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Both normalcy and normality have the definition of "the state of being normal."

From Wiktionary:
Normalcy - "The state of being normal; the fact of being normal; normality."
Normality - "The state of being normal or usual; normalcy."

Is there any functional difference between them?

For example in the sentence:
After a month of extravagant spending, Sam's life returned to ____ .
which is preferable?

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    @WS2 'Normalcy' was never a word until Harding used it as a malapropism in a speech in the 20's 'Return to Normalcy'. Because of that one usage, it has become an accepted ter, in the US, even though 'normality' is preferred. – Mitch Jun 6 '16 at 20:15
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    I would just say "Sam's life returned to normal." – 200_success Jun 6 '16 at 20:36
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    @WS2 Exactly, and I doubt Harding wanted America to return to a state of right angles... – Alan Carmack Jun 6 '16 at 21:39
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    @TrevorD OED says: Regarded by H. W. Fowler as ‘a hybrid derivative of the “spurious hybrid” class..[which] seems to have nothing to recommend it’ ( Dict. Mod. Eng. Usage (1926) 382/2). According to Burchfield ‘Normalcy and normality stand side by side in AmE as legitimate alternatives. In BrE normality is the customary term, and normalcy is widely scorned.’ ( Fowler's Mod. Eng. Usage (1996) 528/1). – WS2 Jun 7 '16 at 6:44
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An interesting comment from 1929 is given in the Oxford English Dictionary:

If..‘normalcy’ is ever to become an accepted word it will presumably be because the late President Harding did not know any better.

OED gives the author as G. N. Clark, writing for the Society for Pure English.

"Normality" means the state of being normal.

"Normalcy" was used by Warren G. Harding in his 1920 election campaign called "Return to Normalcy." When pointed out that the word was a mistake, Harding said he couldn't find the word "normality" in his dictionary. Before his gaff, "normalcy" was used as a mathematics term. In the 90 years since Harding misspoke, the term "normalcy" has become widespread (in the USA, at least) either as an example of a mistake or as a valid synonym for "normality."

I suggest not using "normalcy" unless you know what you are doing, because it is still seen by many as a sign of ill-education.

normalcy
1857, "mathematical condition of being at right angles," from normal + -cy. Associated since c. 1920 with U.S. president Warren G. Harding and derided as an example of his incompetent speaking style. Previously used mostly in the mathematical sense. The word preferred by purists for "a normal situation" is normality (1849).

(Source: Etymology Online)

Harding's usage:

America’s present need is not heroics, but healing; not nostrums, but normalcy; not revolution, but restoration; not agitation, but adjustment; not surgery, but serenity; not the dramatic, but the dispassionate; not experiment, but equipoise; not submergence in internationality, but sustainment in triumphant nationality.

  • Bang-up answer!!!! :) – david macCary richter Jun 7 '16 at 0:57
  • +1 for the answer. But I have been unable to find the comment you quote in the current on-line Oxford English Dictionary . Were you actually quoting from the 1929 edition? – WS2 Jun 7 '16 at 6:48
  • @WS2 The first comment? Yes, it's in the online OED that I access through the public library. It's just below the usage of Mr Harding. – Alan Carmack Jun 7 '16 at 14:22
  • @AlanCarmack Apologies – WS2 Jun 7 '16 at 19:45
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Fowler's Modern English Usage, 3rd edition:

It may come as a surprise to many people that the competing abstract nouns normalcy, normality, and normalness all entered the language at approximately the same time, in the middle of the 19C. The surprise is perhaps reduced when it is noticed that the adj. normal itself, though recorded in the 17C. in the sense of 'rectangular', did not acquire its modern everyday meaning until about 1840. So what we are dealing with here is a group of modern words that has hardly had time for the customary processes of assimilation or rejection to have taken their course.

What is interesting is to look at two different dictionaries from 1828: 1) Johnson and Walker's Dictionary of the English Language, and 2) Webster's.

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