Pat Hayes wrote:
>> Many Thanks, Paola. As John mentioned Feferman is quite well respected.
>
>
> Have you read the CL and Lbase documents? (01)
Yes, read them both. BTW - Do I have to pay to get access to CL now ? (02)
> They both give formal grammars
> and model theories of versions of first-order logic. They say nothing
> about axioms, they do not refer to "open ended schematic systems"
> (whatever those are: what ARE they, by the way?), (03)
Feferman doesn't say much about this. What he does say is " the theory
of operations employed is a version of the partial untyped lambda
calculus." He says a few other things that lead me to believe he's
thinking category theory and I've proposed the logical environment from
Kent's Information Flow Framework (IFF) provides some key insights into
how Feferman might develop such a system. (04)
> they do not describe
> "constraints", and they are written as much in the language of
> mathematics as in natural language. And they both describe logics.
> (Strictly, CL is a family of logics with a common abstract syntax, but
> the point still applies.)
>
>> I believe Feferman's open ended schematic system implies proposition b)
>> and the evolution of formal systems towards logical environments.
>
> What do you mean by a "logical environment"? (05)
Here's a pointer to the IFF logical environment, see figure 1 ... (06)
http://suo.ieee.org/IFF/metalevel/lower/ontology/ontology/version20021205.htm (07)
> BTW, the use of 'ascii-art' as in the above is best restricted to a
> non-proportional font. Your diagram is broken in any font I can find to
> view it in. (08)
Sorry, I put a graphic here ... (09)
http://www.rickmurphy.org/log-env.gif (010)
As I explained to Chris Menzel in a prior thread. This graphic
represents a degenerate version of a logical environment. Kent's, as
referenced above is nicely done and well developed in terms of
transformations. (011)
> However, since it places CL and Lbase under something other
> than 'Logics' (I'm not sure if its under 'Axiomatic' or "Natural
> Language'), it is wrong, since these are in fact both logics. (012)
That's not what they say. They claim to be frameworks. (013)
> Pat
>
>>
>> Rick
>>
>>
>> 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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>>>
>>>
>>
>>
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>
> (014)
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