44 2 From morphology to syntax
become carbon’ and so forth. There are cases that do not fit this analysis (agonizedoesn’t mean ‘cause to become agony’ the same waycolonizemeans ‘cause to become colony’) and there are other subregularities one may wish to consider, but the majority of the 200-300 English words ending in-izefit this pattern well enough to consider it the leading candidate for a semantic definition. What we wish to state is a lexical rule roughly of the following form: for stem X,stem+izemeans ‘cause to become (like) X’. Using the notational conventions that were introduced in1.3, we write this as-ize
-ize
cause_ {become <like/1701> stem_}, "_-ize" mark_ stem_
Herecause_/3290‘efficio’ is a binary relation written with a trailing underscore to distinguish it from ordinary languagecause/1891‘causa’ because it is one of the few cases where we feel the technical sense is sufficiently different from the ordinary, naive sense to merit separate treatment (see2.5). The curly braces denote a single hypergraph node (pictorially, all formulas will correspond to hypergraphs) and the angled brack-ets signify optionality, enclosing the default option.mark_is another technical notion, standing for the relation between signifier (a string, given in doublequotes) and the rele-vant element to be substituted, see2.5. The nodestem_is analogous to the variable X used above.
However, neitherlike/1701norbecomeare primitives (for the four-digit disambigua-tion number following the English binding see Secdisambigua-tion 1.3). like/1701 ‘sicut’ is like
become defined as similar (as opposed to like/3382 ‘amo’) and become is defined as after(=agt[=pat])which for now we will paraphrase as ‘afterwards, agent is_a patient’ (thematic roles will be discussed in2.4). For something likeJohn caramelized the sugarthis would be ‘John caused the sugar to be <similar to> caramel afterwards’.
For the sake of readability, we will continue to make some concessions to En-glish syntax, by adding agreement morphology, an article, a copula, and a preposi-tion if needed, but eventually the reader will get familiar with the syntax of definipreposi-tions that lacks all this niceties, and will fluently read John cause_ after({sugar ăsimilarą caramel}). Sincesimilaris not a primitive of the formal language of definitions, we can take this further by substituting its definition
=agt has property, =pat has property, "to" mark_ =pat Since named nodes are unique in definitions, what this means is that in the construction X (is) similar to Ythe agent will have the sameproperty as the patient. As expected, themark_relation is language-specific, for Hungarian we would want to say that the allative casehoz/hez/hözmarks the patient. (4langcurrently gives the mark_s only for English.)
We can omit the default (since it is a binary relation, this means substitutingis_a) or we can expand it, to yield
-ize cause_ {after({=pat has property, stem_ has property})},
"_-ize" mark_ stem_
2.2 Bound morphemes 45
At this point, all our notions are sufficiently general, including not just the metalinguis-tic stem_ but also the termproperty_, which is really underspecified as to what
property it refers to. This fits well the definition of similar 2794 u A =agt has similar quality, =pat has quality, "to _" mark_ =pat, which is
underspec-ified exactly in this respect: comparesimilar consequencestosimilar balloons. Thehas relation is grammaticalized to different degree in different languages: here we opted for the ordinary meaning has bi1r habeo miec1 288 p V =agt control has
=pat, =agt has =patas opposed to a pure grammatical constructpossorhas_, but its status as a primitive is indicated by the definiendum’s presence in the definiens.
The causative element in-izeis well known (Lieber,1992; Plag,1998), and the idea that we define certain verbs by their result state is standard. Temporal structure can refer to some state beforeorafterthe event, see3.2. Comma-separated linear order, as in
=pat has property, stem_ has property simply means conjunction (see Section1.3), and as such it is independent of the order of the conjuncts.
In the fourth edition (Bullon,2003) LDOCE definescaramelizeas ‘if sugar carameli-zes, it becomes brown and hard when it is heated’. The first edition of LDOCE (Procter, 1978) does not definecaramelizeand has no self-recursion. The self-recursive definitions added to later editions may be a feature from the perspective of the human language learner, but they are definitely a bug from the definition substitution perspective. To parse this definition would lead us nowhere, since the definiendum is part of the definiens, and we don’t have a theory for finding a minimal fixed point in if sugar if sugar if sugar . . . X, X becomes brown and hard when it is heated X becomes brown and hard when it is heated . . .. What happens when it’s not heated? Is it brown? Will it become brown? Is it hard when it’s caramelized? Or will it become hard only when heated? How about caramelizing something other than sugar, say onions? This definition says nothing about the ‘if not sugar’ case, whereas the definition we derived above at least tells us that if onion is caramelized it will share some properties with caramel. 4lang uses the appearance of the definiendum in the definiens to trigger a compiler warning in the handful of cases where we see no further reduction (see2.5), and we see no reason to treatcaramelorcaramelizeas a primitive.
