CHAPTER TWO

Atomic Phonology

Daniel A. Dinnsen

1. The purpose of this paper is to review the developing theory of atomic phonology and differentiate it from other, competing theories of phonology.

The theory of atomic phonology maintains that all linguistic variation requiring distinctly varied formulations of phonological rules is predictable from a set of atomic rules and universal principles of grammar. Within this theory, there is a crucial distinction between atomic and nonatomic rules. Atomic rules are entirely independent rules of grammar which are presumed to be the most basic, most specific rules that can be motivated on empirical grounds. For any given atomic rule, then, there could be no more specific nor equally specific and independent rule effecting a same or otherwise related structural change. Atomic rules thus specify all the necessary initial conditions from which any correct variation on that process for any natural language can be predicted by universal principles. Non-atomic rules are dependent on atomic rules. The dependence on atomic rules derives from the requirement that nonatomic rules are all and only those rules which are complements of atomic rules or complements of their complements. The complement relation may be defined as follows:¹

(1)Two rules are complements, and thus in a complement relation, if just those commonly shared (identical) features in the structural descriptions of the two rules are sufficient to define precisely the same set of input representations defined by the two rules jointly.

This relation is exemplified by the following two rules:

These two rules are complements since just the commonly shared features in their structural descriptions, i.e., [—sonorant] #, equivalently characterize the set of input representations defined by the combined effects of the two rules. However, the following hypothetical rule is not a possible complement of either rule (2) or (3):

The features common to rules (4) and (2) or (3), i.e. [— sonorant] #, do not define the same set of input representations as the pair of rules (2) and (4) or the pair of rules (3) and (4). For example, the class of segments actually defined by rules (2) and (4) would be all stop obstruents and velar fricatives in word-final position. Since such a class excludes at least word-final dental and labial fricatives, it clearly cannot be considered equivalent to the class of all word-final obstruents and thus does not constitute a complement relation.

By assuming that rule (2) is the atomic rule for Terminal Devoicing, it is claimed that rule (2) is a possible, independently verifiable rule of grammar that can be motivated empirically as, for example, in Ferrarese Italian, Turkish, and certain Greek dialects (cf. Dinnsen and Eckman 1977). It also follows that rule (3) is a non-atomic rule and as such is not a possible independently occurring rule of grammar. The claim is, then, that rule (3) will be without any empirical support as an independent rule. This is a particular instance of one of the central claims of atomic phonology, and that is that no two languages will differ solely by the postulation of an atomic rule for one language with another language evidencing the complement rule as an equally independent and necessary rule of grammar. Rule (3), being a dependent rule, can be evidenced, however, if and only if there is also evidence motivating rule (2). Such empirical findings as, for example, in German and Catalan (cf. Dinnsen and Eckman 1977), motivate the distinct, more general formulation of Terminal Devoicing stated in (5):

Rule (5) derives from the conventional conflation of the atomic rule (2) with its non-atomic complement rule (3). Rule (5) is thus predicted to be a possible correct variation on the Terminal Devoicing process. What this illustrates is that within a theory of atomic phonology, rule formulations may vary or differ from the atomic rule only to the extent that that variation follows from the relationship of rules in a complement relation. It is this same constraint that excludes the hypothetical rule (4) as a possible rule or variation of the Terminal Devoicing process. Specifically, since rule (4) is not a possible complement of the atomic rule (2), no relationship can be established between the two rules. Since the atomic rule contains no restrictions based on point of articulation features, it follows that no rule effecting Terminal Devoicing will ever need to incorporate point of articulation features. The apparent absence of any well motivated rule of Terminal Devoicing formulated in terms of point of articulation features bears out the predictions of atomic phonology (cf. Anwar 1974).

