Foundational Concepts: A Working Page

Discerning Relations and Shared Conceptual Frameworks Between Academic Silos

By Bruce Camber, In process

About this Working Page: These pages are knowingly always in process and never complete. Within every discipline there are thought leaders who focus on the first principles within that discipline. Back in 1979 it was the focus of my work at MIT, Harvard and Boston University. Every scholar within each discipline was asked similar questions, essentially Kant’s four:

  1. How did this discipline come to be?
  2. What are its foundational concepts?
  3. Where is this discipline going?
  4. What is the deepest meaning and value of this discipline?

At that time, none of these disciplines had the first 67 doublings (notations) out of the 202 that encapsulate the universe. In December 2011 a first-pass at this model emerged. There were only fleeting thoughts that these 202 notations could be a new paradigm. By focusing on the first 67 doublings, there are many possible directions that can be explored — clusters, domains, groups, layers, platforms, ratios, sets, steps… and more.  Within each perspective, new questions can be asked. This rather-simple, mathematically-integrated view of the universe has actual numbers for physical space, time, mass and energy. It has intellectual space for refining our logic and for integrating our mathematics. I believe there is space to reach, left or right, above and below and across the bias, to build a deeper logical path to one’s own work.

Without such a construct, silos emerge.

All the scholars. This link goes to a very limited listing of scholars who have been introduced to our “Big Board-little universe” project. This project is also known as the mathematically-integrated view of the universe and the Quiet Expansion.  These pages will become a repository to study more deeply each discipline through the current work of its finest scholars and leading thinkers. There will be a close commingling with our notation-by-notation analysis that began in summer of 2017: https://81018.com/1-202/

Currently the embedded links for these disciplines (below) may go to a page within Wikipedia. Eventually any link that takes one outside of this site will become part of our footnotes and eventually an analysis of the work of scholars summarized uniquely within this website.

Infinity.  The most common issue within every discipline is the consideration and definition of infinity. Infinity has a role within each, yet it is often ignored, marginalized, or renormalized. Our assumption is that infinity holds the deep, inherent continuities, symmetries and even harmonies that are apparent in our quantum-imperfect universe and that these continuities, symmetries and harmonies are what we can know about infinity.

So, would you like to help?

Subjects-concepts: How do we relate algebraic geometries, Euclidean geometries, projective geometry, category theory, Mandelbrot set, Julia set, Möbius transformations, Kleinian group, S-matrix theory, unitarity equations, Hermitian analyticity, Golden ratio (Phi), the Fibonacci sequence, fluctuation theory, ratio analysis, pi, cubic-close packing of equal spheres, ring theory, and lattice generation?

Scholars-and-their concepts. How do these concepts fit into the 202 notations?

We will ask very specific questions about each scholar’s work. For example, where does the work of Paul Cohen fit in, particularly his conclusion that the continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory? Or, how do we engage historical scholars like Luigi Bianchi and Sophus Lie currently as represented to us by Bob Coeke of Oxford?

Assumptions: Quine–Putnam indispensability thesis. On occasion, both Quine and Putnam would attend a lecture within the series, Boston Colloquium for Philosophy of Science by Boston University’s Center for Philosophy and History of Science; it had been my group from 1971 through 1980.

 SUBJECTS:LogicPhilosophyMathematicsPhysics*
Logic
• Quine_atom		Quine atom   
Philosophy
Ontology
• Ousia
•_Hypostatic
• Forms
• emergence		 Ontology
• Ousia
•_Hypostatic
• Forms
• emergence		  
Mathematics:
• binary ops
• Bifurcation
• Automaton
• axiom
• groups
• sets
• Scalar fields
• Sphere-Stack
• Automorphics
•_Pointfree_Geometries
•Mereotopology
• Langlands
•Trigonometrics
• ZFC
• topos
• Mandelbrot sets
• Path integral
• Topological space
• Infinity		  • binary ops
• Bifurcation
• Automaton
• axiom
• groups
• sets
• Scalar fields
• Sphere-Stack
• Automorphics
•_Pointfree_ Geometries
• Mereotopology
• Langlands
• Trigonometrics
• ZFC
• topos
• Mandelbrot sets
• Path integral
• Topological space
• Infinity		 
Physics*
• emergence
•_Loop_Quantum_Gravity
• spin foams
• string/M Theory
• Causal set theory
• AdS/CFT
• Quantum Gravity
• Amplituhedron
• Grid
• Strings		   •_Loop_Quantum_Gravity
• spin foams
• string/M Theory
• Causal set theory
• AdS/CFT
• Quantum Gravity
• Amplituhedron
• Grid
• Strings
Theology
Infinity		InfinityInfinityInfinityInfinity

Boston Colloquium for Philosophy of Science

  • Towards a Theory of Emergence for the Physical Sciences, Sebastian De Haro, Philosophy, University of Cambridge, U.K.

  • Emergence in Effective Field Theory and Quantum Gravity, Karen Crowther, Philosophy, University of Geneva, Switzerland
  • Equivalence and Emergence within Dualities in Physics
    Jeremy Butterfield, Trinity College, University of Cambridge, U.K.

Perspectivalism in Philosophy of Mind & Philosophy of Science

The Perspectival Nature of Scientific Representation
Michela Massimi, Philosophy, University of Edinburgh, Scotland

Models in Understanding
Catherine Elgin, Philosophy, Harvard Graduate School of Education

Perspectival Computational Models
Mark Sprevak, Philosophy, University of Edinburgh, Scotland

Views from Nowhere: Problems of Perspective in Contemporary Predictive Processing Accounts of Mind & Life
Maria Brincker, Philosophy, University of Massachusetts Boston