Rules and analogies
The most problematic point concerning current qualitative definitions of productivity is probably the notion of word formation rule itself, dubbed by Schultink as "a morphological process which is the basis of the form-meaning correspondence of some words they know" (1961:113, see above). The crucial question is on which grounds one can assume the existence of such a morphological process. It seems that Schultink's definition is very liberal because it includes both rule-based and analogical formations, which, in standard generative treatments are considered to be two different things. Thus, form-meaning correspondences of individual items are the basis for all kinds of ad-hoc analogies, although one would not want to consider such processes productive. What Schultink probably means is not just any kind of analogical formation but a regular, predictable process which operates in a non-arbitrary manner on a more or less well-defined set of possible input words.

Let us consider the difference between rules and analogies in more detail, a difference that is not always obvious. For example Becker (1990) has argued for the extension of the notion of analogy even to productive proc esses by largely equating the notion of rule with the notion of analogy. In my view this has the considerable disadvantage that it is left unexplained why some analogies are never made, but others are frequently observed.¹
 

Becker acknowledges the existence of this problem, but claims that the only difference between analogies and rules is their productivity. Having stated that it is generally and correctly assumed that analogy works on the basis of existing words, Becker (1993a:189-191) argues that it cannot be correct that existing words play only a role as a model for analogy when they are few, but play no role at all when they are many, as is the case with highly productive rules. Rules must be acquired on the basis of existing words, and are therefore best seen as the "trivial default case of analogical formations" (1993a: 190, my translation). According to this view, the only remaining difference between the traditional generative word formation rule and analogy would then be a quantitative difference: rules yield more forms than analogies. Becker therefore argues for the equation of rules and analogy, which makes the notion of rule redundant because everything can be taken care of by the proportional formula of analogy (see also Becker 1993b).

Although this argumentation for a purely gradual notion of productivity and the elimination of the concept of rule may be attractive because it would considerably streamline morphological theory, it has a number of pitfalls that lead me to reject a purely analogical model of morphology.

The first pitfall concerns the notion of rule, as used by Becker and by the generative morphologists he attacks. It is crucial to distinguish two entirely different senses of the word rule. One is more or less synonymous with regularity and expresses a descriptive generalization. The other sense of rule, and this is the sense standardly used in generative studies, is roughly equivalent to a procedural operation, technically known as a re-write rule. With respect to morphology, rule-based models assume that new words are formed by carrying out a certain manipulation on a given input, yielding a certain, more or less well-specified output. It is this concept of 'rule' as a procedural or derivational device Becker's critique aims at.

However, throughout their history, such procedural-derivational models have been criticized on empirical and theoretical grounds, and recent developments in phonology, morphology, and syntax have shown that representational or declarative models have a number of important advantages over traditional derivational ones. Such models do not transform underlying input strings into surface representations by subjecting them to an ordered set of manipulating procedures (as, for example, in SPE), but make crucial use of representations and conditions that constrain the form of such representations. Examples of the latter models are Optimality Theory in phonology and morphology (Prince and Smolensky 1993), and unification-based phonological and syntactic theories, such as Declarative Phonology (Coleman 1998), Head-Driven Phrase Structure Grammar (Pollard and Sag 1984, Pollard and Sag 1994), Lexical Functional Grammar (Kaplan and Bresnan 1982). In such frameworks, the idea of rule is that of a regularity, not of an operation. We will explore further the capacity of representational models for the description of morphological processes, and substantiate the superiority of output conditions over traditional derivational rules.

Coming back to analogy, I cannot see how such output constraints could be implemented in an analogical model, since they do not work on an item by-item basis, but entail significant generalizations across large numbers of forms. Once the concept of rule as an operation is abandoned, however, Becker's arguments have lost their target because the equation of rule and analogy is, if at all, only possible if rules are conceived as operations.²
 

The second serious drawback of the analogical model is that it fails to make strong predictions about possible and impossible forms. Acknowledging this fact, Becker is forced to make this vice into a virtue by claiming that morphologists cannot make correct predictions about the well-formedness of complex words anyway (1993a:190-191). In support of this claim he argues that acceptability judgments are the only way to tap the distinction between possible and impossible words and raises some well-known objections against such judgments as an analytical tool. In particular, he points out that acceptability is a gradual phenomenon, judgments are often variable across subjects, and even individual subjects are not consistent in their rejection or acceptance of forms. Furthermore, judgments are often dependent on the context or can be influenced by repetition. Although these are interesting considerations, recent work on this methodological issue has convincingly shown that these methodological difficulties can be overcome by a careful planning of the experimental design (see, for example, Bard et al. 1996, Schütze 1996, Cowart 1997).³ Furthermore, predictions about the well-formedness can not only be gleaned from ac ceptability judgments but also from a careful investigation of the regularities of attested formations. Thus even without acceptability judgments one can arrive at rather precise predictions about possible and impossible words, provided that one has discovered the correct regularities and restrictions of the process under discussion.

The third problem with Becker's argumentation is that he obviously assumes that his analogical model is incompatible with generative morphology. I don't see why this should be the case. It is of course true that traditional generative approaches have said very little about analogical formations, but the reason for this lies primarily in the unpredictability of analogy, and not in the denial of their status as morphological formations or in the general impossibility of incorporating analogy into the generative enterprise, as Becker implies. In my view, any competence theory of word formation must certainly include some account of analogical formations, and I don't see any principled argument that would prohibit analyses of the kind Becker proposes for certain paradigmatically motivated processes from being included into such models. This does not mean, however, that the whole model must be analogical in nature.

