Here I am undertaking the limited exercise of looking at three possible general views of root meaning: (1) roots have an inherent or basic meaning; (2) roots have grammatically-conditioned contextual meanings; (3) roots themselves have no meanings (only categorized roots can bear content). Clearly, there are various possible hybrid accounts, which would allow for some roots to have inherent meanings, others to have meanings only in a context, etc. Thanks to an anonymous reviewer for making this point.

3.1 Inherent/Basic/Core Meanings for Roots?

‘Roots possess an inherent meaning (at least in the typical case)’, according to Embick (2015: 47), and ‘At a minimum, there must be a theory of Root meanings, …, to account for the simple fact that Roots possess inherent meanings.’ (ibid: 50; emphasis added). This clearly stated position that roots have an inherent meaning (at least in the typical case) appears to be the exact opposite of the position I assumed in Section 2 (that roots are meaningless in and of themselves, with the minimal bearers of meaning being categorized roots). However, it can be taken in at least two different ways: (a) roots have a semantic content or sense (they encode a concept); (b) roots have a semantically underspecified meaning that underlies the (various) meanings/contents they have in different contexts. As one reads on in the text from which the quotes above are taken, it is not clear exactly which of these two positions Embick is supporting as he also uses the terms ‘basic meaning’ and ‘core meaning’ of a root, each of which is open to several interpretations. What is made clear is that the meaning of a root can alter dependent on the immediate grammatical context in which it appears: ‘categorizers (and perhaps other morphemes local to a Root) play a role in determining which meaning(s) of a Root are active in a given grammatical context.’ (ibid: 47).

Embick gives the following example: ‘In … different grammatical environments there is a shared component of interpretation that is centred on the Root’s “basic” meaning, but perhaps some context-specific differences as well. For example, when the Root √feather in English is employed as the noun ‘feather’, it refers to an object that has a number of properties. Part of what English speakers know about this Root, though, is that in another context, as the adjective ‘feather-y’, it can also have a more restricted meaning, where the weight aspect of √feather is prominent: ‘feather-y’ in this sense means “light or airy”, with no actual objects (feathers) involved … Collectively, the different facets of lexical semantic meaning that are found with Roots in different contexts constitute the phenomenon of Root polysemy …’ (ibid: 48–49; emphasis added). Note first that the conception of ‘context’ here is highly restricted, referring just to grammatical/syntactic context (and with certain further locality restrictions on how far that contextual domain can extend).Footnote 13 And, second, the idea seems to be that all the different polysemes of a root share some component of meaning that comes from the inherent/basic meaning of the root. As regards the particular example, much more could be said: rather than being a more restricted meaning, the ‘feather’ in ‘feather-y’, at least as described above, is broader in denotation, applicable both to actual feathers and to other light airy entities (a classic case of pragmatic broadening, as discussed in Section 2). Also, this is just one meaning of ‘feathery’; consider a sentence like ‘I love that feathery collage’ referring to an art-work made from feathers, whether actual feathers or pieces of wire and fluff artistically modelled into things that look like feathers. There are, doubtless, other possibilities contingent on broader discourse or communication contexts.

