Richard, Rich, Leo and all, (01)
thanks for the articles Richard, here's one link to Pylkkänen's book: (02)
http://www.springerlink.com/content/978-3-540-23891-1#section=319512&page=1&locus=0 (03)
I'd say that Bohm is on the right track and I've learned a lot from
him, but there's some elements that are not required, or could be
replaced by simpler alternatives, such as his "active information". (04)
RC:
But history shows that generalizing from one level to the next is
fraught with inaccuracies. (05)
That's an important notion and it shows that the topic is really
complex and difficult. The goal of the formalization of the layer-cake
intepreration is to clarify the topic, to clarify the ontology of
properties. The simplest syntax I've come up with is the following
(note that when you type P_{n} in LaTex, it is shown as P with the
index n). (06)
Properties are denoted by P,J,K.
Relations are denoted by R
Level n property P is denoted as P_{n}.
The membership relation is denoted by €. (07)
Let property P_{n} be composed of two level n-1 properties J_{n-1} and
K_{n-1}, which are related by the relation R: (08)
P_{n}=R(J_{n-1},K_{n-1}) (09)
Any comments about the syntax? (010)
As another example, I'll translate Rich's above comment into the
language of the layer-cake interpretation. Some levels can be
identified, like the level of the properties of atoms (n), the level
of the properties of molecules (n+1), and the level of the properties
of some combination of molecules (n+2). Let a particular combination
of molecules have some relationally structural property P_{n+2}.
P_{n+2} is composed several level n+1 properties (among which is
J_{n+1}), which are composed of several level n properties (among
which is K_{n}): (011)
K_{n} € J_{n+1} € P_{n+2} (012)
Now, Rich's comment can be translated: (013)
But history shows that identifying the meaning of the membership
relation in "K_{n} € J_{n+1}" with the meaning of the membership
relation in "J_{n+1} € P_{n+2}" is fraught with inaccuracies. (014)
So, what is the difference of € in "K_{n} € J_{n+1}" and in "J_{n+1} €
P_{n+2}"?
That's difficult to say, but still the identification of levels is
useful. It clarifies the ontology of properties. (015)
For instance, consider a bullion of gold. In common parlance everybody
says "of course it has the property of being gold". You can bisect it
in two halves and have two smaller bullions of gold. But when you
proceed in bisecting it, at some point you reach the limit of the
minimal particular that can be gold. From here it is easy to see that
the original bullion was composed of minimal particulars that can be
gold, i.e., when we speak accurately, the original bullion does not
have a property "being gold", but only its minimal parts that are able
to instantiate the property "gold of type x" have that property. (016)
The ontology of properties is opened up: every instantiated structural
property is instantiated in a minimal particular that is able to
possess that property.
I hope that with generalizations such as these, the ontology of
properties is soon compact. My goal is to find out what is the minimal
set of the required generalizations. (017)
-Avril (018)
Lainaus "Richard Vines" <plessons@xxxxxxxxxxxxxxx>: (019)
> Hi Avril:
>
>
>
>> The hierarchy of levels is central to e.g. David
>
>> Bohm's ontology and a good intro to that can be found e.g. from Paavo
>
>> Pylkkänen's Mind, Matter and the Implicate Order.
>
>
>
> Like others, if you have anything on this, this would be interesting.
>
>
>
>> If anyone is aware of citations of systems alike, please let me know,
> thanx!
>
>
>
> Whilst this paper
> <http://www.orgs-evolution-knowledge.net/Index/DocumentKMOrgTheoryPapers/Hal
> lNousala2010AutopoiesisCognitionKnowledgeSelfSustainingOrganizations(final).
> pdf> on autopoiesis is not exactly in line with your request for a “system
> alike’, it still might be useful. Note that this paper is about knowledge in
> higher order sense (i.e. self sustaining organisations). These matters
> remain highly contested. The areas of substantial controversy lie at the
> boundaries between the ontologies of knowledge premised on constructivist
> and the realist world views. I am very interested in the prospects of
> reconciling these positions and think that Karl Popper’s three world
> ontology offers a starting point for this to be explored. I think Popper’s
> ontology can be consistent with both a constructivist and a realist’s
> position, but there are now 30 years on, quite a few missing ingredients for
> it to be coherent.
>
>
>
>> For instance, a level n property P_n is composed of level n-1
>
>> constituents, where the constituents are members of P_n. The
>
>> constituents of a property are lower-level properties and relations.
>
>> P_n = the constituent properties of P_n + the relations between the
>
>> properties. Emergence is a tag for complexity that is not understood
>
>> or explained.
>
>
>
> If you want to read a paper that highlights why emergence is a tag for
> complexity that is not understood or explained, then you might also be
> interested in this piece on chromosome variation
> <http://www.orgs-evolution-knowledge.net/Hall2010ChromosomeVariationGenomics
> SpeciationEvolutionSceloporusLizards.pdf> . Again, it is not quite what you
> are after, but could be useful as background to your views about hierarchy.
>
>
>
>
>
> Richard
>
>
>
> Papers quoted are:
>
> 1. Hall, W.P., Nousala, S. 2010. Autopoiesis and knowledge in
> self-sustaining organizational systems
> <http://www.orgs-evolution-knowledge.net/Index/DocumentKMOrgTheoryPapers/Hal
> lNousala2010AutopoiesisCognitionKnowledgeSelfSustainingOrganizations(final).
> pdf> . 4th International Multi-Conference on Society, Cybernetics and
> Informatics: IMSCI 2010, June 29th - July 2nd, 2010 – Orlando, Fla.
> 2. Hall, W.P. 2010. Chromosome variation, genomics, speciation and
> evolution in
> <http://www.orgs-evolution-knowledge.net/Hall2010ChromosomeVariationGenomics
> SpeciationEvolutionSceloporusLizards.pdf> Seceloporus lizards. Cytogenetics
> and Genome Research (DOI:10.1159/000304050).
>
>
>
>
>
> (020)
--
Always forward towards the supreme maxim of scientific philosophizing (021)
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