Inquiry Into Inquiry

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Re: Michael Harris Does Mathematics Progress ? CommentIn several places I can t find right now I described formalization as an arrow. A related idea occurs in a paper by Susan Awbrey and myself where we discussed a dimension of increasing formalization in our mental models of the world as an obstacle to integrating knowledge across various styles of inquiry. An excerpt follows.Conceptual Barriers to Creating Integrative UniversitiesThe Trivializing of IntegrationFrom reviewing its philosophical sources, we can see that the trivialization of integration hypothesis presents barriers to creating an integrated learning environment. Below we focus on three closely interrelated problematics and the bearing that the triviality of integration hypothesis has on them.Problematic 1 is the tension that arises along a dimension of increasing formalization in our mental models of the world, between what we may call the ‘informal context’ of real-world practice and the ‘formal context’ of specialized study.Problematic 2 is the difficulty in communication that is created by differing mental models of the world, in other words, by the tendency among groups of specialists to form internally coherent but externally disparate systems of mental images.Problematic 3 is a special type of communication difficulty that commonly arises between the ‘Two Cultures’ of the scientific and the humanistic disciplines. Asignificant part of the problem derives from the differential emphasis that each group places on its use of symbolic and conceptual systems, limiting itself to either the denotative or the connotative planes of variation, but seldom integrating the two.ReferencesAwbrey, S.M., and Awbrey, J.L. (May 2001), Conceptual Barriers to Creating Integrative Universities , Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269 284.Abstract. Online.Awbrey, S.M., and Awbrey, J.L. (September 1999), Organizations of Learning orLearning Organizations : The Challenge of Creating Integrative Universities for theNext Century , Second International Conference of the Journal Organization , Re Organizing Knowledge, Trans Forming Institutions : Knowing, Knowledge, and the University in the 21st Century, University of Massachusetts, Amherst, MA. Online.ResourcesDifferential Logic and Dynamic Systems OverviewSurvey of Differential Logiccc: Cybernetics Ontolog Peirce List (1) (2) Structural Modeling Systems Sciencecc: FB | Differential Logic Laws of FormIt is understandable that an engineer should be completely absorbed in his speciality, instead of pouring himself out into the freedom and vastness of the world of thought, even though his machines are being sent off to the ends of the earth; for he no more needs to be capable of applying to his own personal soul what is daring and new in the soul of his subject than a machine is in fact capable of applying to itself the differential calculus on which it is based. The same thing cannot, however, be said about mathematics; for here we have the new method of thought, pure intellect, the very well-spring of the times, the fons et origo of an unfathomable transformation.Robert Musil The Man Without QualitiesRe: Michael Harris Does Mathematics Progress ?Just off-hand, by way of getting grounded and oriented, there are a few questions I d have to ask first.Is mathematics a science, or a form of scientific inquiry?If so, what is the place of mathematics within the sciences?Does science progress?(I mean progress in the sense of progress toward a goal, not necessarily progressivejazz or progressions in music generally.)If so, what is the goal of science?If science has a goal, does mathematics serve it?If so, how?By science or scientific inquiry I meant to focus on species of goal-directed activity with the specific goal of knowledge and to ask whether mathematical arts and crafts and rites fall within that ballpark. We come back to the antic Socratic question of whether we put another quarter in the machine for the sake of an external gain or simply to continue the play for its own sake.In this post I was less concerned with philosophy than with philology which,by the way, is another example of a term that was once seen as hopelesslyantiquated and musty but that has been revived recently.But when you introduce knowledge you have to grapple with truth and objective reality . Philosophy has been so unsuccessful at pinning those down that some would prefer to give up on them altogether. We can choose to call what mathematics generates knowledge but that just leads to the (philological) question of what this has to do with what other practices call knowledge .Not that I don t love wisdom and words, however often their stars may cross, but I invokedMusil rather for the way he syzygied the way of the engineer, the way of the mathematician, and the recursive point where their ways diverge. It s in this frame I thinkof the word entelechy, which I got from readings in Aristotle, Goethe, and Peirce andpromptly gave a personal gloss as end in itself, partly on the influence of Conway s game theory.And that s where I remember all those two-bit pieces I gave up to pinball machines in the early 70s and the critical point in my own trajectory when I realized I would never beat those machines, not