truth.

In other words, the documents are not proof, but
reasonably assumed to be proof.

Now, let's assume you decide that you can actually
prove that you are you by taking a DNA test. One
could reasonably infer that the final proof would
lie there. However that is a wholly fallacious
position, and this is why:

I have here a report from an actual DNA test. It
states, and I quote verbatim:

There are two figures given in the Report:

(i) A Paternity Index - a number which is
the ratio of the likelihood of the
putative father being the true father,
as compared to a male chosen at random
from the population.

(ii) A Relative Chance of Paternity - a
percentage probability based on the
Paternity Index.

1) In this case, the Paternity Index of
137,649 means that X is about 137,649
times more likely to be the father of
Y than is another male chosen at
random from the Australian population.

2) In this case, the probability of X
being the father of Y is 99.9993%.

So, there you have it. 99.9993% is still not 100% proof.
Now, to further complicate matters, even if we grant that
99.9993% is so close to 100% that it doesn't actually
matter, all that has been proven is that you are the
child of parents W and X. You still have not established
that you are you. Only you know that you are you.

Of course, you could always argue that you're an only
child, but again, how do you PROVE that to be true?
Statutory declarations from your parents and other
relatives? Again, they are documents that are not
proof, but can be assumed to be reasonable as proof
for different purposes.

Conclusion: Truth outruns provability.

PART 2: You cannot prove that you are you
+=======================================+

The logical proof for the conclusion of Part 1 is Gödel's First
Incompleteness Theorem. The following section deals with the
applicability of this proof.

Applicability of the logical proof:
+=================================+

The formal proof applies directly to the conclusion of Part 1, viz
truth outruns provability. I have argued at other times that Gödel's
First Incompleteness Theorem applies to the self but this has been
disputed a number of times. However the arguments against it have
been outright assertions based on a fixed notion that the proof only
applies to formal mathematical systems. For the sake of illustration,
I will go into that argument in more detail. When the proof is
presented, it will be in support of the conclusion of Part 1, not in
support of my claim that the theorem does indeed apply to the self.

Other objections have been based entirely on the meaning of two words,
computable and provable. These objections are petty but have been dealt
with below.

Part 1 shows that the self is an incontrovertible instance of truth, and
that all forms of proof are inadequate to prove the self. Furthermore
Part 1 demonstrably shows that the self is the notional equivalent of
"this sentence is unprovable".

Only the knowledge that the self has of itself is adequate. This
knowledge that the self has of itself constitutes a clear self-reference.
"I know that I am I." In this instance, the conclusion is that the truth
of the self is beyond proof.

Since the self is self-referential, it has the fundamental
trait required of a formal system for it to be a Gödelian
self-referential system. The self has been shown by argument
in Part 1 as being equivalent to the statement "this sentence
is unprovable".. The argument in Part 1 should be sufficient
to convince the most hardened opponent that the self is a
Gödelian self-referential system, however additional support
for the position is provided below.

"The proof, published by Kurt Gödel in 1931, of the existence
of formally undecidable propositions in any formal system of
arithmetic. More precisely, his first incompleteness theorem…
states that in any formal system S of arithmetic, there will be
a sentence P of the language of S such that if S is consistent,
neither P nor its negation can be proved in S. …This makes it
possible to show that there must be a sentence P of S which can
be interpreted (very roughly) as saying 'I am not provable'.

A Dictionary Of Philosophy. Second edition. (Pan Books 1984). Page 133.
Source: http://www.faragher.freeserve.co.uk/godeldef2.htm

Part 1 clearly shows that the self is equivalent to the statement
'I am not provable'. That is so despite "formally undecidable
propositions in any formal system of arithmetic".

The next question to be decided is if the self is actually
a formal system that constitutes an adequately axiomatisable
system.

I will define a part of the human mind that directly deals with
encoding and decoding syntactic notions of things like "formula",
"sentence" and "proof"', that also applies axioms, evaluates
assumptions for validity and so on, as being a system - Sf.