The idea that the basic units (the primitives) of a language have (must have) a semantically underspecified meaning has a long history, having been applied to words long before the root-based approach took hold. It is highly intuitive and, if it worked, would make for a neat and unified account of word polysemy, one in which all the polysemes of a word shared a common core of meaning, while differing in whatever other components of meaning make each of them into a fully semantic entity capable of contributing to the truth-conditional content of a sentence/utterance. Furthermore, that common core would function as a constraint on possible senses of a word; any new contextually prompted sense would have to incorporate that core meaning in order to qualify as a possible new sense of the word. On such an account, a word would have an invariant but underspecified (abstract) meaning and any fully semantically specified senses it is used to express would be a result of (broad) context and pragmatic inference fleshing out that core (skeletal) meaning. One of the strongest advocate of this view is Ruhl (1989), who maintains that what people talk of as polysemy is a purely pragmatic phenomenon, entirely context-dependent, and to be explained in those terms, while most words (where words are taken here to be the basic linguistic units) are ‘monosemic’. Ruhl carried out extensive and thorough examination of specific cases, such as the verbs ‘bear’ and ‘run’, often cited as cases of highly polysemous verbs, examining their different meanings in different contexts, and describing their specific senses as cases of pragmatic specialization and generalization, very much at one with (and preceding) the relevance-theoretic account of lexical pragmatics (e.g. Carston 2002, Wilson & Carston 2007). However, the key difference is his commitment to the ‘monosemic principle’ that ‘a word’s semantics should concern what it contributes in all contexts’ (ibid: 87). He says that this single linguistic meaning is impossible to put into words, as it is highly abstract and formal, ‘ … highly remote from all ambient contingencies’, but insists that it must exist.

The psychologists Frisson and Pickering (2001) also favour a ‘radical monosemy’ model, according to which the only element of word meaning/semantics stored in the mental lexicon is an underspecified schematic meaning, which is said to ‘encompass all related senses of a word’ (ibid: 149). This is what a hearer retrieves initially and then at a subsequent stage of processing, ‘context is actively involved in refining the interpretation of a word by changing the underspecified meaning into a specific interpretation’ (ibid: 164), that is, a specific sense is recovered through interaction of the schematic linguistic meaning with contextual information. However, they openly acknowledge that this thin core meaning does not constrain the creation of new senses in context: ‘Because the underspecified meaning is an abstraction over the features of specific senses, a novel interpretation of a word cannot be captured by the underspecified meaning.’ (ibid: 159, their emphasis). Thus, it seems that as new senses arise and become established/conventionalized, a revision, a further attenuating, of the alleged underspecified meaning would be necessary. It is extremely hard, then, to see what purpose this schematic meaning would serve or why the child learning word meanings (via communication, so involving fully semantic senses) would induce such a non-semantic core meaning for a word. In short, the radical monosemy position seems to express a strong intuition but one for which evidence is entirely lacking. As the pragmatic account of the origins of much word polysemy (which includes metaphorically and metonymically related senses) indicates, the inferences may lead to senses whose relations are those of family resemblances without any single shared core. I have argued in more detail elsewhere against any common core meaning for polysemous words (Carston 2020/21), a meaning that seems to have no role in constraining new (pragmatically-derived) senses and which would have to grow ever more schematic and abstract the more new senses that a word acquires.Footnote 14

Whether Ruhl would have embraced recent root-based approaches to syntax and attempted to find a common core meaning for the much larger families of senses that this entails, e.g. ‘run’ in its myriad noun and verb senses, I don’t know, but obviously any such endeavor would be subject to the same difficulties encountered at the word level but much magnified.

Moving back to roots now and the various meanings they can have in ‘grammatical contexts’ (considerably more restricted than the contexts that Ruhl considered and than the notion of communicative context employed quite generally in pragmatics). Most expositions of the position that roots have an inherent core meaning use examples from Semitic languages to illustrate their point because roots and their manifestations in different grammatical contexts are especially clear in these languages. This is due to the wholly consonantal nature of their roots, which cannot occur alone but appear in a range of different ‘templates’ (that is, sequences of consonants and vowels) as words whose meanings are often clearly related, e.g. Arabic √KTB, manifest in the verb ‘kataba’, the noun ‘kitaab’, the adjective ‘kitaabii’, among many others, all of which have meanings related to writing (Embick 2015: 48). An important study in this vein is Arad’s (2003, 2005) account of Hebrew word formation; she takes the meaning of a root to be the common ‘semantic denominator’ or the ‘kernel of meaning’ shared by the words derived from it. Consider, for instance, the following root XŠB and words built on it:

