Heteromorphic Approach to Adjunctions

Saunders Mac Lane famously remarked that “Bourbaki just missed” formulating adjoints in a 1948 appendix (written no doubt by Pierre Samuel) to an early draft of Algebre–which then had to wait until Daniel Kan’s 1958 paper on adjoint functors. But Mac Lane was using the orthodox treatment of adjoints that only contemplates the object-to-object morphisms […]

The new partitional approach to (literally) interpreting quantum mechanics

This paper presents a new `partitional’ approach to understanding or interpreting standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set and, conversely, the math of partitions is a skeletonized set level version of the math of QM.

“Follow the Math” Preprint

The slogan “Follow the money” means that finding the source of an organization’s or person’s money may reveal their true nature. In a similar sense, we use the slogan “Follow the math!” to mean that finding “where the mathematics of QM comes from” reveals a good deal about the key concepts and machinery of the theory.

Partitions, Objective Indefiniteness, and Quantum Reality

  This paper, published in the International Journal for Quantum Foundations, is a shorter introductory paper following up on my recent “Follow the Math!” paper in the Foundations of Physics. The point is to show that the mathematics of QM is the vector (Hilbert) space version of the mathematics of partitions at the set level. […]

Abstraction in Math and Superposition in QM

Abstraction turns equivalence into identity, but there are two ways to do it. The goal is to use the second notion of abstraction to shed some light on the notion of an inde…finite superposition in quantum mechanics.

4Open: Special Issue: Intro. to Logical Entropy

4Open is a relatively new open access interdisciplinary journal (voluntary APCs) covering the 4 fields of mathematics, physics, chemistry, and biology-medicine. A special issue on Logical Entropy was sponsored and edited by Giovanni Manfredi, the Research Director of the CNRS Strasbourg. My paper is the introduction to the volume.

Book Draft: The Logic of Partitions

This book draft is an introduction to the logic of partitions on a set as well as the (quantum) logic of partitions (direct-sum decompositions or DSDs) on a vector space.

Book draft: Quantum Mechanics over Sets

Quantum mechanics overs sets (QM/ℤ₂ or QM/Sets) is a pedagogical or `toy’ model of finite-dimensional quantum mechanics (QM/ℂ) that reproduces in the simplified setting of vector spaces over ℤ₂ the essentials of projective measurements, the double-slit experiment, the indeterminacy principle, entanglement, Bell’s Theorem, the statistics of indistinguishable particles, and so forth,

The Logical Theory of Canonical Maps

The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions.

Negation and Implication in Partition Logic

Our purpose in this paper is to explore the notions of negation and implication in that other mathematical logic of partitions.