Rule inversion and [r]-Insertion
Rhotic varieties of English, of course, preserve the historical situation before /r/-Deletion and most or all of the associated vowel changes. The next closest to this historical period would be an accent which maintained /r/-Deletion as a synchronic phonological rule. Such varieties are rare. For instance, some accents of the Southern USA (Harris 1994) have neither linking nor intrusive [r], so that no [r] is pronounced in soaring, soar in, sawing or saw in; they also lack [r] in forms with historical clusters like beard, harp. But in such cases, [r]-Deletion is not a synchronic process: the absence of [r] has simply led subsequent generations of speakers to set up underlying forms lacking /r/, except word-initially in red, bright. In certain Southern US accents (Wells 1982), [r]-Deletion has also operated intervocalically, giving forms like [vEI] `very'. If such pronunciations occur categorically for a speaker or group, we might propose /r/-less underliers here, too; if they are optional, we might suggest underlying /r/ and an intervocalic deletion rule controlled by formality or speed of speech. Alternatively, we might assume no under lying /r/, and spelling pronunciations in formal styles (as discussed below for RP). However, other speakers of Southern US English (Kenyon and Knott 1953, Wells 1982, Lass 1987) do have linking [r], but not intrusive [r]. In these cases, although there can be no justification for proposing underlying /r/ in non-alternating forms like beard, harp, we might argue for /r/ in soar, letter, spar (but not saw, comma, spa), with a synchronic analogue of /r/-Deletion pre-pausally and pre-consonantally. This might seem to be at odds with my usual mechanism for determining underlying representations, since /r/ will appear underlyingly in underived soar, letter, where it will not surface: however, an argument can be made for this on the grounds of partial surface merger outlined for Scots /ni/ versus /ai/, since there are parallel morphemes like saw, comma which do not attract [r] in any circumstances, and the most appropriate underlying distinction would then be /r/ in the soar class versus final vowel in saw. A similar analysis might be fitting for those speakers of South African English (Wells 1982, Lass 1987), who have linking without intrusive [r]; most, however, seem to replace both with a glottal stop. This might best be accounted for by assuming underlying /r/ only in red and bright words. In soar, saw, letter, comma, spar and spa, there would be no underlying /r/; resulting vowel hiatuses would be broken by [ʔ], with occasional linking [r] reflecting orthographic influence, and again there would be no synchronic /r/-Deletion. We return below to the interaction of /r/ with other synchronic hiatus-breakers.

The great majority of non-rhotic varieties of English, however, have both linking and intrusive [r]. I assume that such varieties arose historically by way of rule inversion (Vennemann 1972) of the earlier /r/ Deletion change, producing a synchronic rule of [r]-Insertion. This hypothesis is by no means new (Johansson 1973, Pullum 1974, Wells 1982), but it has fallen rather into disrepute lately, as many recent discussions of /r/ have adopted alternative solutions. I shall survey some of these in Alternative analyses, but first outline the inversion hypothesis briefly.

Recall that [r] had dropped finally and pre-consonantally, for some speakers at least, by the mid to late eighteenth century. These speakers would still have underlying /r/ in red, bright, very, harp, soar and beer words, but would delete it in the appropriate environments in the last three, producing linking [r] alternations in words like soar, beer. I assume that succeeding generations of speakers would fail to learn underlying /r/ except word-initially and intervocalically, in red, bright, very words; linking [r] would then be derived by a synchronic rule of [r]-Insertion, as informally shown in (1).
(1) 

We shall return to the formulation of [r]-Insertion, and the question of whether it is an exact complementary or inverse of /r/-Deletion, in (1). However, it is important to note here that rule inversion is a phonologist's construct: the two rules under discussion are independent, although diachronically related. In other words, a deletion rule is proposed for the earlier stage, and an insertion rule for the present-day situation, because in each case this represents the best analysis of the varieties involved. The relationship between the two is parallel to that obtaining between the historical Great Vowel Shift and the synchronic Vowel Shift Rule (although in that case rule inversion was not involved): the processes are independently postulated on evidence from the relevant periods, but given a broad diachronic perspective, the present-day rule is the descendant of the earlier one.