Discussing this and other cases, Arad (2003: 9–10) maintains that ‘although the range of meanings in each group is quite varied, all members share a common semantic core. For example, all the words made from the root √xšb are related to some mental activity – whether thought, consideration or calculation.’ The view may seem fairly plausible in this particular case, but there are also word families, clearly built on the same root, whose semantic relatedness is much less evident, making the case for a shared core or kernel of meaning intrinsic to the root much harder to maintain. Consider the following (from Aronoff 2007):

There is also a set of adjectives built on this root, but the nouns and verbs are sufficient for the key point here concerning the alleged core meaning of the root, which is given as ‘press’. Aronoff (2007: 822) puts the point well: ‘The reflex response to problems like this is to posit an 'underspecified' core meaning for the root, which is supplemented idiosyncratically in each lexical entry. It is logically impossible to show that underspecification is wrong, but trying to find a common meaning shared by pickles and highways brings one close to empirical emptiness and this methodological danger recurs frequently in any Semitic language. In any case, there is no need to find a common meaning in order to relate the two words morphologically …’, and he goes on to show how such words can be related via ‘root alternation classes’ without any common meaning, an account that goes well beyond the issue here. With regard to the meanings of the many words formed from √KBŠ, he tells a plausible etymological story about the origins of the ‘highway’ and ‘pickle’ meanings based on how paved roads and pickles were originally made in the relevant societies, both involving ‘pressing’ of one sort or another. The connection between the meanings seems to be essentially pragmatic, involving a series of metaphoric (resemblance) and metonymic (contiguity) relations; the essential point is that ‘there is nothing left of pressing in the meanings of these Hebrew words today’ (ibid: 822) and no role for any such core meaning of the root. See also Panagiotidis (2020: 61–63) for a comparable range of cases in Greek, all based on the root √esth but with no discernible common semantic denominator, and the discussion below of English words based on bound (Latin) roots, e.g. √-ceive, √-fer, √-mit, √-flect; whatever commonalities of meaning they may once have had are long gone, as evident from consideration of, for instance, ‘refer’, ‘infer’, ‘confer’, ‘defer’.

The problem here, as with polysemous words, is that there seems to be no way to isolate any common core meaning for roots and no role for any such element of meaning; as cultural and communicative contexts evolve, leading to the coining of new senses and new words based on the same root, any alleged common core meaning gets more and more attenuated until it disappears altogether. Furthermore, the pragmatics of meaning construction is not constrained by any such core meaning, but proceeds via chains of inference in multiple directions, via narrowing/broadening, metaphor and metonymy. Recall the case of ‘laser’ mentioned above: its meaning has rapidly proliferated from a single concrete noun meaning to various others based on (more or less fanciful) resemblances: ‘a laser stare’, ‘throw a laser’, ‘his laser precision’, etc., and the multiple diverse meanings of words based on the roots √face, √run, √line, and the noun/verb pairs: ‘book’, ‘table’, ‘sand’, ‘ship’, … There just is no common core constituting the meaning of the root in each case, and that isn’t a problem because language users coin new words and new senses (to meet their communicative needs in specific contexts) by adapting and repurposing the senses and words they already have/know, and they can rely on the pragmatic capacities of their interlocutors to understand and grasp these new senses and words.

The idea of a shared semantically-underspecified core meaning hasn’t worked for words and it doesn’t look as if it works for roots either, even when the relevant notion of ‘context’ is radically restricted, as it is here (and in the next position to be considered). Arguably, the identificatory linguistic knowledge that speakers have about the roots in their language is phonological and any apprehension of a root as having meaning is coming from knowledge of the various senses of the words based on that root, whose degree of interrelatedness can vary greatly.

3.2 Allosemy – Grammatically Conditioned Root Polysemy

The third position on root meaning that I’ll look at, in a bit more detail than the previous two (no root meaning, inherent root meaning), is known as ‘allosemy’ (or ‘root polysemy’), viewed by its advocates as a semantic counterpart to ‘allomorphy’, which is where roots can take different phonological forms in different grammatical contexts.

