RESEARCH BASE
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.
1,346 results for "foundations of mathematics" — page 64 of 68
ZG_3_10 — Semantics: Meaning, Reference, and Compositional Analysis
Semantics — the branch of linguistics concerned with meaning — investigates how words, phrases, and sentences encode and convey meaning, how meanings combine compositionally, and how linguistic meaning relates to the wor
ZG_3_00 — Linguistic Theory Structure: Subfolder Summary
ZG_3_18 — Pragmatics and Speech Act Theory
Pragmatics — the study of how context contributes to meaning beyond what is encoded in the literal words of an utterance — and speech act theory — the analysis of language as a form of action — have been foundational to
J_1_08 — Ancient Optics, Lenses, and Light Technology
Ancient civilizations possessed a greater understanding of optics and light than is commonly recognized. Archaeological evidence includes polished crystal lenses (the Nimrud lens, ~750 BCE; Visby lenses, ~11th c. CE), so
J_5_14 — Greek Mathematical Instruments: Precision Tools
Ancient Greek civilization produced the most sophisticated mathematical and scientific instruments of the pre-modern world — devices that embody the Greek integration of theoretical mathematics with practical engineering
J_5_06 — Ancient Measurement Standards and Metrology
Standardized measurement — of length, weight, volume, area, and angle — was fundamental to ancient engineering, trade, taxation, land surveying, and astronomical observation. Every major civilization developed metrologic
J_5_00 — Navigation Measurement Regional: Subfolder Summary
Q_1_11 — Cosmological Redshift and the Hubble Law
The discovery that distant galaxies' light is systematically shifted toward longer (redder) wavelengths was the first observational evidence that the universe is expanding. Vesto Slipher's spectroscopic measurements (191
Q_3_03 — Exoplanets, Habitable Zones, and the Search for Life
The discovery of exoplanets — worlds orbiting stars other than the Sun — has transformed astronomy from a field where planets were known only in our solar system to one cataloging over 5,700 confirmed exoplanets as of 20
Q_0_00 — Cosmology & Astrophysics: Section Summary
INTERDOC_60 — AI Consciousness and Moral Status: The Triadic Framework
As AI systems cross behavioral thresholds once considered markers of intelligence — passing bar exams at the 90th percentile (GPT-4, March 2023), solving protein folding (AlphaFold2, 2020), exhibiting emergent reasoning
INTERDOC_53 — Substrate-Independent Information Patterns: Empirical Cases
A pattern is empirically substrate-independent if the same information content is preserved across changes in the physical material carrying it. Across multiple domains, biology and physics provide concrete instances of
G_4_26 — Consciousness-Technology Integration
The intersection of consciousness studies and technology represents one of the most consequential frontiers of 21st-century science and philosophy. Brain-computer interfaces (BCIs), pioneered by researchers from Jacques
G_3_19 — Hermeneutics: Interpretive Frameworks for Ancient Texts
Hermeneutics — the theory and methodology of interpretation — provides the foundational framework for understanding ancient texts, inscriptions, and symbolic systems. Originating in biblical exegesis and classical philol
G_3_24 — Post-Normal Science: Funtowicz, Ravetz, and Uncertainty
Post-normal science (PNS) is a framework for understanding and managing scientific inquiry when facts are uncertain, values in dispute, stakes high, and decisions urgent — conditions that characterize many of the most cr
G_2_07 — Power Laws, Scale-Free Networks, and Ancient Systems
A power law is a mathematical relationship of the form $P(x) \propto x^{-\alpha}$ in which the frequency of an event is inversely proportional to some power of its size — meaning that small events are extremely common, l
G_2_05 — Graph Theory and Knowledge Network Analysis
Graph theory — the mathematical study of networks of nodes (vertices) connected by edges (links) — provides a rigorous framework for analyzing the structure of connections in systems ranging from ancient social hierarchi
G_2_00 — Analytical Computational: Subfolder Summary
B_1_20 — Trickster Deities: Cross-Cultural Comparison
The trickster is among the most widespread deity archetypes in world mythology, appearing independently across every inhabited continent. Characterized by cunning, boundary-crossing, shapeshifting, and the subversion of
ZD_1_12 — Information Geometry and Fisher Information
Information geometry is the mathematical field that applies differential geometry — the mathematics of curved spaces, manifolds, metrics, and connections — to the study of probability distributions and statistical models
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