Section 2 showed that an adequate model of the initiation and incrementation of community-wide sound change must predict sporadic localized bifurcation (Figure 3), while at the same time preserving the lawful relationship between the strength of the phonetic biases that cause individual innovations and the typological frequency of the corresponding changes (Figure 1). In addition, the model must explain how, once initiated, community-wide sound change advances by intergenerational incrementation (Figure 2), with each successive cohort of speakers using the innovative variant more than the preceding cohort (Labov 1994: 83–84, 112; 2001: Chapter 14). Finally, the model must account for the fact that incrementation is typically monotonic (although, as we will see in Section 5.5, change reversals can and do occur). As part of this, it is generally agreed that the model should be able to produce sigmoid curves, although a number of studies have observed largely linear trajectories of sound change (e.g. Labov et al. 2013).

Thanks to work in Labovian sociolinguistics, the empirical facts of incrementation are known in considerable detail. In general, preadolescent children are conservative: they use the innovative variant less than contemporary teenagers and younger adults. During adolescence, however, speakers rapidly increase their use of the innovative variant, so that, around the age of 17, they reach a level exceeding that of all contemporary age-groups: this is known as the adolescent peak (Labov 2001: Chapter 14; Tagliamonte & D’Arcy 2009). After adolescence, the speaker’s mean use of the variable remains largely stable.

In consequence, apparent-time studies of ongoing sound change typically find the pattern illustrated in Figure 4, which plots the degree of /oʊ/-fronting by age-group in Charleston, South Carolina, at the end of the 20^th century (Baranowski 2007). Among adults, /oʊ/-fronting is inversely correlated with age: each age-group exhibits the amount of fronting that they reached by late adolescence, which was higher than that of the immediately preceding cohort. Preadolescent children are conservative, producing realizations of /oʊ/ within the adult range. In contrast, adolescents have the highest level of fronting, giving rise to the expected peak.

Several quantitative correlations confirm that the adolescent peak is intimately bound with the mechanism of intergenerational incrementation (Labov 2001: Chapter 14; Tagliamonte & D’Arcy 2009). First, the prominence of the adolescent peak at a given point in real time t is directly proportional to the speed (instantaneous velocity) of the change at t. In changes following a logistic trajectory, therefore, the adolescent peak is sharpest at the mid point, when incrementation is fastest. Near floor or ceiling, in contrast, velocity is lower, and so apparent-time curves look flatter. Similarly, if change a advances faster than change b, then a will show a more prominent adolescent peak.1

The fact that speakers cease to increment their use of innovative variants around age 17 can plausibly be imputed to a general decline in linguistic plasticity. In this respect, it is highly suggestive that the age at which the adolescent peak is reached coincides with the critical period for second language acquisition identified by Hartshorne et al. (2018). We know, however, that this decline in linguistic plasticity is not absolute and affects some parts of the grammar less severely than others: in particular, adults appear to perform gradient phonetic adjustments (Harrington 2006) more easily than they learn new categories (Nahkola & Saanilahti 2004) or large-scale patterns such as chain-shifts (Labov 2007). By the same token, the account of intergenerational incrementation presented above is not invalidated by the observation that some individuals exhibit life-span changes, i.e. shifts in variable use after adolescence (e.g. Sankoff & Blondeau 2007; Wagner & Sankoff 2011; Sankoff 2019). The empirical record confirms that, despite the existence of life-span change, generational change is the main mechanism of incrementation: in a study of five variables using data from the Philadelphia Neighborhood Corpus (Labov & Rosenfelder 2013), for example, Fruehwald (2017a) found relatively weak evidence for effects of life-span change, while generational effects proved extremely robust.

I now proceed to show how the desiderata listed in the first paragraph of Section 3.1 are met by a model of initiation and incrementation based on the hypothesis that learners are community-oriented (i.e. they reject individual idiosyncrasies) and momentum-sensitive (i.e. they respond to differences in the use of linguistic variables across age-groups).

This model implements the key insight of Janda & Joseph’s (2003) “big bang” theory: the mechanism that brings new variants into being is not the same as the mechanism that initiates and sustains the incrementation of their use within the community. In particular, I assume that new sound patterns are created by phonologization through Ohalian correction failure; later developments in the life cycle of those patterns (stabilization, domain narrowing, and morphologization or lexicalization in Figure 5) involve input restructuring (Bermúdez-Otero 2015: 382–388). However, whilst correction failure and input restructuring create new variants, they are not responsible for incrementing their level of use; as we shall see presently, that task is performed by momentum-sensitive learning. This division of labour explains why error fails to accumulate under the effect of the permanent biases that cause innovation.

