Dear Guenther,
I believe that this view of how concepts can be defined is easy to understand
but might be
overly optimistic and simplistic.
Numbers may not be the best examples for everyday concepts. We can ask our
biologists,
who has so far been able to define the objective property set of at least a
sparrow.
What worries me even more is, that the problem is pushed to the properties, as
if they were
all obvious, objective and known. So, the approach does neither tell us how we
get to properties,
nor how we can agree ("without secrets") on concepts once they are based on
intuitive properties. Even the
concept of counting seems to me beyond true logical definition. See also David
Wiggins, who claims
that some fundamental concepts exhibit cyclic dependencies in the discussion of
identity, which is
a prerequisite of counting.
I don't think that we can keep out cognitive psychology if we want to describe
a reasonable set of
concepts (and properties) for cultural documentation. I prefer to regard
concepts as an empirical fact,
in the sense that humans are capable to agree with a certain precision on
concepts, however we come
to their formation. As a practictioner, I do not need more than this
ontological commitment.
Best,
Martin
Guenther Goerz wrote:
Dear Christian-Emil,
I think there is no need to be worried. Basically, things are quite
easy to understand and no set theory and no higher order logic are
required, although the proposed scope note for E89 seems to me rather
myterious and not very helpful. I think, the essentials can be
explained in a rather simple way which everybody will be able to
understand.
So let's start with a basic everyday scenario: Given a material object
we can point to --- common agreement about that simple fact assumed
---, we could use
a) a proper noun to address it (like "Emil"), or
b) a common noun or a definite description (as "man")
to refer to it. The second case explains the use of the term "man" by
pointing to examples (and counterexamples). In this way, we can only
address or refer to individuals, but not concepts: you can point to
the sign "IIIIIII" or "VII" or --- taken the cultural history of
number writng systems for granted --- the sign "7" , but not to the
concept of "number 7" oder just the concept of "number". Predication,
of course, is not a definition. If we want to define the concept of
"man" or "number", we need some more linguistic expressivity.
How do we get to concepts? Frege says, by abstraction, in the
following way: Under a given goal or purpose, we name explicitly and
positively certain properties, and we collect individuals which have
the same properties in a class, e.g. we collect all objects
representing the same number of counting signs in a class.
Mathematically spoken, this is an equivalence class partition, but
this can be handled by practicioners without understanding equivalence
relations at all. The decisive point is that we make a
linguistic/logical transition (only, no psychological operation etc.
--- keep in mind that Frege's abstraction was introduced at the time
where psychologism in mathematics was heavily criticzed) in that we
now speak about "abstract objects", but those are nothing else than
equivalence classes where any element may be used as a representative:
take seven strokes at the wall or seven nodes in a quipu or seven eggs
in a basket... No secret at all behind the concept of "number". So,
abstraction is a methodological "facon de parler", we speak about the
same individual objects in a new fashion: Abstracta are
linguistic/logical constructs, i.e. objects of language, and nothing
mental (as the tradition from Aristotle through Ockham --- yes, also
the Nominalists were mentalists --- to Descartes claimed).
If we build sentences which contain a defined concept as, e.g.,
"number", we speak "about" it, e.g. "The number 7 is a prime number"
(given the definition of prime numbers in advance).
This should be sufficient to demystify the Dahlberg diagram (although
I don't agree with everything she claims): We have an object, item of
reference, we use a linguistic sign to refer to it and we build
abstractions ("synthesis") by explicitly naming relevant properties.
Furthermore, we can construct sentences which say something "about" an
item of reference, i.e. by subsuming it under a given class, talk
about values of its properties, etc. So, I think, quite simple, no
artificial popularization level required, and no reason to worry.
The object-centered perspective comes in if we arrange concepts in a
hierarchy, i.e. if we describe prime numbers as a special kind of
numbers, etc., given by a terminological rule "if n is a prime number
then n is a number", etc. Assuming appropriate definitions, then
prime numbers "inherit" all general properties any number has... a
rather obvious idea. As for granularity, there is no general
recommendation except the fact that the degree of detail of a
description depends on the what you want to do with it; even as a
physicist you will not describe a piece of wood in quantum mechanical
terms if you want to build a table, but if you are planning some a
material science experiment you might want to extend your description
to the atomic level for obvious reasons.
Would you think that I left out something VERY important??
Hope this helps,
best wishes,
-- Guenther Goerz
On 4/29/08, Christian-Emil Ore <[email protected]> wrote:
Dear all,
I follow the interesting discussion about E89 Propositional Object and
Symbolic Object, 'refer to' and 'is about'. This is a non trivial topic
and specially interesting for people with background in formal
philosophy or logic. That is ok for me since I have this background (set
theoretical models for higher order type theory).
The introduction of higher level philosophical concepts in the model
may make the model harder to understand for persons without special
training in and/or interest in formal logic. This worries me.
One of the major advantages of CRM is the possibility to use the object
oriented formalism to choose levels of granularity.
It may be so that it could be an idea to have a granularity dimension
also on the philosophical complexity, that is, a kind of popularisation
axis (without throwing out the nicely and concise defined baby with the
water)? This may also make it easier to formulate an operational
compatibility requirement. It may also make CRM easier to understand for
a larger number of museum/cultural heritage persons form whom it was
originally intended (I at least believe).
Regards
hristian-Emil
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