Elements of Number Theory
D. Harbour, 2003
This dissertation argues for the necessity of a morphosemantic theory of number, that is, a theory of number serviceable both to semantics and morphology. The basis for this position, and the empircal core of the dissertation, is the relationship between semantically based noun classification and agreement in Kiowa, an indigenous, endangered language of Oklahoma.
The central claim is that Universal Grammar provides three number features, concerned with unithood, existence of homogenous subsets, and properties of those subsets.
The features are used to analyze a wide variety of data. Semantic topics include the difference between granular and non-granular mass nouns, collective, non-collective and distributive plurals, and cardinality. Syntactic topics include the structure of DP, noun marking, agreement and suppletion. Morphological topics include the inventory of morphological operations, the featural basis of complex syncretisms, the difference between agreement and suppletion, whether features are privative or binary, and the nature of the Kiowa/Tanoan inverse.
Thesis Supervisors: Morris Halle, Alec Marantz
Titles: Institute Professor, Professor of Linguistics
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Table of Contents
1 Framework 12
1.1 Aim: a morphosemantic theory of number 12
1.2 Core claim and overview 17
1.3 Framework 23
1.4 Overview of Kiowa structure 24
1.4.1 The people 25
1.4.2 The language 26
1.4.3 Orthography 32
2 Kiowa’s noun classes 35
2.1 Overview: meaning and features 35
2.2 Preliminaries 36
2.3 The noun classes 38
2.3.1 The SDP class 39
2.3.2 The SDI class 40
2.3.3 The IDP class 40
2.3.4 The IDS class 41
2.3.5 The IDI class 41
2.3.6 The SDS class 41
2.3.7 The PPP class 42
2.3.8 The SSS class 42
2.3.9 The SII class 46
2.4 Semantic coherence of the classes 49
2.4.1 The animate classes 51
2.4.2 Symmetric non-constant classes 56
2.4.3 Symmetric constant classes 59
2.4.4 The default classes 63
2.4.5 Summary 68
2.5 Against a tenth class 69
2.6 Phonological incoherence 72
2.6.1 Inverse allophones 73
2.6.2 Thematic nouns 75
2.6.3 Conclusion 78
3 Number features 79
3.1 Referential cardinality 83
3.1.1 Natural classes 83
3.1.2 Definitions 85
3.1.3 Summary 91
3.2 Class 92
3.2.1 Classification by [+/-singular], [+/-augmented] 92
3.2.2 ClassP and number on D 95
3.2.3 Further derivations I: Other classes 102
3.2.4 Further derivations II: Inverse marking 113
3.2.5 Summary 118
3.3 Mnemonic naturalness 119
3.4 Spurious S/P 122
3.4.1 The meaning of [+/-group] 123
3.4.2 The morphosyntax of [+/-group] 127
3.4.3 Summary 137
3.5 Mass nouns 138
3.5.1 Conjunction 140
3.6 Missing mneumonics 142
3.7 Conclusion 148
4 Agreement and suppletion 150
4.1 Suppletion 151
4.1.1 Number-sensitive predicates 152
4.1.2 Clarification 155
4.2 Analysis of the basic cases 160
4.2.1 Assumptions 160
4.2.2 Analysis 162
4.2.3 Summary 166
4.3 Inverse mismatches 166
4.3.1 Minus-valued classes 167
4.3.2 Plus-valued class 172
4.3.3 Summary 174
4.4 [+/-group]-induced mismatches 174
4.4.1 [+group], non-mass 174
4.4.2 [+group], mass 176
4.5 Harder cases 178
4.5.1 [-group], pluralia tantum 179
4.5.2 Reflexive-induced mismatches 183
4.6 Conclusion 188
4.7 Appendix: adverbs built on suppletive roots 189
5 The agreement prefix 195
5.1 Preliminaries 199
5.1.1 Prefixes 199
5.1.2 Theoretical assumptions 201
5.2 Reduction of explicanda 204
5.2.1 ‘any’ 204
5.2.2 More x deletion 206
5.2.3 3A deletion 208
5.3.4 Person deletion 208
5.3.5 More person deletion 209
5.3 Segmentation I: subregularities 213
5.4 Segmentation II: segments 223
5.4.1 Ditransitives 223
5.4.2 Transitives 231
5.4.3 Intransitives 237
5.5 Vocabulary items 238
6 Conclusions and consequences 239
6.1 Noun classification 239
6.1.1 Gender and declension class 240
6.1.2 Gender-number systems 243
6.2 On privativity 247
6.2.1 Presence~absence privativity 248
6.2.2 Plus~minus privativity 254
6.3 Parting comments 258
A. A Hunting Story 259