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Re: [ontolog-forum] formal systems, common logic and lbase

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "rick@xxxxxxxxxxxxxx" <rick@xxxxxxxxxxxxxx>
Date: Mon, 19 Nov 2007 19:15:18 -0500
Message-id: <47422716.1040002@xxxxxxxxxxxxxx>
Many Thanks, Paola. As John mentioned Feferman is quite well respected. 
You can find more about Fererman here: http://math.stanford.edu/~feferman/    (01)

Given the current structure of CL & LBase, I believe proposition a) is 
where CL & LBase are now: a natural language description of the 
constraints to which the axioms of an open ended schematic system would 
adhere. Proposition b) presumes that we structure a logical environemt 
as illustrated below.    (02)

                Logical Environment
                        |
        -----------------------------------------
        |       |               |               |
Languages    Logics          Models         Theories
                                                 |
                                        -----------------
                                         |                |
                                     Axiomatic    Natural Language
                                                         |
                                                -------------------
                                                |                  |
                                               LBASE         Common Logic    (03)

I believe Feferman's open ended schematic system implies proposition b) 
and the evolution of formal systems towards logical environments.    (04)

Rick    (05)


paola.dimaio@xxxxxxxxx wrote:
> Thanks a lot Rick
> havent had the chance to read the docs yet, but it sounds like a
> fundamental question, although shifts in thinking paradigms may be
> unsettling and painful
> I do think that CL is going to stimulate the transition from NLP to AI
> (so many acronyms)
> and I have come to accept the possibility of a passive logical schema
> but I am still reading
> (and reading and reading)
> I am interested in exploring your a) and b) propositions
> what happend to this chap Feferman? did he get any traction?
> will catch up with the reading and continue with this discussion at
> the first opportunity
> cheers
> PDM
> 
> 
> On 11/17/07, rick@xxxxxxxxxxxxxx <rick@xxxxxxxxxxxxxx> wrote:
>>
>>
>> All:
>>
>> Folks might enjoy the Soloman Feferman lecture Goedel, Nagel, Minds and
>> Machines. After recounting an exchange between Godel and Nagel circa 1956,
>> Feferman describes the implications of the minds vs. machines dichotomy
>> ensuing from the exchange. To avoid the impass resulting from the dichotomy,
>> Feferman proposes the redefinition of a formal system to an "open ended
>> schematic axiomatic system." He claims this redefinition is a constructive
>> step towards an "informative, systematic account at a theoretical level of
>> how the mathematical mind works that squares with experience."  He stresses
>> the importance of a subject neutral theory of operations with basic schemata
>> for language, arithmetic, set theory that would amount to a version of an
>> untyped lambda calculus. Feferman concludes by rejecting any effective
>> machine representation of mind as contemplated by Nagel, Penrose & others.
>>
>> So, what does this mean to Common Logic and LBase ? Seems to me that efforts
>> like Common Logic and LBase would either have to a) be defined within this
>> type of an open ended system, let's say as the natural language description
>> of the constraints to which the axioms that make up the theory of such a
>> system would  adhere; or b) evolve into an open ended system that exhibits
>> characteristics of transformation across languages, logics, models and
>> theories.
>>
>> Rick
>>
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> 
>     (06)


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