I follow Labov (2014a; b) in assuming that language acquisition is community-oriented. This means that, on the basis of her experience of linguistic behaviour in the speech community, the learner internalizes and then follows a mental representation of the collective linguistic norm. Adhering to this internal representation of the community norm leads the learner to reject variants that she perceives as individually idiosyncratic. The most dramatic example of this suppression of individual deviation is found in children’s rejection of features of parental speech that fail to match the local dialect. Labov adduces many instances of this phenomenon: for example, children in new towns like King of Prussia just outside Philadelphia (Payne 1976) and Milton Keynes in England (Williams & Kerswill 1999) abandon their parents’ diverse dialects and converge upon the local norm; similarly, Labov (2006) found no significant differences in variable use between second-generation and third-generation New Yorkers on the Lower East Side, even though the former had non-native parents. Interestingly, there is good evidence that convergence upon the community norm starts very early and that it operates subpersonally and automatically. Nardy et al. (2014), for example, documented the homogenization of variable use in a group of French-speaking kindergarteners: they found that the similarity in usage between any two children was directly proportional to the frequency with which those children interacted, showing no effect of attitudinal parameters such as reported interpersonal attraction or awareness of prescriptive standards.

Community-oriented learning is consistent with the fact that preadolescent children are conservative in their use of variables (Figure 4). This simply reflects the fact that, early in life, their linguistic experience is limited and dominated by the speech of their immediate caregivers, who are mostly adults. In later childhood and adolescence, however, learners gain much wider exposure to the speech community: in the urban areas of developed countries, in particular, this is often facilitated by attendance at large schools. This wider socialization into the community enables learners to build more detailed mental representations of the community norm.

A related assumption of the model is that the learner’s knowledge of the community norm comes to include an age vector: in other words, children and adolescents acquire a mental representation of the differences in variable use between age-groups in their community (Labov 2001: Chapter 14; 2010: 195–195, 344, 369). Until approximately 17 years of age, moreover, the learner crucially retains sufficient linguistic plasticity for the age vector to be enforced in her own speech. This means that the learner undergoes incrementation of her use of innovative variants to the level that is appropriate according to her mentally represented age vector.

To understand how this happens, consider a speech community subject to an ongoing sound change that increases the use of a variant v. Let us now follow the developmental trajectory of a young learner L as she is socialized into this speech community. While L is small, she remains conservative, using v at a relatively low rate like her adult caregivers. As she grows up, however, L is socialized into the wider community, partly through schooling. She is now exposed to the differences in variable use between late adolescents, young adults, and older adults. In consequence, an age vector encoding these intergenerational differences is added to L’s mental representation of the community norm: crucially, this age vector reflects the fact that younger speakers use v more than older speakers. At this point, L’s learning faculty detects a disparity between L’s own usage and the collective norm: L’s use of v matches adult rates but falls below adolescent levels, thus failing to comply with the inverse correlation between speaker age and use of v that holds across the community. Therefore, since the learning faculty is community-oriented, it increments L’s use of v in the direction of the older cohort of adolescents. When the members of that older cohort reach adulthood, however, their linguistic plasticity declines, and so their use of v levels out. Meanwhile, L herself remains plastic, and the incrementation in her use of v continues during her own adolescence. The process is sustained by the orientation of the learning faculty towards the community norm: the older cohort are now adults, and the norm encoded in the age vector is for adolescents to use v more than adults. The result is that, by age 17, L and the other members of her age cohort have reached a peak of v use beyond the level of the immediately preceding generation—only then to undergo a decline in their own linguistic plasticity.2

Figure 6 provides a schematic representation of the age vector in action. Successive cohorts are represented by numbered circles; their dates of birth are shown in the left-hand side column. The apparent-time diagrams in the middle and on the right-hand side provide snapshots of the community at two points in real time separated by a ten-year interval. In the year 2000, the members of cohort 5 are ten years old: they internalize an age vector m (for momentum), encoding the community pattern whereby late adolescents (cohort 4) use the relevant variant more than adults (cohorts 3 and 2). By 2010, the members of cohort 5 are twenty years old: the use of the variant by cohort 4 has not changed in adulthood, while cohort 5 have undergone incrementation during adolescence, so that their distance from older adults (cohorts 4 and 3) complies with m.