3.2.1 Allomorphy

In certain current approaches to the language faculty, in particular, the approach known as Distributed Morphology (DM) (Halle and Marantz 1993; Marantz 1997, 2001, 2013; Harley 2012, 2014a; Embick 2015, 2021, i.a.), once syntax has done its computational work (that is, performed various combinatorial operations, all of them instances of the basic operation of ‘merge’), a structure is ‘spelled out’ or ‘interpreted’ phonologically and semantically. That is, on the one side, it undergoes morpho-phonological operations, resulting in a ‘phonological form’, which interfaces with the articulatory/perceptual systems responsible for its externalization for use in communication, and, on the other hand, it undergoes certain semantic operations that result in a ‘logical form’, which interfaces with conceptual/intentional systems (within the individual’s wider cognitive system), which are responsible for providing the content or meaning of the structures. As well as the central computational (generative) engine of syntax, there are three lists of stored items: the syntactic primitives (roots and grammatical/functional items); vocabulary items (these are the various phonological forms that syntactic primitives may take); the encyclopedia (which provides ‘special’, that is non-compositional, unpredictable semantics). This is roughly summarized in the following diagram:Footnote 15

There is some variation among theorists concerning what the syntactic domains of spell-out are, with some allowing just VP’s and clauses, while others, especially within DM, include much smaller domains (essentially, those phrases that comprise words) as the syntactic domain that is spelled out (Marantz 2001). There is an assumption here that the phonological and the semantic sides of spell-out are symmetrical and each has its ‘allo-’ manifestations, so a given single root (nothing more than an index or address, as hypothesized above) may take any of several (related) morpho-phonological forms, depending on its immediate syntactic context (e.g. ‘receive’ and ‘reception’, ‘wise’ and ‘wisdom’, ‘teach’ and ‘taught’, ‘mouse’ and ‘mice’) and may have any of several (related) meanings (semanticses), also depending on its syntactic context; the first of these, known as ‘allomorphy’, is well-established, while the second, labelled ‘allosemy’, is more recent and somewhat more contentious. The further issue of whether or to what extent the syntactic domains within which these two kinds of allo-forms arise are the same is discussed and disputed within the theory (see, for instance, Marantz 2013), but this is a level of detail that I won’t consider here, my aim being to cast doubt on the very notion of allosemy.

Let’s first look at the allomorphy side of the story and start with a clear case, the English plural (taken from Embick 2015: 172); on this sort of account, the grammatical item ‘plural’ has the following vocabulary items (allomorphs):

The first of these is to be read as ‘the plural’ functor manifests as /-en/ when it occurs in the context of (is suffixed to) the roots √ox, √child, and perhaps others that would need to be included in the unordered set; similarly, mutatis mutandis, for the second line, where the plural has a zero realisation. The third line, which does not specify any grammatical context, gives the ‘elsewhere’ condition or default value for the plural morpheme, that is, if neither of the other contextually specified vocabulary items applies, then the value is /-z/. (Note that this value may itself surface in several distinct forms, e.g. [-z] for ‘dog’, [-s] for ‘cat’, [əz] for ‘class’, but this is entirely a matter of phonological conditioning by the immediately preceding phoneme, e.g. the devoicing caused by the voiceless obstruent [t] of ‘cat’.)

The plural morpheme is, of course, a member of a functional/grammatical category, to do with number (singular/(dual)/plural). Now, what about the other class of basic syntactic elements, which is more central to this paper, namely, roots? On the surface at least, allomorphy seems to work here in essentially the same way,Footnote 16 so, for instance, there are two allomorphs (two vocabulary items) for the root √destroy, roughly indicated here:

That is, this root manifests as /destrʌk-/ in specific nominal and adjectival contexts (‘destruction’, ‘destructive’) and elsewhere it is /destrɔɪ/, the default value. Other cases of root allomorphy discussed in the literature are √mouse with the allomorphs /mais/ manifest in the context of plurality and /maus/ elsewhere (e.g. in the singular and in compounds like ‘mouse-trap’), √thief with the allomorphs /thi:v/ and /thi:f/, √speak with the allomorphs /spi:tʃ/, /spouk/, /spi:k/ in different grammatical contexts (see Siddiqi 2009).

