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1,400 results for "philosophy of mathematics" — page 2 of 70

P_5_08 Verified Philosophy & Meaning

P_5_08 — Philosophy of History

Philosophy of history asks whether history has a pattern, direction, or meaning — and how historical knowledge itself is possible. Two broad orientations have competed since antiquity: cyclical views (civilizations rise

philosophy of history historicism metahistory Hegel dialectic world spirit
P_5_03 Verified Philosophy & Meaning

P_5_03 — Aesthetics — Philosophy of Beauty, Art, and the Sublime

Aesthetics — the philosophical study of beauty, art, taste, and the sublime — has been a central philosophical concern from Plato's suspicion of art as dangerous imitation to contemporary debates about the nature of aest

aesthetics philosophy of art beauty sublime Plato mimesis
ZE_1_13 Verified Ethics & Applied Philosophy

ZE_1_13 — Philosophy of Play, Games, and the Sacred Ludic

The philosophy of play examines one of humanity's most fundamental yet philosophically neglected activities. Johan Huizinga (Homo Ludens, 1938) argued that play is not merely one activity among others but the foundation

philosophy of play Huizinga homo ludens Caillois games sacred play
V_2_08 Verified Mathematics & Information

V_2_08 — Mathematical Proof: History & Philosophy

Mathematical proof — the definitive demonstration that a statement follows necessarily from accepted axioms — is the distinguishing feature of mathematics as a discipline. The axiomatic-deductive method originated with t

mathematical proof axiomatic method Euclid proof by contradiction reductio ad absurdum Four Color Theorem
G_3_20 Verified Modern Frameworks

G_3_20 — Kuhn's Paradigm Shifts: The Structure of Scientific Revolutions

Thomas S. Kuhn's The Structure of Scientific Revolutions (1962) introduced the concept of the paradigm shift — the idea that science does not progress by linear accumulation of facts, but through periodic, discontinuous

paradigm shift Kuhn scientific revolution normal science anomaly incommensurability
V_1_16 Credible Mathematics & Information

V_1_16 — History of Mathematical Notation: Symbols, Conventions, and Communication

The history of mathematical notation reveals that mathematics is not merely a body of truths but also a system of communication whose power depends critically on the symbols used to express it. Good notation does not mer

mathematical notation mathematical symbols history of mathematics numeral systems algebra notation calculus notation
V_1_20 Credible Mathematics & Information

V_1_20 — The History of Zero: Independent Invention & Philosophical Implications

The concept of zero — seemingly trivial yet profoundly revolutionary — was independently invented multiple times across civilizations, and its full development as both a placeholder (indicating an empty position in posit

zero history-of-mathematics placeholder india maya babylon
P_3_14 Verified Philosophy & Meaning

P_3_14 — Hegel: Dialectics, Phenomenology of Spirit, and Historical Reason

Georg Wilhelm Friedrich Hegel (1770-1831), the most ambitious and systematic philosopher of the German Idealist tradition, developed a comprehensive philosophical system in which reality, thought, and history are underst

Hegel Georg Wilhelm Friedrich Hegel dialectic thesis-antithesis-synthesis Phenomenology of Spirit Geist
P_3_12 Verified Philosophy & Meaning

P_3_12 — Medieval Philosophy: Aquinas, Ockham, and Scholastic Thought

Medieval philosophy spans roughly a millennium of intellectual activity (c. 5th-15th centuries CE) dominated by the project of integrating faith and reason — reconciling the philosophical heritage of ancient Greece (espe

medieval philosophy Aquinas Thomas Aquinas Scholasticism Ockham William of Ockham
P_3_08 Verified Philosophy & Meaning

P_3_08 — Pragmatism — American Philosophy

Pragmatism is the most distinctive American contribution to philosophy, originating in the 1870s with Charles Sanders Peirce (1839–1914), developed by William James (1842–1910), and extended by John Dewey (1859–1952). It

pragmatism American philosophy Charles Sanders Peirce William James John Dewey Richard Rorty
P_4_14 Verified Philosophy & Meaning