Finally, there is also psycholinguistic evidence against purely analogical models. Skousen (1989, 1992, 1995), Chandler (1993), and Derwing and Skousen (1989,1994) have presented an analogical single-system approach to morphology in the same spirit as that of Becker (1990). With respect to regular English past tense formation, for example, they argue that speakers add -ed to nonce words not on the basis of a rule but on the basis of an online analogical mechanism. However, recent psycholinguistic studies of regular and irregular inflection such as Marcus et al. (1995) and Jaeger et al. (1996) have presented strong evidence against "single-system theories [such as Skousen's, I.P.] which hypothesize that both regular and irregular past tense forms are computed by the same mechanism" (Jaeger et al. 1996:488). Although it is not quite clear in detail how these results carry over to derivational formations, they nevertheless seriously weaken the analogical case, especially since the analogical model claims that both derivation and inflection are handled by the same mechanism.⁴

I therefore maintain that analogical formations should be distinguished from instantiations of productive word formation rules. I will show that analogical formations nevertheless play a role in certain areas of morphology. Analogical relationships are necessarily paradigmatic in nature, whereas the functioning of word formation rules must often be described as essentially syntagmatic in nature.⁵ This will become evident later, where it is argued that the meaning of the derivative depends on the interaction of the meaning of the base with the templatic meaning of -ize derivatives. This interaction is syntagmatic and not paradigmatic in nature.

The postulation of a word formation rule is ultimately an empirical problem which can only be solved by finding evidence for regular form-meaning correspondences across a reasonably large set of complex words. But even if we have found significant generalizations that give evidence of the existence of a word formation rule, this does not yet tell us anything about the possibility to form new words on the basis of this rule or condition. Thus, in the case of the verbalizing suffix -en the semantic and phonological regularities among the words with this suffix are certainly sufficient to postulate a word formation rule. The meaning of -en derivatives is sufficiently uniform ('make X'), and the morphosyntactic restrictions on possible bases are also quite clear (-en attaches to monosyllabic adjectives that end in an obstruent, especially /t/ and /d/, cf. e.g. Marchand 1969:72, Halle 1973:13). However, this rule is generally regarded as unproductive in modern English (see e.g. Szymanek 1980:416). The nominalizing suffix -th is also a case in point. Although there are clear correspondences between meaning and form, the rules are unproductive (cf. e.g. deep - depth, but steep - *stepth). Such generalizations across existing words are generally referred to as 'redundancy rules' (Jackendoff 1975, Aronoff 1976) or 'via rules' (Vennemann 1972), whose function is to relate morphologically complex words in the lexicon to words with a similar morphological/phonological make-up.⁶

Another, more problematic, example of a redundancy rule is the above-mentioned verb-forming prefix eN-. It is generally assumed that this prefix is no longer productive in 20th century English, but the OED records six new formations in this period. Is there a word formation rule for eN- prefixation, and is it really unproductive? A reasonable answer to this question would be that there is such a (redundancy) rule, and that the small number of neologisms indicates that these are analogical formations, especially since there seem to be no severe structural restrictions that would limit the number of forms that could undergo eN- prefixation, so that one would expect to find many more new derivatives. For instance, the productive verbalizing suffix -ize leads to more than 300 20th century neologisms in the OED. Discussing such quantitative findings takes us to the second set of major approaches to productivity, probabilistic ones.

Before we turn to a discussion of these let us briefly summarize our remarks on productivity as a qualitative notion. Having scrutinized the different criteria put forward in standard definitions of productivity, it can be stated that this notion boils down to the property of a given word formation process or affix to be used to derive a new word in a systematic fashion. Attempts to further qualify this potential by positing criteria like uncountability or unintentionality have turned out to be misguided. Furthermore, the equation of word formation rules with analogy was rejected and the distinction was introduced between redundancy rules and productive rules.

¹ See also Bauer (1993) for discussion.
² Note that I use the terms 'word formation rule' or 'morphological process' in a loose sense, i.e. without committing myself to a derivational or a representational interpretation, or to a specific notion of word formation rule (such as, for example, Aronoffs 1976). This is also the reason why lower-case letters are used.
³ For example, the fact that acceptability is a gradual phenomenon does not speak against the use of acceptability judgments as such. What is important is not absolute acceptance versus absolute rejection, but rather significant differences in the acceptance of forms. The view that there are no perfect, but only best candidate forms is one of the crucial insights of Optimality Theory. It seems that Becker puts up a strawman to argue against.
⁴ For a more detailed critique of Skousen's mathematical definition of analogy see Baayen (1995), who compares Skousen's model with general statistical techniques of data classification, thereby showing that purely analogical mechanisms make incorrect predictions.
⁵ Note that I am not making any claim about the psycholinguistic reality of the distinction between rule and analogy. For example, I can in principle imagine a speaker creating a new word in -ize by local analogy with an existing word with that suffix. But this does not imply that there is no word formation rule for -ize words, but only that it was not accessed in this particular instance.
Interestingly, in most cases the word will conform to the well-formedness conditions of -ize words, so that it is in fact hard to tell whether analogy or some other operation was going on. Only if well-formedness-conditions are violated and strong similarities to particular existing words can be detected is this an indication of the form being created by a psycholinguistic process of analogy. Recent studies of irregular vs. regular inflection (Marcus et al. 1995, Jaeger et al. 1996) have provided new strong evidence for the rule-as an-operation view for regular inflection. How far these results carry over to productive word formation remains to be seen.
⁶ Note that Aronoff (1976:31) reduces the scope of redundancy rules considerably by equating them with his notion of (by definition productive) Word Formation Rule.