JE:-
I strongly suggest you replace your consistent rhetoric (previously I
was
accused of "babbling" and now I am accused of "metaphorical rambling")
with
NON EVASION.

I have not pretended to address your rambling, or if you like the term
better, babbling, with any arguments.

Indeed, there is no point for me
to do so, since my interests lie solely in the incompleteness theorems
and their invocations by your fine self and others.

Going on about
"irreversible linkage", "tautologicity" and what have you, in relation
to the incompleteness theorems is pointless, unless you somehow connect
your ideas to the actual mathematical content of the theorems. Otherwise
you might as well quote the fundamental theorem of arithmetic or
Dirichlet's theorem.

I have read the article with exasperation. AT NO TIME does Torkel
Franzén
even mention the concept of a TAUTOLOGY let alone include
how it necessarily contrasts to a NON tautology within any
RATIONAL system.

Of course not. There is no apparent connection between these things and
the actual mathematical content of the incompleteness theorem.

The closest we seem to get to this seems to be:
"Gödel's proof makes essential use of what is called the diagonal lemma
for
T. This is a general result about T stating that for every formula B(x)
with
one free variable x - meaning that B(x) asserts something about the
unspecified number x - a formula A (known as a fixpoint for B(x)) can be
constructed such that

T |- A<=>B(#A)"

Perhaps you might to like explain why "<=>" does not mean "entirely
reversible" proving just a tautologous logical linkage?

Here Torkel is just explaining a technical theorem pertaining certain
formal theories T. According to the diagonal lemma, as he explains, for
any formula B(x) we can find a formula A such that it is provable in T
that A is true just in case the Gödel number of A has the property
expressed by B(x). What this has to do with "entirely reversible" or
"tautologous logical linkage" cannot be determined unless you provide
some way of relating these notions to the standard logical notions of
formal provability, equivalence, Gödel numberings and so forth.

Franzen clearly noted what he considers to be a CORRECT statement in
WORDS
(i.e. as a non reversible rational proposition with a subject and a
predicate) as to what Gödel had discovered:

"The mathematician Godel proved that a system of axioms can never be
based
on itself: statements from outside the system must be used in order to
prove
its consistency."

This is indeed a correct statement: a consistent system satisfying
certain technical conditions can only be proved consistent by using
principles not contained in the system. However, what this has to do
with "a non reversible rational proposition with a subject and a
predicate" remains completely obscure.

Your argument that "though there are certain marginal set theories with
a
universal set, such a set is not a part of ordinary mathematics or set
theory" was not correct.

Sure it was, as you will find out for yourself if you choose to study
set theory.

It remains easy to see: the universal set is the defined PREDICATE, i.e.
the
INDUCTIVE ASSUMPTION from which everything else exists as just a
deduction
(including all tautologies nested within it).

As usually understood a universal set V is a set such that for every
object a, a is a member of V. The existence of such a set is, on the
face of it, a purely mathematical supposition -

...a false one, as sets are
usually conceived in mathematics, as it happens.

just to be able to replicate genes phylogenetically allowing better
"phylogenetic survival"! IOW the Darwinian selectee is exactly one
fertile
organism and not just any organism.

I don't know if I can agree or not until you tell me (us) what you mean by
"fertile".

Do you mean it in the sense of "viable" - as in "having the potential to
produce likewise viable offspring"?
If you do then my EPT recognition has always, and perfectly obviously
overlapped with yours.

----

IMHO, it is impossible to insist that organisms [of populations that
evolve
by
way of the Principle of Natural (heritable variation) and Selection] who,
individually, were
*not even potentially* reproductive (hence, were never "candidates for
'ancestorhood' or 'forebearship'" ) were "selectees" [i.e., were
selected
positively or negatively from by opportune and adverse types of
pressures/challenges in "individual life|space|time" - as part of the
Evolutionary Patterning Totality], and to be 'evolution-theoretically
sane'
at the same time.

j.wilkins1@uq.edu.au (John Wilkins) wrote:-

This issue has been done to death already, IMO:

http://www.talkorigins.org/faqs/evolphil/tautology.html

That's an incredibly bad article, that needs to be revised and
updated.
One day.

JE:-
I agree entirely. Who wrote it, Dr L Moran?

Some undergraduate...

JE:-
Really, from what university?

John Edser wrote:

I strongly suggest you replace your consistent rhetoric (previously I was
accused of "babbling" and now I am accused of "metaphorical rambling") with
NON EVASION.

I have not pretended to address your rambling, or if you like the term
better, babbling, with any arguments. Indeed, there is no point for me
to do so, since my interests lie solely in the incompleteness theorems
and their invocations by your fine self and others. Going on about
"irreversible linkage", "tautologicity" and what have you, in relation
to the incompleteness theorems is pointless, unless you somehow connect
your ideas to the actual mathematical content of the theorems. [...]

"g" <gillawton@earthlink.net
JE:-
Gil, this is a science list and not just a logic or mathematics list.
What
is required of everybody here, including myself and Mr Koskensilta, are
the
following three things.


i) Defined terms.

ii) Use of self consistent arguments (no contradictions allowed).

iii) Provide verifiable and refutable premises not just premises which
can be verified or non verified.