It should be clear that, if this account of the adolescent peak is correct, the incrementation of sound change in progress does not involve agency on the learner’s part (cf. Section 5). Acquiring a mental representation of the community norm, incrementing the use of innovative variants in line with the age vectors contained in that mental representation, and ceasing incrementation as linguistic plasticity declines is not something that learners do; it is something that happens to them. Since these cognitive processes are not the actions of agents, they do not have motivations or reasons; they only have causes (Schlosser 2019). In much the same way, when human beings with normal vision perform binocular stereopsis, we do not inquire into their reasons or motives, for binocular stereopsis is not an action: it is a subpersonal automatic cognitive process. As in the case of binocular stereopsis, however, we may legitimately wonder why momentum-sensitive learning is part of human nature. This question admits of both narrow and wide answers. Taking a narrow viewpoint, one would simply say that momentum-sensitive learning is just one aspect of the learner’s community orientation: as we have seen, language learning involves discovering and following the community norm, and differences in variable use across age groups are just part of that norm. Taking a wider view of the problem, however, one may ask why learners are community-oriented in the first place. I shall not tackle this larger question here, but will merely suggest that answers are probably to be sought in the evolutionary history of sociality in primates in general and Homo sapiens in particular.

More generally, this account of the incrementation of sound change belongs in the general class of momentum-based selection models. The term momentum is due to Gureckis & Goldstone (2009), who use a model of this type to explain the historical evolution of parental choices for children’s first names (see also Lieberson 2000; discussed in Labov 2010: 194–195). Mitchener (2011) and Stadler et al. (2016) conduct mathematical and computational explorations of momentum-based selection in language change: Mitchener’s model is driven by apparent-time momentum, like the account proposed here, whereas Stadler et al.’s model relies on real-time input, but both produce qualitatively similar dynamics. Stadler (2016) provides further discussion, assessing the evidence for speakers’ knowledge of the momentum of sociolinguistic variables. One of Stadler et al.’s (2016) most important results is that momentum-sensitive learning produces monotonic incrementation and S-shaped curves reliably. The emergence of sigmoid trajectories is due to the fact that a variable’s momentum, reflected in the size of the age vector acquired by the learner, does not remain the same as the change advances in real time: in consequence, incrementation need not be linear. Indeed, Stadler et al. (2016) demonstrate that momentum-sensitive learning gives rise to S-shaped changes under a very broad range of conditions: their model includes a parameter b which modulates the effects of the variable’s momentum on the learner’s acquired level of use; when b ≥ 1, sigmoid trajectories occur systematically.

The most appealing property of community-oriented momentum-sensitive learning is that it predicts the existence of sporadic localized bifurcation.

Recall that the factors that drive mutation are permanently active (Section 2). In consequence, individual innovations occur continually at a basic rate determined by the strength of the relevant biases and their interactions. Community-oriented learners, however, reject individual idiosyncrasies. For this reason, the vast majority of innovations fail to undergo incrementation and propagate: a learner will reject a mutation, even when carried by more than one individual in her social circle, as long as she experiences it as a randomly scattered deviation from the community norm.

From time to time, however, it so happens that, quite by accident, a learner encounters an innovative variant more often in the speech of younger than older speakers: in other words, an accidental skew causes the learner to experience an inverse correlation between the frequency of the mutation and speaker age. If this accidental skew is sufficiently clear and strong, the learner acquires an age vector and incrementation begins. As Mitchener (2011: 395) puts it, “the mechanism of these spontaneous changes is that[,] every so often, children pick up on an accidental correlation between age and speech.” Similarly, Stadler et al. (2016: 188) describe change in a momentum-based model as “self-actuating”. This explains sporadic localized bifurcation: isolated and randomly distributed innovations are actively repressed; innovations that accidentally cluster in a pattern inversely correlated with age are not only adopted, but also actively incremented by the learner.

Crucially, if a mutation occurs at a relatively high rate, its distribution in the speech community has a greater chance of accidentally exhibiting an age skew that is clear and strong enough to trigger the acquisition of an age vector. In consequence, the probability with which innovative variants are selected for incrementation is directly proportional to the basic rate of mutation. Stadler (2016: Chapter 6) establishes this result with the tools of dynamical systems science: he expresses the key insight by saying that momentum-sensitive learning is a “symmetric” (i.e. neutral) selection mechanism operating upon the output of an “asymmetric” (i.e. biased) source of mutations (the same idea appears in Croft 1995: 524). This property enables community-oriented momentum-sensitive learning to preserve Ohala’s explanation of the relative crosslinguistic frequencies of different types of sound change (Figure 1). Similarly, the theory has no difficulty incorporating the insights of competing-motivations models of phonological typology (Section 2).

