Canonically, a language’s morphotactics conforms to the compositional content criterion (Section 1.5.5), according to which the content expressed by a rule sequence is compositional, that is, a function of the content expressed by the individual rules in that sequence. Thus, consider again the Swahili rules of exponence in (1), first seen in Section 2.2. When these rules compose to produce the full exponence rules (FERs) in (2), the resulting composite rules serve unambiguously to realize the summed content of their component rules.

Very often, however, languages present cases in which a FER expresses content some of which cannot be attributed to any of the individual rules that it comprises; indeed, even a simple rule sometimes expresses more content as a FER than when it is used in combination with other rules. In such cases, a language’s morphotactics fails to conform to the compositional content criterion because it allows certain FERs to realize holistic content. In this chapter, I show how a sufficiently rich theory of rule combination makes it possible to accommodate this deviation from canonical morphotactics. I examine the inflection of regular verbs in Breton, which exhibit several examples of holistic content (Section 6.1). I show how the postulation of holistic combinations – special rule combinations expressing supplementary content – affords a straightforward account of this phenomenon in Breton (Section 6.2).Footnote ¹

Some holistic combinations have an emergent character. These are cases in which all of the forms realized by a composite rule (R₂ ◦ R₁) happen to possess a property P that neither R₁ nor R₂ realizes on its own; in such cases the composite rule (R₂ ◦ R₁) is open to reanalysis as a holistic combination realizing P. In Section 6.3, I examine a case of this sort from Limbu.

A particularly compelling case for the postulation of holistic combinations arises in systems in which the same two rules express different supplementary content in different contexts. In Section 6.4, I show that Old English verb inflection is a system of this sort.

6.1 Holistic Content in Breton Verb Inflection

The inflection of regular verbs in Breton provides several clear instances of holistic content. Consider, for example, the finite paradigm of the Breton verb karout ‘love’ in Table 6.1.

The forms in Table 6.1 all arise from the bare stem kar‑ through the application of up to three rules of inflectional exponence. The suffix sequences exhibited by the forms in Table 6.1 are abstracted in Table 6.2. Scrutiny of these sequences reveals the four types of suffixes classified in (3). The irrealis sequences and most of the past indicative sequences show one of the prevocalic suffixes in (3a). Most of the sequences in Table 6.2 exhibit one of the three vocalic suffixes in (3b). In most of the forms containing one of the three vocalic suffixes, this is followed by one of the terminations in (3c). Finally, the portmanteau suffixes in (3d) take the place of an expected suffix sequence in certain forms.

Some of the suffixes in (3) stand in a biunique relation to the content that they express; a suffix of this sort always expresses the same content and is the only suffix expressing exactly that content. Suffixes of this sort include the prevocalic suffix ‑f, the terminations ‑mp and ‑nt, and all of the portmanteau suffixes. The prevocalic suffix ‑j and most of the other terminations (‑n, ‑s, ‑c’h, ‑r, and ‑d) are alike in that each of these always expresses the same content but is not the only suffix expressing that content; for example, ‑j always expresses past tense, but some portmanteaus also express past tense, either to the exclusion of ‑j (‑is and ‑as) or in combination with it (‑out). The termination ‑t is ambiguous, expressing second‑person plural subject agreement in some forms but third‑person singular subject agreement in one form.

The form–content relations involving the prevocalic suffixes in (3a), the terminations in (3c), and the portmanteaus in (3d) are summarized in Table 6.3. While these are comparatively straightforward, the form–content relations involving the vocalic suffixes in (3b) are somewhat more complicated. Forms containing the vocalic suffix ‑e include all irrealis forms, all imperfect indicative forms, the impersonal present indicative form (karer ‘one loves, on aime’), and the third‑person imperative forms (karet ‘s/he must love’, karent ‘they must love’). Forms containing the vocalic suffix ‑i include second‑person plural forms of the present indicative and imperative as well as some future‑tense forms. Forms containing the vocalic suffix ‑o include some present indicative forms, some future‑tense forms, plural and impersonal past indicative forms, and the first‑person plural imperative form. The vocalic suffixes’ somewhat miscellaneous distribution is summarized in Table 6.4.

