ǵneh₃-sk-
“to know, to recognize”know, recognize
Root for knowing, yielding Latin gnoscere/noscere, Greek gignoskein, English know.
Discussion
The PIE form *ǵneh₃-sk- (to come to know, to recognise, to learn by inquiry) is an inchoative derivative of *ǵneh₃- (to know), formed with the *-sk- suffix that in PIE marked the beginning of an action or a gradual process. The meaning is "to begin to know" — the process of learning, as distinct from the state of knowing.
Latin (g)nōscere (to come to know, to get to know, to learn) continues the inchoative form directly: the g- is etymological but was often dropped in classical Latin. The compound cognōscere (to know thoroughly) gave English: cognition (the process of knowing), recognise (to know again), incognito (unknown, unrecognised), connoisseur (one who knows — through French from Latin cognōscere), and reconnaissance (a knowing-again, a scouting expedition to learn the terrain).
The word noble (from Latin nōbilis, earlier gnōbilis — "knowable, well-known, famous") is from the same root: a noble person is one whose name is known. The semantic chain know → known → famous → noble encodes a social reality in which knowledge and visibility conferred rank.
English know (OE cnāwan, from PGmc *knēaną) continues the root natively through Germanic, making know and cognition etymological cousins from the same PIE root.
English can (OE cunnan, "to know how" — from PGmc *kunnaną, from the same PIE root) connects ability to knowledge: what you can do is what you know how to do. The word cunning (originally "knowing, skilled") and the archaic ken ("to know, to recognise" — as in "beyond my ken") extend the native Germanic family.
The *-sk- inchoative suffix survives productively in Latin -scere verbs (adolēscere "to begin to grow up," cognōscere "to begin to know"), confirming its PIE origin as a marker of process and becoming.
Notes
Pokorny 376-378. English know, can, cunning, cognition, notice, noble.