In order to demonstrate the existence of Sf, one should only need
point to what is going on inside your own head...

Answer this question:

"Ten plus five minus two equals what?"

If you get 13, there is direct evidence that Sf decoded the
syntactic notions of a formula from an encoded sentence, also
applied axioms (add and subtract rules) and possibly performed
a verification process before it accepted the output as correct,
then encoded it back to a formula, which Sf expressed as the
number 13.

A) The human mind Sf can encode and decode syntactic notions
of things like "formula", "sentence" and "proof"', can apply
axioms (rules), evaluate assumptions for validity and so on
to arrive at a rational output.

To apply the logical proof to the self, the following assumption
is required:

ASSUMPTION: The human mind Sf can encode sequences of numbers
and can computably generate axioms. Consequently it can encode
the syntactic notions of "formula", "sentence" and "proof".

Logical Proof - Truth Outruns Provability
+=======================================+

Purpose: To prove that truth outruns provability

Definitions:

Computable: Capable of being computed, numbered, or reckoned.
Note: The definition of computable does not imply machine
computation. The mind is capable of performing
such computations and can apply rules (axioms)
to those computations independently of a machine.

Provable: Capable of being proved; Capable of being established as
truth.

Truth: Conformity to fact or reality; exact accordance with
that which is, or has been; or shall be. Conformity to
rule; exactness.

Proof. Given a computably generated set of axioms, let PROVABLE be the set
of numbers which encode sentences which are provable from the given axioms.

Thus for any sentence s,

(1) < s > is in PROVABLE iff s is provable.

Since the set of axioms is computably generable,
so is the set of proofs which use these axioms and
so is the set of provable theorems and hence
so is PROVABLE, the set of encodings of provable theorems.
Since computable implies definable in adequate theories, PROVABLE
is definable.
Let s be the sentence "This sentence is unprovable".
By Tarski, s exists since it is the solution of:
(2) s iff < s > is not in PROVABLE.
Thus
(3) s iff < s > is not in PROVABLE iff s is not
provable.
Now (excluded middle again) s is either true or false.
If s is false, then by (3), s is provable.
This is impossible since provable sentences are true.
Thus s is true.
Thus by (3), s is not provable.
Hence s is true but unprovable.

Source:
http://www.math.hawaii.edu/~dale/god...Incompleteness
For Tarski, see same page.

Conclusion: There are statements that are true but cannot be proved.
Corollary: Truth outruns provability.


> nice try, troll,

Me? A troll?

<aside>
WEIL


--
Kadaitcha Man: Registered Linux User #344402
Akhenaten: Registered Linux Machine #235500
gentoo Linux kernel 2.6.5 <-- rolled my own

Kadaitcha Man

"James Q. Morrissey" <mellon_collie2003@btopenworld.com> wrote in message
news:c98n6r$clp$1@sparta.btinternet.com...
> > > > This statement cannot be proved.
> > >
> > > which one, and why?
> >
> > You work it out, you ------- moron. Of course, you'll have to contend
with
> > self-referential logic, not just notions of basic syntax, so I don't
fancy
> > your chances of figuring it out.
> >
> > I would not be surprised if you were ameriKKKan. ameriKKKans have such a
> > tenuous grasp on language that the meaning of even the most mildly
twisted
> > notion escapes them.
>
> this is the point where i stopped reading

You are a liar.

> because it became obvious that not
> only were you bigoted (i'm british, actually)

Shame on you, eh.

> but you were ignorant,
> arrogant,

And that's a revelation to you, is it?

> and instead of having any interest in debate

Actually, the statement "this statement cannot be proved" is very
interesting. It leads into major discussions about truth outrunning
provability. In fact, entire bodies of human and mathematical philosphies
are founded upon it. More shame on you, eh.

> were concerned solely
> with dishing out abuse instead of arguing any kind of case.

Here, choke on this, ----tard... focus the single, beady, close-set eye that
sits in the middle of your steeply sloping forehead on the words 'Part 1
demonstrably shows that the self is the notional equivalent of "this
sentence is unprovable".'

