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Language Learning › Learn Sindarin › Sindarin Lessons ›

Supplement 8: Vocabulary — Emotions & Abstract Concepts

Tolkien's Emotional Vocabulary Tolkien embedded his own theological and philosophical views directly in his Elvish emotional vocabulary. Words like estel (hope as trust, not wishful thinking) carry dense meaning that can only be understood by reading what Tolkien wrote about them in Morgoth's Ring and related texts. Learning Sindarin emotional vocabulary is therefore also a study in Tolkienian theology and moral philosophy. The emotional register of Sindarin is particularly rich...
sindarin vocabulary emotions philosophy intermediate May 30, 2026
Maths › 03. Logic and Foundations ›

14.4 Implications

14.4 Implications for Formal Systems Gödel’s theorems change how we understand formal systems. They do not weaken logic. They clarify its limits and force a more precise view of what formal reasoning can achieve. Separation of Truth and Provability Before Gödel, it was natural to expect that every true mathematical statement could be proved. The incompleteness theorem shows this expectation fails for sufficiently strong systems. There exist sentences $A$ such...
logic foundations incompleteness philosophy mathematics May 2, 2026
Maths › 00. General Mathematics ›

00. Preface

This volume defines the ground layer of mathematics. It focuses on how mathematics is expressed, structured, and practiced before any specialization. The scope follows MSC 00 and concentrates on classification, exposition, philosophy, and general methods that recur across all fields . Mathematics operates as a language, a system of structures, and a method of reasoning. Each of these aspects appears in every branch, whether one studies algebra, analysis, geometry, or...
mathematics foundations philosophy methods May 2, 2026
Maths ›

00. General Mathematics

This volume establishes the meta-layer of mathematics. It covers language, structure, methodology, and cross-cutting tools that apply across all branches. The scope follows MSC 00: classification, exposition, philosophy, and general methods. Part I. What Mathematics Is Chapter 1. Nature of Mathematical Objects 1.1 Abstract objects and structures 1.2 Sets, types, and universes 1.3 Equality, identity, and equivalence 1.4 Finite vs infinite objects 1.5 Constructive vs classical viewpoints Chapter 2. Mathematical...
mathematics foundations philosophy methods May 2, 2026