Etymology
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say (v.)

Middle English seien, from Old English secgan "to utter, inform, speak, tell, relate," from Proto-Germanic *sagjanan "to say" (source also of Old Saxon seggian, Old Norse segja, Danish sige, Old Frisian sedsa, Middle Dutch segghen, Dutch zeggen, Old High German sagen, German sagen "to say").

Watkins has this from a PIE *sokwyo-, from a root *sekw- (3) "to say, utter" (source also of Hittite shakiya- "to declare," Lithuanian sakyti "to say," Old Church Slavonic sociti "to vindicate, show," Old Irish insce "speech," Old Latin inseque "to tell say"). Some further see this as identical to the PIE root *sekw- (1) "to follow" (with semantic development to "see" and then "speak"). But others doubt it and Boutkan gives it "No certain PIE etymology."

The past tense form said developed from Old English segde. Impersonal use (it is said) was in Old English. The notion in shall we say, etc. (1580s) is "suppose, take for granted." On that analogy, impersonal say is used as an introduction word, or parenthetically, with a clause and meaning "suppose, assume" (c. 1600). Its colloquial use as an expression of surprise, etc. is by 1830.

Not attested before 1930 in use with inanimate objects (clocks, signs, etc.) as subjects. You said it! "you're right" is attested by 1919; you can say that again as a phrase expressing agreement is by 1925, American English colloquial. You don't say(so) as an expression of astonishment (often ironic) is attested by 1779. The Society of American Florists' advertising slogan say it with flowers dates to 1918 from it grew other say it with constructions.

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say (n.)

1570s, "what someone says," hence "what one has in him to say, a declaration or statement," from say (v.). The Old English noun secge meant "speech."

The meaning "right or authority to be heard in a matter or influence a decision" is from 1610s in have a say; earlier in this sense was have a saying (late 15c.). Extended form say-so "personal assertion" is recorded by 1630s; in the sense of "power, authority" it is by 1896. 

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says 
third person singular of say (v.), c. 1300, eventually replacing saith.
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sayable (adj.)

"capable of being spoken," 1858; see say (v.) + -able.

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said (adj.)

"named or mentioned before," c. 1300, past-participle adjective from say (v.). Expression all is said and done is from 1550s.

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soothsayer (n.)
mid-14c., zoþ ziggere (Kentish), "one who speaks truth,;" late 14c., sothseggere, "fortune-teller;" see sooth + say. Old English had soðsagu "act of speaking the truth."
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naysayer (n.)

"one who refuses or denies," 1721, from verb naysay (implied from 1530s in naysaying); from nay + say (v.). The verbal phrase say (someone) no "refuse, deny" is from c. 1300. Nay-say (n.) "refusal" is from 1630s.

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unsaid (adj.)
Old English unsæd, from un- (1) "not" + past participle of say (v.). Similar formation in Middle Dutch ongeseit, German ungesagt, Old Norse usagðr.
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hearsay (n.)
"information communicated by another, gossip," mid-15c., from phrase to hear say (Middle English heren seien, Old English herdon secgan). The notion is "hear (some people) say;" from hear (v.) + say (v.). As an adjective from 1570s. Hearsay evidence (1670s) is that which the witness gives not from his own perception but what was told to him. Compare similar formation in Dutch hooren zeggen, German hörensagen.
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gainsay (v.)
"contradict, deny, dispute," c. 1300, literally "say against," from gain- (Old English gegn- "against;" see again) + say (v.). In Middle English it translates Latin contradicere. "Solitary survival of a once common prefix" [Weekley]. It also figured in such now-obsolete compounds as gain-taking "taking back again," gainclap "a counterstroke," gainbuy "redeem," Gaincoming "Second Advent," and gainstand "to oppose." Related: Gainsaid; gainsaying.
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