that way, not ever, and I turned to the more collaboratory ends of teaching machines how to learn and reason. On A Related Note The Music Of The Primes Now there s a progression of progressions I could enjoy, musically speaking, ad infinitum, and yet this pilgrim would consider it progress, mathematically speaking, if he could understand why the sequentiae should be sequenced as they are. Would that understanding add to my enjoyment? On jugera ResourcesDifferential Logic and Dynamic Systems OverviewSurvey of Differential Logiccc: Cybernetics Ontolog Peirce List (1) (2) Structural Modeling Systems Sciencecc: FB | Differential Logic Laws of Form Re: Peirce List John Sowa : Modal Logic Is An Immense Swamp Dear John,Best title I ve read in a long time! But the really immense swamp critter here is theNaturally Evolved Organon known as ornery natural language which resists any augmentation by mathematics and keeps trying to get by with a motley assortment of evolution s legacy software.The way physics adapted to quantitative change was not by adding tense operators toDescartes analytic geometry but by Leibniz and Newton developing the differential calculus. The way logic will handle qualitative change is by finding the appropriate logical analogue of differential calculus. I took a few steps in that direction with the work linked on the following page.Survey of Differential Logiccc: Cybernetics Ontolog Forum Peirce List Structural Modeling Systems Sciencecc: FB | Differential Logic Laws of Form Re: Definition and Determination (18) (19) (20)Re: FB | The Ecology of Systems Thinking Richard SaundersDon t you think some little bit of unconscious knowledge and logic comes preloaded, àpriori, courtesy of our parents DNA? Is that simply experience one or more generations removed?Dear Richard,Excerpt 21 comes from a lecture on Kant in a series of lectures On the Logic of Science. Peirce s survey of conditions for the possibility of science reaches back through his time s run of the mill dualism of deductive and inductive logic to encompass Aristotle s notice of abductive reasoning. This deeper perspective helps Peirce walk the line between empirical and rational sides of science without tumbling into either ism and it aids him in his quest for the questying beast of Kant s synthetic àpriori. In this setting and under this sum of influences Peirce is led to his prescient theory of information, enabling him to integrate form and matter, intension and extension, into a unified whole.With all that in mind, when Peirce says, all our thought begins with experience, the mind furnishes no material for thought whatever , we have to understand he is using material in the Aristotelian sense of matter versus form. Saying the mind furnishes no material for thought still leaves room for the mind to furnish form for thought. Much the same point is made in our contemporary literatures of cognitive psychology and linguistics under rubrics like poverty of the stimulus and under-determination of theories by data .ResourcesCollection Of Source MaterialsExcerpts on DefinitionExcerpts on DeterminationSurvey of Definition and DeterminationInquiry Driven Systems The Formative Tensioncc: Inquiry List Peirce List (1) (2) (3) (4)cc: Cybernetics (1) (2) Ontolog Forum Structural Modeling (1) (2) Systems Sciencecc: FB | Inquiry Driven Systems Laws of Form Re: Peirce List Robert MartyThank you for this information. I happen to have a work in progress (not yet written) on the question of determination. I discovered that Peirce gave a quite remarkable definition in CP8.361. We thus learn that the Object determines (i.e. renders definitely to be such as it willbe,) the Sign in a particular manner. (CP8.361, in CP8.342 379, from M-20b, 1908).It fits very well with what he writes in Excerpt 21. Hence universal and necessary elements of experience are not determined from without. But are they, therefore, determined from within? Are they determined at all? Does not this very conception of determination imply causality and thus beg the whole question of causality at the very outset? Not at all. The determination here meant is not real determination but logical determination. A cognition àpriori is one which any experience contains reason for and therefore which no experience determines but which contains elements such as the mind introduces in working up the materials of sense, or rather as they are not new materials, they are the working up. (C.S.Peirce, Chronological Edition, CE1, 246 247).I have hosted this working paper on my personal website: The Semiotics.Online, entitled Determine What Determine Means.I appreciate any suggestion or criticism, as usual.Dear Robert,Excerpt 21 comes from Peirce s Harvard Lectures On the Logic of Science (1865). It begins with a question about the possibility of knowledge àpriori and draws conclusions about the grounds of validity for necessary and universal judgements. For ease of discussion Icopy the full excerpt below.Is there any knowledge àpriori? All our thought begins with experience, the mind furnishes no material for thought whatever. This is acknowledged by all the philosophers with whom we need concern ourselves at all. The mind only works over the materials furnished by sense; no dream is so strange but that all its elementary parts are reminiscences of