Views
4 years ago

mathematics

mathematics

Two archetypes of

Two archetypes of „grammar „ grammar“ The grammar of Panini was considered an ideal of grammar writing by Bloomfield, the founding father of American linguistics, who had proposed an axiomatic system of grammatical terms in 1926 (A set of postulates for the Science of Language) and reviewed a book on Panini and Candra in 1929. Another more philosophical current was concerned by the logics underlying both our thinking and our language. Based on Aristotelian and Renaissance thinkers the “Grammaire “ Grammaire générale et raisonnée” raisonnée” (A General and Rational Grammar) of Port Royal (cf. Arnauld and Lancelot, 1660) developed the idea that basic logical schemata underlie human rationality. rationality 4

Philosophically motivated models Chomsky (1966) sees these authors as the precursors of his own “rational” grammar. The aspect of thinking is however reduced by Chomsky to hierarchical patterns (phrase structures) and transformations based on the intuition of the speaker about grammaticality and synonymy / ambiguity. Other followers of a rational grammar were the models proposed by Montague (1970), and Barwise &Perry (1983). The program they followed may be referred to philosophical trends in the Vienna Vienna circle, e.g., to Carnap’s “Logische Logische Syntax” (1934); i.e. they start from advanced logical calculi (e.g. intensional logics). The family of “cognitive semantics” proposed by Fillmore, Langacker, Langacker, Lakoff and Talmy link cognitive capacities (perception, motor-control, motor control, memory, imagination) systematically with grammatical features. In contraposition to Chomsky, Chomsky, Lakoff dismisses formal languages (including logics) as tools of grammar grammar writing and starts from a kind of “natural logic” or from folk- theories of the mind. 5

Work package 6 - Case Study: Mathematics - Molto
MATHEMATICS CLUB - Trinity Grammar School
A-level Mathematics - Wakefield Grammar School Foundation
Teaching and Learning Mathematics in Multilingual Classrooms
MATHEMATICAL LOGIC QUARTERLY - CUNY
LATINO/A AND BLACK STUDENTS AND MATHEMATICS
Brochure (PDF) - Institute for Mathematics & Education - University ...
Work package 6 - Case Study: Mathematics - Molto
Mathematical Notions and Terminology - Hampden-Sydney College
article in Mathematics Teaching in the Middle School
High-level languages - Mathematics and Computer Science
to Download Complete Issue - Eurasia Journal of Mathematics ...
Mathematics Newsletter - Department of Mathematics - North ...
Vedic Mathematics - Department of Mathematics and Computer ...
Headstart's High Five Mathematize
The Moment of Proof: Mathematical Epiphanies
Institute of Mathematical Statistics
Download - NIE Mathematics & Mathematics Education
Download - NIE Mathematics & Mathematics Education
Roadmap: Applied Mathematics - Computational Mathematics ...
Roadmap: Applied Mathematics - Computational Mathematics ...