Similarly for the bound root √-ceive or √683, which manifests as /sep/ in certain nominal and adjectival contexts (as in ‘reception’ / ‘perception’ and ‘receptive’ / ‘perceptive’) and as /si:v/ elsewhere, its default value (as in ‘receive’, ‘receiver’, ‘perceive’ and ‘perceiver’). This nicely captures a generalization: the /si:v/ ~ /sep/ alternation is a property of the –ceive root itself, which is why it behaves the same way across lexical items that share this root (e.g. deceive, conceive, perceive) and in imaginary nonce items formed from –ceive (e.g. acceive, acception). Contextual allomorphy, then, is a real phenomenon, such that there are distinct vocabulary items (phonological forms) for a single morpheme X (whether a functional item or a root) dependent on the immediate grammatical context Y that the morpheme occurs in, as schematized in (9) (from Embick 2015: 178):

There are important further components of the theory of allomorphy, in particular concerning the ‘locality conditions’ on the structures within which the morpheme X and the context Y can interact (that is, constraints on the domains within which they can ‘see each other’); I think/hope that this important and somewhat contentious issue, which I do not attempt to address here, does not affect my central concern which is to consider the grounds for a semantic parallel to allomorphy (for discussion of these locality issues, see Marantz (2013), Embick (2015, chapt. 7)).

In the next section, the focus is on allosemy, the hypothesized semantic counterpart to allomorphy. After introducing the idea, I look at some putative examples of allosemy, drawing on work from Borer (2014b) and Panagiotidis (2020) in finding striking differences between the way these work (or, in fact, do not work) as compared with the examples of allomorphy just considered. Then, at a more general level, stepping away from specific cases, I question the underlying assumption informing this work, namely, that there is a Phon/Sem symmetry in language, arguing instead for a significant asymmetry. In short, the position taken here is that there isn’t such a phenomenon as allosemy (root polysemy), that roots themselves have no meanings (inherent or grammatically conditioned), and that the bearers of content/meaning are structural domains as defined in Section 2 (Borer’s C-core of categorizers), the established/stored non-compositional meanings of these structures (words) having been originally pragmatically inferred in specific communicative contexts.

3.2.2 ‘Allosemy’—the Idea and its ProblemsFootnote 17

Apparently paradoxically, some linguists talk of roots as being both meaningless (as discussed above) and polysemous (Marantz 2013, p.103; Panagiotidis & Nobrega forthcoming). How can this be? The idea is that roots are meaningless in isolation but have meanings in a grammatical context, often several distinct meanings, each dependent on the local grammatical context in which the root appears. Marantz characterizes the ‘theory of contextual allosemy’ as ‘the theory about what governs the choice of meaning for a polysemous root.’ (2013: 103). Note that if there are such meanings for roots, they are ‘special’ (non-compositional), as for the meanings at issue in Section 2 above; roots themselves have no structure, no parts to compose, so any such meaning(s) must be atomic. That is, as with allomorphs, allosemes are unpredictable and so have to be listed together with the syntactic contexts in which they are realized.Footnote 18

In support of the view that contextual allomorphy and contextual allosemy arise in the same local grammatical domains, Marantz (2013: 102–103) discusses the root √house, which has the two allomorphs: /hauz/ as in the verb ‘house’ and the default (elsewhere) /haus/ as in the noun ‘house’ and compounds like ‘housework’. In parallel to this, he points out, their meanings are not compositionally related: ‘no literal house nor even a literal container is implied by the verb’ (p. 102); that is, √house has two contextual allosemes (polysemes): house (the dwelling) and house* (roughly: ‘give shelter/harbour’). So far, so good (although, of course, this case is at least as well explained by the account in Section 2 on which roots themselves have no meaning, contextual or otherwise). This is not to say that the two phenomena must always occur together: consider ‘relief’/ ‘relieve’, ‘belief’ / ‘believe’ (allomorphy without allosemy), on the one hand, and the noun/verb pairs ‘field’/ ‘field’ (= catch or stop) and ‘pinch’/ ‘pinch’ (= steal) (allosemy without allomorphy), on the other hand.

