In logic and affirmation is a positive judgment -- the union of the subject and predicate of a proposition.
In law, an affirmation is a solemn declaration allowed to those who conscientiously object to taking an oath. An affirmation has exactly the same legal effect as an oath, but is usually taken to lack religious implications of an oath. The Constitution of the United States twice refers to an "oath or affirmation": once when saying that search warrants must be supported by such evidence, and once when saying that before entering office, the president must take a certain oath or affirmation.
Based on an article from a well-known encyclopedia published in 1911.