projectivity
|pro-ject-iv-i-ty|
/prəˌdʒɛkˈtɪvɪti/
the quality of being projective (literally 'thrown forward')
Etymology
'projectivity' originates from Latin, specifically from 'projectus' (past participle of 'proicere'/'projecere'), where 'pro-' meant 'forward' and 'iacere'/'jec-' meant 'to throw'.
'projectivity' developed via Late Latin/Medieval Latin forms such as 'projectivitas' and passed into French (e.g. 'projectivité') and Middle English before becoming the modern English 'projectivity'; the adjectival base 'projective' (from Latin via French) combined with the noun-forming suffix '-ity'.
Initially related to the literal sense of 'being thrown forward' (from the Latin root), it evolved to denote abstract qualities associated with 'projection' — e.g., geometric projective maps, algebraic projective property, and semantic projection — yielding the modern technical senses of 'projectivity'.
Meanings by Part of Speech
Noun 1
in projective geometry, a projectivity is a projective transformation (a bijection of a projective space that preserves the cross-ratio); a map or correspondence that is projective in nature.
The projectivity taking one line to another was represented by a 3x3 matrix in homogeneous coordinates.
Synonyms
Noun 2
in algebra (module theory), projectivity denotes the property of being a projective object (for example, a projective module); the quality of possessing the lifting property that defines projective objects.
The projectivity of the module was used to split the exact sequence in the proof.
Synonyms
Noun 3
in linguistics and semantics, projectivity refers to the tendency of certain meanings or semantic features (e.g., presuppositions) to 'project' from phrases to larger linguistic contexts (to remain constant under operators like negation).
Researchers studied the projectivity of presuppositions to see which elements survive under negation.
Synonyms
Last updated: 2025/11/16 18:22