On The Principles of Mathematical Linguistics By, Miguel A. Sanchez-Rey Abstract The aim of the article is comple te rev isi on of the met hod s and usage of the mathematics in linguist ic theory . Revisi on that takes into princip le strict and precis e adher ence to mathe matical forma lism and empiricis m. Such formalism means more novelty than the conv entio nal use of stand ard metho ds in linguistic s that has been persist ent in the last half- century. Stress ing formal and Boolean logi c, numb er theory, p. d. e.' s, geomet ri c, and topologi cal appl icat ions in dyna mical systems to the structur e and nature of the langu age acquisiti on devic e, internal and external merge, the unraveling of the neural cellular rules that lead to langu age acquisitio n, and the reso lution of D.A.R.P.A.' s first grand mathe matica l challe nge stating a formulaic express ion, as an experimen tal conje cture , of the human cognitive organ. The resolution of D.A.R.P.A's problem implies three natural laws that are a resu lt of this bio log ica l sys tem, and as a con seq uen ce to breaking symmetr y. It's resol ution , as will be explained , solve s the five fund ament al prob lems of Bio- linguistics and an unraveling of the Minimalist Program. July 15th, 2010 Keywords: Minimalism, Bio-linguistics, Bio-Physics, Cognitive Science, Neuroscience, Bare Phrase Structure, Interfaces, I-language, Le xicon, Faculty of Language, Language of Thought, Language Acquisition Device, Universal Grammar, Mind/Brain, Module, Computational Device, Cognitive Organ, Architec ture, Internal Merge, External Merge, Numeration, Recursion, Headedness, Externalization, Inclusiveness Condition, Last Resort, Reductionism, Neural System, Binary Switches, Parametric Settings, Genotype, Phenotype, Epigenetics, Developmental Constraints, Natural Selection, Symmetry Breaking, Natural Law, Differential Topology, Algebraic Topology, Differential Geometry, Dynamical Systems, Non-Linear Dynamics, Number Theory, Homology, Julia set, Fatou set, Mandelbrot set, Frac tals, Simplexes, Observables, Lagrangian, Line Integral, Action Integral, Measure Space, Banach Space, Hilbert Space, Lie Groups, Bo olean Algebra 1
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8/12/2019 On the Principles of Mathematical Linguistics