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2 results

  • Chapter 1 - Interaction between Language and the Other Symbolic Forms

  • from Part I - Cassirer’s Philosophy of Culture
  • Edited by Simon Truwant, Katholieke Universiteit Leuven, Belgium
  • Book:
    Interpreting Cassirer
    Published online:
    17 April 2021
    Print publication:
    01 April 2021, pp 13-33

  • Summary

    This chapter explores the ways in which language is related to the other symbolic forms in Cassirer’s philosophy of culture. Like myth, religion, art, and science, language is a distinct symbolic form, yet at the same time it always appears in the context of other human activities. This means that whenever we talk about language as a symbolic form, we are forced to think of it relationally, in and through the different aspects of language that come into focus through the perspectives of the other forms. Leib distinguishes three constitutive functions of language: its sign function, its mediation between the “I” and the world, and its ability to encapsulate a “worldview” as a totality for consciousness. On the basis of these functions, he shows how language, as a medium for expression, reorganizes itself when aligning with myth, religion, art, science, and history. Ultimately, Leib argues that myth is an immanent possibility of language that remains active even in today’s “labile equilibrium” of culture.

  • On Characteristic Polynomials of Geometric Frobenius Associated to Drinfeld Modules

  • Liang-Chung Hsia, Jing Yu
  • Journal:
    Compositio Mathematica / Volume 122 / Issue 3 / July 2000
    Published online by Cambridge University Press:
    04 December 2007, pp. 261-280
    Print publication:
    July 2000
    • Article
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  • Let K be a function field over finite field ${\Bbb F}_q$ and let ${\Bbb A}$ be a ring consisting of elements of K regular away from a fixed place ∞ of K. Let φ be a Drinfeld ${\Bbb A}$-module defined over an ${\Bbb A}$-field L. In the case where L is a finite ${\Bbb A}$-field, we study the characteristic polynomial $P$φ(X) of the geometric Frobenius. A formula for the sign of the constant term of $P$φ(X) in terms of ‘leading coefficient’ of φ is given. General formula to determine signs of other coefficients of $P$φ(X) is also derived. In the case where L is a global ${\Bbb A}$-field of generic characteristic, we apply these formulae to compute the Dirichlet density of places where the Frobenius traces have the maximal possible degree permitted by the ‘Riemann hypothesis’.