2013년 제 5차 콜로퀴엄, Robert P. Malouf(San Diego State University)
2013년 제 5차 콜로퀴엄
- 발표자: Robert P. Malouf(San Diego State University)
- 제 목: The Low Entropy Conjecture
- 일 시: 2013. 8.14.(수) 오후 4시~
- 장 소: 8동 301호(두산인문관 3층 대형강의실)
- 초 록:
Cross-linguistically, inflectional morphology exhibits spectacular complexity in both the structure of individual words and the organization of systems that words participate in. One approach to understanding the evident variety of this syntagmatic and pardigmatic complexity is to develop taxonomies of the attested strategies for organizing words and paradigms. In classical paradigm-based models of morphology, a morphological system is represented via two distinct components: a set of exemplary full paradigms that exhibit the inflectional classes of a language, and sets of diagnostic principal parts which can be used to deduce which inflectional class a given lexeme belongs to. Given the right wordforms of a novel lexeme, such models provide a general strategy for filling in the rest of the paradigm that exploits the implicational structure of inflectional systems in a way that can be quite effective. Paradigm-based models also provide measure of morphological complexity: languages with a greater number of possible exponents, inflectional classes, and principal parts will require more wordforms to be memorized by the language user (and recorded by the lexicographer). However, from the point of view of the fluent language user, this is an artificial measure of complexity. Speakers of morphologically complex languages do often have to produce wordforms that they have never heard before, but they rarely have to predict all forms of a given lexeme. On the contrary, speakers must produce some subset of the complete paradigm of a lexeme given knowledge of some other subset, a task which often will not require completely resolving a lexeme’s inflectional class membership.
In this talk we will discuss the consequences of an alternative approach to morphological complexity which directly quantifies the difficulty that a system poses for language users (rather than lexicographers) using the information theoretic notion of information entropy. The average entropy of a paradigm is the uncertainty in guessing the realization for a particular cell of the paradigm of a particular lexeme (given knowledge of the possible exponents). This gives one measure of the complexity of a morphological system — systems with more exponents and more inflection classes will in general have higher expected entropy — but it presupposes a problem that speakers will never encounter. In order to know that a lexeme exists, the speaker must have heard at least one wordform, so in the worst case a speaker will be faced with predicting a wordform based on knowledge of one other wordform of that lexeme. Thus our measure of morphological complexity is the average conditional entropy, the average uncertainty in guessing the realization of one randomly selected cell in the paradigm of a lexeme given the realization of one other randomly selected cell.
Viewed from this perspective, languages which appear to differ greatly in their morphological complexity — the number of exponents, inflectional classes, and principal parts — are actually quite similar in terms of the challenge they pose for a language user who already knows how the system works. Our conjecture is that all morphological systems are (in fact, must be) simple enough for speakers to use, and that this simplicity is reflected by their low average conditional entropy. This leads to our possibly provocative conclusion: in addition to focusing on morphological complexity, we should be looking at morphological simplicity. That is, as a complement to cataloging the ways in which morphological systems can be baroque and (apparently) dysfunctional, we must explore the multitude of ways that languages have shaped this complexity to meet the communicative needs of language users.