One point which perhaps requires further comment is a point which frequently arises in discussions over the characterization of complement rules. And that is, it might appear to some that the construct ‘complement rule’ reduces to rules that simply differ in the coefficient specification of a single feature. This is certainly true in the case of rules (2) and (3) above. In fact, any two rules that differ solely in the coefficient specification of a single binary feature will be complements. But, what is not true is that all complement rules differ in the coefficient specification of just one feature. To see this, consider the following two rules which account for certain vocalic alternations in various Swiss German dialects (cf. Robinson 1976; Keel 1976, 1977):

These two rules are complements despite the fact that they differ in more than one feature specification. The focus of each rule is, of course, identical; and while the determinants differ explicitly in the coefficient specification of the feature [sonorant], they also differ in other respects. That is, rule (6) explicitly requires specification for the features [nasal] and [lateral] while rule (7) does not. Similarly, rule (7) explicitly requires a specification for the feature [coronal] while rule (6) does not. These two rules do, however, have more features common to their structural descriptions than may be initially evident and that permit their characterization as complements. That is, in this language, r’s are redundantly [+ coronal], and obstruents are redundantly [— nasal, — lateral]. Therefore, since the features common to the determinants of both rules are actually [+ consonant, — nasal, — lateral, + coronal], i.e., lower in the environment before coronal obstruents and r, and since this is precisely the same set of contexts defined by the two rules, they are quite properly complements. These two rules are incidentally confutable as rule (8)—the well known rule of lowering for the Schaffhausen dialect (cf. Robinson 1976: 148; Kiparsky 1968b):

This discussion of the lowering rules also reveals some of the implications of atomic phonology for the characterization of linguistic change by means of rule simplification or generalization (cf. Dinnsen 1976a). That is, atomic phonology maintains that all cases of rule simplification are derivable by means of the independently necessary mechanism of rule addition—but rule addition of a highly limited sort, namely complement rule addition. In this particular instance, the rule lowering o before r, i.e., rule (6), can be established as the atomic rule (cf. Robinson 1976; Keel 1976, 1977). Subsequently and in other dialects rule (7) was added lowering o before coronal obstruents. Given the same degree of applicability for the two rules, they can be conflated as the generalized rule (8). Rule (8) also serves to illustrate that not all cases of a generalized rule will differ from the atomic rule or some predecessor rule in only one feature specification. While the feature [sonorant] is lost from the formulation of rule (8), the feature [coronal] must be added.

The discussion above is intended to demonstrate that there are examples of complement rules that differ in more than one feature. It may be suspected, however, that after consulting the redundant or implied features, the rules then do differ in only one feature. To dispel this view, consider the following highly plausible rules:

In a language where roundness is a redundant property of non-low vowels, these two rules would differ in the coefficient specifications of both the features [back] and [round]; yet these rules are complements since the commonly shared features of the rules, namely non-low vowels in closed syllables, define precisely the same set of input representations defined by the two rules jointly.

This discussion, thus, suggests that the characterization of “complement rule” given in (1) does not reduce simply to any statement that counts the number or type of differences in feature specifications.

2. The inclusion of the construct “complement rule” in a theory of phonology has many significant empirical consequences, as has been argued in earlier papers. For example, it is generally recognized that rules are added to grammars as optional rules (Kiparsky 1971; Norman 1973). If rule generalization is a special case of rule addition as predicted by a theory of atomic phonology, one would expect that in the course of rule simplification certain component parts or expansions of the generalized rule should evidence optionality corresponding to complement rules. These predictions are also borne out in Keel (1976), Keel and Shannon (1976), and Dinnsen (1976a).

3. Moreover, within standard theory, rule generalization is characterized by two formally distinct mechanisms, i.e., generalization by feature loss and generalization by Greek letter variables. There is, however, absolutely no empirical basis whatever for distinguishing these types of simplification. Within a theory of atomic phonology both types of simplification are derived in the same way—by complement rule addition (cf. Dinnsen 1976a). It is thus not surprising that the two putative types of simplification are empirically indistinguishable.

4. The theory of atomic phonology also provides for the principled exclusion of certain rule formulations which within the standard theory are judged to constitute linguistically significant generalizations but which are otherwise empirically indefensible. This exclusion follows from the general requirement that any rule R is a possible rule of grammar if and only if R is atomic or is in a complement relation with an atomic rule. For example, in Dinnsen (1977a) it was argued that the well known rule of French Truncation proposed by Schane (1968a) abbreviates two rules which cannot possibly be related within atomic phonology.

(In word-final position, true consonants are truncated before consonants and liquids, vowels are truncated before vowels and glides, and liquids and glides are never truncated.)