Let us now take stock. We have fulfilled all the desiderata stated in Section 3.1: community-oriented momentum-sensitive learning

We may further observe that the theory of sound change outlined in Sections 2 and 3 operates at a relatively high level of abstraction. The account of individual innovation adopted in Section 2 relies on phonetic biases arising from physical law and from universal properties of human physiology and cognition; individual differences in language processing styles play no role (cf. Yu 2013). Similarly, the model of the initiation and incrementation of community-wide sound change proposed in Section 3 ignores all differences between speakers beyond those associated with broad demographic categories like age; personal identity and individual agency are not involved (cf. Eckert 2012). We may therefore wonder whether we might make further explanatory gains by adopting a less abstract approach, incorporating individual differences into the theory. In the following sections I argue against such a move. Section 4 shows that the solution to the problem of sporadic localized change is not to be sought in individual patterns of articulation, pace Baker et al. (2011). Section 5 provides evidence that, even if individual speakers use socially meaningful variables to signal their identities and construct personae, it is not their stylistic agency that drives the intergenerational incrementation of sound change, pace Eckert (2019). The broad methodological point is stated in Section 6 by means of an analogy from physics: the explanatory success of macroscopic models of sound change can be gauged in part by the extent to which they incorporate only those microscopic facts that are truly relevant and causally efficient.

I have asserted that the intergenerational incrementation of sound change in progress is caused by a subpersonal automatic cognitive mechanism of momentum-sensitive learning which does not involve speaker agency (Section 3.2). Eckert (2019) proposes a different hypothesis, according to which incrementation is driven by speakers’ stylistic activity. In her theory, variants acquire indexical value through differential use by social groups (Silverstein 2003; Eckert 2008), and as a result are endowed with social meaning (Eckert 2012); once an innovation possesses social meaning, it can be deployed by individual speakers to signal their stances and to construct personae; this stylistic activity in turn causes the use of the variant to increase and spread. Individuals do not control the social meaning assigned to a linguistic variant, but their stylistic agency drives incrementation and propagation. This section argues against these claims. I provide evidence indicating that intergenerational incrementation cannot be propelled by the social evaluation of variants. I further show that community-oriented momentum-sensitive learning, coupled with the purely mechanical effects of density of communication (Bloomfield 1933: 46ff; Labov 2001: 19–20; Trudgill 2008; 2014), suffices to account for major macroscopic patterns of propagation such as class stratification (Labov 2006: 397), the curvilinear pattern (Labov 1972: 294–295; 2001: 31–33, 171–172), and even some instances of change reversal.

This debate does not concern the undeniable fact that individual speakers’ personal attitudes may affect their use of linguistic variants: see Eckert & Labov (2017: 5–14) for a review of the evidence from production. Similarly, the fact that some linguistic variables acquire social meaning is not in dispute: social meaning can be directly observed in perceptual studies, notably by means of the matched guise technique (Lambert et al. 1960; see e.g. Campbell-Kibler 2006). I take these to be established empirical facts. The question, rather, is how far their consequences reach. In particular, to what extent should we incorporate social meaning into models seeking to explain general macroscopic facts about the initiation, incrementation, and propagation of sound change?

In tackling this question, the first problem we encounter is methodological. Assuming that we can somehow control for automatic accommodation, we can estimate the relative effect of style on production by comparing an individual’s usage across different social settings (e.g. Eckert & Labov 2017: 5–10). It is far more difficult, however, to determine the extent to which an individual’s (or a social group’s) overall mean level of use of a variant depends on the social meaning of the latter. This is in part because an individual’s position in the community’s spectrum of variation will reflect the combined effects of both attitudes and exposure, but the two are hard to disentangle, as people with different attitudes socialize in different ways, and vice versa (Pierrehumbert 2016: §3.3): a high-schooler’s stance in respect of higher education, for example, will affect her stylistic practice (Roberts 2016: 56–57), but also the composition of her social network. In consequence, it should not come as a surprise that, in statistical analyses of variation at the community level, attitudinal variables can exhibit a strong linear relationship with demographic variables like class (Baranowski 2017: 328–329). This collinearity is further explored in Section 5.3 below, which also discusses the case of sociolinguistically exceptional individuals (Eckert & Labov 2017: 12–14).

