Etymology
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bullshit (n.)

also bull shit, "eloquent and insincere rhetoric," 1914, American English slang; see bull (n.1) + shit (n.), probably because it smells. But bull in the sense of "trivial or false statements" (1914), which usually is associated with this, might be a continuation of Middle English bull "false talk, fraud" (see bull (n.3)).

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scatology (n.)

"obscene literature," 1876, with -logy "treatise, study" + Greek skat-, stem of skōr (genitive skatos) "excrement," from PIE *sker- "excrement, dung" (source also of Latin stercus "dung"), on the notion of "to cut off;" see shear (v.), and compare shit (v.). Late 19c. dictionaries also give it a sense of "science of fossil excrement." Related: Scatological (1886).

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batshit 
also bat-shit, by 1967 as a variant of bullshit (n.) in the slang sense; from bat (n.2) + shit (n.). By early 1980s as "crazy," the sense shift is for uncertain reasons; perhaps from the notion of guano as an explosive or health problems caused by inhaling powdered bat feces in caves and mines. Also compare batty "crazy" (early 20c.), from the expression bats in (one's) belfry.
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turd (n.)

Old English tord "piece of excrement," from Proto-Germanic *turdam (source also of Middle Dutch torde "piece of excrement," Old Norse tord-yfill, Dutch tort-wevel "dung beetle"), from PIE *drtom, past participle of root *der- "to split, flay, peel;" thus "that which is separated ("torn off") from the body" (compare shit (v.) from root meaning "to split;" Greek skatos from root meaning "to cut off; see scatology). As a type of something worthless and vile, it is attested from mid-13c. Meaning "despicable person" is recorded from mid-15c.

A tord ne yeue ic for eu alle ["The Owl and the Nightingale," c. 1250]
Alle thingis ... I deme as toordis, that I wynne Crist. [Wyclif, Philippians iii.8, 1382; KJV has "I count all things ... but dung, that I may win Christ"]
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crap (v.)

"to defecate," 1846, from a cluster of older nouns, now dialectal or obsolete, applied to things cast off or discarded (such as "weeds growing among corn" (early 15c.), "residue from renderings" (late 15c.), underworld slang for "money" (18c.), and in Shropshire, "dregs of beer or ale"), all probably from Middle English crappe "grain that was trodden underfoot in a barn, chaff" (mid-15c.), from French crape "siftings," from Old French crappe, from Medieval Latin crappa, crapinum "chaff." Related: Crapped; crapping.

For connection of the idea of defecation with that of shedding or casting off from the body, compare shit (v.). Despite the etymological legend, the word is not from the name of Thomas Crapper (1837-1910) who was, however, a busy plumber and may have had some minor role in the development of modern toilets. The name Crapper is a northern form of Cropper (attested from 1221), an occupational surname, obviously, but the exact reference is unclear. Crap (v.) as a variant of crop (v.) was noted early 19c, as a peculiarity of speech in Scotland and what was then the U.S. Southwest (Arkansas, etc.).

Draw out yere sword, thou vile South'ron!
   Red wat wi' blude o' my kin!
That sword it crapped the bonniest flower
   E'er lifted its head to the sun!
[Allan Cunningham (1784-1842), "The Young Maxwell"]
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*skei- 
Proto-Indo-European root meaning "to cut, split," extension of root *sek- "to cut."

It forms all or part of: abscissa; conscience; conscious; ecu; escudo; escutcheon; esquire; nescience; nescient; nice; omniscience; omniscient; plebiscite; prescience; prescient; rescind; rescission; science; scienter; scilicet; sciolist; scission; schism; schist; schizo-; schizophrenia; scudo; sheath; sheathe; sheave (n.) "grooved wheel to receive a cord, pulley;" shed (v.) "cast off;" shin (n.) "fore part of the lower leg;" shingle (n.1) "thin piece of wood;" shit (v.); shive; shiver (n.1) "small piece, splinter, fragment, chip;" shoddy; shyster; skene; ski; skive (v.1) "split or cut into strips, pare off, grind away;" squire.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit chindhi, chinatti "to break, split up;" Avestan a-sista- "unsplit, unharmed," Greek skhizein "to split, cleave, part, separate;" Latin scindere "to cut, rend, tear asunder, split;" Armenian c'tim "to tear, scratch;" Lithuanian skiesti "to separate, divide;" Old Church Slavonic cediti "to strain;" Old English scitan, Old Norse skita "to defecate;" Old English sceað, Old High German sceida "sheath;" Old Irish sceid "to vomit, spit;" Welsh chwydu "to break open."
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S.O.L. 

initialism (acronym) from shit out of luck (though sometimes euphemised), 1917, World War I military slang. "Applicable to everything from death to being late for mess" [Russell Lord, "Captain Boyd's Battery, A.E.F.," c. 1920]

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skite (n.)
"contemptible person," 1790, Scottish and Northern, earlier "sudden stroke or blow" (1785), perhaps from Old Norse skyt-, from skjota "to shoot" (see shoot (v.)). Old Norse skita "to shit" might have had some influence on the sense of the English word.
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gore (n.1)
"thick, clotted blood," Old English gor "dirt, dung, filth, shit," a Germanic word (cognates: Middle Dutch goor "filth, mud;" Old Norse gor "cud;" Old High German gor "animal dung"), of uncertain origin. Sense of "clotted blood" (especially shed in battle) developed by 1560s (gore-blood is from 1550s).
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not (adv.)

negative particle, a word expressing negation, denial, refusal, or prohibition, mid-13c., unstressed variant of noht, naht "in no way" (see naught). As an interjection to negate what was said before or reveal it as sarcasm, it is attested by 1900, popularized 1989 by "Wayne's World" sketches on "Saturday Night Live" TV show.

Not, spoken with emphasis, often stands for the negation of a whole sentence referred to: as, I hope not (that is, I hope that the state of things you describe does not exist). [Century Dictionary, 1895]

To not know X from Y (one's ass from one's elbow, shit from Shinola, etc.) was a construction attested from c. 1930 in modern use; but compare Middle English not know an A from a windmill (c. 1400). Double negative construction not un- was derided by Orwell, but is persistent and ancient in English, popular with Milton and the Anglo-Saxon poets.

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