ABSTRACT
Since the term "invariance" seems to mean different things to different people, we need a way of discussing the problem that allows for a variety of types of invariance. It seems to me that geometry already has evolved a very useful framework for this purpose that can easily be adapted to the study of speech and language. In this formulation, invariance is defined in terms of specific transformations. This approach makes it possible to specify many abstract properties of an object—in particular, the ones that make it a linguistic-phonetic object—without necessity to describe the properties of the object that differentiate it from others in its space. After presenting this framework, several of the most fully developed theories of the phonetic space will be recast in terms of this descriptive scheme. The final goal will be to present a brief account of a new phonetic theory that will attempt to explain many properties of the phonetic space. This theory will be directly justified in terms of the invariance framework. It will be argued that the phonetic space must have certain properties of invariance in order for phonetic objects to play their role in the communicative function of language.
