This thesis takes as its starting point proposals to model inflectional paradigms as geometrical structures, wherein systematic homonymies are constrained to occupy contiguous regions. It defines a precise criterion for assessing systematicity and shows, for a range of largely Indo-European and Afro-Asiatic data, that such models are observationally adequate in modelling systematic homonymies within a single inflectional dimension, and to a lesser extent, between different inflectional dimensions. This is taken to indicate that widely assumed characterizations of inflectional categories in terms of cross-classifying binary features are incorrect, inasmuch as such characterizations fail to predict the linearizability of natural classes of properties belonging to those categories. The same inadequacy besets attempts to account for systematic homonymies by means of rules that convert or 'refer' one morpho-syntactic representation to another. Rather it is argued that the linearizability of natural classes of properties suggests that inflectional categories are structured as a sub-classification of those properties, but that a phenomenon of 're-marking' serves to define, under strict constraints, additional natural classes beyond those defined by the sub-classification itself. The specific sub- classifications indicated by observed patterns of homonymy are language-specific. In addition, the properties so sub-classified under a single node may in certain cases be drawn from separate morpho-syntactic categories. This is taken to indicate that the terminal nodes of a morphological sub-classification are not morpho-syntactic feature complexes but purely morphological functions performing a discontinuous mapping between morpho-syntactic and morpho-phonological representations. The systematicity of homonymy patterns, then, is shown to be evidence for a linguistic level of 'pure morphology'.

This thesis takes as its starting point proposals to model inflectional paradigms as geometrical structures, wherein systematic homonymies are constrained to occupy contiguous regions. It defines a precise criterion for assessing systematicity and shows, for a range of largely Indo-European and Afro-Asiatic data, that such models are observationally adequate in modelling systematic homonymies within a single inflectional dimension, and to a lesser extent, between different inflectional dimensions. This is taken to indicate that widely assumed characterizations of inflectional categories in terms of cross-classifying binary features are incorrect, inasmuch as such characterizations fail to predict the linearizability of natural classes of properties belonging to those categories. The same inadequacy besets attempts to account for systematic homonymies by means of rules that convert or 'refer' one morpho-syntactic representation to another. Rather it is argued that the linearizability of natural classes of properties suggests that inflectional categories are structured as a sub-classification of those properties, but that a phenomenon of 're-marking' serves to define, under strict constraints, additional natural classes beyond those defined by the sub-classification itself. The specific sub- classifications indicated by observed patterns of homonymy are language-specific. In addition, the properties so sub-classified under a single node may in certain cases be drawn from separate morpho-syntactic categories. This is taken to indicate that the terminal nodes of a morphological sub-classification are not morpho-syntactic feature complexes but purely morphological functions performing a discontinuous mapping between morpho-syntactic and morpho-phonological representations. The systematicity of homonymy patterns, then, is shown to be evidence for a linguistic level of 'pure morphology'.