Let us briefly discuss some of the challenges that arose in providing semantics for mor-phological operations such as-ize-suffixation. First, the rule is not uniform: there are no-table subregularities and exceptions, such asagonize, cannibalize, editorialize, . . .which do not at all fit the proposed semantics. Some of them lack an object, others may have a prepositional object (editorializeaboutsomething), yet others seem to be built on stems that are no longer actively part of the language?extempore, ?proselyte, *tantal(os).
Stating a rule of -ize suffixation runs into problems of both underapplication and overapplication. There are seemingly excellent base candidates like meat from which we don’t obtain*meatizeeven though ‘cause something to become (like) meat’ would be a perfectly reasonable meaning, and the process actually exists (food producers are sometimes known to add wood pulp to meat products). This lack of productivity has
46 2 From morphology to syntax
led Chomsky,1970to proposing the Lexicalist Hypothesis that puts in the lexicon all processes that lack full generativity (see Bruening,2018for cogent criticism).
Conversely, no English speaker can extract a stem*ostracforostracize, and frankly, knowing thatostrakonmeans potsherd in Ancient Greek is not particularly helpful with-out a longer explanation. The problem is by no means specific to-ize, The same problem is seen with many suffixes like-ify(*modify, *ratify, ossify) and even compounding (no cranforcranberry).
The rule-application approach also runs into subtle, and on occasion less subtle, prob-lems at the string rewriting level. We use the standard underscore symbol ‘_’ for rule focus, and doublequotes for string material, so that in an expressionx mark_ y we can have some form (string)xand some meaningy. The expression of meanings, our main subject in this book, can be done by formulas as in1.3, by vectors as in1.4, or by graphs as in1.5, we will see this in a great deal more detail as we go along.
For the expression of forms, our notation is at best indicative of intention, rather than a fully fleshed-out proposal for the appropriate morphophonological formalism. Creating such a formalism is a problem we don’t take on board, since this would require importing a huge amount of technical machinery from phonology, and would not lead us closer to our goal of providing the semantics. (InS19we argued that both morphophonology and semantics are well suited for finite state devices, but we leave this to the side here.) The intention of the shorthand"_-ize", while clear to the linguist, can only be made explicit in terms of machinery that we are not too keen on developing, as it goes far beyond what we could call ‘naive’.
That said, in the metatheory we’ll make use of several standard distinctions of mor-phology such as between roots, stems, and fully formed words, and between derivational and inflectional affixes. These distinctions, however, are not part of the naive theory of grammar, which begins and ends with words (see2.5). We have already seen examples of roots in1.2, where we discussed a pair of Hungarian suffixes-itand-ulwhich turn roots into transitive (resp. intransitive) verbs quite systematically (there are several hundred examples in the Hungarian vocabulary, more than for the average English derivational affix included in LDV). It is a standard assumption of morphology that roots themselves are categoryless, and obtain their lexical category only in the process of adding deriva-tional affixes. In2.1we already discussed the4langsystem of lexical categories, and as we shall see, there are many elements in the4langlexicon that are better thought of as roots than as stems/lexemes or fully formed words. But given our focus on English, a ridiculously inadequate choice for the study of morphology, we will rarely encounter roots in this book. (For a more systematic study of (Latinate) English morphology, see Quirk et al.,1985Appendix I; Plag,2003; Hamawand,2011; Schulte,2015.)
What is stem_ in the definition of affixes? Ideally, it should be a string vari-able, which in a rule for caramelizewill select the part before-ize, i.e.caramel. This clearly doesn’t work well for most cases, as there is also some truncation going on:
deputy/deputize, colony/colonize . . . removes y;economical/economize removes ical, feminizeinvolves removal of ine orinity; and so on. Here we take string to be no
2.2 Bound morphemes 47
more than a call to associative memory, something that will be matched by feminine, femininity, feminist, feminismand perhaps eveneffeminate. The string associated to this element may be "femin". We use the maximal common substring, but treat this as a hack, and certainly don’t want to elevate it to the status of a principle. Stems, in this sense, belong in thenaivetheory of grammar, see2.5.