Rule inversion in this case reflects problems of learnability, and the reasonable expectation of speakers that forms which sound the same should behave the same. After [r]-Deletion, speakers would be unable to distinguish spar from spa, or soar from saw, or to tell which was the form which should appear with [r] in intervocalic contexts. It is hardly surprising that they should regularize their system, by introducing [r] intervocalically, regardless of whether the underlying form in question was [r]-final or vowel-final. Since this in turn would lead to surface convergence of underlyingly distinct forms, we would expect a further regularization at the underlying level, with final /r/ lost altogether (in line, incidentally, with the assumptions of my model of Lexical Phonology on the formation of underlying representations), and [r] supplied between schwa or a long low vowel, and any following vowel. This leads automatically to the innovation of [r]-Insertion, and to intrusive [r].

Intrusive [r], like linking [r], appears both word-internally (banana[r]y, withdraw[r]al) and across word boundaries (law[r] and order, India[r] and Africa). For many speakers, it is extraordinarily productive, operating in foreign words, acronyms, and when speaking (or singing, in the case of Latin) foreign languages: some examples are given in (2) (and see Jespersen 1909).
(2) 

Intrusive [r] is clearly contextually restricted, in that it appears only after /ɑ: ɔ: ə/: however, when any other vowel is reduced to schwa, it does attract intrusive [r]; data from a number of non-rhotic varieties appear in (3). [r] also interacts productively with other phonological processes and with other hiatus breakers.
(3) 

We have already considered its complementarity with [ʔ] in South African English; the contexts of insertion for [r] are also precisely those not available for [j], which appears after high and mid-front vowels, and [w], the preferred hiatus breaker after high and mid-back vowels. An example of such interaction is given in (4). In potato and, a speaker with a final long-mid monophthong in potato will introduce [w], but reduction to schwa will trigger [r]-insertion. In potato hot, [h] may be pronounced, and if so no hiatus arises; but if it is elided, then either [w] or [r] will again be introduced, depending on the quality of the preceding vowel.
(4) 
 

These connections of /r w j h/ in Modern English are especially interesting given Lutz's (1994) suggestion that these relatively weak consonants have all undergone parallel weakening during the history of English, both positionally and structurally. Whereas in Old English they could appear in onset or coda position, they have undergone gradual attrition in codas, vocalizing and fusing in various ways with preceding vowels. One might add that /l/, the other English liquid, is undergoing vocalization in various English dialects (Tollfree 1995, Harris 1994); there is also an intrusive [l], reported in Bristol forms like America[l], Anna[l] (and historically, the name Bristol itself) ± hence the old joke about the Bristollian with three daughters called Idle, Evil and Normal. Intrusive [l] is also fairly productive in some American English varieties, including South Central Pennsylvania, Newark and Delaware (Gick 1997), where earlier patterns of word-final vocalization with intervocalic linking [l] have been reanalyzed for some speakers as productive [l]-intrusion in over lapping but not identical environments to those triggering [r]-Insertion elsewhere: thus, we find draw[l]ing, Sau[l] is, saw[l] is, Ha[l] is, how[l] is.

