The Necessity of Unity: Why Comprehension Requires Imposed Boundaries

Authors: Marcovich, Barry John

Subject Terms: cognition, structural pattern, life identity, Logic and Foundations of Mathematics, cognitive boundaries, Social and Behavioral Sciences, self-imposed boundaries, Psychology, unity as imposition, Causal Speed Limit, identity projection, identity, cross-disciplinary framework, continuum and discreteness, fractal identity, Neuroscience and Neurobiology, Philosophy of Mind, system coherence, Systems Biology, epistemology, Life Sciences, philosophy of mind, fractal structure, intelligence, Structural Invariance, FOS: Philosophy, ethics and religion, FOS: Psychology, philosophy of science, 0 ↔ ∞ = 1, comprehension, Fractal Identity, Information theory, paradox, autopoiesis, multi-scale, paradoxes, self-maintenance, mathematics foundations, observer limits, Systems Theory, Evolutionary Synthesis, Philosophy of Science, Cell and Developmental Biology, Autopoiesis, recursion, structural invariance, systems theory, unity, Cognitive Psychology, Philosophy, imposed unity, operational identity, Cognitive Science, Arts and Humanities, complexity, Pseudo-1

The Limits of Mathematical Freedom: Why the Independence of Mathematical Practice Does Not Establish the Existence of Infinite Objects

Authors: Burnstein, Daniel

Subject Terms: Quantum-Geometry Dynamics QGD MPDT Minimally Physically Derivable Theories mathematical independence pure mathematics philosophy of mathematics physical construction criterion mathematical existence Axiom of Infinity effective autonomy top-down causation mathematical practice two-domain principle border condition category error continuum import physical axiom mathematical axiom warehouse analogy Penelope Maddy Second Philosophy fruitfulness criterion ultraviolet divergences renormalisation singularities cosmological constant problem measurement problem string theory landscape Physically Derivable Set Theory PDST ZFC Gödel incompleteness physical proof Euclidean space emergence discrete space preons computable analysis mathematical freedom mathematical ontology foundations of mathematics foundations of physics philosophy of physics

TFC depreciated

Authors: Moore, Douglas Joseph Huntington

Subject Terms: Philosophy of Science, Foundations of Mathematics, Mathematical Logic, Category Theory, Geometry and Topology, History and Philosophy of Mathematics, Theoretical Computer Science, Mathematical Physics, Ontology, Systems Theory, Leibniz, Analysis Situs, First-Classness, First Calculus, qualitative calculus, ontological type, Generic Entity, Indeterminate Dyad, monadology, co-syllogistic reasoning, concrete adjunction, H-diagrams, dispositional dyads, operational ontology, Geometric Algebra, Category Theory, operational calculus, Heaviside, qualitative mathematics, foundations of science

The Unrealizable Prescription: Physically Derivable Set Theory as the Replacement for ZFC

Authors: Burnstein, Daniel

Subject Terms: Quantum-Geometry Dynamics QGD MPDT Minimally Physically Derivable Theories ZFC Zermelo-Fraenkel set theory Axiom of Infinity physical construction criterion unrealizable prescription PDST Physically Derivable Set Theory hereditarily finite sets constructivism physical constructivism finitary mathematics Banach-Tarski paradox Gödel incompleteness axiom of choice continuum hypothesis uncountable cardinals Russell's paradox infinite sets foundations of mathematics foundations of set theory philosophy of mathematics discrete spacetime finite universe mathematical existence mathematical ontology computability decidability

The First Calculus: Formalising Leibniz's Unfinished Qualitative Calculus

Authors: Moore, Douglas Joseph Huntington

Subject Terms: Philosophy of Science, Foundations of Mathematics, Mathematical Logic, Category Theory, Geometry and Topology, History and Philosophy of Mathematics, Theoretical Computer Science, Mathematical Physics, Ontology, Systems Theory, Leibniz, Analysis Situs, First-Classness, First Calculus, qualitative calculus, ontological type, Generic Entity, Indeterminate Dyad, monadology, co-syllogistic reasoning, concrete adjunction, H-diagrams, dispositional dyads, operational ontology, Geometric Algebra, Category Theory, operational calculus, Heaviside, qualitative mathematics, foundations of science