The Truncation rule abbreviates the following two sub-rules:

The exclusion of the French Truncation rule follows from the non-complement character of its two sub-rules in (12). The sub-rules in (12) are not in a complement relation since the features common to their structural descriptions define a set of input representations not specified by the two rules. A consideration of only the commonly shared features in the two sub-rules would suggest the following rule formulation:

Rule (13) is clearly not equivalent to Truncation in terms of potential input representations. Rule (13) would, for example, specify incorrectly the deletion of consonants before vowels and glides, the deletion of vowels before consonants, and the deletion of liquids and glides. It should, therefore, be clear that atomic phonology excludes in a principled manner the Truncation rule as a possible account of any natural language fact.

The correctness of this exclusion is supported by Schane’s (1974) re-analysis which does not involve the conflation of non-complement rules. The numerous empirical reasons offered by Schane for rejecting the earlier analysis are summarized in Dinnsen (1977a: 12).

5. The construct ‘complement rule’ has similar constraining effects for such other descriptive devices as the so-called ‘neighborhood convention’ or mirror-image rules (cf. Bach 1968, Anderson 1974, Langacker 1969). A mirror-image rule schematically represented as (14) abbreviates the two rules (14a and b):

The claim embodied in this device is that it is linguistically significant for a language to evidence two rules with symmetric determinants and which are identical in all other respects. It is argued in Dinnsen (1977a), however, that there is no empirical justification whatever for relating rules abbreviated as mirror-image rules and further that within the theory of atomic phonology such empirically indefensible relationships are excluded on principled grounds.

The general arguments against mirror-image rules can be stated succinctly as follows:

(15) a. In some cases, the sub-rules of mirror-image rules cannot be independently motivated (Norman 1976).

b.In others, the conjunctive vs. disjunctive application of the sub-rules is unpredictable (Norman 1976, Anderson 1974, Miller 1976).

c.Yet other cases reduce to ‘non-rules’ (Harms 1973, Norman 1976).

d.There is apparently no evidence of an implicational relation between any of the sub-rules in a mirror-image relation.

e.There is apparently no evidence of the sub-rules of any putative mirror-image rule simplifying in precisely the same way at the same time.

f.And finally, it may even be that the structural description of certain putative mirror-image rules is non-mirror-image or ‘constant’ (cf. Miller 1976).

To illustrate how atomic phonology excludes in principle mirror-image rules, consider, for example, the rule of Spanish glide formation proposed by Harris (1969:33) as a “first approximation of the correct rules”:²

(Effectively an unstressed vowel becomes a glide adjacent to a stressed vowel, and the first of two unstressed vowels becomes a glide.)

This rule abbreviates the following two ordered sub-rules:

The commonly shared features of these two sub-rules would define the following rule:

(An unstressed vowel between vowels becomes a glide.)

Rule (19) clearly does not define the same set of input representations as (17) and (18) thus failing to establish a complement relationship between the two rules. Rule (16) is therefore correctly excluded as a possible rule of grammar within the theory of atomic phonology.

6. The construct ‘complement relation’ also contributes to the explanation of certain aspects of the historical phenomena known as ‘drag chains.’ A drag chain is a complex series of related sound shifts which serve the function of filling vacated slots in a phoneme inventory. Within a standard theory framework, drag chains have been characterized as a special case of simplification utilizing Greek letter variables (King 1969a). For example, in the historical development of Corsican (Rohlfs 1966), three such sound shifts are evident.³ During stage I, short voiced stops spirantized. During stage II, short voiceless stops voiced. And finally, long voiceless stops shortened (Rohlfs 1966:323).⁴ This drag chain may be schematized as follows:

To see that this is indeed a special case of simplification, note the following rule formulations:

(21) Stage I

(22) Stage II

(23) Stage III

There is, however, another logically possible sound shift which seemingly corresponds to a drag chain and which can be characterized in a standard theory framework as a simplification, i.e., short voiced stops spirantize and long voiceless stops voice. The rule for such a ‘drag chain’ would be formulated as follows:

Such a drag chain, while possible within standard theory, appears to be unattested in any natural language history. However, its unattested character must be regarded as an accident in standard theory. The standard theory thus fails to explain why certain drag chains can be evidenced and why certain others cannot. Atomic phonology, on the other hand, provides a principled explanation of this fact. That is, the characterization of especially stages II and III of the Corsican drag chain entail rule formulations which abbreviate rules in a complement relation whereas the characterization of the presumably unattested drag chain (24) entails a rule formulation abbreviating rules not in a complement relation. Rule (24) is thus properly excluded as a possible rule of grammar. For further discussion of yet other drag chains and their characterization within atomic phonology, see Walsh (1976a,b).

