ontolog-forum
[Top] [All Lists]

Re: [ontolog-forum] HOL decidability [Was: using SKOS for controlled val

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Tue, 12 Oct 2010 22:14:27 -0700
Message-id: <20101013051433.1509A138CD8@xxxxxxxxxxxxxxxxx>
Iterate means "for each in order" for the ill-iterate.      (01)

I was discussing a mapping function that would produce one prime for each
one iteration.  It's called a one-to-one-mapping.  Now read the whole post
again because your rant below has gotten too far off base to spend time
reading.      (02)

Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2    (03)

-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Christopher
Menzel
Sent: Tuesday, October 12, 2010 9:12 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] HOL decidability [Was: using SKOS for
controlled values for controlledvocabulary]    (04)

On 12/10/2010 10:18 PM, Rich Cooper wrote:
>> ...
>>> Not so fast!  I'm sure you remember that the set of primes is
>>> infinite, and that there is no (known) function that can iterate
>>> them. 
>>
>> Of course there is.  For any given number n>1, it is easy to test
>> whether n is prime.  For a particularly crude algorithm, for each i<n
>> (i>1), look for a number j<n (j>1) such that ij=n.  If you fail to
>> find such an i, then n is prime.  To construct a list of the primes,
>> apply the above procedure to each number in turn, starting with 2,
>> adding the primes you discover to the list as you go.  This informal
>> procedure is easily expressed formally as a recursive function; one
>> typically demonstrates this in the first week or two of a course on
>> computability.
> 
> RC: I didn’t say there was no way to calculate them;     (05)

The procedure above simply identifies and lists them.  I'm not sure
what you mean by calculating them.    (06)

> I said there is no function that *iterates* them.      (07)

Doesn't "iterate" mean "list"?  If it doesn't what does it mean?    (08)

> And your algorithm above iterates *integers* till it starts to factor,
> then continues to factor forever without returning if the number is
> unfactorable (i.e., if its prime).      (09)

Uh, no it doesn't.  If n is prime, the procedure simply halts when i
reaches n-1 and fails to find a j<n such that ij=n.    (010)

>>> Godel showed that there are theorems which though true cannot be
>>> proven,  
> 
>> No, he didn't.   First of all, theorems are by definition statements
>> that have been proved. 
> 
> RC: From Google:
> 
> Definition:A proposition that has been or is to be proved on the basis
> of certain assumptions Context:In Book 1 of Elements, Euclid's
> proposition 41 is the theorem "if a parallelogram has the same base with
> a triangle and is in the same parallels, then the parallelogram is
> double the triangle."
> school.discoveryeducation.com/lessonplans/programs/conceptsInGeometry/    (011)

Uh, right.  Theorems are statements that have been proven.  Isn't that
what I said?  That's why "theorem which...cannot be proven" is an oxymoron.    (012)

>> CM: So what you are trying to say is that Gödel showed that there are
>> arithmetical statements which, though true, cannot be proven.  But
>> that's not true either.  Provability is relative to a system and *any*
>> arithmetical statement can be proven in some system or other -- just
>> take that statement as an axiom.
> 
> RC: The “some system or other” is the whole point.  That is the part
> that you can’t iterate over for every observed case.  There are
> primes, remember, and you will encounter them in iteration of
> supersets of the primes.    (013)

Word salad.    (014)

>> CM: Here's what Gödel proved: Given any consistent, decidable set S
>> of axioms in the language of arithmetic** capable of proving a
>> certain minimal amount of arithmetic, there will be statements in the
>> language that are neither provable nor disprovable *in S*.  From this
>> it follows that, for any such set S, there are statements that are
>> true in the natural numbers but which S cannot prove.
> 
> RC: The plurality of Systems, as you called them, are ordered in pairs
> with the integers (a superset of primes), but not with the primes.
> That is how Godel constructed his proof.  So there are true theorems
> that can’t be proven (factored) and false theorems that can’t be
> disproved (factored), because in association with the integers, they
> occasionally designate a prime – which by definition can’t be
> factored.       (015)

Abject nonsense.    (016)

>>> and theorems which though false cannot be disproved, all based
>>> on the primes.
>> 
>> CM: This is just nonsense.  The key to Gödel's result, for a given
>> system S, is the "arithmetization" of S's syntax, which refers to any
>> method of encoding the terms and formulas of S (and, indeed,
>> sequences of such) as numbers.  This one to represent the proof
>> theoretic apparatus of S in S itself as actual functions and
>> relations on the numbers. 
> 
> RC: I didn’t say anything about defining S in S itself, you did, and
> your formulation of Godel is not the only way to formulate it.  So by
> enabling self reference, it’s nice that you have moved ahead of the
> conversation, but not relevant to the issue at hand, which neither
> requires nor disallows self reference.      (017)

*sigh*  You toss precise technical vocabulary about with only the
vaguest inkling of its true meaning, making claims that are not only
syntactically tortured but semantically DOA.  I'd hoped that perhaps a
clear and forthright accounting of your errors and confusions in regard
to mathematical logic combined with a dash of mild ridicule might get
you to hit the books instead of shooting your mouth off in ignorance of
the subject.  I see now I was mistaken.  In the face of correction, you
will simply dig yourself a deeper hole.    (018)

I will therefore cease replying to you, no matter the topic, as it is
clear that discussion with you is a waste of time and bandwidth, at
least in regard to technical matters on which you feign expertise.  I
hope at least that folks in this forum have been properly alerted to
this and I apologize to them for not seeing the pointlessness of my
efforts sooner.    (019)

-chris    (020)


_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (021)



_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (022)

<Prev in Thread] Current Thread [Next in Thread>