Linked from

The 24 pages that link to Consistency, each with the reason it gives.

• Causal inferenceRelated: It connects observed data to the potential outcomes used to define causal effects.

• AxiomRelated: Axioms and inference rules together determine whether contradictions can be derived.

• Hilbert's programRelated: Proving consistency was a central aim of Hilbert's project.

• Paraconsistent logicRelated: Paraconsistency separates tolerating inconsistency from treating every theory as acceptable.

• Kurt GödelRelated: Consistency is a key condition in Gödel’s incompleteness results.

• SoundnessRelated: Consistency is weaker: a theory can avoid contradiction yet prove false claims.

• Proof by contradictionRelated: The argument treats contradiction as impossible within the accepted assumptions and rules.

• Formal systemRelated: A system deriving contradictions can undermine the reliability of its theorems.

• Foundations of mathematicsRelated: Consistency is a central standard for evaluating foundational systems.

• Axiomatic methodRelated: Consistency is a central test of whether an axiom system avoids incompatible conclusions.

• FormalismRelated: Consistency is a key condition for a formal system to serve as a viable mathematical theory.

• Foundations of GeometryRelated: A geometric axiom system is useful only if its assumptions do not yield contradictions.

• Philosophy of mathematicsRelated: Foundational programs must address whether their formal systems avoid contradiction.

• Axiomatic systemRelated: Consistency rules out systems that prove both a statement and its negation.

• Deductive systemRelated: Consistency rules out systems whose derivations collapse into contradictory conclusions.

• Hilbert's axiomsRelated: A model of Hilbert's axioms can establish their consistency relative to its underlying number system.

• Goodstein's theoremRelated: The unprovability result is established relative to the consistency of Peano arithmetic.

• Gödel sentenceRelated: Consistency is among the conditions connecting the sentence’s unprovability to its truth.

• Tarski's undefinability theoremRelated: Consistency is among the assumptions that prevent a theory from proving its own liar-like sentence.

• Cut-elimination theoremRelated: In standard classical sequent calculi, cut elimination rules out a cut-free derivation of the empty sequent.

• Axiom (general principle)Related: A useful axiom system must avoid deriving incompatible claims.

• Löb's theoremRelated: Consistency is a central background condition in results about formal provability, though not the theorem’s conclusion.

• Axiom (mathematics and logic)Related: A contradiction among consequences undermines the theory's use as a foundation.