Hi Doug,

Thanks for you post, you seem to be honestly trying to understand what
I meant by the statement "there is no function that can iterate the
primes", and perhaps I should have originally said "directly, without
iterating other types", which seems to have set off this mess. But I
expected Menzel to make an honest answer instead of an ad hominem attack.

The point is that there is no function which takes primes as its domain
and ranges over the primes. For example, you could write a loop like this:

For I := 2,3,5,7,11,13,...

Do f(I);

Which would loop the domain of f(I) over the primes, but only in a
fixed set of primes given at compile time, not over an infinite set of primes,
limited only by computer word length precision. Your example function

G(I) := [calculate new value of nextPrime];

is a good example because it does not exist as an iterator. There
is no G(I) which will directly calculate the Ith prime (without ineffectively iterating
over something other than primes in an inner loop), as in:

I := 1;

Do G(I);

I didn't say that primes are not computable; I said there is no iterator
of them.

As to expressiveness, the idea is to generate an infinite set of
sentences based on combinations of a finite set of primitives, such as AND, OR,
NOT, and a finite set of variables and constant symbols.

Associating this sequence of primes with expressions made up of the
primitives of logic (e.g., AND, OR, NOT and variables), you can generate an
infinite number of primes (which by definition are not factorable) and which
cannot be expressed as combinations of the primitive symbols.

The result demonstrates that the newly generated primes are unique
expressions that cannot be formed from combinations of the finite set of FOL primitives.

The only feasible conclusion is that there is an infinite number of
sentences (since there is an infinite number of primes) which CANNOT be
expressed as combinations of the finite starting set of AND, OR, NOT and
variables and constants.

Therefore there are expressions (like in Escher's drawings) which are
not well formed, yet which express sentences that have meaning to the observer.
Just not to observers who refuse to look at them - the observer has to
understand that the Escher drawings are expressions which are not in reality,
but which do have meaning nonetheless.

Encapsulation of a function that iterates other things than primes is
merely a distraction from the claim. It doesn't change the fact that
there is no DIRECT iterator of primes.

Q.E.D.

If anything looks strange to you, please comment. I can see you
are posting in good faith.

-Rich

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

-----Original Message-----

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of doug foxvog

Sent: Thursday, October 14, 2010 5:46 AM

To: [ontolog-forum]

Subject: Re: [ontolog-forum] HOL decidability [Was: using SKOS forcontrolled
values for controlledvocabulary]

It appears that Rich Cooper's definition of "iterate" is to
loop with

a counter that advances from one element of a set to the next. It
is

unclear what restriction there is on the step that does the advancement.

It probably has to be a fixed value (like a FORTRAN DO statement), but

may not be restricted to the number 1. Rich, do you allow
positive

integers other than 1, negative integers, and non-integers as iterative

steps? It evidently does not include taking the next element from
a

list.

Rich Cooper's "iterate" does not cover the more advanced C
FOR statement

which allows an arbitrary reassignment of the loop counter for each

step of the loop. If this were allowed, the following would be an

iteration of primes.

nextPrime = 2;

for (i = 2, i < upperLimit, i = nextPrime)

[calculate new value of nextPrime];

If the loop counter for Rich Cooper's iterate has to be a fixed value,

the statement that "there is no function that can iterate the
primes

directly" seems to simply mean that there is not a fixed integer

difference between all primes.

Rich, please clarify if this your meaning of the term
"iterate", or

if not, what restrictions you place on the assignment of the next

value in the iteration. If it has to be taking the next value
from

a list, wouldn't the list of calculated primes be acceptable?
That

could have been done in the 1970s with C, although not in the 1950s

with FORTRAN II. E.g.:

sieve[0] = 2;

primeCounter = 0;

for (i = sieve[primeCounter++], i < upperLimit,

i = sieve[primeCounter++])

<calculate next prime and store it into
sieve[primeCounter]>;

My definition of "iterate" would consider this to iterate
through the

primes.

== doug foxvog

On Thu, October 14, 2010 1:19, Randall R Schulz said:

> On Wednesday October 13 2010, Rich Cooper wrote:

>> The whole point is that there is no function that will iterate
the

>> primes directly. The code you wrote will EVENTUALLY
iterate primes

>> as a BYPRODUCT of iterating integers and testing them, but
that code

>> doesn't produce each prime directly, once per iteration,
without

>> iterating other types.

>

> Then there is no iterator that directly iterates anything. It's
all

> by-products of something else down to the level of electrons and
holes

> cascading through the semiconductor material from which
transistors are

> fabricated. And while the electrons are (putatively) primitive,

> semiconductor materials are aggregates and the phenomenon of

> semiconductivity is a bulk property, so there are deeper levels
even

> than that.

>

>

>> The method you are using is often called Eratosthenes' Sieve,
which

>> is a well known method to calculate primes, but NOT to iterate
them.

>> The difference is in what is being enumerated
inside the code.

>

> I gotta' say, this sounds like an entirely specious distinction to
me.

> But what do I know? I've only been writing computer code for 34
years.

>

>

>> -Rich

>

>

> Randall Schulz

>

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=============================================================

doug foxvog doug@xxxxxxxxxx
http://ProgressiveAustin.org

"I speak as an American to the leaders of my own nation. The great

initiative in this war is ours. The initiative to stop it must be
ours."

- Dr. Martin Luther King Jr.

=============================================================

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doug foxvog doug@xxxxxxxxxx
http://ProgressiveAustin.org

"I speak as an American to the leaders of my own nation. The great

initiative in this war is ours. The initiative to stop it must be
ours."

- Dr. Martin Luther King Jr.

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