From Philosophical Program to Formal Science: The Complete Axiomatization, Dual Realization and Machine Verification of YuanXian Theory (YXT)

Authors: Acharya, Zhenyuan

Subject Terms: Computer Science → Formal Methods, Computer Science → Theorem Proving and Automated Reasoning, Mathematics → Logic and Foundations, Physics → Mathematical Physics, YuanXian Theory, YXT, True-Circle Self-Consistency, Self-Referential Mind-Field Type Theory, YXTT, T^64 Torus, Fine Structure Constant, Riemann Hypothesis, Total Energy of the Universe, Formal Verification, Lean 4, Homotopy Type Theory, ZFC Extension, Unified Theory, Machine-Verifiable Mathematics, Mathematics → Foundations of Mathematics, Philosophy → Philosophy of Science / Philosophy of Physics, Physics → Theoretical Physics

The Qualitative Alternative to the Quantitative Calculu

Authors: Moore, Douglas Joseph Huntington

Contributors: Moore, Douglas Joseph Huntington

Subject Terms: Mathematical Physics, Geometry and Topology, History and Philosophy of Mathematics, Foundations of Physics, Metaphysics, Logic, Philosophy of Science, Theoretical Biology, First Calculus, First-Classness, ontological gender, analysis situs, monadology, qualitative mathematics, geometric algebra, Minkowski spacetime, de Sitter geometry, quantum mechanics, relativity, genetic code, Leibniz, dyadology, naturality, complementary oppositions

Unified Theory of Ontological Zero (UTOZ): Zero as Actual-Potential Concurrency; 0α as Source-Origin and 0β as Transition-Threshold

Authors: Soto, Armando

Subject Terms: Mathematics/methods, Mathematical model, Ontological Zero, Zero, UTOZ, actual-potential concurrency, source-origin, transition-threshold, 0α, 0β, 0>1, trace, non-depletion, non-annihilative change, threshold ontology, philosophy of mathematics, foundations of mathematics, infinitesimal, signed zero, limits, formal zero, emergence, time, Now, identity over time, Augmentative Prospective, Unified Informational Dynamics Theory, UInDT, informational dynamics, Boundary/Horizon, source-expression, potentiality, continuity, transformation, ontology, Mathematical logic, FOS: Mathematics, Mathematical analysis, Mathematics

The Distribution of Prime Numbers: A Physical Constructivist Account

Authors: Burnstein, Daniel

Subject Terms: prime numbers, prime distribution, physical constructivism, construction modes, dynamic constraint, discrete construction space, Minimal Physically Derivable Theories, MPDT, Uniqueness Theorem, Riemann Hypothesis, additive construction mode, multiplicative construction mode, factoring mode, finite domain, Quantum-Geometry Dynamics, philosophy of mathematics, foundations of mathematics, prime gaps, sieve of Eratosthenes, large prime finding, primorial, cryptography, computational number theory, prime-richness score, prime numbers, prime distribution, physical constructivism, construction modes, dynamic constraint, discrete construction space, Minimal Physically Derivable Theories, MPDT, Uniqueness Theorem, Riemann Hypothesis, additive construction mode, multiplicative construction mode, factoring mode, finite domain, Quantum-Geometry Dynamics, philosophy of mathematics, foundations of mathematics