In view of these observations about the relation of form to content in Breton verb paradigms, it is reasonable to assume that Breton conjugation is based on the system of simple rules of exponence in (4). Because certain rules in (4) do not express the same content in all of their uses, they are not directly associated with any specific content. For instance, the rule ⟦‑o⟧ is represented in (4) as applying to a verb to realize the empty set through the suffixation of ‑o. But in combination with the impersonal rule ⟦‑r⟧, ⟦‑o⟧ realizes the future indicative (as in karor ‘one will love’); in combination with first‑person plural rule ⟦‑mp⟧, it realizes the present indicative (karomp ‘we love’); in combination with both the past‑tense rule ⟦‑j⟧ and the ⟦‑mp⟧ rule, it realizes the past indicative (karjomp ‘we loved’); if it serves on its own as a FER, it realizes the third-person singular future indicative (karo ‘s/he will love’); and so on.

It is clear that in this system, holistic content abounds. Consider the seven affix sequences in Table 6.5. The form of the first‑person plural present indicative suffix sequence ‑o‑mp in kar‑o‑mp ‘we love’ is defined by the successive application of the rules ⟦‑o⟧ and ⟦‑mp⟧, but neither of these rules expresses tense or mood on its own; instead, it is the combination of ⟦‑o⟧ and ⟦‑mp⟧ that expresses the additional content {ind prs}. By contrast, it is the combination of the rules ⟦‑e⟧ and ⟦‑r⟧ that expresses the content {ind prs} in the definition of the impersonal present indicative suffix sequence ‑e‑r in kar‑e‑r (‘one loves, on aime’). And even though ⟦‑d⟧ and ⟦‑r⟧ are both expressions of an impersonal subject, the combination of ⟦‑e⟧ and ⟦‑d⟧ expresses different content from the combination of ⟦‑e⟧ and ⟦‑r⟧: in the definition of the suffix sequence ‑e‑d in kar‑e‑d (‘one loved, on aimait’), the combination of ⟦‑e⟧ and ⟦‑d⟧ expresses the content {ind impf}.

The additional content expressed by the combination of two rules may differ from the additional content expressed by those two rules when they are together in combination with some third rule. Thus, the suffix sequence ‑j‑o‑mp whose form is defined by the successive application of ⟦‑j⟧, ⟦‑o⟧, and ⟦‑mp⟧ expresses the first-person plural past indicative (not the first-person plural present indicative expressed by ⟦‑o⟧ and ⟦‑mp⟧ in the absence of ⟦‑j⟧); similarly, the suffix sequence ‑j‑e‑d whose form is defined by the successive application of ⟦‑j⟧, ⟦‑e⟧, and ⟦‑d⟧ expresses the impersonal past irrealis (not the impersonal imperfect indicative expressed by ⟦‑e⟧ and ⟦‑d⟧ in the absence of ⟦‑j⟧).

Finally, a solitary rule may serve as a FER expressing more specific content than that same rule expresses in combination with other rules. As FERs, ⟦-i⟧ and ⟦-o⟧ respectively express the second- and third-person singular future indicative though both appear in rule combinations expressing other person/number/tense/mood combinations. Thus, as FERs, ⟦-i⟧ and ⟦-o⟧ are instances of solitary specialization (Section 1.5.5).

Any adequate theory of morphotactics must account for facts of these sorts, which show that the compositional content criterion is a canonical tendency and not a theorem of some inviolable set of principles.

6.2 Accounting for Holistic Content by Means of Content Supplementations

In order to account for the fact that an inflectional rule may express supplementary content, I employ the supplementation operator Ⓢ defined in Section 2.3. This may apply to a simple inflectional rule serving as a solitary specialization, as in (5a), or to the composition of two inflectional rules serving as a holistic combination, as in (5b).

The patterns of content supplementation in (5) afford a straightforward account of the holistic content expressed by the inflectional morphology of Breton regular verbs.

For the inflection of indicative nonpast and imperative forms, the rules in (4) participate in the definition of the FERs specified in Table 6.6; all of these FERs involve supplementary content, and they fall into five main groups according to the nature of their addend (= their supplementary content). The holistic combinations listed in part (a) of the table share the addend {ind prs}; those in part (b), the addend {ind fut}; and those in part (c), the addend {ind impf}. The sole holistic combination in part (d) supplies {ind} as supplementary content for the combination of past‑tense ⟦‑j⟧ with the rule introducing the second‑person singular portmanteau suffix ‑out. In each of the FERs in part (e), the supplementary content includes a person/number specification; note that these FERs include three holistic combinations and three solitary specializations.

