From Rules of Grammar to Laws of Nature

Joachim Lambek
McGill University, Montreal, QC, Canada

Series: Languages and Linguistics
BISAC: MAT015000

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We look at questions debated by pre-Socratic philosophers, emphasize their linguistic motivation and point out attempted answers by modern physics. We pursue a mathematical treatment of the syntax and morphology of natural languages, investigate the foundations of mathematics and speculate about a quaternionic approach to special relativistic quantum mechanics. (Imprint: Novinka )

Abstract (pp. vii)

Introduction (pp. ix-xii)

I. The Mental Dictionary (pp.1-16)

Chapter 1. Kinship Terms pp.1-3

Chapter 2. Number Words pp.4-5

Chapter 3. Nouns pp.6-8

Chapter 4. Verbs pp.9-10

Chapter 5. Adjectives and Participles pp.11-12

Chapter 6. Adverbs and Prepositions pp.13-14

Chapter 7. Capulet Semantics pp.14-16

II. Verbal Inflections pp.17

Chapter 8. Mediterranean Conjugation pp.17-18

Chapter 9. Latin Conjugation pp.19

Chapter 10. Turkish Conjugation pp.20-21

Chapter 11. Hebrew Conjugation pp.22-24

Part III. From Word to Sentence pp.25

Chapter 12. Production Grammars pp.25-27

Chapter 13. Anaphora pp.28-30

Chapter 14. Syntactic Calculus pp.31-33

Chapter 15. Pregroup Grammars pp.34-35

Chapter 16. Multiple Pregroups pp.36-38

Part IV. Mathematical Background pp.39

Chapter 17. Arithmetic versus Geometry pp.39-40

Chapter 18. Algebraic Preliminaries pp.41

Chapter 19. Quaternions pp.42-44

Chapter 20. Infinitesimals pp.45-46

Chapter 21. What is a Calculation? pp.47-52

Part V. Speculations about Six Dimensions pp.53

Chapter 22. Classifying Fundamental Particles pp.53-55

Chapter 23. The Lorentz Category pp.56-57

Chapter 24. Six-Dimensional Special Relativity pp.58-59

Chapter 25. Six-Dimensional Relativistic Quantum Mechanics pp.60-61

Chapter 26. The Spread of Time pp.62-64

Part VI. Foundations of Mathematics (with Phil Scott) pp.65

Chapter 27. Philosophy of Mathematics pp.65-66

Chapter 28. Godel’s Argument Re-Examined pp.67-68

Chapter 29. Constructive Nominalism pp.69-72

Epilogue pp.73-74

Acknowledgements pp.75-76

References pp.77-96

Index pp.97-104

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