From Entropy to Echo: Lecture Series on CODES

Authors: Bostick, Devin

Subject Terms: CODES Framework, Resonance Intelligence Core (RIC), Structured Resonance, Determinism, Probability vs Coherence, PAS (Phase Alignment Score), CHORDLOCK, ΔPAS_zeta, AURA_OUT, ELF (Echo Loop Feedback), SPIRALCORE, TEMPOLOCK, GLYPHLOCK, Logic and Proof Theory, Incompleteness, Entropy and Negentropy, Memory and Identity, Consciousness, Error and Drift Collapse, Biology and Evolution, Death, Intelligence, Law and Governance, Mathematics Foundations, Physics Foundations, Cosmology, Complex Systems, Theoretical physics

Relation: https://zenodo.org/records/17102687; oai:zenodo.org:17102687; https://doi.org/10.5281/zenodo.17102687

Availability: https://doi.org/10.5281/zenodo.17102687
https://zenodo.org/records/17102687

Building the Foundations: Effective Approaches in Mathematics Teacher Preparation

Authors: Olawale, Editor: B. E.

Source: Open Books and Proceedings ; Building the Foundations: Effective Approaches in Mathematics Teacher Preparation; i-189 ; 3079-8450 ; 10.38140/10.38140/obp3-2025c

Subject Terms: Mathematics foundations, effctive approaches, mathematics teacher preparation

File Description: application/pdf

Relation: https://pubs.ufs.ac.za/index.php/ijgs/article/view/1809/1170; https://pubs.ufs.ac.za/index.php/ijgs/article/view/1809

Availability: https://pubs.ufs.ac.za/index.php/ijgs/article/view/1809
https://doi.org/10.38140/obp3-2025

The 3–4–5 Triangle and 10368 (2⁷·3⁴): A Practical Engineering Note

Authors: Delph, Andrew

Subject Terms: Mathematics — Geometry — Euclidean geometry (right triangles, circle radii/areas) Mathematics — Number Theory — Diophantine equations / Pythagorean triples Mathematics — Foundations / Notation — Alternative radix systems (duodecimal/base-12)

Relation: https://zenodo.org/records/17009996; oai:zenodo.org:17009996; https://doi.org/10.5281/zenodo.17009996

Availability: https://doi.org/10.5281/zenodo.17009996
https://zenodo.org/records/17009996

The Logical Origin of Positive Integers: Identity and Distinction

Authors: Chan, H.-K.

Subject Terms: positive integers, pure definition, identity, distinction, recursive definition, philosophy of mathematics, foundations of arithmetic, first-order logic with equality

The Zimmerman Framework: Unified Physics from Z² = CUBE × SPHERE

Authors: Zimmerman, Carl

Subject Terms: Bekenstein bound, geometric closure, first principles, mathematics foundations, music theory, consciousness, origin of life, genetic code, unified physics, Z² geometry, horizon thermodynamics, gauge symmetry, MOND, CUBE × SPHERE, cosmology, time

Fermat's Last Theorem: A Physical Constructivist Proof

Authors: Burnstein, Daniel

Subject Terms: Fermat's Last Theorem, physical constructivism, construction modes, Minimal Physically Derivable Theories, MPDT, Uniqueness Theorem, prescription, integer structure, finite causal sequences, irreversibility, Quantum-Geometry Dynamics, QGD, philosophy of mathematics, foundations of mathematics, axiomatic foundations

First Calculus Supplementary Material, Book III: Dyadology — The Universal Geometric Product integrating ontological gender arithmetic (M/F) and geometric algebra in one operation

Authors: Moore, Douglas Joseph Huntington

Contributors: Moore, Douglas Joseph Huntington

Subject Terms: First Calculus, ontological gender, universal geometric product, dyadology, First-Classness (FC), complementary oppositions, qualitative mathematics, Clifford algebra Cl(1,1), geometric algebra foundations, Minkowski signature, scalar emergence, metric–composition duality, dispositional algebra, pseudoscalar structure, right-side mathematics, Mathematics – Foundations of Mathematics Mathematics – Algebra – Clifford and Geometric Algebras Mathematical Physics – Geometric Methods Philosophy of Mathematics Philosophy of Physics Philosophy of Biology Mathematical foundations of Genetic code Theoretical Physics – Mathematical Structures Logic and Non-Classical Logical Systems History and Philosophy of Science, (4-(m-Chlorophenylcarbamoyloxy)-2-butynyl)trimethylammonium Chloride

