RE: SUO: Irreducible Triadicity
Matthew,
The catch in my email was the phrase "without any loss of logical
content".
There is, after all, a big difference between saying, for example, 'all
landscapes can be represented by still black-and-white photographs' and
claiming that such representations *necessarily* capture the visual
experience of all landscapes without loss of content (e.g. color,
3-dimensionality, passage of time).
I do not believe that Pat's critique of Burch's attempt to reconstruct
Peirce made so strong a claim for reduction to dyadic relations.
Nor in the measurement example you gave, do I see how we can address this
without loss unless we add to the dyadic relation between object and
measuring instrument the *tertium quid* of the interpreting observer.
This is not to deny that *some* representation in concatenated dyadic
relations is possible (and of course computationally convenient if our
medium of representation is a relational database). But I would question
whether such a representation can exhaust the content of the measurement
problem such that it would be adequate for e.g. quantum physics.
Of course, for the limited problem before us, constructing a
well-specified upper level artifact, it may be sufficient to declare the
presuppositions that limit it and let those with problems that cannot be
accommodated shop elsewhere.
Lee
On Mon, 19 Mar 2001, West, Matthew MR SSI-GREA-UK wrote:
> Dear Lee,
>
> I thought we had gotten beyond this. Indeed I thought we had got to the
> point where it was demonstrated (by Pat, but by me previously) that in
> representation terms anything can be reduced to dyadic relations.
>
> This caused a change in tack to saying that there are axioms that require
> more than 2 arguments (not a particular surprise to me). The question
> remaining is then whether there are any axioms that cannot be reduced to
> some set of independent axioms that involve only 3 elements.
>
> Regards
> Matthew
> ===============================================================
> Matthew West http://www.matthew-west.org.uk/
>
> Principal Consultant Shell Visiting Professor
> Operations & Asset Management The Keyworth Institute
> Shell Services International The University of Leeds
> http://www.shellservices.com/ http://www.keyworth.leeds.ac.uk/
>
> H3229, Shell Centre, London, SE1 7NA, UK.
> Tel: +44 207 934 4490 Fax: 7929 Mobile: +44 7796 336538
> ===============================================================
>
> > -----Original Message-----
> > From: Josiah Lee Auspitz [mailto:lee@textwise.com]
> > Sent: 17 March 2001 13:24
> > To: West, Matthew MR SSI-GREA-UK
> > Cc: Standard-Upper-Ontology (E-mail); lee@sabre.org
> > Subject: Re: SUO: Irreducible Triadicity
> >
> >
> >
> > Matthew,
> >
> > The "triadic" issue in the example you have given is whether we can
> > analyze this example into triads which add up to the whole
> > picture without
> > any loss of logical content. In listing the attributes of
> > the measurement
> > problem you have already done this, if we can show that each
> > element of
> > the problem-- time of observation, measurement device,
> > measurement scale,
> > place of observation, observing subject, observed object etc.-- is
> > reducible to the pattern O(for object)-R(for representamen)-I (for
> > interpretant), where any R can also be seen as an O for some further
> > O-R-I, and any I can be seen as an O or R for some further
> > O-R-I, and any
> > O may also be an R or an I, and so on, this whole business being the
> > continuum of semiosis, infinitely extendable and infinitesimally
> > refinable.
> >
> > Lee
> >
> > On Sat, 17 Mar 2001, West, Matthew MR SSI-GREA-UK wrote:
> >
> > >
> > > Dear Colleagues,
> > >
> > > This has been a very interesting discussion, in which I
> > have learnt some
> > > things, and been surprised at some things that I thought
> > were common ground
> > > but were not.
> > >
> > > Firstly the good news. I think I now understand what John
> > means when he says
> > > "mediating". He means an activity, or the result of an
> > activity, in which
> > > more than two things are necessarily involved form an
> > ontological viewpoint.
> > >
> > > Pat has explained some theoretical background to graph
> > theory from which I
> > > draw (actually I already knew this) that there is more than
> > one way that the
> > > world can be represented as a graph (or some other
> > formalism) and that the
> > > triadic iirreducibility only applies when you take one particular
> > > representation.
> > >
> > > I have one unanswered question. Part of the claim about irreducible
> > > triadicity is that anything that is higher than triadic can
> > be reduced to
> > > triadic. Pat and Nicola (I think) have suggested that there
> > is no reason why
> > > the limit should be 3 for ontological dependence. So I have
> > presented a test
> > > example about measurement. Measurement is just about the
> > most complicated
> > > thing I have come across in my years of analysis, and I am
> > prepared to
> > > believe that if the information about a measurement can be
> > reduced to triads
> > > that are independent, then it is likely that anything else
> > can. On the other
> > > hand John has not responded to this example, which I repeat below.