The second problem is both methodological and substantive. It arises over the fact that, as noted above, social meaning can be detected directly in perception (e.g. by means of matched guise experiments) and indirectly in production (e.g. by analyses of style-shifting). It turns out, however, that these two procedures do not necessarily converge on the same result. Notably, Haddican et al. (2013) relied on production data to infer the indexical values associated with the fronting and diphthongization of /uː/ and /oː/ in York, but Lawrence (2017) found a poor match between these indexical values and the social meaning that York listeners assigned to the variables in a perceptual task. One possible account of this mismatch (Hall-Lew 2017) is that it reflects the personal stylistic agency of the participants in Lawrence’s experiment: the hallmark of indexical value would be its “mutability” because individuals are constantly “reinterpreting variables […] in a continual process of bricolage” (Eckert 2012: 94). Adopting this account, however, is tantamount to conceding the argument of this section: if personal stylistic agency causes social evaluation to diverge from community-level production patterns, it can hardly be the main cause of those patterns.

Setting these issues aside, the next section identifies two major empirical problems for the claim that the intergenerational incrementation of ongoing sound change depends on the social meaning of variants.

First, the social evaluation of variants is often either too fine-grained or too coarse to serve as the engine of incrementation of ongoing change. For example, Labov (2002: 281–283) and Eckert & Labov (2017: 22–23) cite the case of the Northern Cities Shift, a large-scale pattern that involves a set of five vowel phonemes rotating in phonetic space. Observations of speakers’ stylistic practice indicate that social meaning attaches to the realizations of single phonemes or, at most, of pairs of adjacent phonemes. This is consistent with the fact that, in areas where the shift is propagated mainly by contact between adult speakers, such as the St. Louis corridor, the pattern spreads only in a fragmentary fashion (Labov 2007: §4). In the Inland North, however, where the shift advances by intergenerational incrementation in the course of language acquisition (Section 3.1), the integrity of the pattern is highly preserved (Labov 2007: 372, 375, 378). This would come as a surprise if intergenerational incrementation itself were propelled by social meaning, rather than by momentum-based learning (Section 3.2).

Just as the granularity of social meaning is too fine to drive the incrementation of the Northern Cities Shift in the Inland North, it is too coarse to account for ongoing shifts in the use of Velar Nasal Plus in North West England. This phenomenon consists of the conservative realization of etymological ŋɡ as [ŋɡ] rather than [ŋ] in positions where it is not followed by a vowel belonging to the same stem-level domain, so that si[ŋɡ]-er rhymes with fi[ŋɡ]er (Bermúdez-Otero 2011: 2020–2025; Bermúdez-Otero & Trousdale 2012: 697–699). In a recent matched-guise experiment, Bailey (2019a) found that Velar Nasal Plus is becoming available to carry social meaning: older speakers exhibit identical responses to [ŋɡ] and [ŋ] guises, but younger speakers show an incipient evaluative distinction. At the same time, sociolinguistic interviews show an increase in the use of [ŋɡ] in apparent time. It transpires, however, that the ongoing incrementation of Velar Nasal Plus is not driven by its incipient indexicality: natural and laboratory data reveal that this incrementation is strictly confined to prepausal position (Bailey 2019b), whereas social evaluation attaches to the [ŋɡ] variant in all contexts, including those in which the variable remains stable (Bailey 2019a).

Finally, sociolinguistic and ethnographic studies of the social meaning of linguistic variants often highlight their oppositional value: e.g. Labov (1963) reports that the inhabitants of Martha’s Vineyard use centralized diphthongs to signal a commitment to the island’s traditional way of life and a rejection of the influence of newcomers from the mainland, while Zhang (2005) finds that the replacement of neutral tones with full tones by Beijing yuppies indexes their positive stance towards the cosmopolitan culture of Hong Kong in contrast with the perceived insularity of state managers. Thus, Eckert (2012: 98) emphasizes how the personal stylistic agency of speakers manifests itself in “lifelong projects of self-construction and differentiation”. However, the predominantly oppositional character of social meaning suggests that indexicality cannot be the primary driver of incrementation in the case of ordinary sound changes advancing monotonically towards completion, for in such situations the lagging groups end up converging with the leading groups.3 If oppositional indexicality drove propagation, one would at least have to ask why we do not see more cases of arrested incrementation ushering in stable linguistic polarization.

