Actually, you don't have to do that. Indeed, that's what many
researchers are trying to avoid. The idea is to find a logical
representation that can capture as many different 'flavours' of parthood
as possible. In principle, it can be done; no one's been able to sort
out the details yet, however, without falling off a logical cliff.
Just to name one approach, one can use a "context logic" to represent
contexts. In each context, one can use a "belief logic" to represent
different and possibly mutually inconsistent notions of parthood. But
inside of all that, one needs a logical notion of parthood that is both
formal, but broad enough to represent everything we need it to.
This is a huge undertaking. No single researcher would be daft enough
to think he/she can do it alone. But we're all poking at the problem
from different directions - hopefully someday we'll poke our way through
to a solution.
Cheers.
Fil
klaus krippendorff wrote:
> ok, if you are interested in the part/whole LOGIC, then you can abstract
> anything you like from the multiple meanings of part* from the context of
> its use and you are in mathematics proper. this is a world with stated
> rules, a world without people talking with each other and using the word
> part in the way they think appropriate
>
> klaus krippendorff
> gregory bateson term professor for cybernetics, language, and culture
> the annenberg school for communication
> university of pennsylvania
> 3620 walnut street
> philadelphia, pa 19104.6220
> phone: 215.898.7051 (O); 215.545.9356 (H)
> fax: 215.898.2024 (O); 215.545.9357 (H)
> usa
>
>
> -----Original Message-----
> From: PhD-Design - This list is for discussion of PhD studies and
> related research in Design [mailto:[log in to unmask]]On Behalf
> Of Filippo Salustri
> Sent: Wednesday, March 31, 2004 4:30 AM
> To: [log in to unmask]
> Subject: Re: parts, wholes, reflection, etc.
>
>
> Klaus,
>
> Set theory is a bad example. Lesniewski originally developed mereology,
> like, 100 years ago cuz set theory sucks so bad at explaining parthood.
> And of all the set theories I've ever heard of (yes, there's many of
> 'em), there isn't one that has survived Godel's Incompleteness Theorems,
> which is to say there is no set theory that is both logically valid and
> complete.
>
> What's that mean to us who don't use formal logic? It means that no
> matter what, right at the most basic, academic, scientific, formal
> level, there ain't no way to guarantee a right answer if you rely on set
> theory.
>
> Systems theory is the same way.
>
> Indeed, even mathematics is, at some level, all wrong. Consider the
> notion of an "indeterminate number". For example: x^0=1 and 0^x=0, so
> 0^0=....um - an indeterminate number. What is up with that? And that's
> just algebra, which is a basis of calculus, which is how we describe
> pretty much every physical system there is these days.
>
> By comparison, mereology and mereotopology and related systems (a) all
> fundamentally avoid many of the pitfalls that mess up set theory, and
> (b) remains very much underdeveloped compared to set theory. So there
> is still hope that some day, some other approach (maybe mereology, maybe
> something else) will provide a MUCH better account of parthood than is
> currently possible with set theory.
>
> And on the multiple meanings of 'part':
> Klaus, that's exactly my point! There are many meanings of part. The
> problem is that we confuse the label 'part' with the concepts - the
> meanings - we attribute to it.
>
> I think of one meaning; you think of another. But if the only 'label'
> we have to use is the single label 'part', then we're *bound* to
> misunderstand one another. So most certainly, context is an important
> way to disambiguate the various uses of the label. This is especially
> so in cases where people interact. Indeed, one of the reasons I believe
> in the importance of context in thinking about parthood is exactly
> because I have struggled and continue to struggle with the logical
> representation of parthood! See? Logic is really useful! :-)
>
> Cheers.
> Fil
>
> klaus krippendorff wrote:
>
>>i think the part/whole logic is well developed, for example in set theory,
>>or in systems theory.
>>
>>this does not mean that ordinary language conforms to formal-logical
>>distinctions.
