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The first two are based on wiktionary

false

From Middle English false, from Old English fals (“false, fraud, falsehood”), from Latin falsus (“counterfeit, false; falsehood”), perfect passive participle of fallō (“deceive”).

Uncommon before the 12 century, the word was reinforced in Middle English by Norman fals (compare Old French faus), eventually displacing native Middle English les, lese (“false”), from Old English lēas; See lease, leasing. For spelling, the -e (on -lse) is so the end is pronounced /ls/, rather than /lz/ as in falls, and does not change the vowel (‘a’). Compare else, pulse, convulse.

fallo

From Proto-Indo-European *gʰwel- (“to lie, deceive”). Cognate with Ancient Greek φῆλος (phẽlos, “deceitful”), Sanskrit वृ (vṛ, “twist, crook”), Avestan 𐬰𐬎𐬭𐬀𐬵 (zurah, “injustice”), Lithuanian ẑulas (“rough”), Latvian zvel'u (“to turn aside”), Old Church Slavonic зълъ (zŭlŭ, “evil”)

But here is another etymology from myEtymology.com

false

the English word false

derived from the Latin word falsus (wrong, lying, fictitious)

derived from the Latin word fallere (deceive; slip by; disappoint)

derived from the Latin word facere (to make; act, take action, be active; compose, write; classify; do, make; create; make, build, construct; produce; produce by growth; bring forth)

derived from the Proto-Indo-European root *dhē-

The third etymology is from etymonline.

false

late 12c., from O.Fr. fals, faus (12c., Mod.Fr. faux) "false, fake, incorrect, mistaken, treacherous, deceitful," from L. falsus "deceived, erroneous, mistaken," pp. of fallere "deceive, disappoint," of uncertain origin (see fail). Adopted into other Germanic languages (cf. Ger. falsch, Du. valsch, Dan. falsk), though English is the only one in which the active sense of "deceitful" (a secondary sense in Latin) has predominated. False alarm recorded from 1570s. Related: Falsely; falseness.

fail

early 13c., from O.Fr. falir (11c., Mod.Fr. faillir) "be lacking, miss, not succeed," from V.L. *fallire, from L. fallere "to trip, cause to fall;" figuratively "to deceive, trick, dupe, cheat, elude; fail, be lacking or defective."

Related: Failed; failing. Replaced O.E. abreoðan. The noun (e.g. without fail) is from late 13c., from O.Fr. faile "deficiency," from falir. The Anglo-French form of the verb, failer, came to be used as a noun, hence failure.

I just don't know which PIE form of "false" is the right one.

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You might find this information helpful (or, maybe it just muddies the water even more). Either way, that website can be a good resource for these kinds of questions. –  J.R. Sep 12 '12 at 9:09
    
@J.R. Thnaks!I will add it to the question. –  archenoo Sep 12 '12 at 9:34
    
@archenoo, which IE languages do you know? –  Alex B. Sep 12 '12 at 13:54
    
@AlexB. I know English(as a second language) and a little about others, namely, Latin(just know about the case and declension system), Greek(with an unfinished textbook), German(a layman but willing to continue), Russian(only the alphabet).I am interested in these languages ,especially the connections among them, because they are all daughter languages from one ancestor. –  archenoo Sep 12 '12 at 15:20
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2 Answers

up vote 4 down vote accepted

I asked you which IE languages you know - in order to critically evaluate these three hypotheses, a strong background in the history of Latin (at least) is necessary. There are three major textbooks on the history of Latin - Baldi 1999, Sihler 1995, and Weiss 2009.

The first hypothesis is best supported by evidence - and, in fact, pretty standard now (for example, de Vaan 2008).

The Anlaut (word-initial) PIE *gwh> Lat. f sound correspondence is well documented, cf. Latin formus 'warm' - MnE warm; Greek thermos; Rus. zhar 'heat', goret' 'burn' etc. We still don't really know how PIE *gwh turned into Latin f (via *χw?) but this correspondence is regular.

We may ignore the perfectum fefelli because it's a relatively new coinage (double ll), cf. pello-pepuli, fero-tetuli (Meiser 1998), although reduplicated perfectum is usually archaic/rare in Latin.

The second "hypothesis" does not stand to scrutiny - supposedly, Latin fallo is derived from Latin facio. The person who came up with that hypothesis doesn't know Latin morphology at all. I don't know of any rule of Latin word-formation that could explain such a connection.

The third hypothesis does not have any explanation - it stops at Latin fallo.

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Here's the OED's etymology:

Etymology: late Old English fals adj. and n., < Latin fals-us false (neuter fals-um , used subst. in sense fraud, falsehood), originally past participle of fallĕre to deceive; compare Old Norse fals n. The adj. is found in Old English only in one doubtful instance (see sense A. 13); its frequent use begins in the 12th cent., and was probably due to a fresh adoption through the Old French fals, faus (modern French faux = Provencal fals, Spanish, Portuguese, Italian falso). The continental Germanic languages adopted the word in an altered form: Middle High German valsch, modern German falsch (compare Old High German gifalscôn to falsify), Old Frisian falsch, Dutch valsch, late Icelandic (15th cent.) falskr, Danish, Swedish falsk.

The etymological sense of Latin falsus is ‘deceived, mistaken’ (of persons), ‘erroneous’ (of opinions, etc.). The transition to the active sense ‘deceitful’ is shown in phrases like falsa fides ‘breach of trust, faithlessness’, where the n. has a subjective and an objective sense. In mod. English the sense ‘mendacious’ is so prominent that the word must often be avoided as discourteous in contexts where the etymological equivalent in other Germanic languages or in Romanic would be quite unobjectionable. Some of the uses are adopted < French, and represent senses that never became English.

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Thanks for your answer!!It contains more details about the history of "false". –  archenoo Sep 12 '12 at 9:50
    
Though no PIE root; the OED doesn't go in for that, since it was pretty speculative in the 19th century. I can't find a PIE root *ghwel- in either Buck or Watkins, and I don't have Pokorny. So we may have to let that one lie until somebody can look it up. –  John Lawler Sep 12 '12 at 15:56
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@JohnLawler, a list of PIE roots based on Pokorny is here utexas.edu/cola/centers/lrc/ielex/PokornyMaster-X.html The dictionary itself is available here archive.org/details/indogermanisches01pokouoft –  Alex B. Sep 12 '12 at 18:17
    
Thank you, Alex. I hadn't searched for it. And here's what UT reports: 489 *gu̯hel- 'to want, wish'; 489-90 *g̑hu̯el- 'to bend, swerve'. You'd think that 'to bend, swerve' would wind up meaning 'false', wouldn't you? But it's actually 'to want, wish', which refers to how we keep deluding ourselves and others by believing our own fantasies. –  John Lawler Sep 12 '12 at 18:27
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Could be. Either one could work. That's what's tricky about PIE root attribution; after a few millennia of accumulating accidents, any meaning can get to be any other meaning, by accident. –  John Lawler Sep 12 '12 at 21:21
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