different between completeness vs utterness

English

Etymology

complete +? -ness

Noun

completeness (usually uncountable, plural completenesses)

1. the state or condition of being complete
2. (logic) The property of a logical theory that whenever a wff is valid then it must also be a theorem. Symbolically, letting T represent a theory within logic L, this can be represented as the property that whenever ${\displaystyle T\vDash \phi }$ is true, then ${\displaystyle T\vdash \phi }$ must also be true, for any wff ? of logic L.

   • THEOREM 37°. (Gödel's completeness theorem 1930.) In the predicate calculus H:
     (a) If ${\displaystyle \vDash F}$ [or even if ${\displaystyle \aleph _{0}}$-${\displaystyle \vDash F}$], then ${\displaystyle \vdash F}$. If ${\displaystyle E_{1},...,E_{k}\vDash F}$ [or even if ${\displaystyle E_{1},...,E_{k}\ \aleph _{0}}$-${\displaystyle \vDash F}$], then ${\displaystyle E_{1},...,E_{k}\vdash F}$.
     (b) [...]

Synonyms

• (state of being complete): completion, fulfillment; see also Thesaurus:completion

Antonyms

• incompleteness, unfinishedness; see also Thesaurus:incompletion

Translations

English

Etymology

utter +? -ness

Noun

utterness (uncountable)

1. The state or condition of being utter.

   We were appalled by the utterness of the destruction.

Synonyms

• completeness
• totality