Let us suppose that this problem can be circumvented by positing an additional mechanism that depolarizes the social evaluation of the variable and brings the lagging groups up to the level of use of the leading groups: perhaps the indexical value of variables is diluted as their use spreads. Such a scenario still predicts that interspeaker variation will increase in magnitude during the initial phase of the change, as propagation gathers momentum under the effect of oppositional indexicality. This prediction, however, is in direct conflict with the empirical evidence currently available. The relevant information is not abundant: as Fruehwald (2017b) notes, many studies of ongoing sound change follow the variable’s central tendency over time, but few track the evolution of its dispersion. Using data from the Philadelphia Neighborhood Corpus, however, Fruehwald (2017b) monitored intra- and inter-speaker variance during the incrementation of prefortis /aɪ/-raising and preconsonantal /eɪ/-raising in Philadelphia from the late 19^th to the late 20^th century. Crucially, he found that, for both variables, intra- and inter-speaker variance remained stable during this period: see the schematic representation in Figure 7. This observation rules out oppositional indexicality as the main incrementation engine for sound change.

The situation may be illuminated by an analogy, somewhat similar to a comparison proposed by Labov (2002: 283). An ordinary sound change undergoing monotonic incrementation to completion may be likened to a large swell wave coursing through the open sea: its origin, amplification, and propagation from a distant fetch of ocean are like the initiation and incrementation of sound change driven by community-oriented momentum-based learning. In contrast, the short-wave roughness on the surface of the swell is caused by local winds; this is like the effect of personal identity and agency on the ongoing change. Both phenomena are real, interesting, and important,4 but they operate at measurably different scales and are to a significant extent causally independent from each other.

In agreement with this conclusion, Holmes-Elliott’s (2020) panel study of children and adolescents in Hastings shows parallel trajectories of steady incrementation for GOOSE-fronting, which is socially unmarked, whereas incrementation is less consistent and robust precisely for those variables that are subject to strong social evaluation.

Pursuing these arguments, the following sections provide empirical evidence of macroscopic patterns of propagation that are best explained mechanically by the principle of density of communication, rather than in terms of social meaning.

One of the most salient phenomena in the propagation of sound change is stratification by class: since Labov’s seminal study of New York City in the early 1960s, this observation has been replicated time after time (Labov 2006: 397). But what causes class stratification: density of communication or social meaning? A number of conceptual arguments suggest that the role of density of communication is primary and dominant.

At the birth of a variable, sociolinguistic differentiation must precede sociolinguistic evaluation both temporally and causally. If a variant were distributed uniformly across the speech community, it would have no indexical value and so could not acquire social meaning. Differences in the social distribution of variants must thus arise first by mechanical means (Labov 2006: 397). This is easily explained on a background of neutral propagation by probability matching (Labov 1994: 580–583; see also Kauhanen 2017: §2), consistent with the community orientation of the learner (Section 3.2). As proposed in Section 3.3, the locus of initiation, where incrementation begins, consists of a small set of learners who acquire an age vector upon exposure to an accidental pattern of age-skewed variation. Subsequently, other speakers in the larger community become exposed to the change in inverse proportion to their status distance from the locus of initiation, simply because average density of interaction decreases with distance on the status scale. This mechanical effect endows the innovative variant with first-order indexicality (Eckert 2008: 463; after Silverstein 2003), which can come to be cognitively represented in the minds of some members of the community. Once we have reached this stage, further developments become possible: knowledge of the variable’s value as a first-order index may lead some speakers to endow it with additional social meanings, and those speaker’s productions may accordingly start to display attitudinal effects.

Moreover, it seems reasonable to expect that, in a large proportion of cases, those attitudinal effects may at most amplify, but will not qualitatively alter, the pattern of class stratification created mechanically by density of contact. This is because attitudinal variables often exhibit strong linear relationships with status. This appears to be true, in particular, of two important individual variables: attitudes to local traditional life-styles and attitudes to education. In Eckert’s (1989; 2000) study of Belten High, for example, jocks, characterized by their educational aspirations and cooperative relations with teachers, came mostly from the upper half of the local socioeconomic hierarchy, whilst burnouts came mostly from the lower half (Eckert 2012: 92).

In sum, class stratification is one of the most salient facts about the propagation of sound change. The arguments we have considered so far suggest that it emerges mechanically from the impact of socioeconomic distance on density of communication; the effects of personal identity and agency are causally secondary and smaller in scale.

