Joseph -- On Tue, Oct 18, 2011 at 11:14 AM, Joseph Brenner <joe.bren...@bluewin.ch>wrote:
> ** > Dear Gavin, Loet and Colleagues, > > Gavin raises a fair question as to the reasons for my objection to the use > of category theory > with respect to information. My answer is that it suffers from the same > limitations as standard truth-functional logic, set theory and mereology: > > Logic: absolute separation of premisses and conclusion > Set Theory: absolute separation of set and elements of the set > Mereology: absolute separation of part and who > Category Theory: exhaustivity and absolute separation of elements of > different categories. (The logics of topoi are Boolean logics). > 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 <garr...@xtra.co.nz> > *To:* 'Joseph Brenner' <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. > > > > > > > _______________________________________________ > fis mailing list > fis@listas.unizar.es > https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis > >
_______________________________________________ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