>>your example "partly" = in some measure or degree
>>but also: "partial" = (a) favoring one thing more than another (b)
>
> referring
>
>>to a part rather than the whole
>>"participate" = to take part in something
>>"particle" = a basic unit of matter, a minute quantity
>>
>>there is no single meaning of "part*"
>>as michael says, it depends on the context to which i would add of the
>>conversation among real people, who coordinate their meanings
>>
>>klaus krippendorff
>>gregory bateson term professor for cybernetics, language, and culture
>>the annenberg school for communication
>>university of pennsylvania
>>3620 walnut street
>>philadelphia, pa 19104.6220
>>phone: 215.898.7051 (O); 215.545.9356 (H)
>>fax: 215.898.2024 (O); 215.545.9357 (H)
>>usa
>>
>>
>>-----Original Message-----
>>From: PhD-Design - This list is for discussion of PhD studies and
>>related research in Design [mailto:[log in to unmask]]On Behalf
>>Of Filippo A. Salustri
>>Sent: Tuesday, March 30, 2004 10:51 AM
>>To: [log in to unmask]
>>Subject: Re: parts, wholes, reflection, etc.
>>
>>
>>Hi all,
>>
>>It's clear that there are many, many approaches to the part/whole thing.
>>Besides the work mentioned by previous posts, there is also all work of
>>people like Barry Smith, Tony Galton, AG Cohn, Eschenbach, Artale,
>>Franconi, et al, Lesniewski (who invented 'mereology'), and so on.
>>
>>My acquaintance with the work in logic and AI assures me that no one has
>>developed a sensible logic that covers 'parthood' without somehow
>>disrupting topology - or vice versa.
>>
>>Also, the different researchers all tend to make certain limiting
>>assumptions of their domains of interest. In the end, there's 2
>>perspectives one has to choose from.
>>
>>1. parthood is axiomatic; ie, you cannot explain why x is a part of y, you
>>just state it as factual.
>>
>>2. parthood is derived from some other fundamental/axiomatic
>
> characteristic
>
>>(perhaps 'connection' - ie, topology)
>>
>>The difficult is that in conventional parlance, we tend to blend together
>
> a
>
>>wild assortment of different kinds of parthood, but we do not do so to the
>>point where the different kinds of parthood blend into an amorphous blob.
>>
>>This vagueness is further muddied by language artefacts. For example, one
>>might say "The bicycle is partly steel" which suggests that "steel" is a
>>part of "bicycle". Do we adopt a linguistic position - ie, we say it that
>>way so we need a way to represent it that way? Or do we adopt a more
>>semantically based position - ie, "The bicycle is partly steel" => "The
>>bicycle has parts that are made of steel" ?
>>
>>As an engineer, the "semantic approach" works better for me. But as a
>>designer, I'd also have to say that 'your mileage may vary'.
>>
>>Cheers.
>>Fil
>>--
>>Prof. Filippo A. Salustri, Ph.D., P.Eng.
>>Department of Mechanical and Industrial Engineering
>>Ryerson University Tel: 416/979-5000 x7749
>>350 Victoria St. Fax: 416/979-5265
>>Toronto, ON email: [log in to unmask]
>>M5B 2K3 Canada http://deed.ryerson.ca/~fil/
>>
>
>
> --
> Filippo A. Salustri, Ph.D., P.Eng.
> Department of Mechanical and Industrial Engineering
> Ryerson University
> 350 Victoria St, Toronto, ON, M5B 2K3, Canada
> Tel: 416/979-5000 ext 7749
> Fax: 416/979-5265
> Email: [log in to unmask]
> http://deed.ryerson.ca/~fil/
--
Filippo A. Salustri, Ph.D., P.Eng.
Department of Mechanical and Industrial Engineering
Ryerson University
350 Victoria St, Toronto, ON, M5B 2K3, Canada
Tel: 416/979-5000 ext 7749
Fax: 416/979-5265
Email: [log in to unmask]
http://deed.ryerson.ca/~fil/
|