P_4_14 — Maat and Ancient Egyptian Philosophy: Order, Truth, and Justice

Maat (also Ma'at) is the ancient Egyptian concept of cosmic order, truth, justice, balance, and righteous conduct that governed the universe, society, and individual ethics for over three millennia — from the Old Kingdom

Maat ancient Egypt Egyptian philosophy cosmic order truth justice
P_4_13 Verified Philosophy & Meaning

P_4_13 — Chinese Philosophy — Dao, Confucius, and Beyond

Chinese philosophy encompasses one of the world's richest and longest-continuous intellectual traditions, spanning from the Zhou dynasty (~1046–256 BCE) to the present. The foundational period — the Hundred Schools of Th

Chinese philosophy Daoism Taoism Confucius Confucianism Laozi
P_4_02 Credible Philosophy & Meaning

P_4_02 — Perennial Philosophy and Universal Wisdom

The Perennial Philosophy — philosophia perennis — is the thesis that beneath the surface diversity of the world's religious and spiritual traditions lies a SINGLE, universal truth about the nature of reality and human ex

perennial philosophy philosophia perennis Huxley Leibniz Steuco mysticism
P_1_13 Verified Philosophy & Meaning

P_1_13 — Paradoxes in Philosophy: Zeno, Liar, Ship of Theseus, Sorites

A paradox is an argument that proceeds from apparently acceptable premises via apparently valid reasoning to a conclusion that is apparently unacceptable — forcing us either to reject a premise, identify a flaw in the re

paradox Zeno Achilles and tortoise dichotomy liar paradox Ship of Theseus
P_5_14 Verified Philosophy & Meaning

P_5_14 — African Philosophy Beyond Ubuntu: Sage, Négritude, and Ethnophilosophy

African philosophy extends far beyond the Ubuntu concept most familiar to Western audiences. It is a diverse, complex, frequently contested field encompassing multiple traditions, methods, and debates. The "Great Debate"

African philosophy sage philosophy négritude ethnophilosophy Ubuntu Paulin Hountondji
P_5_20 Verified Philosophy & Meaning

P_5_20 — Cicero: Roman Oratory, Natural Law, and Republican Philosophy

Marcus Tullius Cicero (106–43 BCE) — Roman statesman, orator, philosopher, and lawyer — stands as one of the most influential figures in Western intellectual history, bridging Greek philosophy and Roman practice, and tra

cicero roman republic oratory rhetoric natural law stoicism
P_5_18 Verified Philosophy & Meaning

P_5_18 — Comparative Religion & the Science of Sacred Traditions

Comparative religion — the systematic study of the world's religious traditions through cross-cultural analysis — emerged as an academic discipline in the 19th century with Friedrich Max Müller's translation of the Sacre

comparative religion history of religions Mircea Eliade Joseph Campbell phenomenology of religion sacred and profane
P_2_06 Verified Philosophy & Meaning

P_2_06 — Political Philosophy: Justice, Power, and Authority

Political philosophy examines the nature of justice, power, authority, and the proper organization of collective human life. Plato (Republic, c. 375 BCE) argued that justice consists in each part of the soul and the city

political philosophy justice power authority legitimacy sovereignty
ZA_2_01 Verified Physics & Quantum

ZA_2_01 — Time: Physics and Philosophy

Time is arguably the deepest unsolved problem in physics and philosophy. Physics reveals: (1) time is relative, not absolute — Einstein showed it flows at different rates depending on velocity and gravity; (2) the fundam

time arrow of time entropy relativity block universe presentism
V_1_08 Verified Mathematics & Information

V_1_08 — Mathematical Puzzles & Recreational Mathematics

Mathematical puzzles — problems posed for amusement, education, or intellectual challenge — have served as engines of mathematical discovery for over 4,000 years. The Rhind Mathematical Papyrus (c. 1650 BCE, Egypt) conta

mathematical puzzles recreational mathematics Rhind Papyrus Archimedes cattle problem Fibonacci rabbits Tower of Hanoi