Henkin Semantics
Henkin semantics offers a flexible alternative to standard first-order semantics, allowing quantifiers to range over restricted domains within models. This generalization enhances expressive power in formal logic.
Hasty Generalization Fallacy
A hasty generalization occurs when a conclusion is drawn from insufficient or biased evidence, essentially making a broad claim based on a tiny sample size.
Harmony in Logic and Philosophy
Harmony in logic signifies a balance in introduction and elimination rules for logical connectives. This ensures connectives neither over-promise nor under-deliver, maintaining logical integrity and consistency in reasoning.
The Halting Problem
The halting problem asks if it's possible to determine if any given program will halt or run forever. Alan Turing proved this fundamental problem to be undecidable.
Grelling Paradox
The Grelling paradox explores self-reference in language. It questions whether the word 'heterological' (not describing itself) applies to itself, leading to a logical contradiction.
Gödel’s Slingshot Argument
Gödel's slingshot argument challenges theories distinguishing facts from true propositions. It questions the coherence of fine-grained semantic distinctions, impacting truth and reference theories.
Gödel’s Second Incompleteness Theorem
Gödel's second incompleteness theorem states that no consistent formal system strong enough to include basic arithmetic can prove its own consistency. This profound result builds upon his first incompleteness theorem.
Gödel’s First Incompleteness Theorem
Gödel's First Incompleteness Theorem states that any consistent formal system capable of basic arithmetic contains true statements that are unprovable within the system itself. This reveals inherent limitations of formal…
Gödel-Dummett Logic
A distinct intuitionistic logic, Gödel-Dummett logic incorporates a principle of maximal elements. This allows it to articulate specific intermediate truth values situated between absolute true and false.
Gödel Sentence
A self-referential sentence in formal systems, a Gödel sentence demonstrates incompleteness theorems by asserting its own unprovability within that system. It's a cornerstone of mathematical logic.