On Revisiting Gödel's Incompleteness and Turing's Undecidability of the Halting Problem

Authors: Zerradi, Marouane

Subject Terms: Gödel incompleteness theorems Turing halting problem Diagonal lemma Foundational mathematics Metamathematics Peano arithmetic Self-reference Zermelo-Fraenkel set theory Philosophy of mathematics, Doubled Diagonal Lemma Gödelian Dilemma Provability Predicate Rosser Provability Predicate Diagonal Lemma Strong Representability Derivability Conditions Gödel Incompleteness Theorems Halting Problem Arithmetization of Syntax Substitution Function Peano Arithmetic ZFω Metatheory Impredicative Comprehension Axiom of Separation Axiom of Infinity Potential Infinity Actual Infinity Bag Mindset Diagonal Arguments Self-Reference Fixed Point Theorems Recursive Function Theory Löwenheim-Skolem Theorem Non-Standard Models Uncountability Cantor's Diagonal Argument Power Set Axiom Countable Models Philosophy of Mathematics Foundations of Mathematics Platonism Aristotelian Logic Ontological Commitment Logicism Principia Mathematica Type Theory Incomplete Symbols Potentialism Church-Turing Thesis Universal Turing Machine Computability Theory Simulation Index Undecidability, Foundations of Mathematics Gödel's Incompleteness Theorems Halting Problem Diagonalization Doubled Diagonal Lemma ZF_ω Impredicativity Comprehension Schema Axiom of Infinity Peano Arithmetic Recursive Functions Turing Machines Potential Infinity Vicious Circle Principle Church-Turing Thesis Philosophy of Mathematics

First Calculus Supplementary Material, Book I: Methodology — First-Classness, Axioms, Postulates, Principles

Authors: Moore, Douglas Joseph Huntington

Contributors: Moore, Douglas Joseph Huntington

Subject Terms: First Calculus, Supplementary Material, Methodology, First-Classness (FC), FC-constraint, normative authority, Euclid-style development, axiom, postulate, principle, Principle of Sufficient Reason (PSR), Leibniz, analytic vs dialectical reasoning, complementary oppositions, qualitative mathematics, foundations of mathematics, foundations of physics, Substance Theory, Disposition of the Quantum Object (DQO)

Critique of Cantor's Method and Presentation of an Enumeration of Functions over N

Authors: Lynch, Thomas Walker

Subject Terms: Mathematics → Logic, Mathematics → Foundations of Mathematics, Philosophy → Logic, Computer Science → Theory of Computation

Relation: https://zenodo.org/records/15090739; oai:zenodo.org:15090739; https://doi.org/10.5281/zenodo.15090739

Availability: https://doi.org/10.5281/zenodo.15090739
https://zenodo.org/records/15090739

The Other Zero: Unified Theory of Ontological Zero (UTOZ): Zero as Actual-Potential Concurrency; 0α as Source-Origin and 0β as Transition-Threshold

Authors: Soto, Armando

Subject Terms: Philosophy, Databases and Information Systems, Computer Sciences, Physical Sciences and Mathematics, FOS: Mathematics, Arts and Humanities, Logic and Foundations of Mathematics, Other Mathematics, Ontological Zero Zero UTOZ actual-potential concurrency source-origin transition-threshold 0α 0β 0>1 trace non-depletion non-annihilative change threshold ontology philosophy of mathematics foundations of mathematics infinitesimal signed zero limits formal zero emergence time Now identity over time Augmentative Prospective Unified Informational Dynamics Theory UInDT informational dynamics Boundary/Horizon source-expression potentiality continuity transformation ontology, Mathematics, FOS: Philosophy, ethics and religion, Philosophy of Science