The definition of the other indicative past‑tense forms and that of the irrealis forms involve the rule combinations in Table 6.7. Three rules function as carrier rules in these combinations: these are the holistic combination Ⓢ_{ind}(⟦‑o⟧ ◦ ⟦‑j⟧), the composite rule (⟦‑e⟧ ◦ ⟦‑f⟧), and the holistic combination Ⓢ_{irr}(⟦‑e⟧ ◦ ⟦‑j⟧) on the left side of the table. Each of these serves as the carrier rule for various termination rules. Termination rules compose with the rule Ⓢ_{ind}(⟦‑o⟧ ◦ ⟦‑j⟧) in part (a) of the table to provide FERs for the definition of indicative past‑tense forms. Termination rules compose with the composite (⟦‑e⟧ ◦ ⟦‑f⟧) to provide FERs for the definition of irrealis present‑tense forms. And termination rules compose with the combination Ⓢ_{irr}(⟦‑e⟧ ◦ ⟦‑j⟧) to provide FERs for the definition of irrealis past‑tense forms. The composite (⟦‑e⟧ ◦ ⟦‑f⟧) and the holistic combination Ⓢ_{irr}(⟦‑e⟧ ◦ ⟦‑j⟧) serve on their own as default FERs for two third-person singular forms – specifically, that of the present irrealis (e.g. karfe ‘s/he would love’) and that of the past irrealis (e.g. karje ‘s/he would have loved’).

The rules in (4) and in Tables 6.6 and 6.7 define all but a handful of the forms of karout ‘love’ in Table 6.1. To account for the two suffixless forms (the third‑person singular present indicative form kar ‘s/he loves’ and the second-person singular imperative form kar ‘love!’), I assume that the definition of the Breton paradigm function PF includes the clause in (6). This assumption excludes the possibility that any otherwise applicable rule of overt affixation in (4) (e.g. ⟦‑i⟧, ⟦‑o⟧, ⟦‑e⟧, ⟦‑s⟧, ⟦‑t⟧, or ⟦‑out⟧) might apply in the definition of these forms.

I additionally assume that the plural imperative forms have the shape they do as an effect of systematic syncretism – specifically, that the definition of the Breton paradigm function includes the clauses in (7), according to which (i) a regular verb’s first‑ and second‑person plural imperative forms are syncretic with the corresponding present indicative forms; and (ii) its third‑person plural imperative form is syncretic with the corresponding imperfect indicative form.

With these additional assumptions, it is now possible to account for the definition of every one of the forms of the paradigm of karout ‘love’ in Table 6.1: each form in Table 6.1 is defined by the corresponding FER in Table 6.8.

This analysis correctly accounts for the fact that combinations of rules may realize content some parts of which cannot be directly attributed to any of the individual rules being combined. That is, it accounts for the possibility that a word’s morphology may express holistic content – content that fails to conform to the canonical expectation of compositionality. Notice, in addition, that this analysis correctly accounts for the fact that the mode of combination exhibited by two rules, and hence also the content that they express, may vary with the presence or absence of some additional rule. For instance, the holistic combination Ⓢ_{{ind prs}}(⟦‑mp⟧ ◦ ⟦‑o⟧) expresses {ind prs 1pl} through the suffixation of ‑o‑mp while the composite (⟦‑mp⟧ ◦ Ⓢ_{ind}(⟦‑o⟧ ◦ ⟦‑j⟧)) expresses {ind pst 1pl} through the suffixation of ‑j‑o‑mp. Similarly, the holistic combination Ⓢ_{{ind impf}}(⟦‑d⟧ ◦ ⟦‑e⟧) expresses {ind impf imps} through the suffixation of ‑e‑d while the composite (⟦‑d⟧ ◦ Ⓢ_{irr}(⟦‑e⟧ ◦ ⟦‑j⟧)) expresses {irr pst imps} through the suffixation of ‑j‑e‑d. Such facts show that the same rules may enter into different kinds of combinations, and in doing so, may express different kinds of supplementary content.