Setting aside allomorphy for now, the following seem like good candidates for root allosemy (with the grammatical contexts that condition the allosemes in each case presented very informally here):

It’s worth emphasizing that what is being claimed here is that these are meanings of the root itself, albeit contextually conditioned.

What about the special non-compositional meanings of complex words such as ‘reactionary’, ‘natualize’, and ‘recital’, discussed in Section 2? Recall that these, as well as the cases just discussed (‘fetch’, ‘liquid’, ‘book’), all fall within Borer’s ‘syntactic domain of Content’ account. Where do they fit into an allosemy account? Presumably, they simply don’t: the meaning ‘make a citizen’ isn’t an alloseme of √nature or √nat (whichever of these is the root here) and ‘backward-looking’ isn’t an alloseme of √(re)act, because in these cases the special meaning doesn’t arise in an appropriately local context of the root, there being several categories intervening between the root and the categorization at which the atomic meaning arises.Footnote 19 If that is right, then contextual allosemy is quite limited in the range of non-compositional meanings of words based on a single root that it encompasses, meanings all of which might be thought of as associated with that root.

Even allowing for the limited nature of the phenomenon, specific problems arise. Consider the following cases of allosemy for the root ‘-ceive’, or √683, as presented by Harley (2014a: 245):

The first line is to be read: the (inherently meaningless) root ‘-ceive’ (√683) gets a contextual meaning paraphraseable as “think” when it occurs within a verbal domain and is immediately preceded by the prefix ‘con- ‘, and the same goes, mutatis mutandis, for the other cases. As already noted, it’s important to be clear that the claim is that the Content (i.e. encyclopaedic meaning) here belongs to the root ‘-ceive’ itself rather than to the whole formation ‘conceive’ or ‘deceive’, whose verbal prefixes merely constitute the domains in which it is realized. This seems problematic. As emphasised by Panagiotidis (2020: 61) in a discussion of the Hebrew case above in (5), there is no ‘elsewhere’ condition here as there is for allomorphy, that is, no default meaning: the contextual meanings of ‘-ceive’ are all, in effect, specific ‘special meanings’; they are the atomic Contents conceive, receive, deceive, etc.  Furthermore, the "think" alloseme realized in the context of [con-] does not apply to the "become pregnant" sense of 'conceive'/ ‘conception' and the "get" alloseme realized in the context of [re-] does not apply to the "social event" sense of ‘reception’. There is no nice generalization across cases here as there is for the allomorphy of √-ceive (i.e. /si:v/ and /sep/), which holds for all occurrences of the root in the specific syntactic contexts given by the rules.  These issues arise for numerous other cases (of Latinate roots), e.g. √-mit in ‘commit’, ‘permit’, ‘transmit’, ‘emit’, etc.; √-volve in ‘revolve’, ‘devolve’, ‘involve’, ‘evolve’, etc.; √-tract in ‘detract’, ‘contract’, ‘subtract’, ‘retract’, etc. In contrast with allomorphy, allosemy seems unexplanatory.

A further point of interest is that the meanings of these roots are semantically unrelated, so talk of root polysemy seems misplaced, at least if the word ‘polysemy’ is being used in its well-established sense of a single linguistic unit which has several interrelated meanings, thereby distinguishing it from homonymy (accidental coincidence of form with unrelated meanings). As far as I can tell, it is not the intention of allosemy supporters to obliterate the polysemy/homonymy distinction; I don’t think anyone is suggesting, for instance, that the root √bank has as two of its allosemes the financial and the riverside meanings. It seems, then, that what is being captured by the allosemy cases above is etymological relatedness rather than any current semantic/pragmatic relatedness.Footnote 20