The preceding discussions should serve to review some of the essential claims of atomic phonology, the problems and issues that it addresses, and how it differs from standard theory. The remainder of this paper will attempt to distinguish atomic phonology from other presumably competing theories.

7. One of the fundamental claims of Natural Generative Phonology as developed by Hooper (1976) is that naturalness constraints on phonemic systems are the same as those on phonological rules.

(25) We need not separate the notion of naturalness in phonemic systems from the naturalness of rules. (Hooper 1976:136)

This same position is also identifiable in Natural Phonology as indicated in the following statement from [Donegan] Miller (1972:165):

(26) What should emerge from this paper, at least, is that the principles governing possible phonological inventories can be identified with the processes themselves, and thus, ultimately, with the intrinsic character of the human speech capacity.

The distinguishing claim of atomic phonology is that the constraints on rule formulations are relatively independent of constraints on inventories. These two claims are substantively different and can be evaluated on empirical grounds.

Hooper (1976:136-37) proposes the following rule as a natural constraint on both phonemic systems and phonological rules:

The ‘<+continuant>’ specification in this rule means, as stated by Hooper,

(28) The rule may affect only fricatives, or it may affect all obstruents, but it may not affect ONLY stops (except trivially where a language has only stops).
... if stops undergo a context sensitive process involving voicing, fricatives do as well.

The predictions which follow from rule (27) for phonemic inventories appear to recapitulate some of the implicational restrictions on inventories proposed by Jakobson (1942) and would appear to be correct. However, as a constraint on phonological rules, rule (27) makes incorrect predictions. (27) predicts, for example, that there could be no language with the following characteristics:

(29) a. A voice contrast in obstruent stops and fricatives with the contrast neutralized in word-final stops only,

b.No voice contrast in obstruents with only certain stops voiced intervocalically.

The fact is, however, that Ferrarese Italian evidences precisely the characteristics of (29a) and Korean evidences those of (29b). For discussion of the Italian and Korean facts, see Dinnsen and Eckman (1977) and references therein.

Rule (27) also predicts that there should be languages evidencing the following characteristics:

(30) a. Voicing is contrastive, but the contrast is neutralized in favor of [+voice] intervocalically (part (a) only),

b.Voicing is contrastive, but the contrast is neutralized in fricatives only in favor of [+voice] intervocalically (part (a) with [+continuant]).

Hooper fails, however, to cite any known language evidencing the characteristics stated in (30). It appears, moreover, that languages like (30a) and (30b) are completely without empirical attestation (cf. Dinnsen and Eckman 1977). It is interesting, too, that the inadequacies of Hooper’s proposal cannot evidently be remedied by reformulating (27) with the specification <—continuant>. While such a reformulation would correctly provide for languages like (29a and b), it would fail to account for languages like Old English evidencing the effects of an intervocalic fricative voicing rule. The reformulation would moreover be inconsistent with the previously established constraints on phonemic systems. The end result for Hooper’s theory or any other theory failing to recognize the distinction between constraints governing inventories and rule formulations is that such theories either make false predictions or predictions that are without empirical support.

Within atomic phonology where this distinction is recognized, a correct account of the facts of voicing and devoicing is available. That is, languages like Ferrarese Italian are accounted for by the postulation of rule (2) as the atomic rule for Terminal Devoicing. Korean is accounted for by the postulation of an intervocalic voicing rule restricted to unaspirated stops (cf. Dinnsen and Eckman 1977). The unattested character of those languages in (30) is explained by the universal constraining principle (31).

(31) All intervocalic voicing rules are allophonic (Dinnsen and Eckman 1977).⁵

The same principle explains the apparent restriction on the intervocalic voicing rule of Old English. That is, Old English evidences a voice contrast in obstruent stops only and an alternation between voiced fricatives medially and voiceless fricatives finally. While it would appear that intervocalic voicing in Old English is restricted to fricatives, the rule can be formulated generally to voice all obstruents between vowels with the universal principle permitting the rule to apply only to the extent that its effect is allophonic, that is, to fricatives.

