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What do the terms "exponent" and "formative" mean in linguistics?

I've seen the term "exponent" used in linguistics texts, and found a definition at Wikipedia. "An exponent is a phonological manifestation of a morphosyntactic property. In non-technical language, it is the expression of one or more grammatical properties by sound."

The article goes on to give examples of the different types of exponents:

"Identity (e.g. deer + PLURAL = deer)
Affixation (e.g. look + PAST = looked)
Internal Modification (e.g. sing + past = sang)
Reduplication (e.g. toó ‘man’ totóo ‘people’ (from Pangasinin, cited in WALS)"

But the article cites no references or sources, I have been unable to find authoritative references and sources elsewhere, and I have been unable to find a definition of linguistic "formatives" and how they are related to linguistic exponents.

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    Could you provide some context for 'formative'? – robert Aug 5 '13 at 9:14
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It depends on your theory of morphology.

Laurie Bauer uses the term "formative" to describe "a recurrent element of form which correlates with derivational behaviour in some way and yet cannot be identified with a morph" (Bauer 2003: 330).

However, as he himself admits, this is an untraditional use and usually the term "formative" is equivalent to a morph or a morpheme.

When I hear/see the words "exponent" (or "exponence"), the first name that comes to my mind is of Peter Matthews. Here's how he defines an exponent. "If x marks y, x is defined as an exponent of y." Thus, under his proposal, a formative could be an exponent of some morphosyntactic property. E.g. formative "s" could be a plural exponent.

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This should really be a comment to Alex B's answer, but the system won't let me comment yet...

It's true that the meaning of "formative" or "exponent" depends on your theory of morphology. But in practice, the most widespread reason why people use these terms is to try to avoid theories of morphology — and especially to avoid the controversial and hopelessly theoretically loaded terms "morph" and "morpheme".

Most people tend to use "formative" for any chunk of phonology that recurs across several words with a consistent behaviour (usually a sequence of one or more segments, though some people are more liberal about what counts) — as in Bauer's definition, except (crucially) remaining agnostic over whether it's a morph or not (rather than, like Bauer, insisting it can't be). It gives you a way to talk about things like the re- and -fer of English refer, without claiming that they do or don't mean anything and without getting into an argument (like Aronoff 1976 did) over whether they deserve to be called "morphemes". Or to talk neutrally about things like the theme vowels in a verb conjugation, or the apparent genitive suffixes that appear between the halves of many German compounds. Or to talk about anything without taking a stand on whether it's an independent word or a stem or an affix or a clitic or whatever.

People don't use "exponent" quite as consistently, but it tends to be the flip side of "formative": talking about the phonological realizations of a meaning or of a morphosyntactic feature, while not taking a stand on what the phonological realization has to be like. Maybe it's a string of segments (a formative), but maybe it's just a single phonological feature, or a shift in the position of stress, or nothing at all (people talk about "zero exponents", while talking about "zero formatives" would be weird), or maybe it's even deleting something from the phonological representation. Maybe this particular phonological representation for the feature [past] recurs consistently across verbs, or maybe it occurs in just this one verb — doesn't matter, we can still just call it an "exponent".

To oversimplify: "Formative" talks about form with minimal assumptions about meaning. "Exponent" talks about (the form of) meanings with minimal assumptions about form.

Except for all the linguists who use the terms differently. :-)

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    Actually, I don't see why the information in your post could not be considered an answer. – James Grossmann Aug 18 '13 at 1:23
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from A Dictionary of Linguistics and Phonetics by David Christal:

exponence (n.) A concept in a hierarchical linguistic analysis, referring to the relationship of correspondence between linguistic units at a higher level of analysis and units at a lower level. For example, words can be said to have phonological units (such as phonemes) as their exponents, and the exponents of the latter are phonetic features. The term representation is equivalent. In this sense, abstract units are expounded by other abstract units or by physical units. An alternative emphasis restricts the application of the term to the physical expression of any abstract unit (i.e. at any level), e.g. a morph being the exponent of a morpheme, a phone of a phoneme, a particular formative (such as -s) of a syntactic category (such as ‘plural’), the item going of the lexeme go. There are plainly many possible types of exponence relationships (e.g. to handle the ‘fusion’ or ‘overlapping’ of exponents). This sense of the term receives a specific technical status in Hallidayan linguistic theory (see systemic grammar), referring to one of the scales of analysis which interrelates the categories of the theory, viz. the relationship postulated between these categories and the raw data. For example, the lexical item table is an instance of (an ‘exponent’ of) the class of nouns. Other scales in this approach are labelled rank and delicacy.

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