If I label terms differently (which I take great pains to avoid doing
but
I
may have to define new concepts with new labels because the concept has
not
been previously employed) then all that has to be done is for the
respondent
to provide the more accepted label.

John,
Much good will and much deserved respect.

But with all due good will and deserved respect, please allow me to assert
that my best efforts, so far, to believe that any human could define any
"natural" universal set would require that he know all things within that
set, lest he fail to have tweaked his definition sufficiently to encompass
the very last twit of it.

snip

What I do not personally ACCEPT, albeit I approve with much enthusiasm
YOUR right to accept it, if you wish -- is that there can be "the"
definition
of anything in nature derivable by any human mind, nor "the" definition of
anything in pure logic derived by any human mind.

"John Wilkins" <j.wilkins1@uq.edu.au> wrote in message
news:eolnpd$29es$1@darwin.ediacara.org...

(MUCHISIMOS SNIPPOS)

That's my stand this week, anyway.

Well, your this-week-stand surely reads like a carefully studied
treatment of it. Well received.

I have not pretended to address your rambling, or if you like the term
better, babbling, with any arguments. Indeed, there is no point for me
to do so, since my interests lie solely in the incompleteness theorems
and their invocations by your fine self and others. Going on about
"irreversible linkage", "tautologicity" and what have you, in relation
to the incompleteness theorems is pointless, unless you somehow connect
your ideas to the actual mathematical content of the theorems. [...]

One problem I see with this is that the connection with
the supposed topic of discussion (biological evolution)
grows pretty tenuous.

Godel's theorem originally came up here recently because it
has been claimed (Lucas, Penrose) that it places limits on
machines which mean that they cannot perform the same
functions that the human mind can - and therefore are
unlikely to ever compete with our species for its ecological
niche - unless they can /also/ master some mystical/quantum
do-dah.

I have claimed that is baseless nonsense: Godel's theorems
are esoteric math about the completeness of axiomatic systems
that has diddley-squat to do with whether machines can match
and exceed the capabilities of modern humans.

Discussion of Godel's theorem which *doesn't* relate to this
whole issue will probably interest only a minority of subscribers.

People being attracted from abroad by debatable material
in John's posts is all very well - but my council to most
of them would be: please don't feed the Edser.

One problem I see with this is that the connection with
the supposed topic of discussion (biological evolution)
grows pretty tenuous.

People being attracted from abroad by debatable material
in John's posts is all very well - but my council to most
of them would be: please don't feed the Edser.

That's an incredibly bad article, that needs to be revised and
updated.
One day.

JE:-
I agree entirely. Who wrote it, Dr L Moran?

Some undergraduate...

JE:-
Really, from what university?

He would have been at Monash University at the time.

People being attracted from abroad by debatable material
in John's posts is all very well - but my council to most
of them would be: please don't feed the Edser.

You'll be happy to know I'm now done with Edser.

j.wilkins1@uq.edu.au (John Wilkins) wrote:-


That's an incredibly bad article, that needs to be revised and
updated.
One day.

JE:-
I agree entirely. Who wrote it, Dr L Moran?

Some undergraduate...

JE:-
Really, from what university?

He would have been at Monash University at the time.

JE:-
The university of the same name here in Australia?

I expect so. Sir John Monash is not widely known outside Australia...

You will be unhappy to know that I am not done with you.

Tim Tyler wrote:
One problem I see with this is that the connection with
the supposed topic of discussion (biological evolution)
grows pretty tenuous.

Indeed, but that can hardly be avoided; Gödel's theorems don't have
anything to do with evolution in the first place.

People being attracted from abroad by debatable material
in John's posts is all very well - but my council to most
of them would be: please don't feed the Edser.

You'll be happy to know I'm now done with Edser.

--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

j.wilkins1@uq.edu.au (John Wilkins) wrote:
That's an incredibly bad article, that needs to be revised and
updated.
One day.

JE:-
I agree entirely. Who wrote it, Dr L Moran?

Some undergraduate...

JE:-
Really, from what university?

He would have been at Monash University at the time.

JE:-
The university of the same name here in Australia?

I expect so. Sir John Monash is not widely known outside Australia...

snip
Indeed, but that can hardly be avoided; Gödel's theorems don't have
anything to do with evolution in the first place.

snip
Mathematical
formalism is supposed to be the language of sciences (biology included).
Formalization of biology (such as ALIFE, and AI), therefore, would have
to be viewed under the very same light of Godel's Incompleteness, just as
any other mathematical theories. But unlike certain theories where a model
is the set of natural numbers, biology formalization might be
syntactically
possible, without us knowing an infinite (biological) model. And this
formalization-without-model would indeed reveal the weakness of reasoning
in general, and Incompleteness in particular.

So the relationship between the two (biology processes and Gödel's
theorems)
might not be in that much "don't have anything to do [with each other]",
as
we initially suspect.