The postulation of atomic rules for Devoicing and Intervocalic voicing and the inclusion of such universal principles as (31) constitutes a strong empirical claim by predicting the principled exclusion of, at least, the following language-types:

(32) a. (30a)

b.(30b)

c.A language with a voice contrast in both stops and fricatives and an alternation between voiced fricatives medially and voiceless fricatives finally (a rule devoicing fricatives finally).

d.A language with no voice contrast in obstruents and an alternation between voiced fricatives medially and voiceless fricatives finally (a rule voicing fricatives medially).

The exclusion of the logically possible language-types (32a and b) follows from principle (31) since the rules would have a neutralizing effect. The logically possible language-types cited in (32c and d) are excluded since each would require the postulation of a non-atomic rule with no associated atomic rule.

8. There are a number of descriptive devices from various theories which would seem to parallel the role of the ‘complement relation’ in atomic phonology, but which in fact make different empirical claims. The descriptive devices of interest here include (a) the ‘natural process’ notation [!+F] ([Donegan] Miller 1972, Donegan and Stampe 1977a), (b) the simplex-feature hypothesis (Sanders 1974b), (c) hierarchies (Chen 1973, Foley 1972, Zwicky 1972a).

The ‘natural process’ notation [!+F] of Natural Phonology could conceivably be incorporated into the Intervocalic Voicing rule expressing some of the same implicational claims as an atomic rule along with the principle of rule complementation. The Voicing rule could be formulated roughly as follows:⁶

The prediction is that fricatives may or may not undergo the rule, but if they do, stops must also undergo it. Both Natural Phonology and atomic phonology make the same empirical prediction in this particular instance. However, Natural Phonology fails to account for a related language fact where atomic phonology provides a principled explanation of that fact. Specifically, Natural Phonology cannot explain the apparent restriction of the Old English intervocalic voicing rule to fricatives, unless it incorporates universal principles such as (31) governing the application of phonological rules. In atomic phonology, this apparent restriction is but a consequence of the universal principle governing the application of a generalized voicing rule.

The preceding discussion can also be related to the simplex-feature hypothesis proposed by Sanders (1974b). In its strong form, this hypothesis excludes reference to a positively specified class in one instance and the negative specification of that same class in some other instance. For example, intervocalic voicing would presumably be characterized as follows:

Such a characterization permits reference to obstruent stops or to all obstruents by the loss of the feature STOP. To this extent, there is overlap between the predictions of atomic phonology and the simplex feature hypothesis. However, in the case of the simplex-feature hypothesis, just as in the preceding discussion, there is no explanation for the apparent restriction on the Old English rule voicing fricatives—unless the universal principle (31) governing certain rule applications is incorporated.

Appeal to implicational hierarchies has long been evident in many theories of phonology, and atomic phonology is no exception.⁷ It is, however, the contention of atomic phonology that the form and configuration of any defensible hierarchy is inferable/derivable from an atomic rule and the associated principle of rule complementation. Furthermore, since different processes will require the postulation of different atomic rules, it follows necessarily that any inferential hierarchy will be process-dependent.

The schematization of the Corsican drag chain, for example, given in (20) represents an implicational hierarchy. The implication is that if long voiceless stops weaken, then so do all the segments arranged to the left. The validity of this implication is not in question here. Rather, the questions should be raised relative to this phenomenon: “Why does the weakening of long voiceless stops imply the weakening of specifically short voiceless stops and not some other set of segments, and why does the weakening of short voiceless stops imply specifically the weakening of short voiced stops?” Put differently: “Why couldn’t the hierarchy be arranged differently with a different set of implications such as the following?”

The answer seems to be that hierarchies can only establish implicational relations between classes which are in a complement relation.

Consider the hierarchy proposed by Chen (1973) for vowel nasalization where vowels are assigned an integer value along a height continuum as follows:

A formalism is developed by Chen such that the nasalization of any vowel with a relatively high integer value implies the nasalization of all vowels with a lesser value. Precisely this configuration of the hierarchy is inferable from the postulation of an atomic rule for vowel nasalization defined on low vowels and the successive extension of the rule by complementation (cf. Dinnsen 1976a).

