Jespersen's Cycle - why is it defined cycle?

Question

In his excellent work, Negation in English and Other Languages (1917), Otto Jespersen has discovered a pattern that describes how linguistic negation shifts between several stages:

1. Negation is expressed by a single negative marker (NEG1);
2. Negation is expressed by NEG1 in a combination with a negative adverb or noun phrase (NEG2);
3. NEG2 takes on the function of expressing negation by itself; NEG1 becomes optional;
4. NEG1 becomes extinct and NEG2 expresses negation on its own.

However, I'm confused with its name. To me, a cycle is something that repeats over and over. As far as I understood, there's no evidence of more than a single iteration here. It seems that only certain languages (including English) have completed their first iteration, and the others (a majority) have not yet even completed their first iteration.

Hence, the question: why they called it a cycle?

UPD, thanks to Gaston Ümlaut: The term itself has been suggested by Östen Dahl in his work "Typology of Sentence Negation" (1979).

Answer 1

This is Negation by Association. It happens all the time. Probably it's unavoidable, given the variety of language changes that can occur over centuries, the variety of negative expressions, and the ubiquity of negation.

As to whether it's technically a "cycle", it certainly is a repetitive phenomenon, happening quite frequently. But of course it doesn't happen repeatedly to the same forms; this is the kind of cycle we mean when we talk about digestive cycles.

Like negation by association, digestion happens frequently, and in the same order of events, with similar inputs and similar outputs. But it doesn't have to be recursive.

Answer 2

It's called a 'cycle' because the output at the end of stage 4 is able to feed the input at stage 1 (a single negative marker), so a new cycle could easily begin at this point, with the whole process repeating. This is made explicit by Jespersen in the first paragraph of chapter one of the work cited in the question (Negation in English and Other Languages (1917)). Jespersen himself only referred to this as a 'curious fluctuation'; the term 'Jespersen cycle' was coined by Östen Dahl in 'Typology of Sentence Negation' in Linguistics, 17 pp. 79-106.

So the pattern has the form of a cycle; but whether or not this cycle actually happens, repetitively, is another question that can be examined empirically, and has been in some depth: see e.g. Schwenter, Breitbarth & Haegeman, Dahl, Vossen, and many others accessible by web search.