Moving now to a different sort of case: the meanings of ‘conversions’ such as those discussed in Section 2 would, presumably, also be listed as allosemes of the root, so, for example:

But what about the sense of the verb ‘dust’ in ‘to dust the cake (with sugar)’? There is no syntactic context to distinguish this “sprinkle” sense from the “remove” sense – it is entirely a matter of discourse context, general knowledge and pragmatics. This could arise (perhaps has arisen already in some instances) for many verbs, which, in principle, allow for both a removing X and an adding X meaning, e.g. ‘seed’, ‘skin’, ‘shell’, ‘pit’, ‘pebble’, ‘weed’. Similarly, it is easy to envisage a further sense for ‘sand’ arising and becoming established, as in ‘Let’s sand this area so the kids can play here’ meaning to cover (or pile up) with sand.Footnote 21 Nothing about the immediate syntactic context will distinguish the operative alloseme here. The point applies generally to any number of cases of denominal verbs, so ‘brick’ gets different meanings according to speaker/hearer’s concerns as in ‘They cleared the debris and bricked the wall’ (= make/repair something with bricks), ‘She bricked the papers so they would all fit in her bag’ (= make something into (the shape of) bricks). Unlike the √-ceive case, these noun/verb alternations are instances of polysemy (in the sense of having related meanings), but again there is no default meaning, no generalization across cases, just a list of non-compositional meanings whose realization is not a matter of grammatically specifiable contexts but of fine-grained communicative contexts.

Another issue concerns what exactly constitutes a ‘syntactic’ or ‘grammatical’ domain, especially when overt categorizers are involved. Consider, for instance, the nouns ‘fracture’ and ‘fraction’, both formed directly from the root √fract and with very different meanings (albeit both to do with ‘breaking’); these meanings would appear to be prime candidates for contextual allosemes of √fract, but how are the two local grammatical contexts to be distinguished? The functors ‘-ure’ and ‘-tion’ are both nominalizers of the root and do not seem to have any obviously different formal syntactic/semantic (syn/sem) features, both apparently realizing states, processes, and results (see Lieber (2004:39) who talks of them as rival affixes which are semantically interchangeable). If this is right, it looks as if it will be necessary to involve phonological components, /tjur/ and /šən/, in conditioning the choice of root meaning, but this is precluded by the assumed architecture of the grammar and its interfaces (see the diagram at (6) above). There seem to be several other noun pairs built on a single root, to which this concern pertains: creature/creation; fissure/fission; denture/dentition; juncture, junction; nature/nation.Footnote 22 Other pairs that may raise the same problem, but involve different pairs of affixes are ‘proposal’/ ‘proposition’, ‘sensory’/ ‘sensual’, ‘credal’/ ‘credible’. Another manifestation of the same issue (that is, the required ‘grammatical’ nature of the conditioning context) arises for the multiply polysemous words/roots ‘run’, ‘bear’, and ‘line’. Consider √run and its myriad meanings when in an immediate verbal context: ‘run a mile’, ‘run a business’, ‘run a bath’, ‘run a tight ship’, ‘run for president’, ‘run for New Zealand’ (in the commonwealth games), ‘run an argument/idea’, and more. It looks very unlikely that each of these different meanings for ‘run’ and hence potential allosemes of √run can be distinguished entirely on the basis of immediate grammatical context, but rather that considerations of discourse context and real world knowledge have to be brought to bear, a far more expansive notion of context than anything needed for allomorphy and one which has, therefore, been excluded also for allosemy (see Harley (2014b: 469) for brief discussion of the exclusion of ‘discourse context’ from the theory of allosemy).