PART 1: You cannot prove that you are you
+=======================================+

If you cannot prove that you are you, how can you logically
expect anyone to prove that God exists?

This is a two part proof. Part 1 is an argument. Part 2 is
a logical proof of the conclusion of Part 1.

1) You cannot prove that you are you.
Corollary 1 of 1): Only you know that you are you.
Corollary 2 of 1): Truth outruns provability.

Proof by argument:
Assume you are requested to prove your identity
to someone or some government agency.

Assume you provide bank statements, photo drivers'
license, birth certificate and passport.

Those things are erroneously labelled as proof.

They are actually only reasonable evidence of who
you are, and the assumption of proof is ascribed to
the documents. That is to say, the documents are
not proof, but are assumed to be reasonable as proof.
This can be further illustrated by the fact that
false documentation is often accepted as "proof" of
identity.

The corollary of that argument is that if these
documents were indeed proof of identity, then false
documentation would not be accepted as proof at all,
in any scenario. That is to say, lies cannot prove
truth.

In other words, the documents are not proof, but
reasonably assumed to be proof.

Now, let's assume you decide that you can actually
prove that you are you by taking a DNA test. One
could reasonably infer that the final proof would
lie there. However that is a wholly fallacious
position, and this is why:

I have here a report from an actual DNA test. It
states, and I quote verbatim:

There are two figures given in the Report:

(i) A Paternity Index - a number which is
the ratio of the likelihood of the
putative father being the true father,
as compared to a male chosen at random
from the population.

(ii) A Relative Chance of Paternity - a
percentage probability based on the
Paternity Index.

1) In this case, the Paternity Index of
137,649 means that X is about 137,649
times more likely to be the father of
Y than is another male chosen at
random from the Australian population.

2) In this case, the probability of X
being the father of Y is 99.9993%.

So, there you have it. 99.9993% is still not 100% proof.
Now, to further complicate matters, even if we grant that
99.9993% is so close to 100% that it doesn't actually
matter, all that has been proven is that you are the
child of parents W and X. You still have not established
that you are you. Only you know that you are you.

Of course, you could always argue that you're an only
child, but again, how do you PROVE that to be true?
Statutory declarations from your parents and other
relatives? Again, they are documents that are not
proof, but can be assumed to be reasonable as proof
for different purposes.

Conclusion: Truth outruns provability.

PART 2: You cannot prove that you are you
+=======================================+

The logical proof for the conclusion of Part 1 is Gödel's First
Incompleteness Theorem. The following section deals with the
applicability of this proof.

Applicability of the logical proof:
+=================================+

The formal proof applies directly to the conclusion of Part 1, viz
truth outruns provability. I have argued at other times that Gödel's
First Incompleteness Theorem applies to the self but this has been
disputed a number of times. However the arguments against it have
been outright assertions based on a fixed notion that the proof only
applies to formal mathematical systems. For the sake of illustration,
I will go into that argument in more detail. When the proof is
presented, it will be in support of the conclusion of Part 1, not in
support of my claim that the theorem does indeed apply to the self.

Other objections have been based entirely on the meaning of two words,
computable and provable. These objections are petty but have been dealt
with below.

Part 1 shows that the self is an incontrovertible instance of truth, and
that all forms of proof are inadequate to prove the self. Furthermore
Part 1 demonstrably shows that the self is the notional equivalent of
"this sentence is unprovable".

Only the knowledge that the self has of itself is adequate. This
knowledge that the self has of itself constitutes a clear self-reference.
"I know that I am I." In this instance, the conclusion is that the truth
of the self is beyond proof.

Since the self is self-referential, it has the fundamental
trait required of a formal system for it to be a Gödelian
self-referential system. The self has been shown by argument
in Part 1 as being equivalent to the statement "this sentence
is unprovable".. The argument in Part 1 should be sufficient
to convince the most hardened opponent that the self is a
Gödelian self-referential system, however additional support
for the position is provided below.

