Holism: Understanding Systems as Wholes
Holism posits that systems and their properties are best understood as integrated wholes, rather than merely the sum of their individual components. This perspective is crucial in fields like philosophy,…
Hilbert’s Program
An ambitious project by David Hilbert to formalize all mathematics and prove its consistency using finitary methods. It aimed to secure the foundations of mathematics.
Higher-Order Variables in Logic
A higher-order variable represents functions, predicates, or relations, distinguishing it from variables that denote individual objects. This concept is fundamental in higher-order logic, enabling more expressive and abstract reasoning.
Higher-Order Vagueness
Higher-order vagueness concerns the application of vagueness itself, especially with predicates that are borderline cases of borderline cases. It explores the fuzzy boundaries of fuzzy concepts.
Higher-Order Quantifiers
A higher-order quantifier binds variables that range over properties, relations, or functions, rather than individuals. This allows for more expressive logical statements and complex reasoning.
Higher-Order Logic
Higher-order logic extends first-order logic by enabling quantification over predicates and other higher-order entities. It offers greater expressive power for formal reasoning and knowledge representation.
Understanding Hierarchy: Concepts, Types, and Applications
A hierarchy ranks entities based on criteria, seen in organizational structures and set theory. Tarski's and cumulative hierarchies are key examples. It organizes complex systems effectively.
Heterological: Understanding Self-Referential Paradoxes
Explore heterological, an adjective describing terms that do not apply to themselves. Discover its implications in language, logic, and the fascinating world of paradoxes and self-reference.
Hereditary Property
A hereditary property in mathematics and logic is a characteristic that, if held by an object, is also present in all its constituent subobjects or elements. This concept is fundamental…
Henkin Sentence
A Henkin sentence is a self-referential statement that asserts its own provability within a formal system. It's a foundational concept in Gödel's incompleteness theorems, demonstrating limits of formalization.