appearance, the collocation of these alone are we capable of originating.In one sense, therefore, everything may be said to be inferred from experience; everything that we know, or think or guess or make up may be said to be inferred by some process valid or fallacious from the impressions of sense. But though everything in this loose sense is inferred from experience, yet everything does not require experience to be as it is in order to afford data for the inference. Give me the relations of any geometrical intuition you please and you give me the data for proving all the propositions of geometry. In other words, everything is not determined by experience.And this admits of proof. For suppose there may be universal and necessary judgements; as for example the moon must be made of green cheese. But there is no element of necessity in an impression of sense for necessity implies that things would be the same as they are were certain accidental circumstances different from what they are. I may here note that it is very common to misstate this point, as though the necessity here intended were a necessity of thinking. But it is not meant to say that what we feel compelled to think we are absolutely compelled to think, as this would imply; but that if we think a fact must be we cannot have observed that it must be. The principle is thus reduced to an analytical one. In the same way universality implies that the event would be the same were the things within certain limits different from what they are.Hence universal and necessary elements of experience are not determined from without. But are they, therefore, determined from within? Are they determined at all? Does not this very conception of determination imply causality and thus beg the whole question of causality at the very outset? Not at all. The determination here meant is not real determination but logical determination. A cognition àpriori is one which any experience contains reason for and therefore which no experience determines but which contains elements such as the mind introduces in working up the materials of sense, or rather as they are not new materials, they are the working up. (C.S.Peirce, Chronological Edition, CE1, 246 247).ReferenceCharles Sanders Peirce, Harvard Lectures On the Logic of Science (1865), Writings of Charles S. Peirce : A Chronological Edition, Volume1, 1857 1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.ResourcesCollection Of Source MaterialsExcerpts on DefinitionExcerpts on DeterminationSurvey of Definition and Determinationcc: Inquiry List Peirce List (1) (2) (3) (4)cc: Cybernetics (1) (2) Ontolog Forum Structural Modeling (1) (2) Systems Sciencecc: FB | Inquiry Driven Systems Laws of Form Re: Peirce List Edwina TaborskyI needed to start thinking of semiotics and sign relations in the light of cybernetics and systems theory. That required me to convert from understanding a sign relation as a relation among three sets, the Object, Sign, and Interpretant domains, to thinking of a sign relation as involving three active systems, Object, Sign, and Interpretant systems, respectively. Various discussions in sundry places led me by a commodius vicus of recirculation back to the environs of old notes I gathered on the topics of Definition and Determination, that being on the occasion of a return to graduate school in a system engineering program where I needed to start thinking of semiotics and sign relations in the light of cybernetics and systems theory.That required me to convert from understanding a sign relation as a relation among three sets, the Object, Sign, and Interpretant domains, to thinking of a sign relation as involving three active systems, Object, Sign, and Interpretant systems, respectively.It will take a few posts to recover my notes from the Internet Archive (Wayback Machine), after which I ll present the excerpts in a more digestible fashion and discuss more fully their implications. Just for starters, a link-repaired version of the anchor post for this series is copied below.Definition and Determination 1It looks like we might be due for one of our recurring reviews on the closely related subjects of definition and determination, with special reference to what Peirce himself wrote on the topics.Arisbe List ArchiveHere is a collection of excerpts on the subject of determination, mostly from Peirce but with a sampling of thoughts from other thinkers before and after him, on account of the larger questions of determinacy I was pursuing at the timeExcerpts on Determination May 2001 Aug 2001Collection Of Source MaterialsOne naturally looks to the Baldwin and Century dictionaries for Peirce-connected definitions of definition but I d like to start with a series of texts I think are closer to Peirce s own thoughts on definition, where he is not duty-bound to give a compendious account of every significant thinker s point of view. It may be a while before I get all the excerpts copied out.Excerpts on DefinitionExcerpts on Determinationcc: Inquiry List Peirce List (1) (2) (3) (4)cc: Cybernetics (1) (2) Ontolog Forum Structural Modeling (1) (2) Systems Sciencecc: FB | Inquiry Driven Systems Laws of Form Enter your email address to follow this blog and receive notifications of new posts by email. Email Address:

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