Dear Joseph,
Perhaps, this is a repeat of a previous discussion and my problem may be
based on my confusion of the semantics: both "logic" and "category theory"
seem to indicate a static (epistemic) scheme in contrast to a calculus. Of
course, these schemes allow for updates, but that leads to comparative
statics and not yet to dynamics.
The assumption in comparative static is that time can be exogenized. In the
constructivist tradition time is constructed in terms of the communication
of frequencies among systems which tick with their own self-referential (and
potentially changing) clocks. Newtonian time and calculus can, for example,
be considered as a specific construct of 17th century natural philosophy.
("The time of the Lord is the best of all times" as in Bach's Actus
tragicus.)
I am making this remark because Shannon's information theory provides us
with a calculus based primarily and mainly on discrete time-events. Why
would one go back to comparative statics? How is "Logic in Reality" to be
assessed from this perspective?
Best wishes,
Loet
_____
Loet Leydesdorff
Professor, University of Amsterdam
Amsterdam School of Communications Research (ASCoR),
Kloveniersburgwal 48, 1012 CX Amsterdam.
Tel.: +31-20- 525 6598; fax: +31-842239111
<mailto:l...@leydesdorff.net> l...@leydesdorff.net ;
<http://www.leydesdorff.net/> http://www.leydesdorff.net/
From: fis-boun...@listas.unizar.es [mailto:fis-boun...@listas.unizar.es] On
Behalf Of Joseph Brenner
Sent: Friday, October 28, 2011 9:37 AM
To: Stanley Salthe; fis
Subject: Re: [Fis] Category Theory and Information. Back to Basics
Dear Stan,
To return to your question, I think that there is a disjunction between our
usual logics and the actual, changing world but that it is fatal only in
those logics. Logic in Reality reduces to standard logic for simple process
phenomena involving minimal interactive aspects - those which science
handles easily. But LIR applies to more complex phenomena whose evolution I
would not consider outside science. Could we say that LIR is a way of
bringing change better within science?
Thus my answer to your question is yes. LIR, to use your phrase, encompasses
change as it happens. It describes logical characteristics of the evolution
of processes in a multi-dimensional configuration space. The elements of the
logic are changing values of the actuality and potentiality of the elements
in interaction (e.g., system and environment). The disjunction thus becomes,
itself, a process describable by LIR.
I do not expect that people who wish to retain the characteristics of
standard category theory can accept the above any more than those who
require that logic refer only to propositions and their truth-values. I have
said that a conceptual mathematical theory applicable to my Logic in Reality
is both possible in principle and desirable. I only insist that none such
yet exists, since what does exist is eliminative with respect to the
interactive realities LIR attempts to discuss, among them information.
Cheers,
Joseph
----- Original Message -----
From: Stanley N Salthe <mailto:ssal...@binghamton.edu>
To: joe.bren...@bluewin.ch ; fis@listas.unizar.es
Sent: Tuesday, October 18, 2011 11:16 PM
Subject: Re: [Fis] Category Theory and Information. Back to Basics
Joseph --
SS: Your objection seems to me to imply a fatal disjunction between our
usual logics -- the basis of science -- and the actual (changing) world.
For example, in biological ontogeny we begin at one scale, and GRADUALLy
assemble a larger scale. During this transition the system is ambiguous as
to scale. It is CHANGE which faults our thinking here, not the idea that a
developing embryo can be modeled as existing at more than one scale. I
suppose you can then tell us that your system of logic (LIR) takes care of
this, by encompassing change as it happens. Yes?
STAN
For complex process phenomena such as information, involving
complementarity, overlap or physical interactions between elements, these
doctrines fail. The "mathematical conceptualization" they provide does not
capture the non-Markovian aspects of the processes involved for which no
algorithm can be written. If any algebra is possible, it must be a
non-Boolean one, something like that used in quantum mechanics extended to
the macroscopic level.
I have proposed a new categorial ontology in which the key categorial
feature is NON-separability. This concept would seem to apply to some of the
approaches to information which have been proposed recently, e.g. those of
Deacon and Ulanowicz. I would greatly welcome the opportunity to see if my
approach and its logic stand up to further scrutiny.
As Loet suggests, we must avoid confounding such a (more qualitative)
discourse with the standard one and translate meaningfully between them.
However this means, as a minimum, accepting the existence and validity of
both, as well as the possibility in principle of some areas of overlap,
without conflation.
Best,
Joseph
----- Original Message -----
From: Gavin Ritz
To: 'Joseph Brenner'
Sent: Tuesday, October 18, 2011 10:45 AM
Subject: RE: [Fis] Chemo-informatics as the source of morphogenesis -
bothpractical and logical.
Hi there Joseph
This takes us
back to the question of the primacy of quantitative over qualitative
properties, or, better, over qualitative + quantitative properties.
Is this not a good reason to use category theory and a Topos (part of an
object), does not the axiom of "limits" and the axiom of "exponentiation-
map objects" deal philosophically with "quantity and limit" and "quality and
variety" concepts respectively.
Is this not the goal of category theory to explain the concepts in a
conceptual mathematical way.
Regards
Gavin
This for
me is the real area for discussion, and points to the need for both lines
being pursued, without excluding either.
----- Original Message -----
From: Gavin Ritz <mailto:garr...@xtra.co.nz>
To: 'Joseph Brenner' <mailto:joe.bren...@bluewin.ch>
Sent: Tuesday, October 18, 2011 10:45 AM
Subject: RE: [Fis] Chemo-informatics as the source of morphogenesis -
bothpractical and logical.
Hi there Joseph
This takes us
back to the question of the primacy of quantitative over qualitative
properties, or, better, over qualitative + quantitative properties.
Is this not a good reason to use category theory and a Topos (part of an
object), does not the axiom of "limits" and the axiom of "exponentiation-
map objects" deal philosophically with "quantity and limit" and "quality and
variety" concepts respectively.
Is this not the goal of category theory to explain the concepts in a
conceptual mathematical way.
Regards
Gavin
This for
me is the real area for discussion, and points to the need for both lines
being pursued, without excluding either.
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