In her stringent critique of Harley’s (2014a) applications of allosemy, Borer (2014b) points out further problems that the approach faces when dealing with idiomatic phrases (e.g. ‘spill the beans’, ‘kick the bucket’),Footnote 23 the key point being that these structures receive their idiomatic meanings as a whole. She extends the point to morphologically complex and simple words quite generally:

Clearly, neither kick nor bucket are assigned Content in the context of the idiom kick the bucket. Rather, what is assigned Content is the constituent as a whole. By a similar rationale, neither nat nor ceive are assigned Content, nor, for that matter, are nature and natural within naturalize when the relevant Content is naturalize – become a citizen. Rather, Content is assigned to receive or to naturalize as a whole. But if that is the case, then there is little reason to assume that roots are ever assigned Content, with or without context. Content, rather, is always associated with (labeled) syntactic constituents, at times with considerable internal complexity. To the extent that we perceive the ‘root’ realized as dog to have Content, then, this is not because the root itself has Content but rather, [N √dog] has Content, distinct, we note, from that associated with [v √dog]. (Borer, ibid: 356)

This is, of course, the position I have adopted in Section 2: given an adequate account of the syntactic domain of Content, as developed by Borer (2013a, b), together with a store of such Contents (established non-compositional meanings), and a process for matching the two, there is no need for anything like allosemy.Footnote 24 So, given the problems with specific alleged cases of allosemy and its, at best, very limited explanatory range, the Borerian account seems preferable.Footnote 25

Leaving aside the details of specific cases now, the question arises: why is it that this alleged allomorphy/allosemy symmetry is seen by many theorists, especially those working within the DM framework, as a desideratum of the theory, which it very clearly is (see, in particular, Marantz (2013: 97))? Certainly, the architecture of DM, itself reflective of the architecture of the broader minimalist program in generative grammar (syntax kept minimal with much of the action now playing out at the phon/sem interfaces) (Chomsky 1995a, 2021; Allott & Lohndal forthcoming), does seem to point to such a symmetry (see the diagram in (6)), with the syntax cyclically sending chunks of structure off simultaneously to both kinds of spell-out (interpretation). Theory-internal considerations of economy and elegance, then, appear to favour a phon/sem symmetry, and thus, given the undoubted reality of allomorphy, the existence of a parallel phenomenon of allosemy.

I think there are significant grounds for doubting that there is such a symmetry, that the semantic interface works in the same way as the phonological interface. First, recall that there are really two kinds of allomorphy, syntactically conditioned (e.g. the different plurals for ‘boy’, ‘child’, ‘sheep’) and phonologically conditioned (e.g. the distinct manifestations of the plural /-z/: [-s], [-z], [iz] (Embick 2015: 173–176)). Similarly for the allomorphy of the bound root √-fer, with distinct syntactically conditioned stress patterns (as in ‘refer’ vs. ‘reference’, ‘referential’) and, arguably, phonologically conditioned allomorphs /fɚ/ and ‘fɚr/ as in ‘refer’ and ‘referral’. Given the symmetry assumption, one might wonder what parallel there might be to this phonologically conditioned allomorphy on the allosemy side. Apart from the (alleged) syntactically conditioned meanings, the only other ‘conditioning’ factor available on the meaning side seems to be semantic/pragmatic. But there is no parallel here. Phonologically conditioned allomorphs are a small definitive set, the predictable outcome of facts about human articulation: the plural of the nonsense word ‘jelit’ will be pronounced [s], the plural of ‘dax’ will be pronounced [iz]. ‘Semantically or pragmatically conditioned’ meanings, on the other hand, are indefinite in number (new ones arising every day for ever-evolving speaker-hearer purposes, some recurring, many one-off and transient), unpredictable ahead of specific contexts of utterance—we can’t predict what ‘jelit’ or ‘dax’ may come to mean, nor for that matter the meanings that ‘mouse’, ‘swipe’, ‘remote’ or any other word may acquire in use. There is no phon/sem parallel here.

Arguments coming from a rather different direction, point to an intrinsic asymmetry between the phonology and the (conceptual) semantics of a language. As Studdert-Kennedy (2000) says: ‘… a purely semantic representation of any language is indeed impossible, because a phonetic structure is intrinsic to every word. Every language has phonologically permissible words that happen not to hav