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Search 3,721 documents across 34 fields — every claim tier-rated by evidence
3,633 are the core, quality-scored corpus (34 lettered sections — see How We Work); the remaining 88 are cross-corpus synthesis documents (68 InterDocs, 12 Connections, 8 Theories) also indexed here.
1,400 results for "philosophy of mathematics" — page 3 of 70
V_1_10 — Ancient Greek Mathematics
Ancient Greek mathematics (c. 600 BCE – 500 CE) transformed mathematics from a collection of empirical recipes into a deductive science built on axioms, definitions, and rigorous proof. Thales of Miletus (c. 624–546 BCE)
V_1_13 — Women in Mathematics History
Women have made profound contributions to mathematics throughout history despite systematic exclusion from universities, academies, and professional recognition. Hypatia of Alexandria (c. 350–415 CE), the first well-docu
V_1_11 — Islamic Golden Age Mathematics
Islamic Golden Age mathematics (c. 750–1500 CE) preserved, synthesized, and dramatically extended the mathematical traditions of Greece, India, Persia, and Mesopotamia, creating entirely new fields and transmitting the r
V_4_01 — Discrete Mathematics and Logic
Discrete mathematics — the study of mathematical structures that are countable, separated, or distinct (as opposed to continuous) — provides the theoretical bedrock for computer science, digital communication, and rigoro
V_2_22 — Imaginary Numbers: From "Truly Imaginary" to Physically Necessary
In 1545, the Italian mathematician Girolamo Cardano encountered expressions involving the square root of a negative number while solving cubic equations in his Ars Magna. He used the expression — computed with it, obtain
V_2_20 — Gödel's Incompleteness Theorems — Philosophical Implications
Kurt Gödel's incompleteness theorems, published in 1931 in the paper "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I," constitute one of the most profound results in the history of l
G_3_21 — Critical Realism: Roy Bhaskar and Stratified Ontology
Critical realism is a philosophical movement founded by Roy Bhaskar (1944–2014) that proposes a stratified ontology — reality consists of three nested domains (the Real, the Actual, and the Empirical) — and argues that s
ZD_1_09 — Conway's Game of Life and Recreational Mathematics
Conway's Game of Life (1970), a two-dimensional cellular automaton devised by mathematician John Horton Conway (1937–2020), stands as perhaps the most famous example of how astonishingly complex behavior can arise from e
P_3_02 — Pre-Socratic Philosophy — The Birth of Western Thought
The Pre-Socratic philosophers (c. 624–370 BCE) inaugurated Western philosophy by replacing mythological explanations of the natural world with rational inquiry into a single unifying principle (archê). From Thales' ident
P_4_11 — Indian Darshanas — Six Orthodox Systems of Hindu Philosophy
The Indian philosophical tradition produced six orthodox (āstika) systems (darśanas, literally "viewpoints") that accept the authority of the Vedas: Samkhya, Yoga, Nyaya, Vaisheshika, Mimamsa, and Vedanta. Alongside thre
P_5_04 — Process Philosophy — Whitehead and the Metaphysics of Becoming
Process philosophy, most fully developed in Alfred North Whitehead's Process and Reality (1929), proposes that reality is fundamentally constituted not by enduring substances but by dynamic events — "actual occasions of
P_5_17 — Process Philosophy: Whitehead, Becoming, and the Metaphysics of Experience
Process philosophy — the metaphysical tradition holding that reality is fundamentally composed of processes, events, and becomings rather than static substances, objects, or things — represents one of the most ambitious
P_2_17 — Philosophy of Law: Jurisprudence and Legal Theory
Jurisprudence — the philosophical study of law's nature, authority, and relationship to morality — addresses foundational questions: What makes a rule a "law"? Is law necessarily connected to morality? How should judges
ZE_1_03 — Feminist Philosophy and Ethics of Care
Feminist philosophy is not a single doctrine but a constellation of projects united by the conviction that mainstream Western philosophy has been shaped by patriarchal assumptions — that dominant categories, frameworks,
ZE_2_09 — Philosophy of Sovereignty
Sovereignty — the concept of supreme authority within a territory — has undergone radical transformation from its theological origins to contemporary debates about humanitarian intervention, indigenous self-determination
V_1_19 — Non-Western Mathematical Traditions
The standard Eurocentric narrative of mathematics — from Greek geometry to the European Scientific Revolution — obscures the fact that many foundational mathematical innovations originated in India, China, the Islamic wo
V_1_06 — Mathematics of Music: Harmonic Ratios & Tuning Systems
The relationship between mathematics and music is among the oldest in intellectual history. Pythagoras (c. 570–495 BCE) is traditionally credited with discovering that consonant musical intervals correspond to simple num
V_3_10 — Tensor Calculus and Differential Geometry: The Mathematics of Curved Spaces
Tensor calculus and differential geometry provide the mathematical language for describing curved spaces — from the geometry of Earth's surface to the curvature of spacetime in general relativity. Developed through the w
X_4_18 — Fractal Physiology: The Mathematics of Healthy Life
The body is a fractal machine. From capillaries that branch like river deltas to the 70 m² of lung surface packed into a 4-litre chest cavity, and from the beat-to-beat complexity of a healthy heart to the trabecular sca
W_5_35 — I Ching: The Book of Changes, Divination, and Binary Philosophy
The I Ching (Yìjīng, 易經, "Classic of Changes") is among the oldest continuously used texts in human history, with roots extending to the Western Zhou dynasty (c. 1000–750 BCE) and legendary attribution to Fu Xi (trigrams
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