Of particular interest here is the fact that in the inflection of a Breton verb, parallel forms may not express parallel content because of the different ways in which the rules defining those forms combine. Given the forms kar-o-mp ‘we love’ and kar-i-mp ‘we will love’, one might expect the parallel forms kar-o-t and kar-i-t to express the parallel content ‘you (pl.) love’ and ‘you (pl.) will love’. And yet, it is karot that means ‘you (pl.) will love’ and karit that means ‘you (pl.) love’. The forms karomp, karimp, karot, and karit involve the four simple rules ⟦‑o⟧, ⟦‑i⟧, ⟦‑mp⟧, and ⟦‑t⟧, but these rules combine in different ways in the definition of these forms (Table 6.9). The holistic combination of ⟦‑mp⟧ with ⟦‑o⟧ has {ind prs} as its addend (as in part (a) of Table 6.9), but the holistic combination of ⟦‑t⟧ with ⟦‑o⟧ has {ind fut 2pl} as its addend (as in part (b) of the table); by contrast, the holistic combination of ⟦‑mp⟧ with ⟦‑i⟧ has {ind fut} as its addend (as in part (c)), but the holistic combination of ⟦‑t⟧ with ⟦‑i⟧ has {ind prs 2pl} as its addend (as in part (d)).Footnote ²

6.3 Emergent Supplementary Content in Limbu Verb Inflection

There are cases in which holistic combinations have an emergent character; these are cases in which the composition of a rule R₂ expressing property P₂ with a rule R₁ expressing property P₁ only applies in the definition of forms that possess an additional property P₃, even though on their own, R₁ and R₂ both apply in the definition of forms that do not necessarily possess P₃. In such cases, R₁ and R₂ might be assumed to enter into the holistic combination Ⓢ_{P₃}(R₂ ◦ R₁). Emergent content supplementations of this sort are not unusual; consider an example from Limbu.

In the inflection of transitive verbs in Limbu (Section 3.2), the ⟦a‑⟧ rule in (8a) expresses first‑person involvement through the prefixation of a‑, identifying either the agent argument (as in (9a)) or the patient argument (as in (9b)) as first person; similarly, the ⟦kɛ‑⟧ rule in (8b) expresses second‑person involvement through the prefixation of kɛ‑ (~ gɛ‑ after a vowel), identifying either a second‑person agent (as in (10a)) or a second‑person patient (as in (10b)). One might therefore expect that a form such as a‑gɛ‑huʔ, which carries both a‑ and kɛ‑ and no other overt morphology, should be ambiguous between a first‑person agent/second‑person patient interpretation and a second‑person agent/first‑person patient interpretation; yet, a‑gɛ‑huʔ only means ‘you teach me/us’ (as in (11a)). The other interpretation is instead expressed by means of the portmanteau rule ⟦‑nɛ⟧ in (12), which signals a first‑person agent acting on a second‑person patient, as in (11b); see van Driem (Reference van Driem1987: 80). This shows that although the ⟦a‑⟧ and ⟦kɛ‑⟧ rules are both indeterminate with respect to the argument whose person they encode, their combination ⟦a‑gɛ‑⟧ is not similarly indeterminate; that is, the combination of ⟦a‑⟧ with ⟦kɛ‑⟧, though representable as the composite rule (⟦a‑⟧ ◦ ⟦kɛ‑⟧) in (13a), might also be represented as the emergent content supplementation Ⓢ_{{{agt 2}{pat 1}}}(⟦a‑⟧ ◦ ⟦kɛ‑⟧) in (13b). Consider these alternatives.

If the morphotactics of Limbu involves the composite rule (13a) rather than the emergent content supplementation (13b), the realization of the form cell (14a) as the realized cell (14b) involves the competition of (13a) with (12) – a competition that Pāṇini’s principle resolves in favor of (12). But if the Limbu system instead involves the emergent content supplementation (13b), this rule doesn’t compete with (12); the realization of (14a) by (14b) is, in that case, computationally simpler. That is, the composite rule (13a) is a default that is subject to override by (12), but the emergent content supplementation (13b) is not subject to override by (12), since its domain is disjoint from that of (12). On the assumption that it is more efficient for speakers to memorize frequently recurring form/content correspondences rather than to recompute them extemporaneously, it is reasonable to assume that (13b) would be the preferred mode of combination for ⟦a‑⟧ and ⟦kɛ‑⟧ in Limbu. (See Section 11.1 for related discussion.)

