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Re: [ontolog-forum] Foundation Ontology Primitives

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Sun, 7 Feb 2010 17:07:37 -0600
Message-id: <F822519D-B021-4742-A133-AADE6E6765FA@xxxxxxxx>
On Feb 6, 2010, at 7:36 PM, Rob Freeman wrote:
> ...
> On Sun, Feb 7, 2010 at 8:14 AM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
>> ...
>> PC> I have often (when trying to be careful) used the term "intended
>> > meaning" to emphasize that the "meaning" of an ontology term should
>> > be what the ontologist intended it to be (unless s/he made a logical
>> > error -- which should be detectable by testing).
>> I agree. But computer algorithms only deal with formal symbols, and it's 
>irrelevant whether those symbols came from pure or applied math. The computer 
>has no access to what's in the head of theprogrammer or ontologist.
> I agree completely. The results showing no theory can explain all theories 
>apply to manipulations of symbols, and are quite general.    (01)

There is no result showing that "no theory can explain all theories", mostly 
because there is no formal notion of what it is for one theory to "explain" 
another (unless you are, once again, using your own terminology to make 
statements for which standard conventional terminology already exists).    (02)

> But now it gets more interesting...
>> ... no program can embody any "meaning" that goes
>> beyond or outside what is or can be specified in axioms.
> I have to quibble with this. Words are slippery. At best I think anyone 
>reading it could be easily confused. We have to remember, as you said:
> On Wed, Jan 20, 2010 at 4:57 AM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
> "For some pairs of (M,T), the predicate Will_Halt can be
> determined by a proof in FOL.  But for others, the theorem
> prover will loop forever.  But any (M,T) that is undecidable
> in FOL will be just as undecidable in English or any other
> language, formal or informal."
> If you define "meaning" to be what is specified by axioms, it may be 
>technically true that 'no program can embody any "meaning" that goes beyond or 
>outside what is or can be specified in axioms.' But we have to remember there 
>are at least some properties of computable processes which are not specified, 
>other than by running the process itself.    (03)

Well, I have no clear idea what you mean by a process specifying a property; 
perhaps an example would help.    (04)

But the bigger problem, once again, is that you continue to conflate programs, 
processes, and problems, and doing so makes a serious muddle of your claims.      (05)

PROGRAMS are static; they are pieces of code in some specific language that can 
be run on a computer.    (06)

"PROCESS" can mean a dozen different things, but the kind of process that seems 
most relevant to what you are trying to say is the actual running of a program 
(easiest case: a Turing machine computation), that is, the series of 
transitions undergone by an actual or theoretical computer (a Turing machine) 
as it runs a program (set of Turing machine instructions) on specific input 
(the initial state of a Turing machine tape).  Such processes are the things 
that halt or fail to halt.  Computers and programs are often said to halt or 
not and that's fine, but this usage is derivative.  In particular, to say that 
a Turing Machine M (or its program P) halts on given input I is just to say 
that the process that ensues when M is started on I eventually halts.    (07)

Finally, PROBLEMS are the things that are or are not decidable by a computer 
program.  The halting problem for Turing Machines, in particular, is the 
problem of determining, for any arbitrary Turing machine M (with program P), 
whether M halts on arbitrary input I.    (08)

You really should keep these clearly separated if you have any hopes of getting 
your ideas across.    (09)

> Whether you choose to interpret that to mean computable processes are 
>limited, or whether you choose to interpret it as I do to mean computable 
>processes are more powerful, it is undeniable that some things about programs 
>can only be specified by the program itself.    (010)

I hereby deny it -- mostly because there is no clear sense attached to the idea 
of a program specifying "things" about itself.  There is of course a well-known 
notion of a program spec, and I reckon there are clever ways of writing 
"self-referential" programs that in some sense specify their own functionality. 
 But that certainly doesn't sound like what you are talking about.  And that, 
once again, is the chief frustration with reading your posts.  You make grand 
sounding claims but leave critical terms undefined, so there is really no clear 
substance for the reader to grasp.    (011)

>> ... any meaning that cannot be specified in axioms cannot be programmed on a 
>computer ...
> Same thing. All the steps of a program my be individually specifiable with 
>axioms, I grant you, but it is fundamental to the nature of computation that 
>some aspects of computation, like halting, will not be known until after the 
>program is run.    (012)

What do you mean "after the program is run"?  If the program never halts, then 
there will never *be* a point *after which* it is run.  *If* the program 
eventually halts, we can know that (in theory), simply by running it.  The 
whole problem is that, if the program never halts, we may not be able to tell, 
at any point in the process of running the program, whether or not we simply 
haven't waited long enough for it to halt.  There is no "aspect of computation" 
here that emerges in virtue of running the program.    (013)

> I won't go on to argue at length again here what I think that means for 
>knowledge representation: essentially that a learning process, because it is a 
>process, may be the only complete representation.    (014)

The idea that a process is a representation is opaque.  Representations are 
linguistic or graphical things and processes are not -- at least, in any sense 
of those terms commonly in use.    (015)

Chris Menzel    (016)

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