Baranowski’s (2017) study of GOOSE- and GOAT-fronting in Manchester provides strong empirical support for this conclusion. Unlike the majority of English dialects, Manchester shows advanced fronting of /uː/ before coda /l/, as in school and pool. The variable is stable in apparent time and exhibits strong stratification by class: the speakers’ degree of /uː/-fronting before /l/ correlates inversely with their socioeconomic status (Figure 8).

Unusually, Baranowski’s study directly compared the effects of socioeconomic status and those of attitudes to Manchester. Status was operationalized in terms of occupation (Baranowski 2017: 303). Attitudes to Manchester were operationalized in terms of the responses to questions such as “how Mancunian do you feel?” (Baranowski 2017: 326). As expected, attitudinal scores displayed a fairly large correlation with status, but not so strong as to prevent both variables from being entered into the same mixed-effects linear regression (Baranowski 2017: 328, 330–331). Baranowski ran three regressions with the F2 of GOOSE before /l/ as the the dependent variable: the first included status as a predictor, but not attitudes; the second included attitudes, but not status; and the third included both. The first model outperformed the second according to both the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Crucially, the third, more complex, model did not emerge as a clear winner over the first: it was favoured by AIC but not BIC. In this light, “we cannot confidently conclude that adding attitudes to social class improves the explanation of the variation” (Baranowski 2017: 331). In the case of GOAT-fronting, which also displayed strong class stratification, the results were even clearer: an ANOVA comparison showed that a model including both class and attitudes was not significantly different from one with class alone.

As Baranowski (2017: note 13) acknowledges, a critic might object that a different selection or operationalization of attitudinal variables might have resulted in a bigger effect of attitudes. Note, however, that this argument cuts both ways: the operational definition of class is itself not trivial, and so, had the effect of attitudes proved significant, an opponent might just as well have objected that this effect could disappear in a study using a better operationalization of class (Baranowski & Turton 2018). All one can conclude from such prudential considerations, well motivated though they are, is that it would be highly desirable for many more studies like Baranowski’s to be conducted until the overall picture emerges clearly by simple preponderance of evidence.

In the meantime, it is useful and enlightening to pursue the implications of the hypothesis that many, perhaps most, sociolinguistic variables behave like GOOSE and GOAT in Manchester. This scenario invites us to consider in greater depth the following question: why is there such a strong correlation between status and attitudes, and why does status outperform attitudes as a predictor of variation? The conceptual considerations explored at the beginning of this section suggest a plausible answer. First, status exerts a causal effect upon attitudes: for example, parental occupation and income partially determine the chances of an American student becoming a jock or a burnout. In consequence, status shapes linguistic variation both primarily through the mechanical effects of interpersonal contact and secondarily through its effect on attitudes. Figure 9 represents a subset of the relevant causal relations.5

This depiction of the causal chain is fully compatible with the existence of sociolinguistically exceptional individuals and with the possibility that many of them owe their exceptionality to their personal stylistic agency (Eckert & Labov 2017: 12–14). Those exceptional speakers may be expected to exert a limited influence on the community pattern anyway. First, a few special cases contribute far less to the average than the mass of the ordinary. Secondly, and more importantly, the community-oriented learner, like a statistician suspicious of outliers, actively rejects individual idiosyncrasies (Labov 2014a; b; and see again Section 3.2 above).

A special case of class stratification is the curvilinear pattern (Labov 1972: 294–295; 2001: 31–33, 171–172), in which an ongoing sound change is led by the social classes that occupy the interior of the socioeconomic hierarchy, whilst the lowest- and highest-status groups lag behind. Figure 10 illustrates this phenomenon with data from the cot-caught merger in Charleston (Baranowski 2013): the loss of the contrast is led by the lower and middle segments of the middle class (LM and MM), whilst the working (WC), upper-middle (UM), and upper (UC) classes are relatively conservative, exhibiting higher distinction scores.

The curvilinear pattern is very commonly observed in sound changes fulfilling two requirements: first, they operate below the level of social awareness; secondly, they are in progress, advancing rapidly by intergenerational incrementation. The cot-caught merger in Charleston fits this description exactly. It does not elicit overt comments (Baranowski 2013: 288, 291), and it displays the expected distribution in apparent time: distinction scores rise smoothly with age among speakers up to 50, and older speakers retain the contrast (Baranowski 2013: 275). In this respect, the cot-caught merger stands in stark contrast with a similar ongoing change in Charleston: the pin-pen merger. The latter also shows vigorous incrementation in apparent time, but it operates above the level of social awareness, prompting overt remarks from speakers (Baranowski 2013: 287). Significantly, the pin-pen merger fails to conform to the curvilinear pattern, instead displaying an inverse monotonic correlation with socioeconomic status (Baranowski 2013: 282–283, 291).

