- Text
- Mathematics,
- Cognitive,
- Cultural,
- Wildgen,
- Grammar,
- Mathematical,
- Languages,
- Chomsky,
- Thom,
- Linguistic

mathematics

Descriptive mathematical grammars (Harris) For Zellig Harris language phenomena contain already features like discrete, linear organization, combinational power, and restrictions of this power, which ask for a mathematical treatment. As grammar was for Harris primarily concerned with forms (phonological, morphological, syntactic, and textual), their contexts and the operations of replacement and transformation of linear order, algebra was the best choice as basic tool in “mathematical linguistics”. Similar to Bloomfield (under the impact of behaviourist psychology) he considered meaning as not accessible to scientific methods and as a consequence a formal treatment of meaning seemed to be devoid of scientific interest. Chomsky has at least partially followed this formalist tradition, insofar as a semantic interpretation is only attached to the basic syntactic device. 6

The “morphological turn” by René Thom The epistemological background of René Thom is Poincaré’s philosophy of sciences and **mathematics** and his idea of qualitative analysis. analysis. This idea had come-up come up when it became obvious that one may write down differential equations capturing the dynamics of a large system (the universe; cf. Laplace’s formula of the world), but that it is normally not possible to solve a system of such equations with spatial and temporal dynamics. One can, however, specify major characteristics of these systems such as the type of singularities which show-up. show up. Under special conditions one may find attractors, i.e., stable states to which many process lines converge. This led to theories about structural stability. stability. Many basic systems, cf. the damped pendulum may be reduced to rather simple gradient dynamics with a point-attractor. point attractor. 7

- Page 1 and 2: Wolfgang Wildgen Mathematics and gr
- Page 3 and 4: Mathematics and grammar in the hist
- Page 5: Philosophically motivated models Ch
- Page 9 and 10: The catastrophe controversy The mor
- Page 11 and 12: Morphogenetic patterns in language
- Page 13 and 14: Composition is therefore in princip
- Page 15 and 16: Are there formal universals underly
- Page 17 and 18: Chomsky comparable with Thom In Cho
- Page 19 and 20: Language contains (implicitly) math
- Page 21 and 22: The mythical semantics are rather f
- Page 23 and 24: The phase of „pure meaning“ mea
- Page 25 and 26: 3. Mathematics (as languages) has t
- Page 27 and 28: Major differences of functionality
- Page 29 and 30: Mathematics Selection of technologi
- Page 31 and 32: 2. Both are culturally relative, bu
- Page 33 and 34: Some publications of the author Wil
- Page 35: Montague, R. (1970). « Universal G