Section IV. Re-envisioning Nature; Re-envisioning Science
Track 2: Intuition in Mathematics and Physics
Mathematics and physics are in need of being re-envisioned imaginatively by taking our deepest intuitions into account. Take physics. Physicist focus on “lifeless nature” and hence, from a methodological point of view they exclude from their description of nature all characteristics of “nature alive” such as feeling, creativity, purpose, value. Whitehead writes: “As a method this procedure is entirely justifiable, provided that we recognize the limitations involved.” However, the overwhelming success of physics has led to disregarding its limitations, and to turning the methodological exclusion of live into an ontological exclusion, denying the existence in nature of feeling, creativity, purpose, value. But our deepest intuitions, which rule all human practices, from the playgrounds to the law courts, involve feeling, creativity, purpose, value. So, Whitehead writes, “the science of nature stands opposed to the presuppositions of humanism,” and in the light of this alienation of humans from nature, only two options seem left. Either we declare our deepest intuitions of feeling, creativity, purpose, value, to be illusions, or we declare the human soul to be part of a non-natural world: the supernatural world as opposed to the natural world, a religious escape; or the world of mind as opposed to the world of matter, a Cartesian escape; or the practical world of values as opposed to the theoretical world of facts, a Kantian escape. There is, however, a third option: the refusal to accept the strict separation of lifeless nature from nature alive, and the endeavor to turn the bifurcating opposition between physics and intuition into a fruitful contrast.
- Whitehead quote: “The transitions to new fruitfulness of understanding are achieved by recurrence to the utmost depths of intuition for the refreshment of imagination.
Track 2 Outline
Friday, June 5, from 2 to 3.30 pm :
The Interplay of Logic and Intuition in Mathematics, Measurement and Intuition in Physics, and Rationality and Intuition in philosophy – Ronny Desmet
Friday, June 5, from 4 to 5.50 pm :
Mathematical Beauty as a Paradigm for All Beauty – Jean Paul Van Bendegem
Saturday, June 6, from 11 to 12.30 am :
This Session consists of two Lectures by the authors of Foundations of Relational Realism:
- Lecture 1. The Ontology of Contextualized Potentiality: Whiteheadian Internal Relations in Quantum Mechanics – Michael Epperson
- Lecture 2. Sheaves of Boolean Internal Relational Frames: A Local-to-Global, Whiteheadian Approach to Quantum Geometry – Elias Zafiris
Saturday, June 6, from 2 to 3.30 pm :
This Session consists of three Lectures by Ron Phipps:
- Lecture 1. Whitehead’s Concept of Metaphysics and Its Creative Relationship with Science.
Whitehead’s concept of metaphysics will be discussed in light of Whitehead’s historic letter to his personal assistant at Harvard, Henry S. Leonard. Phipps will discuss the contrasts between logical positivism and logical empiricism with Whitehead’s speculative metaphysics; this contrast will include Leonard”s deeply insightful formal comments to the letter. Phipps will discuss Leonard’s work with Gödel to integrate propositional and modal logic, the logic of truth and that of potentiality and possibility. He will introduce the concept of “integrative philosophy” as best capturing Whitehead’s monumental philosophic enterprise. This lecture may take 20 minutes or so with 10 minutes for discussion.
- Lecture 2. Whitehead’s transformation of the Ontology of Geometry.
This lecture will include Whitehead’s method of extensive abstraction, Leonard’s calculus of individuals, which led to the mathematical field of mereology, and Karl Menger’s “Menger’s sponges.” (Karl Menger was a member of the Vienna School and a colleague of Kurt Godel.) This may take 15 minutes of presentation and 5 – 10 minutes of discussion.
- Lecture 3. Implications of Whitehead’s Metaphysics to Theoretical Physics.
An outline of the revolutionary and transformative implications of the creative development of Whitehead’s mature metaphysics to the following areas of theoretical physics: cosmology, particle theory, including the standard model), quantum theory, Einstein’s relativity theory, the Higgs field, the interactions of physical and emergent mental attributes. This will include a model of a spatially infinite, temporally eternal, qualitatively open and organically integrated universe rich in finite domains of causal potentialities of atomic occasions (“puffs of becoming”) perpetually emerging and perpetually perishing. The talk may be about 25 minutes and discussion for the rest of the session.
Saturday, June 6, from 4 to 5.50 pm :
This session consists of three Lectures of 20 minutes by Gary Herstein, each time followed by 10 minutes of discussion:
- Lecture 1. Intuition and Radical Empiricism
- Lecture 2. The Measurement Problem of Cosmology
- Lecture 3. Intuitions, Models, and Explanations
Sunday, June 7, from 11 to 12.30 am :
Actualization of Potential –
Peter Fimmel (presenter), Rob Valenza (respondent), Gary Herstein (moderator) & Hank Keeton (Organizer):
Peter Fimmel will present his theory of the Actualization-of-Potential (AoP), emerging from the counter-intuitive physical consequences of Dirac’s equation for the electron. Rob Valenza will respond by engaging the photon and its internal-external temporal attributes. Gary Herstein will moderate from the perspective of Whitehead’s bimetric theory of gravity. Audience participation required.
Sunday, June 7, from 2 to 3.30 pm :
This session consists of three Lectures of 20 minutes by Arran Gare, each time followed by 10 minutes of discussion:
- Lecture 1. Revisiting Grassmann. The Roots of Grassmann’s Conception of Mathematics in Schelling’s Process Metaphysics.
Grassmann was a major influence on Whitehead’s early work, and I will try to show that understanding the tradition of thought of which Grassmann’s extension theory was a development can both clarify and be clarified by Whitehead’s claims that ‘Mathematics is the most powerful technique for the understanding of pattern, and for the analysis of the relationships of pattern’ and ‘mathematics is concerned with certain forms of process issuing into forms which are components for further process.’
- Lecture 2. From Grassmann to Robert Rosen via Category Theory
Category Theory was developed after Whitehead, but facilitates far better than logic and set theory the idea of mathematics as the study of pattern, the relationships of pattern and forms of transition. William Lawvere, the great champion of Category Theory, traces it back to Grassmann. Robert Rosen, who studied with Saunders Mac Lane, extended Category Theory into a general theory of modeling and then attempted to develop models adequate to living processes characterized by final causes, work that is now coming to be more appreciated by mathematicians and biologists. I will attempt to explain Rosen’s ideas on this.
- Lecture 3. New Developments in Mathematics
Rosen’s work has inspired new developments in mathematics associated with the ‘biomathics’ movement, and a further questioning of the very idea of what mathematics is. Such work requires a ‘synthetic’ philosophy of mathematics. I will attempt to characterize some of these developments.
Sunday, June 7, from 4 to 5.50 pm :
This session consists of two Lectures of 35 minutes, followed by Q&A time:
- Lecture 1. A Whiteheadian Evaluation of John Conway and Simon Kochen’s Freewill Theorem – Robert Valenza
Robert Valenza will begin with a presentation that lays out the background technical issues and then provides a relatively simple and accessible (for the broad audience) account of the Freewill Theorem, its relationship to Bell’s Theorem, and its likely significance (e.g. as supportive of a panexperientialist perspective).
- Lecture 2. Summing Up – Timothy Eastman
Timothy Eastman will then make a presentation that attempts to bridge the following: Philip Clayton’s Plenary Session, Desmet’s Session 1, and the Epperson-Zafiris Session 3 (with reference to their new work ‘Foundations of Relational Realism’).