Foundational Concepts: A Working Page

Discerning Relations and Shared Conceptual Frameworks Between Academic Silos

By Bruce Camber, February 2019

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 of that discipline. Back in 1979 it was the focus of my work at MIT, Harvard and Boston University.   Every scholar within a discipline was asking similar questions: (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. This model was 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. Our mathematically-integrated view of the universe creates actual physical space and intellectual space for refining our logic and for integrating our mathematics. 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 who have been introduced to our “Big Board-little universe” project, also known as the mathematically-integrated view of the universe, will also be listed here.  These pages will become a repository to more deeply study each discipline through the current work of its leaders. 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 linked disciplines below may go to a page within Wikipedia. Eventually all links that take one outside of this site will be within the footnotes only. Eventually, these links will go to the particular work of scholars summarized uniquely within this website.

A common issue within each discipline is their consideration and definition of infinity. Infinity has a role within each yet it is often ignored, marginalized, or renormalized. Our assumption is that infinity is the deep, inherent continuities, symmetries and even harmonies that are apparent in our quantum-imperfect universe.

So, want to help?

Subjects-concepts :  Where are 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, picubic-close packing of equal spheres, ring theory, and lattice generation?

Scholars-their concepts. How does it fit into the 202 notations? Also, 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? Just as a test, how do we engage historical scholars like Luigi Bianchi and Sophus Lie as represented 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 GravityKaren 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

Friday,  April 12th, 2019
STH B24 (Oxnam Room), 745 Commonwealth Ave.

1:00 pm – 5:00 pm

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