The First Science Project
Research since January 2010
I have worked full time on the First Science Project since January 2010. It began as a book, The First Science and the Generic Code (see Books), an exploratory book setting the path for the next phase of the project. That phase produced the First Calculus, earlier called the Generic Calculus, and the corpus described on this page: papers, supplementary books and computational verification packages.
For about three centuries the sciences have advanced on the quantitative calculus, the mathematics of number, measurement and rate of change. The First Science Project develops a complementary qualitative calculus, the First Calculus: a mathematics of organisation, disposition and relation. It rests on one principle, First-Classness: nothing in a system is intrinsically privileged, so there is no preferred origin, no special container and no external vantage point. The starting point is the Generic Entity, a single entity of wholly undetermined character, taken before number, order or any distinguished element is admitted. From First-Classness the calculus derives the complementary opposition of toHave (F) and toBe (M), the monads, and four elementary dyadic types.
The papers apply the calculus to logic, philosophy, physics, biology and computing. The Corpus Index on Zenodo is a living register of every paper, supplementary book and verification package, with all their versions. New papers and versions are added to it as they are deposited. The Corpus page on this site links to it.
Recent papers
Generic Logic: Completion and Ground in the AUG/UGG Composite
Starting from the Generic Entity, it develops having and being into four directed dyadic types. Generic adjunction (AUG) yields the balance law; generic unjunction (UGG) has two termini and a supplied FM completion. The Stoic sage is the principal test case: the paper reconstructs the architecture of infallible assent without making infallibility a personal faculty.
From Mathematical Logic to Logical Mathematics: Adjunction, Ramification, and First-Class Completion
Compares the concrete adjunction of the First Calculus with categorical adjunction and with Russell’s ramified theory of types. It proposes Qualitative Logic leading to Logical Mathematics, and reads the Stoic criterion of body and the five indemonstrables as the logical antecedent of the concrete adjunction.
Neither Haecceity nor Non-Individual: Dispositional Individuation and the Identity of Indiscernibles
The Principle of the Identity of Indiscernibles is usually tested against cases such as Kant’s droplets and Black’s spheres, in which numerically distinct entities share every qualitative property. The paper adds a fourth response to the three standard ones (primitive thisness, weak discernibility, non-individuals), derived from First-Classness: the entities are numerically distinct because of a dispositional asymmetry, the complementary opposition between having content (F, toHave) and being content (M, toBe).
Twistor Incidence and the First Calculus: Penrose, Neiman, and the AUG/UGG Spacetime Codons
A bridge paper between twistor theory and the First Calculus, written for the MONORG programme. It identifies the Penrose sector, twistor incidence in conformal Minkowski space, with the autonomous codon AUG/C, and the Neiman sector, de Sitter twistors, with the non-autonomous codon UGG/G’. The two codons couple as a spacetime molecule.
The First Calculus, the Minkowski Signature, and Penrose’s Twistor Programme
Compares Roger Penrose’s twistor programme with the First Calculus. Read from its dispositional side, the First Calculus gives spacetime as a projected triad whose three dispositions correspond to the timelike, spacelike and lightlike cases, with a fourth, singular disposition completing the frame. It recovers fundamental chirality, the demotion of the located point, and a Lorentzian structure beneath the metric.
Foundations
The First Calculus: Dyadology and Generic Adjunction
Develops a constructive qualitative calculus complementary to the quantitative calculus of modern science. From the Generic Entity and First-Classness it derives the opposition of toHave and toBe, the Indeterminate Dyad, the sea of monads, four primitive dispositional dyads, and the H-diagram, an arrow-theoretic calculus of qualitative organisation. It reconstructs Leibniz’s unfinished Analysis Situs in operational form, and relates the calculus to Category Theory, Geometric Algebra and Heaviside’s operational calculus.
Monads as Generic Substratum: A Foundational Reconstruction of Leibniz’s Monadology
Completes the formalisation of Leibniz’s Monadology within the First-Classness framework. It establishes the monad as a gendered entity constrained by First-Classness, and fixes what the monadology requires of the dyadology that follows, naming the four dyads as the next alphabet. It sets the terms for Leibniz’s envisaged Analysis Situs, a geometry of position without number, and gives the qualitative foundation that precedes the quantitative Second Calculus.
Dispositions of the Quantum Object
Defines the Generic Entity as an attribute-free object constrained by First-Classness. It derives ontological gender as the articulation that preserves First-Classness, with toBe (M) and toHave (F) held in balanced indeterminacy, and develops a dispositional monadology in which qualified entities arise as selections from an indeterminate substrate compatible with First-Classness.
Applications
Biology
First-Classness yields the redundancy architecture of the universal genetic code
Imposing First-Classness (no entity, position or relation is intrinsically privileged) on a four-element dispositional algebra forces a unique partition of the 64 codons into synonymous families of sizes 1, 2, 3, 4 and 6. This reproduces the degeneracy pattern of the universal genetic code without biological input. The two singletons (AUG, UGG) appear as conformal singularities, the three stop codons as the structural residue of coding closure, and the 61/3 sense/stop split is derived. The constructive verification scripts are a separate Zenodo record.
Genomic codon usage is structurally consistent with First-Classness across the tree of life
Tests the First-Classness derivation of the genetic code’s 21-family degeneracy partition against codon usage data from 70,950 species. Within-family codon usage uniformity follows the ordering 2-fold < 4-fold < Ser 6-fold < 3-fold < Leu/Arg 6-fold, and the three split six-fold families (serine, leucine, arginine) show stable internal structure across all kingdoms of life. Accepted for publication in the Journal of Molecular Evolution (online version active: DOI 10.1007/s00239-026-10343-2).
Physics
Logic-Driven Physics: An Operational Companion to the Standard Model for Reconstructing Particle Structure
Applies the First Calculus and the genetic-code algebra to particle physics. It constrains particle constructions by colour geometry and dyadic structure, and proposes a monorg framework in which particle triads are the primary objects, keeping quantitative dynamics as the complementary partner. A computation package accompanies the paper.
Computing
Dispositional Typing: Eliminating Unsafe Annotations through First-Class Role Algebra
Applies First-Classness to memory safety in programs. It induces a four-element role algebra, the unique minimal closed system that refines the lvalue/rvalue distinction while privileging no pole, with composition fixed by the balance law. The algebra grounds a static memory-safety analysis that needs no programmer annotations and adds under 2% to compilation time. An implementation accompanies the paper.
Supplementary books
Four Supplementary Material books develop the system step by step, in the manner of a classical treatise: Book I, Methodology; Book II, Monadology; Book III, Dyadology; and Book IV, Colour Geometry, which treats the codon square and the codon triple, particle triads (monorgs) and genetic triads (biorgs).
Method
The results are derived at the level of theorems and then checked by computation. Reproducible verification packages accompany the biology, physics and computing papers. The work builds on Leibniz’s monadology and Analysis Situs and on Stoic logic, which is treated in Generic Logic and in From Mathematical Logic to Logical Mathematics.