Despite the general productivity of [r]-insertion, some speakers of, for instance, RP (Gimson 1980, Wells 1982) seem to suspend it, particularly word-internally. This suspension depends in part on the phonological context, since linking and intrusive [r] are disfavored by another [r] in the immediate environment, as in the emperor of Japan, a roar of laughter (Jones 1956: 197, Wells 1982). Johansson (1973) and Pullum (1974) argue that this is best analyzed as a restriction on the [r]-epenthesis rule, whereby [r] fails to appear in dissimilatory contexts; /r/s, and indeed liquids in general, are very commonly involved in dissimilation. However, the suspension of intrusive [r] in particular appears to depend primarily on the sociolinguistic context, and particularly on formality. Most straightforwardly, we might assume that [r]-Insertion can be blocked by reference to the spelling: an RP speaker saying withdrawal may be, or become aware that there is no orthographic and therefore not supply phonetic [r]. This hypothesis is consistent with the fact that suspension of intrusive [r] seems most common in more formal speech, where spelling consciousness may be greater. It is also in accord with recent work by Giegerich (1992, in press), who argues on the basis of alternations between schwa and full vowels that spelling may inform or even drive phonological rule applications. Orthographic 5r4 is certainly used differently by non-rhotic and rhotic speakers: for rhotic speakers, it means essentially `say [r] here', whereas for non-rhotic speakers it can signal a property of the preceding vowel, and can therefore be used for disambiguation, as in (5).
(5) 
 

Conversely, the spelling of historical vowel plus [r] sequences is breaking down in some respects for non-rhotic speakers. We find variant spellings, like versus , and confusion as to whether [pælɑ:və] should be spelled with final , (like pavlova)or (like howdah) (6). If speakers are suspending [r] Insertion by referring to the orthography, no wonder they are only partially successful.
(6) 

Additionally, we might account for variable lack of intrusive [r] with reference to adaptive rules (Andersen 1973, Disterheft 1990), which were also discussed briefly in connection with inter-dialectal communication. Disterheft is particularly concerned with the question of how linguistic change can take place without prejudicing inter-generational communication, and concludes that the mechanism responsible involves adaptive rules, `ad hoc rules used by learners to disguise output which, because of improper rule formulation, does not match that of their models. They adapt forms/structures to correspond to what community norms dictate' (1990: 182). These rules smooth the transition between generations, so that even catastrophic changes do not jeopardize communication. They do not stop or reverse a change, but temporarily obscure the effects of some abductive innovation: in other words (Disterheft 1990: 184), adaptive rules are the diachronic correlate of accommodation. In the speech community, the adaptive rules will gradually become optional, used only in formal situations or when talking to older people; and ultimately, they are lost as the novel form becomes the norm. In addition, speakers with the change and the adaptive rule in their grammars are assumed to correct children producing the innovatory forms less frequently. All this means that the change will become apparent only very gradually.

Let us apply this hypothesis to the case of [r]. At the point when younger speakers were innovating [r]-Insertion, older speakers with the deletion rule would still be producing linking but not intrusive [r]. Younger speakers with intrusion might be corrected, and respond by setting up an adaptive rule, so that intrusive [r], although the result of a new rule, and subsequent rule inversion and change at the underlying level, would seem to creep very gradually into the language. Intrusive [r] has been stigmatized from its earliest stages (see Muggle stone 1995): Hullah (1870: 53-4) considers it `a characteristic of cockney breeding, as Maidarill (for Maida Hill - not unpardonable in an omnibus conductor), and Victoriarour Queen - quite unpardonable in an educated gentleman'. It is still generally frowned upon by present-day Standard British English speakers at least, and modern RP speakers might therefore still use some sort of adaptive rule, in formal situations or with older interlocutors. This seems even more likely given Campbell and Ringen's (1981) hypothesis that sound changes or phonological processes may be suspended as part of assimilation to a prestige model, and that this tendency may also be spelling-based. Note, however, that being sensitive to public opinion about a particular feature, and indeed disapproving of it oneself, does not guard against producing it, as Sweet's quotation in (7) makes admirably clear.

(7) I have for some years been in search of a `correct speaker'. It is very like going after the great sea-serpent ... I am inclined to the conclusion that the animal known as a `correct speaker' is not only extraordinarily shy and difficult of capture, but that he may be put in the same category as the `rigid moralist' and `every schoolboy' - that he is an abstraction, a figment of the brain (Sweet 1881: 5-6)