6.4 Holistic Content in Old English Verb Inflection

In certain cases, the same two rules may combine to express different holistic content in different contexts. Some striking instances of this sort appear in Old English verb inflection.Footnote ³

The finite inflection of Old English verbs distinguishes three moods (indicative, subjunctive, imperative), two tenses (present, past), and two numbers, with person distinguished in the singular of the indicative (present and past); the imperative is restricted to the present tense. Typically of Germanic languages, Old English makes a distinction between weak verbs (whose past stem is marked by a dental suffix) and strong verbs (whose past stem is instead distinguished by ablaut). The finite paradigms of the five verbs in Table 6.10 are representative.Footnote ⁴

Each of the verbs in Table 6.10 exhibits three stems in its finite paradigm (Table 6.11): a present stem (in present-tense forms, whether indicative, subjunctive, or imperative), a default past stem (in past-tense forms, both in the subjunctive and in the plural and second‑person singular of the indicative), and a singular past stem (in the first and third persons of the singular past indicative). In the inflection of weak verbs, the default past stem and the singular past stem are syncretic.

The suffixal morphology in Table 6.10 exhibits varying patterns of similarity among the five paradigms. In the present tense, the strong verbs smītan, clēofan, singan, and the weak class 1 verb dēman are alike, but differ from the weak class 2 verb leornian. In the singular of the past indicative, the suffixal morphology of the strong verbs differs from that of the weak verbs. In the plural of the past indicative and in the past subjunctive, all five verbs exhibit the same suffixal morphology. Within the context of this variety, the suffixal inflection of Old English verbs presents several instances of holistic content; of particular interest is the fact that in more than one instance, the same two rules may enter into two distinct holistic combinations.

I assume that the fragment of Old English verb morphology in Table 6.10 involves the simple rules of inflectional exponence in (15)–(17). The vocalic suffixes in (15) serve as carrier rules; ⟦‑e⟧ also applies on its own, as a FER. The ⟦‑e⟧ rule expresses content only in combination with one or more other rules; thus, when ⟦‑e⟧ applies on its own, it does so by default, signaling the inapplicability of any other rule. The dependent rules in (16) combine with the carrier rules as in (18)–(21); as we shall see, these combinations involve several examples of the expression of holistic content. The identity rules in (17) override rules of overt suffixation in the definition of particular forms – specifically, in the first and third persons singular of the indicative past of strong verbs and in singular imperatives. (For convenience of reference, I distinguish the two rules in (17) by means of the subscripts ‘pst’ and ‘imp’.)

The combined rules in (18) apply in the inflection of all five verbs. Rule (18a) is simply the composite rule (⟦‑n⟧ ◦ ⟦‑o⟧), which realizes indicative past plural forms through the suffixation of ‑on. In the holistic combination (18b), ⟦‑n⟧ combines with ⟦‑e⟧ to yield a rule realizing the subjunctive plural through the suffixation of ‑en. This is an example of emergent content supplementation, since neither ⟦‑n⟧ nor ⟦‑e⟧ realizes subjunctive mood on its own, but in combination, they only realize plural subjunctives. In the inflection of all five verbs, the subjunctive singular is realized by default through the application of ⟦‑e⟧.

In the singular of the indicative past, strong verbs and weak verbs behave differently. In the inflection of strong verbs, the default rule ⟦‑e⟧ realizes the second‑person singular of the indicative past; but in the first and third persons of the singular indicative past, the application of this rule is overridden by the identity rule ⟦X→X⟧_pst. In the inflection of weak verbs, the default rule ⟦‑e⟧ applies in the first and third persons of the singular indicative past; in the second person, however, its application is overridden by that of the holistic combination in (19).

In the present tense, strong verbs show the same suffixal morphology as weak class 1 verbs. In the inflection of such verbs, the holistic combinations in (20) define second‑person singular indicative present forms in ‑est, third‑person singular indicative present forms in ‑eþ, and plural indicative present forms in ‑aþ. Note that two distinct rules combine ⟦‑st⟧ with ⟦‑e⟧: the holistic combination in (19) defines ‑est as a second‑person singular suffix for the indicative past of weak verbs (dēmdest ‘you judged’, leornodest ‘you learned’), but the holistic combination (20a) defines ‑est as the default second‑person singular suffix for the indicative present (applying in the definition of smītest ‘you smite’, clīefest ‘you cleave’, singest ‘you sing’, and dēmest ‘you judge’ but overridden in leornast ‘you learn’).

Besides sharing the morphology defined by the rules in (20), strong verbs and weak class 1 verbs are alike in their present‑tense inflection in other ways as well:

• their first‑person singular indicative present forms and their singular subjunctive present forms are defined by the default rule ⟦‑e⟧;

• their imperative singular forms are defined by ⟦X→X⟧_imp; and

• their plural subjunctive present forms are defined by means of the same rule (18b) as defines the plural subjunctive forms of all verbs in the past tense.

