Share this entry

Share this page

incompleteness theorem

Syllabification: in·com·plete·ness the·o·rem
(also Gödel's incompleteness theorem)

Definition of incompleteness theorem in English:

noun

Logic
The theorem that in any sufficiently powerful, logically consistent formulation of logic or mathematics there must be true formulas that are neither provable nor disprovable. The theorem entails the corollary that the consistency of a logical system cannot be proved within that system.
Example sentences
  • The incompleteness theorem thus raises doubts about any philosophy of mathematics (formalist or otherwise) that requires a single deductive system for all of arithmetic - a single formal method for deriving every arithmetic truth.
  • Gödel's incompleteness theorem tells us that within mathematics there are statements that are unknowable, or undecidable.
  • The fallout, however, from this mathematical bomb was even more perilous than that from the incompleteness theorem.

Definition of incompleteness theorem in:

Share this entry

Share this page

 

What do you find interesting about this word or phrase?

Comments that don't adhere to our Community Guidelines may be moderated or removed.

Get more from Oxford Dictionaries

Subscribe to remove adverts and access premium resources

Word of the day orthoepy
Pronunciation: ˈɔːθəʊɛpi
noun
the correct or accepted pronunciation of words