In short, implicational hierarchies of this sort do not appear to be necessary and independent of the constraints on rule formulation. On the contrary, they are totally derivable within atomic phonology. The argument for an independent construct ‘hierarchy’ in phonological theory must lie in the establishment of a universal process-independent hierarchy governing the formulation of all rules in all languages. The prospects of such a development are clearly remote. A case in point is the comprehensive dialect study by Keel (1977) of the extensive variation from the Swiss German rule lowering [o to ɔ] in various phonological contexts. In his study, it is demonstrated that all the dialects lower at least before [r], supporting the postulation of rule (6) noted earlier as the atomic rule. Keel notes, however, that an implicational hierarchy can be inferred that is capable of characterizing this variation. The hierarchy may be formulated as follows:

Some of the variation that this hierarchy represents may be summarized as follows: [o] lowers to [ɔ]

(38) a. before r and only r, or

b.before r and nasals, or

c.before r and coronal obstruents, or

d.before r and laterals, or

e.before r and all obstruents.

The implicational restrictions that obtain are the following: If [o] lowers to [ɔ]

39) a. before non-coronal obstruents, then it also lowers before coronal obstruents and r.

b.before nasals, then it also lowers before r.

c.before laterals, then it also lowers before r.

d.before coronal obstruents, then it also lowers before r.

Precisely these implicational restrictions and thus the hierarchy in (37) follow from the postulation of rule (6) as the atomic rule and the identification of those rules in a complement relation with (6) or with some rule that is itself a complement of (6) (cf. Keel 1977).

Aside from the fact that atomic phonology is capable of deriving the empirically correct set of implicational restrictions on the vowel lowering rule, this case has special significance inasmuch as the empirically well-supported hierarchy in (37) violates the often cited (e.g., Householder 1974 and references therein), purportedly universal hierarchy given below:

The violation obtains relative to the implications expressed in (40) between [r] and presumably obstruents such as fricatives. That is, if (40) is a valid process-independent hierarchy, it should follow for the vowel lowering process that if [o] lowers before obstruents and [r], then it should also lower before nasals and laterals. The fact is, however, that no implicational relation can be established between obstruents and nasals or between obstruents and laterals as regards the lowering of [o] since there are dialects that lower before all obstruents and [r] without lowering before nasals or laterals (Keel 1977:63,73,82,89).

The point here is that different processes will evidence different implicational restrictions supporting the process-dependent character of such restrictions and that any such implicational restrictions (hierarchies) are derivable from the postulation of an atomic rule and the identification of rules in a complement relation with the atomic rule.

9. A few words are in order concerning functional constraints on rule formulations as set forth in Houlihan and Iverson (1977) and in their contribution to this volume. While we are all interested to some extent in determining the correct constraints on rules, Houlihan and Iverson’s particular program differs significantly from that of atomic phonology. That is, their interests so far have been limited to constraining on principled grounds what a given phonological rule type may produce. Atomic phonology, on the other hand, maintains in general the weaker position that the structural change of any given phonological rule must be stated axiomatically in the atomic rule. The contentions of atomic phonology appear at least to be consistent with the facts, where Functionally Constrained Phonology does not.

Houlihan and Iverson advance the following constraint and corollary as bidirectionals:

(41) Markedness Constraint. Phonologically-conditioned neutralization rules convert relatively marked segments into relatively unmarked segments.
Corollary. Phonologically-conditioned rules which produce exclusively segments that are marked relative to the input segments are allophonic.

This constraint clearly excludes the possibility of a neutralization rule producing exclusively marked segments. However, the facts of a particular vocalic alternation in the Western dialect of Catalan suggest that this constraint is too strong by virtue of incorrectly excluding a defensible rule of grammar. The Western dialect evidences a neutralization of the distinction between [a] and [e] in favor of [e] when in word-final, unstressed, closed syllables (cf. Moll 1952:102).⁸ The following data illustrate the alternation between [a] and [e]:

This alternation is equally productive in verbs (cf. Moll 1952: 224-25, 237). The rule accounting for this alternation is neutralizing since there is a contrast between [e] and [a] in open syllables and [e] does not alternate in the same contexts:

Assuming, then, that [a] is relatively less marked than [e], Western Catalan evidences a neutralization rule which produces only marked segments—thus casting doubt on the correctness of such constraints as the Markedness Constraint. Additional counterexamples to the Markedness Constraint are presented in Jonathan Kaye’s contribution to this volume.

