From the second edition (1989):
(ˈfæləsɪ) Forms: 5–7 falacy(e, 6–7 fallacie, (7 fallecie), 7– fallacy. [ad. L. fallācia, n. of quality f. fallax deceptive: see fallace a. First in 15th c. replacing the older fallace n.]

1. Deception, guile, trickery; a deception, trick; a false statement, a lie. Obs.

1481 Caxton Reynard (Arb.) 67 Ha reynart how wel can ye your falacye and salutacion doon. 1607 Topsell Four-f. Beasts (1673) 159 Then make they a narrow bridge covered with earth‥that the beasts may dread no fallacy. 1671 Milton P.R. i. 155 Winning by Conquest what the first man lost By fallacy surprized. 1749 Fielding Tom Jones xvi. ix, Her utter detestation of all fallacy.

2.a. Deceitfulness (obs.). b. Deceptiveness, aptness to mislead, unreliability.

1641 J. Johnson (title), The Academy of Love, describing the Folly of younge Men and the Fallacy of Women. 1654 Whitlock Zootomia 220 Let us not affirm their existence, and ὄτι on the Fallacies of Sense. c1800 K. White Rem. (1837) 381 The fallacy of human friendship. 1849 M. Somerville Connex. Phys. Sc. xxv. 264 A consciousness of the fallacy of our senses.

3. a. A deceptive or misleading argument, a sophism. In Logic esp. a flaw, material or formal, which vitiates a syllogism; any of the species or types to which such flaws are reducible. Also, sophistical reasoning, sophistry. In certain phrases in the formal terminology of Logic, as fallacy of accident (see quots.); fallacy of composition (see composition 4b); fallacy of division, the fallacy that whatever is true of a whole must be true of any part or member of that whole.
Not in Wilson's Logic (1552) which has ‘deceipt’, ‘deceiptfulness’, as the equivalent of fallacia in this sense.

[1552 R. Ascham Let. 12 July in H. Ellis Orig. Lett. Lit. Men (1843) 12 Lest the fallax of composicion and division‥inverte the sentence. 1562 Turner Herbal ii. 100a, It is a false fallacie‥ to argue from a parte to the hole. 1599 Blundevil Logike 166 Fallacia Accidentis‥: which may bee englished thus: the fallax of the Accident.] 1612 Brinsley Lud. Lit. xvii. (1627) 208 To helpe to answer the subtilties or fallacies. a1665 J. Goodwin Filled w. the Spirit (1867) 160, I shall‥proceed to shew the fallacies and other weaknesses of those pretences. 1685 tr. Arnauld & Nicole's Logic III. xix. 108 To judge of a thing which only agrees with it by accident. This Sophism is call'd in Schools Fallacia accidentis, the Fallacy of the Accident. Ibid. 109 To pass from sence divided to sence compos'd‥is call'd Fallacia Compositionis, Fallacy of Composition. Ibid., To pass‥from sence compos'd to sence divided‥is call'd‥Fallacy of division. 1776 Adam Smith W.N. ii. iv. I. 357 The fallacy which seems to have misled those gentlemen. 1870 W. S. Jevons Elem. Lessons Logic xxi. 176 The fallacy of accident consists in arguing erroneously from a general rule to a special case, where a certain accidental circumstance renders the rule inapplicable. 1884 tr. Lotze's Logic 284 The commonest fallacy is ambiguity of the middle term. 1961 J. G. Brennan Handbk. Logic (ed. 2) x. 213 The Gambler's Fallacy may be construed as an example of the fallacy of division. 1967 Philosophy XLII. 7 An avoidance of the fallacy of accident or secundum quid.

b. Also in extended use (cf. 4, 5): fallacy of misplaced argument (see quot. 1942); fallacy of misplaced concreteness (see quots.); fallacy of simple location, acc. to A. N. Whitehead, an assumption that underlies the whole of science since the 17th century, viz. a form of materialism which holds that the space-time location of a material object is not dependent on reference to other space-time regions; fallacy of the inversion of parts (see quot. 1867); fallacy of the perfect dictionary (see quot. 1938).

1867 J. S. Mill Exam. Hamilton's Philos. (ed. 3) vii. 127 There is a mode of controversy which I do not remember to have seen in any enumeration of Fallacies, but which will some day find a place there, under some such name as the Inversion of Parts. It consists in indignantly vindicating as against your adversary the very principle which he is asserting against yourself. 1925 A. N. Whitehead Sci. & Mod. World (1926) iii. 64 The accidental error of mistaking the abstract for the concrete‥is an example of what I will call the ‘Fallacy of Misplaced Concreteness’. [Ibid. iv. 72 There is no element whatever which possesses this character of simple location.] 1927 B. Russell Analysis of Matter xxxii. 340 Dr. Whitehead‥is not open to such a charge; his ‘fallacy of simple location’, when avoided, leads to a world-structure quite different from that of common sense and early science. 1929 A. N. Whitehead Process & Reality i. i. 9 The ‘fallacy of misplaced concreteness’‥consists in neglecting the degree of abstraction involved when an actual entity is considered merely so far as it exemplifies certain categories of thought. 1938 —— Modes of Thought 235 The very natural belief, that mankind has consciously entertained all the fundamental ideas which are applicable to its experience. Further it is held that human language, in single words or in phrases, explicitly expresses these ideas. I will term this presupposition, the Fallacy of the Perfect Dictionary. 1942 R. G. Collingwood New Leviathan iv. 73 The fallacy of arguing about questions like this is what I call the Fallacy of Misplaced Argument; which may be defined as the fallacy of arguing about any object immediately given to consciousness.

4. A delusive notion, an error, esp. one founded on false reasoning. Also, the condition of being deceived, error.

1590 Shakes. Com. Err. ii. ii. 188 Ile entertaine the free'd [Globe ed. offer'd] fallacie. 1665 Glanvill Sceps. Sci. xiii. 75 We being then thus obnoxious to fallacy in our apprehensions and judgments. 1735–8 Bolingbroke On Parties Ded. 22 When They cannot impose a Fallacy, endeavour‥to hinder Men from discerning a Truth. 1825 Syd. Smith Wks. (1859) II. 59/2 A vast number of absurd and mischievous fallacies. 1844 H. H. Wilson Brit. India I. 413 In adducing the authority of Hindu writers in favour of the doctrine, two sources of fallacy are discernible.

5. a. Sophistical nature, unsoundness (of arguments); erroneousness, delusiveness (of opinions, expectations, etc.).

1777 Priestley Disc. Philos. Necess. Pref. 30, I was enabled to see the fallacy of most of the arguments. 1825 McCulloch Pol. Econ. ii. 158 The returns under the population acts have shown the fallacy of these opinions. 1850 Prescott Peru II. 193 Expectations of wealth, of which almost every succeeding expedition had proved the fallacy.

b. Proneness to err, fallibility. Obs. rare.

1651 N. Bacon Disc. Govt. Eng. ii. xxvii. (1739) 120 Finding the fallacy of the infallible Chair, he hearkens unto other Doctors. 1796 Gouv. Morris in Sparks Life & Writ. (1832) III. 87 Experience has taught me a sincere faith in the fallacy of human opinions.

6. Comb., as fallacy-monger.

1849 Cobden Speeches 10 When the revolutions broke out, these fallacy-mongers exclaimed.