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 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 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
Re: [Fis] Category Theory and Information. Back to Basics
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
Re: [Fis] Category Theory and Information. Back to Basics
Joseph -- On Fri, Oct 28, 2011 at 3:37 AM, Joseph Brenner joe.bren...@bluewin.chwrote: ** 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. So, just to get a clearer statement -- we can have a differential equation describing some kind of change. But here the constants are fixed, and so the change is predetermined, and used to describe only average, standard or characteristic changes. So, you seem to be saying that in LIR format one can describe changes where the constraints are not fixed. If so, would the changes of the constants be in some way predetermined? Or could that be open as well? 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. Does the above comment give some hint of what would be required, or accomplished by this math? STAN Cheers, Joseph - Original Message - *From:* Stanley N Salthe 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
Re: [Fis] Category Theory and Information. Back to Basics
Hi Joseph 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 whole Category Theory: exhaustivity and absolute separation of elements of different categories. (The logics of topoi are Boolean logics). From my limited working with Category Theory, it covers all the aspects you mention above, the logic by the subobject classifier, sets as objects, plus the arrows as functions. Associativity and identity as parts and wholes, plus the axioms of a Topos, which is part (is the part of the whole) of an object etc. (quantity, quality, variety, truth testing, unbounded-ness) The whole point of category theory is to be able to map dynamical systems. For complex process phenomena such as information, I don't understand what's the complex part of 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. Is this not the whole point of Category theory. Regards Gavin 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 mailto:joe.bren...@bluewin.ch 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. ___ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
