Differential Logic and Dynamic Systems • Discussion 2

Re: Michael HarrisDoes Mathematics “Progress”?Comment

In 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 Universities

The Trivializing of Integration

From 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.  A significant 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.


  • Awbrey, 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.  AbstractOnline.
  • Awbrey, S.M., and Awbrey, J.L. (September 1999), “Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next 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.


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This entry was posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

2 Responses to Differential Logic and Dynamic Systems • Discussion 2

  1. Pingback: Survey of Differential Logic • 3 | Inquiry Into Inquiry

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