It is the meaning marked by this string, or more precisely, the meaning common to all words that are reached by the associative call, that is relevant for the use of the entry, as it is this meaning that must be used in linking the semantics of the derived word to the semantics of the stem or root. This linking, which we treat as a rule of lexical redundancy, rather than a generative rule, is imperfect, not so much because of the under- and -overapplication issues discussed above, but rather because the semantics computed along these lines is itself incomplete. Considereditorialize. In ordinary use, e.g[T]his newspaper has editorialized about the disturbing achievement gaps between boys and girlsit is true that the meaning includes ‘the newspaper made (the disturbing gaps) the subject of an editorial’, but there is a lot more to this. On the grammatical side, the use ofaboutis clearly necessary, something that will have to be made part of the full lexical entry of the wordeditorialize(see 2.4). But even more important, the meaning has shifted to ‘use the editorial format as a means to publicly address an issue’.
This phenomenon,lexicalization, is the main driver of non-compositionality. Once a word enters the lexicon (permanent, community-wide repository of words), it can accrue meanings that go beyond the compositional meaning. This is evident for accrual of en-cyclopedic knowledge:cook/2152is not just a person who makes food in a professional manner, but also someone we picture as wearing achef’s uniform, complete with atoque blanche.
Paul Kiparsky (pc) calls attention to P. 3.2.135a¯a kves tacch¯ılataddharmatatsa¯adhu-ka¯ari˙su which defines a class of agent nouns as denoting “habitual, professional, or skilled” actors. This would apply well for many agent nominals, not just those derived by zero-affixation as incook/2130Ñcook/2152or by the even more productive-er/3627 (see2.1), and the less productive, but semantically more transparent-ist. In6.4we will discuss how these can be compressed in a two-way disjunction betweenperson and professional.
Since both grammatical and extragrammatical information can accrue, it should be no surprise that lexical information does too. This is particularly clear in the case of compound words: afoursquarebuilding is not just one that has four squares, but rather one that ‘has a solid appearance’, a foursquare position is ‘unyielding, firm’.
There is simply no way to derive the ‘solid and strong’ (Collins) or ‘frank, forthright, blunt’ (Webster) aspects either fromfouror fromsquare. There may be some plausible story about how solid buildings gave rise to this meaning, but it is not even true that square buildings are more solid than cylindrical or hexagonal ones (as English can use bastion as a descriptor of strength/firmness just as well), and such stories are at best post hocjustifications for the lexical fact. InS19:5.2,6.4we used the notion ofsubdirect composition to describe this phenomenon. Since this is the single most important
ele-48 2 From morphology to syntax
ment in any formulation of non-compositionality, be it formulaic (1.3), geometric (1.4), or algebraic (1.5), we will spend some time illustrating it from different standpoints. We will stay with binary operations, since, as argued in (Kornai,2012) in detail, we never need to use ternary and higher arity operations.
(a) Direct product (b) Subdirect product
Fig. 2.1: Direct and subdirect products of the same two intervalsr0,12sandr0,8s
Given algebraic structuresS1 andS2, we form theirdirect productS “S1ˆS2by taking the base set to be the Cartesian product of the base sets of theSiand performing operations coordinatewise. WhenS1 is the intervalr0,12sandS2 is the intervalr0,8s, the result is the rectangleSshown in blue in panel (a) of Fig.2.1. Thesubdirect product is a subalgebraS1of the direct productSthat spans all coordinates, i.e. a subsetS1ĂS that is closed under the operations and satisfiesπipS1q “Sifori“1,2, whereπiis the i-thprojection(a mapping that discards all coordinates other than thei-th). An example is shown in panel (b).
When the elements of the structures are formulas f and g, their direct product is simply their conjunctionf,g. When they are polytopes in n-space, their direct product is their intersection. When they are hypergraphs, their direct product is their unification.
Subdirect products are, by their very nature, underdefined: a typical subdirect product of formulasfandgmay bef,g,h, wherehexpresses the additional non-compositional content accrued in the process of lexicalization.
What needs to be emphasized here is that ‘compositional’ versus ‘non-compositional’
is not a simple yes/no distinction, but rather a matter of degree: for the compositional case the contribution of h is negligible (either not there to begin with, or just irrel-evant from the perspective of syntax, semantics, or both), whereas in the truly non-compositional caseshnarrows the definition substantively. Recall Frege’s definition of compositionality (S19:1.1):
The meaning of a complex expression is determined by its structure and the meanings of its constituents.