"The proof, published by Kurt Gödel in 1931, of the existence
of formally undecidable propositions in any formal system of
arithmetic. More precisely, his first incompleteness theorem…
states that in any formal system S of arithmetic, there will be
a sentence P of the language of S such that if S is consistent,
neither P nor its negation can be proved in S. …This makes it
possible to show that there must be a sentence P of S which can
be interpreted (very roughly) as saying 'I am not provable'.

A Dictionary Of Philosophy. Second edition. (Pan Books 1984). Page 133.
Source: http://www.faragher.freeserve.co.uk/godeldef2.htm

Part 1 clearly shows that the self is equivalent to the statement
'I am not provable'. That is so despite "formally undecidable
propositions in any formal system of arithmetic".

The next question to be decided is if the self is actually
a formal system that constitutes an adequately axiomatisable
system.

I will define a part of the human mind that directly deals with
encoding and decoding syntactic notions of things like "formula",
"sentence" and "proof"', that also applies axioms, evaluates
assumptions for validity and so on, as being a system - Sf.

In order to demonstrate the existence of Sf, one should only need
point to what is going on inside your own head...

Answer this question:

"Ten plus five minus two equals what?"

If you get 13, there is direct evidence that Sf decoded the
syntactic notions of a formula from an encoded sentence, also
applied axioms (add and subtract rules) and possibly performed
a verification process before it accepted the output as correct,
then encoded it back to a formula, which Sf expressed as the
number 13.

A) The human mind Sf can encode and decode syntactic notions
of things like "formula", "sentence" and "proof"', can apply
axioms (rules), evaluate assumptions for validity and so on
to arrive at a rational output.

To apply the logical proof to the self, the following assumption
is required:

ASSUMPTION: The human mind Sf can encode sequences of numbers
and can computably generate axioms. Consequently it can encode
the syntactic notions of "formula", "sentence" and "proof".

Logical Proof - Truth Outruns Provability
+=======================================+

Purpose: To prove that truth outruns provability

Definitions:

Computable: Capable of being computed, numbered, or reckoned.
Note: The definition of computable does not imply machine
computation. The mind is capable of performing
such computations and can apply rules (axioms)
to those computations independently of a machine.

Provable: Capable of being proved; Capable of being established as
truth.

Truth: Conformity to fact or reality; exact accordance with
that which is, or has been; or shall be. Conformity to
rule; exactness.

Proof. Given a computably generated set of axioms, let PROVABLE be the set
of numbers which encode sentences which are provable from the given axioms.

Thus for any sentence s,

(1) < s > is in PROVABLE iff s is provable.

Since the set of axioms is computably generable,
so is the set of proofs which use these axioms and
so is the set of provable theorems and hence
so is PROVABLE, the set of encodings of provable theorems.
Since computable implies definable in adequate theories, PROVABLE
is definable.
Let s be the sentence "This sentence is unprovable".
By Tarski, s exists since it is the solution of:
(2) s iff < s > is not in PROVABLE.
Thus
(3) s iff < s > is not in PROVABLE iff s is not
provable.
Now (excluded middle again) s is either true or false.
If s is false, then by (3), s is provable.
This is impossible since provable sentences are true.
Thus s is true.
Thus by (3), s is not provable.
Hence s is true but unprovable.

Source:
http://www.math.hawaii.edu/~dale/god...Incompleteness
For Tarski, see same page.

Conclusion: There are statements that are true but cannot be proved.
Corollary: Truth outruns provability.


> nice try, troll,

Me? A troll?

<aside>
WEIL


--
Kadaitcha Man: Registered Linux User #344402
Akhenaten: Registered Linux Machine #235500
gentoo Linux kernel 2.6.5 <-- rolled my own

Bobby D. Bryant

On Fri, 28 May 2004 02:43:13 +0000, Xomicron wrote:

> I am waiting for evolutionists to support their assertion that modern
> man has somehow been able to observe changes that have taken place in
> living beings regardless that modern man is supposedly a result of
> those changes in the first place.

Do you reject indirect observations?


