provability

Thân thiện

The mathematician wrote a proof to demonstrate the provability of the theorem.

Definition

Noun: The quality or state of being capable of being demonstrated or logically proved. It refers to the inherent characteristic of a statement, proposition, or argument that allows it to be shown to be true through evidence, logical reasoning, or formal proof.

Usage

"Provability" is a formal term used primarily in logic, mathematics, philosophy, and scientific discourse. It describes whether a given claim can, in principle, be proven, not whether it has already been proven. It is often discussed in contrast to concepts like truth, belief, or axiomatic acceptance.

Examples

• In mathematical logic, the provability of a theorem within a formal system is a central concern.
• The philosopher questioned the provability of ethical statements using purely empirical evidence.
• A key difference between a hypothesis and a law in science often lies in its degree of provability and supporting evidence.

Advanced Usage

• Provability Logic: A branch of modal logic that formalizes reasoning about provability. It uses a box operator (□) to mean "it is provable that..."
• Gödel's Incompleteness Theorems: These famous theorems address the limits of provability within sufficiently powerful formal systems, showing that some true statements are unprovable within the system itself.

Variants and Related Words

• Provable (adjective): Capable of being proved.
  • The conjecture was not yet a provable theorem.
• Prove (verb): To demonstrate the truth or existence of something by evidence or argument.
• Proof (noun): Evidence or argument establishing a fact or the truth of a statement.

Synonyms

• Demonstrability
• Verifiability (Note: Often implies empirical verification, while provability can be purely logical.)
• Confirmability

Antonyms

• Unprovability
• Improvability
• Falsifiability (in specific philosophical contexts, as a contrasting methodological concept)

Học thuật

Noun

1. capability of being demonstrated or logically proved

Từ đồng nghĩa

• demonstrability