Verbs belonging to weak class 2 are very different in their present‑tense inflection, which involves the combined rules in (21). In the definition of the first‑person singular indicative present and singular subjunctive present forms of leornian, the composite (⟦‑e⟧ ◦ ⟦‑i⟧) in (21a) overrides ⟦‑e⟧; in the definition of the other indicative present forms, the combinations in (21b–d) override those in (20). Note that two distinct rules combine ⟦‑þ⟧ with ⟦‑a⟧: the holistic combination in (20c) defines ‑aþ as the default suffixal expression of the plural indicative present (smītaþ ‘we/you/they smite’, clēofaþ ‘we/you/they cleave’, singaþ ‘we/you/they sing’, dēmaþ ‘we/you/they judge’), but the holistic combination in (21c) defines ‑aþ as the suffixal expression of the third person singular indicative present of weak class 2 verbs (leorn‑a‑þ ‘s/he learns’).

Outside the weak class 2, the plural present forms of the indicative and subjunctive are defined by the content supplementations (20c) and (18b). In the inflection of weak class 2 verbs, these forms are defined by (21d,e) – the respective composites of (20c) and (18b) with ⟦‑i⟧. Because the domains-of-definition of (21d,e) are narrower than those of (20c) and (18b), (21d,e) override (20c) and (18b) in the definition of plural present forms of weak class 2 verbs. Finally, the solitary specialization in (21f) overrides both ⟦X→X⟧_imp and (21a) in defining imperative singular forms of weak class 2 verbs.

Plural imperative forms are invariably identical to their plural present indicative counterparts. I assume that this is a systematic syncretism enforced by clause (22) in the definition of the Old English paradigm function PF.

This analysis accounts for all of the forms in Table 6.10. For each cell A in Table 6.10, the corresponding cell in Table 6.12 lists the FER defining the form in A.

In this analysis, the suffixal morphology of the forms leornodest ‘you learned’ and smītest ‘you smite’ in both cases involves the simple rules ⟦‑e⟧ and ⟦‑st⟧ in (15) and (16); but because these rules enter into two different holistic combinations, the suffix sequence -e-st is an exponent of different property sets in leornodest and smītest, as parts (a) and (b) of Table 6.13 show. Similarly, the suffixal morphology of the forms smītaþ ‘we/you/they smite’ and leornaþ ‘s/he learns’ in both cases involves the rules ⟦‑a⟧ and ⟦‑þ⟧ in (15) and (16); here, too, the rules enter into two different holistic combinations, as in parts (c) and (d) of Table 6.13. Finally, like the analysis of Limbu proposed in Section 6.3, this analysis of Old English verb morphology derives computational simplicity from the use of holistic combination, treating the combination of rules ⟦‑n⟧ and ⟦‑e⟧ not simply as a composite rule spelling out the default exponence of plural number, but as a holistic combination spelling out the (present or past) exponence of the plural subjunctive; the definition of smiten ‘we/you/they smote (sbjv)’ in part (e) of Table 6.13 illustrates this.

The notion of holistic combination highlights an important reason why the morpheme concept (and in particular, its theorem that a word form’s content is the sum of the content associated with its component morphemes) is wrong. The morpheme concept entails that a word form is endowed with the summed content of its individual formatives. But holistic combinations show that word forms with different content don’t necessarily differ in content because they are composed of different exponents; even if they involve the very same exponents, they may instead differ because the rules introducing those exponents are combined in different ways.

6.5 Conclusion

In this chapter, deviations from the compositional content criterion have been shown to necessitate a mode of rule combination distinct from ordinary composition, namely that of holistic combination. Breton conjugation is an example of an inflectional system whose morphotactics makes extensive use of this mode of combination. I analyze such systems by means of a supplementation operator Ⓢ_γ, whose application to a rule R realizing content τ produces the content supplementation Ⓢ_γ(R), a rule whose formal effect is like that of R but which realizes the more specific content [τ ⊔ γ]. If R is a composite rule, the content supplementation Ⓢ_γ(R) is a rule of holistic combination; if R is a simple rule, Ⓢ_γ(R) is instead a solitary specialization. Evidence from Old English shows that the same two rules may enter into more than one holistic combination.

In the following chapter, I present evidence motivating another special mode of rule combination – that of aggregation. Aggregation inherently deviates from the stem operand criterion (Section 1.5.6), but it brings apparent deviations from the affix directionality criterion (Section 1.5.10) into conformity with it.