> Only an uninformed fanatic says that evolution can be proved
> scientifically.

Only the uniformed think empirical scientists deal in proof.


> Christians believe in creationism because we believe in the veracity of
> the Bible but we also have scientific evidence to support our position.

Why do you keep it secret?



> Evolutionists don't "know" anything about man's origins. They guess,
> suppose, etc. but they don't "know."

Actually, scientists build models that explain observations.


> Honest scientists have become weary and embarrassed at the confusing,
> convoluted and contradictory claptrap that often passes as science.

Name three.


--
Bobby Bryant
Austin, Texas

Bobby D. Bryant

On Fri, 28 May 2004 02:43:13 +0000, Xomicron wrote:

> I am waiting for evolutionists to support their assertion that modern
> man has somehow been able to observe changes that have taken place in
> living beings regardless that modern man is supposedly a result of
> those changes in the first place.

Do you reject indirect observations?


> Only an uninformed fanatic says that evolution can be proved
> scientifically.

Only the uniformed think empirical scientists deal in proof.


> Christians believe in creationism because we believe in the veracity of
> the Bible but we also have scientific evidence to support our position.

Why do you keep it secret?



> Evolutionists don't "know" anything about man's origins. They guess,
> suppose, etc. but they don't "know."

Actually, scientists build models that explain observations.


> Honest scientists have become weary and embarrassed at the confusing,
> convoluted and contradictory claptrap that often passes as science.

Name three.


--
Bobby Bryant
Austin, Texas

Bobby D. Bryant

On Fri, 28 May 2004 02:43:13 +0000, Xomicron wrote:

> I am waiting for evolutionists to support their assertion that modern
> man has somehow been able to observe changes that have taken place in
> living beings regardless that modern man is supposedly a result of
> those changes in the first place.

Do you reject indirect observations?


> Only an uninformed fanatic says that evolution can be proved
> scientifically.

Only the uniformed think empirical scientists deal in proof.


> Christians believe in creationism because we believe in the veracity of
> the Bible but we also have scientific evidence to support our position.

Why do you keep it secret?



> Evolutionists don't "know" anything about man's origins. They guess,
> suppose, etc. but they don't "know."

Actually, scientists build models that explain observations.


> Honest scientists have become weary and embarrassed at the confusing,
> convoluted and contradictory claptrap that often passes as science.

Name three.


--
Bobby Bryant
Austin, Texas

Bobby D. Bryant

On Fri, 28 May 2004 02:43:13 +0000, Xomicron wrote:

> I am waiting for evolutionists to support their assertion that modern
> man has somehow been able to observe changes that have taken place in
> living beings regardless that modern man is supposedly a result of
> those changes in the first place.

Do you reject indirect observations?


> Only an uninformed fanatic says that evolution can be proved
> scientifically.

Only the uniformed think empirical scientists deal in proof.


> Christians believe in creationism because we believe in the veracity of
> the Bible but we also have scientific evidence to support our position.

Why do you keep it secret?



> Evolutionists don't "know" anything about man's origins. They guess,
> suppose, etc. but they don't "know."

Actually, scientists build models that explain observations.


> Honest scientists have become weary and embarrassed at the confusing,
> convoluted and contradictory claptrap that often passes as science.

Name three.


--
Bobby Bryant
Austin, Texas

Timberwoof

In article <c98dol.1684.1@kadaitcha.ath.cx>,
"Kadaitcha Man" <nospam@kadaitcha.cx> wrote:

> "Shiva" <shiva87@hotmail.com> wrote
>
> > Science tries
> > to prove things through experiments that can be repeated.
>
> Oh well. There go quantum and string theories.

Well, yes. And no. "String Theories" are mostly hypotheses. They have
made some predictions, but these are difficult to prove yet. But the
status of string theory as hypothesis has no bearing on the status of
evolutionary theory as fact.

--
Timberwoof <me at timberwoof dot com>
http://www.timberwoof.com
Baloney Detection Kit: http://www.xenu.net/archive/baloney_detection.html