> > >
> > > > MW: OK. In that case please show me how a measurement can be
> > > > reduced to triads. A Measurement is an activity that:
> > > >
> > > > has a subject (the thing measured)
> > > > an observer (doing the measuring)
> > > > an instrument (e.g. thermometer)
> > > > a measure (what about the thing is being measured, e.g.
> > temperature)
> > > > a result (the value e.g. 20)
> > > > a Unit of Measure (e.g. Celsius)
> > > > the time when the measurement was taken.
> > >
> > > I would be interested to see whether and how this can be
> > reduced to triadic
> > > or less ontologically dependent elements. If it can't, then
> > there is at
> > > least one case where this does not apply (which is enough)
> > or perhaps as Pat
> > > has been suggesting there has been confusion between graph
> > theory and
> > > ontology.
> > >
> > > Well I guess the next question is "does it really matter?".
> > By this I mean,
> > > does it really matter that there are different mappings
> > from the world onto
> > > graph theoretic representations.
> > >
> > > Unfortunately the answer is "yes", as we discovered in
> > Shell some 10-15
> > > years ago. At about that time many of the 200 or so
> > companies in the Shell
> > > Group were getting into relational databases, mostly
> > developing much the
> > > same systems to do much the same thing in different
> > countries. Something
> > > that we noticed to our horror was that all these systems
> > were generally
> > > incompatible, and that generally they were not
> > transferrable either. We
> > > (then the corporate data management group) were asked to
> > look at why this
> > > was the case.
> > >
> > > The databases were generally documented in data models.
> > (Data Models can be
> > > seen as graphs with entity types as nodes, relationship
> > types as edges, and
> > > attribute types as leaf nodes.) When we examined the data
> > models we found
> > > that one of the (many) problems was that people had mapped
> > the real world
> > > onto these constructs in a variety of ways. Let us take
> > activities as an
> > > example:
> > >
> > > 1) as a relationship type, with the participants at either
> > end of the
> > > relationship.
> > > 2) as a "transaction" - an entity type with a number of dependent
> > > relationships.
> > > 3) as an independent entity type with non-dependent
> > relationships to the
> > > objects involved.
> > > 4) a mixture of 2 & 3.
> > >
> > > 1)
> > >
> > > o------------o o----------o
> > > | | throws | |
> > > | person |>-------------<| ball |
> > > | | | |
> > > o------------o o----------o
> > >
> > > 2)
> > >
> > > o------------o o----------o
> > > | | thrower | |
> > > | |>--------------| person |
> > > | throws | | |
> > > | | o----------o
> > > | | o----------o
> > > | | thrown | |
> > > | |>--------------| ball |
> > > | | | |
> > > o------------o o----------o
> > >
> > > and even 3)
> > >
> > > o------------o o----------o o----------o
> > > | | | | | |
> > > | |--------------<| thrower |>---------| person |
> > > | throws | | | | |
> > > | | o----------o o----------o
> > > | | o----------o o----------o
> > > | | | | | |
> > > | |--------------<| thrown |>---------| ball |
> > > | | | | | |
> > > o------------o o----------o o----------o
> > >
> > > Of course these different structures are not directly compatible
> > > and in many cases arbitrary combinations of these different
> > approaches
> > > were taken.
> > >
> > > So one of the things we did was to study the differences
> > between these
> > > (and other) representations. The conclusions to these have been
> > > implemented in the EPISTLE Core Model. Incidently, the ECM V4.0
> > > has just been published, and can be found at:
> > >
> > http://www.stepcom.ncl.ac.uk/epistle/data/epistle_core_model_v
> ersion_4.htm
> >
> > Regards
> > Matthew
> > ===============================================================
> > Matthew West http://www.matthew-west.org.uk/
> >
> > Principal Consultant Shell Visiting Professor
> > Operations & Asset Management The Keyworth Institute
> > Shell Services International The University of Leeds
> > http://www.shellservices.com/ http://www.keyworth.leeds.ac.uk/
> >
> > H3229, Shell Centre, London, SE1 7NA, UK.
> > Tel: +44 207 934 4490 Fax: 7929 Mobile: +44 7796 336538
> > ===============================================================
> >
>
Josiah Lee Auspitz
17 Chapel Street
Somerville, MA 02144
617-628-6228
fax -9441
email: lee@sabre.org
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