On the mathematical foundations of crash-proof grammars
-
Tommi Tsz-Cheung Leung
Abstract
This paper looks at how the particular computational mechanism of Crash-Proof Syntax (CPS) (Frampton & Gutmann 1999, 2002) as an instantiation of the Minimalist Program (Chomsky 1995) can be understood from the point of view of mathematical foundation that captured the spotlight among mathematicians during the nineteenth century. I claim that CPS can be analyzed as an analogy with Classical Peano’s Axioms that generate the theory of natural numbers. Instead of its computational efficiency, CPS is driven by the economization of axioms of formal systems. Further comparisons between syntax and natural numbers reveal that the central tenets of CPS can be defined mathematically on one hand, and highlight the significance of the ‘third factor’ as the design feature of language (Chomsky 2005) on the other hand.
Abstract
This paper looks at how the particular computational mechanism of Crash-Proof Syntax (CPS) (Frampton & Gutmann 1999, 2002) as an instantiation of the Minimalist Program (Chomsky 1995) can be understood from the point of view of mathematical foundation that captured the spotlight among mathematicians during the nineteenth century. I claim that CPS can be analyzed as an analogy with Classical Peano’s Axioms that generate the theory of natural numbers. Instead of its computational efficiency, CPS is driven by the economization of axioms of formal systems. Further comparisons between syntax and natural numbers reveal that the central tenets of CPS can be defined mathematically on one hand, and highlight the significance of the ‘third factor’ as the design feature of language (Chomsky 2005) on the other hand.
Chapters in this book
- Prelim pages i
- Table of contents v
- Preface & Acknowledgments ix
- List of contributors xi
- Exploring crash-proof grammars 1
-
Part I Applications of crash-proof grammar
- Computation efficiency and feature inheritance in crash-proof syntax 15
- Implications of grammatical gender for the theory of uninterpretable features 31
- The Empty Left Edge Condition 59
-
Part II The crash-proof debate
- Grammaticality, interfaces, and UG 89
- A tale of two minimalisms 105
- Uninterpretable features 125
- Syntactic relations in Survive-minimalism 143
- Toward a strongly derivational syntax 167
- On the mathematical foundations of crash-proof grammars 213
- Crash-proof syntax and filters 245
- Crash-free syntax and crash phenomena in model-theoretic grammar 269
- Index 299
Chapters in this book
- Prelim pages i
- Table of contents v
- Preface & Acknowledgments ix
- List of contributors xi
- Exploring crash-proof grammars 1
-
Part I Applications of crash-proof grammar
- Computation efficiency and feature inheritance in crash-proof syntax 15
- Implications of grammatical gender for the theory of uninterpretable features 31
- The Empty Left Edge Condition 59
-
Part II The crash-proof debate
- Grammaticality, interfaces, and UG 89
- A tale of two minimalisms 105
- Uninterpretable features 125
- Syntactic relations in Survive-minimalism 143
- Toward a strongly derivational syntax 167
- On the mathematical foundations of crash-proof grammars 213
- Crash-proof syntax and filters 245
- Crash-free syntax and crash phenomena in model-theoretic grammar 269
- Index 299