Why should it be the case that sound changes are likely to follow the curvilinear pattern while they are in progress if they operate from below? Labov (2001) contemplates two possibilites. One is purely mechanical: the curvilinear pattern is created by density of communication (Labov 2001: 191–192). The other involves covert social meaning: changes are led by members of the interior status groups because these are in the best position to “display the symbols of nonconformity in a larger pattern of upward social mobility” (Labov 2001: 516–517). A strong argument favours the first of these two answers: changes from below tend to exhibit curvilinear propagation because this is the pattern most likely to arise mechanically from the topology and dynamics of the social network.

Support for this assertion may be found in Kauhanen’s (2017) mathematical and computational exploration of neutral change, i.e. change propagated by probability matching in the absence of social evaluation. Kauhanen demonstrates that neutral change exhibiting realistic patterns of incrementation and propagation occurs spontaneously in a network if the latter satisfies two properties, one topological, the other dynamic. First, the network must be strongly clusterized: some nodes occupy a relatively central position by virtue of having a large number of connections; other nodes have fewer connections and so count as more peripheral. Secondly, the network must undergo rewiring: periodically, some nodes are removed, and others are created. Crucially, neutral change in such a network will typically irradiate from the centre: over time, propagation is easy from the centre to the periphery, but hard in the opposite direction (Kauhanen 2017: 349–351).

Admittedly, Kauhanen conceives of the nodes in his model as individual speakers, but extrapolating his results to a coarser level of granularity leads to an interesting scenario. If nodes consist of groups of speakers of similar socioeconomic status, then middle-status nodes are more likely than high- or low-status nodes to occupy central positions in the network (in the technical sense). This is because, with density of communication falling in direct proportion to status distance, only intermediate-status nodes are likely to have strong connections with other nodes throughout the social scale. Accordingly, propagation is more likely to be successful precisely for those innovations that originate in the intermediate-status groups. If this extrapolation is correct, the curvilinear pattern is the hallmark of mechanical propagation in a social network clusterized by class.

I have argued that many macroscopic patterns of propagation submit to largely mechanical explanations. In such cases, attitudinal variables may have significant small-scale effects, but the large-scale evolution of the community depends mainly on supra-individual topological properties of the social network, notably density of communication as determined by demographic variables such as class. As highlighted in Hall-Lew (2017), however, the acid test for this approach to propagation lies in accounting for scenarios of change reversal, in which the use of a variant starts to decline after a period of consistent growth. Labov et al.’s (2013) survey of twentieth-century Philadelphia highlights two cases: /aʊ/-raising and /oʊ/-fronting, both led by women in the first half of the century, went into reversal in the second half.

Change reversal is problematic because, according to the model of momentum-based learning outlined in Section 3.2, intergenerational incrementation, once initiated, is self-sustaining. Crucially, however, the model also predicts that incrementation may cease and even go into reverse if, for any reason, a new cohort of adolescents comes to be exposed to a community pattern in which the use of the innovative variant by adults no longer decreases monotonically with speaker age. Such a situation can be brought about by population changes (e.g. migration) or changes in network topology (e.g. shifts in class segregation). In a simple scenario, for example, the arrival of a large contingent of young immigrants of working age lacking the local variant may invert the age vector acquired by the current adolescent cohort.

What role, if any, population changes or shifts in network topology may have had in the reversal of /aʊ/-raising and /oʊ/-fronting in Philadelphia is at present unclear (Labov et al. 2013: 51–52, 59–60; Tamminga 2019). However, an instance of reversal in which population change was demonstrably decisive, in combination with network topology, is the retreat from the Southern Vowel Shift in Raleigh, North Carolina. In this case, the reversal was triggered by an influx of white-collar workers from the North and was crucially facilitated by social segregation by status, as affluent local residents and their children interacted more frequently with affluent Northern immigrants than with the local working-class population (Dodsworth & Kohn 2012). This confirms that, as Hall-Lew (2017) argues, the reversal of sound change is impossible in the absence of social change. It is, however, quite feasible for the relevant social change to operate mechanically, while attitudinal variables add small-scale effects.