Defining productivity: Qualitative approaches
The following account of the notion of productivity is partly based on the useful summary presented by Rainer (1987), but also includes more recent approaches such as van Marie (1985, 1986), Corbin (1987), Baayen (1989, 1991,1992), Baayen and Lieber (1991), Baayen and Renouf (1996).

Two major questions will play a role, the first being whether productivity is a quantitative or a qualitative notion, the second whether productivity is a derived property of morphological rules or not. If productivity is of a qualitative nature, a process or affix could be said to either have this property or not. However, it has frequently been argued that productivity is a gradual phenomenon, which means that morphological processes are either more or less productive than others, and that completely unproductive or fully productive processes only mark the end-points of a scale.¹ I will lay out the qualitative concept of productivity. We will turn to approaches that have attempted to devise quantitative measures of productivity.

The second important problem is whether productivity is a theoretical primitive, i.e. a non-derivable property of word formation rules, or an epiphenomenon, i.e. a property that results from other mechanisms. It is clear, for example, that the productivity of a rule is never unrestricted in the sense that any given word may serve as its base. In particular, there can be phonological, morphological, syntactic, and semantic conditions on possible bases, or on the derivatives themselves, which limit the productivity of the process. In view of such structural restrictions, Paul (1896:704) already pointed out that it is crucial to determine the limits within which affixes are productive.² This type of reasoning has led to the frequently uttered postulate that "The degree of productivity of a WF-rule [word formation rule, I.P.] can be seen as inversely proportional to the amount of competence restrictions on that WF-rule" (Booij 1977:5). Ac cording to this position, one would only have to define the word formation rule with its proper restrictions and the degree of productivity would naturally fall out.

Definitions of productivity can be found in any standard morphology textbook. Bauer, for example, says that a word formation process is productive "if it can be used synchronically in the production of new forms" (Bauer 1983:18). Spencer considers a rule productive if it is "regularly and actively used in the creation of totally new words" (Spencer 1991:49).³ These more recent definitions can be regarded as reflections of a more sophisticated one proposed earlier by Schultink (1961). Since Schultink's definition incorporates important aspects of the problem and has become something like the classic definition, it will also be used here as a reference point for our discussion. Schultink writes:

Onder produktiviteit als morfologisch fenomeen verstaan we dan de voor taalgebruikers bestaande mogelijkheid door middel van het mor fologisch procédé dat aan de vorm-betekeniscorrespondentie van som mige hun bekende woorden ten grondslag ligt, onopzettelijk een in principe niet telbaar aantal nieuwe formaties te vormen.
(Schultink 1961:113, footnote omitted)

[Productivity as morphological phenomenon is the possibility which language users have to form an in principle uncountable number of new words unintentionally, by means of a morphological process which is the basis of the form-meaning correspondence of some words they know.]
(Translation by Booij 1977:4)

Schultink's definition captures the important insight that the vocabulary of a language can be expanded in a regular fashion on the basis of already existing lexical elements, but is problematic in several respects. Since these problems are inherent in many qualitative and quantitative definitions of productivity, it is worthwhile discussing them in more detail.

¹ Botha (1968:138) lists the numerous qualifying terms linguists have used to refer to the different degrees of productivity, such as "quasi-", "marginally", "semi-", "fully", "most", "quite", "immensely", and "very productive". As we will see below, the theoretical status as well as the practical utility of these labels for the linguist is doubtful.
² Speaking about suffixes Paul remarks "Es kommt also darauf an, festzustellen, innerhalb welcher Grenzen das Suffix produktiv ist" (Paul 1896:704).
³ See also Adams (1973:197), who uses "the epithet 'productive' to describe a pattern, meaning that when occasion demands, the pattern may be used as a model for new items."