10. In conclusion, following this review of atomic phonology and the discussions of how it differs from some of the other competing theories, it should at least be evident that atomic phonology constitutes some strong claims constraining phonological systems. It is true, too, that atomic phonology is not as highly constrained in certain areas as some of the other theories. However, in those cases where the weaker position has been adopted, this presumably is warranted on empirical grounds. In any case, it is hoped that the basic tenets and claims of atomic phonology are sufficiently explicit to permit its empirical differentiation from the other theories and that any choice between competing theories can be an empirical one.

Naturally, as atomic phonology is a new and developing theory, many questions remain open. For example, the question of rule ordering is left entirely open. Rule order and rule formulations are not wholly independent. In fact, it must be clear now to anyone involved in the recent rule ordering controversy that the question of how rules apply relative to one another cannot reasonably be pursued in the absence of severe constraints on what constitutes an admissible rule formulation. It seems that the debate over rule ordering has reached an impasse primarily because, for any given analysis supporting some hypothesis on rule ordering, an alternative analysis involving different rule formulations is available which supports an opposing hypothesis. The discovery of atomic rules would substantially limit the range of possible analyses by establishing clear cases of necessary and independent rule formulations against which competing hypotheses about rule interactions could be tested.

Another area which remains largely open is the principled determination of atomic rules. All that is available at present is a methodological principle for identifying atomic rules. This principle is, however, strictly empirical, and thus, the claims derivable from it are clearly vulnerable to empirical disconfirmation. Inasmuch as many of the atomic rules correspond with what others would refer to as ‘natural rules’, it may be fruitful to pursue ‘phonetic explanations’ for at least some atomic rules. At present, however, the character of phonetic explanations is sufficiently nebulous that this particular avenue does not permit a totally satisfactory principled determination of atomic rules. The explanation of atomic rules may, of course, lie in other areas as well. Until these explanatory bases are more accessible, the methodological basis for determining atomic rules will at least encourage extensive typological investigations which would in the final analysis be pertinent to the evaluation of any theory of phonology.

NOTES

I am especially indebted to Thomas Walsh for his numerous and valuable discussions with me about many of the issues raised in this paper. I have also benefited from comments on this topic received at various times from Fred Eckman, Gerald Sanders, and Arnold Zwicky.

This work was supported in part by a grant from the Office of Research and Graduate Development, Indiana University.

1. This relation between rules can be equated largely with Trubetzkoy’s concept ‘bilateral opposition’ (Trubetzkoy 1969: 68-69).

2. While this rule admittedly is deficient in certain respects, the deficiencies do not detract from the point that can be illustrated by this or any mirror-image rule.

3. Various aspects of this gradation process are still productive as synchronic rules (cf. Dinnsen and Eckman 1977).

4. These stops are assumed to be long as opposed to a geminate cluster in order to relate this particular shift to the others and because there are no other consonant clusters in the language where both members are stops.

5. An intervocalic voicing rule is any purely phonological phenomenon which introduces the feature [+voice] (and only that feature) onto an obstruent between vocalic segments. A rule is ‘allophonic’ in the traditional sense of accounting for the complementary distribution of phonetically similar sounds or inasmuch as it produces an output representation whose input is uniquely recoverable.

Although principle (31) may be totally derivable from the more general Markedness Constraint proposed by Houlihan and Iverson (1977 and their contribution to this volume), I have opted for the less general statement of (31) since it is at least empirically well supported, while the Markedness Constraint engenders some apparently serious empirical difficulties (cf. section 9 of this paper and Jonathan Kaye’s contribution to the volume).

6. It may be that Natural phonologists would have to formulate this rule with [!+continuant] instead of [!—continuant], given the connection between constraints on inventories and rules discussed in the previous section. Whatever the choice, Natural Phonology will fail to account for languages like Old English or Korean.

7. For examples of hierarchies, see Zwicky (1972a), Foley (1972), Householder (1974), and Chen (1973), and references therein.

8. This example was pointed out to me by Thomas Walsh.