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______________________________________________________________________ The "Zeitschrift für
Semiotik"
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Dietrich Marsal Jorge Bogarin Cornelie Leopold Dietrich Marsal Pirmin Stekeler-Weithofer Wilhelm F. Niebel Hans G. Knapp Analysis Literary report Documentation: Christian Weyers In hindsight: Study Dietrich Marsal, University of Stuttgart Summary. The article introduces the reader to the following papers by discussing the question, "What is mathematics?", from different points of view. What is mathematics to the layman and what does the pure and the applied mathematician think about it? Does mathematics continue to be the science of numbers? Why does mathematics appear to be so difficult? Is the mathematician a monomaniac? Why do mathematicians often dislike the views of philosophers about mathematics? The reproach of physicists and engineers that mathematics is inadequate for them because of exaggerated exactness motivates various conceptions of mathematical rigor and suggests a distinction of the mathematics of the mathematician from the mathematics of the logician. Despite all such efforts, the question, "What is mathematics?", cannot be answered to complete satisfaction. Sign, number and being: semiotics as an ontologic theoretical foundation of mathematics Jorge Bogarin, University of Stuttgart Summary. It is not through the solution of special problems, but through the
clarification of the theoretical foundations that semiotics can contribute to mathematics.
It can provide a system of coordinates or a framework in which ontological implications
and questions about contexts of justification and new paradigms can be intelligibly
discussed. The present paper uses Peircean semiotics to show how such a theoretical
framework could be. Semiotics and the foundations of mathematics Cornelie Leopold, University of Kaiserslautern Summary. The discussion of the foundations of mathematics is characterized by differing attitudes towards the ontological nature of mathematical objects and by contrasting epistemological positions. With the aid of semiotics the conception of mathematics as a science based on signs leads to a new basis in the discussion of foundations. Ontological aspects of mathematical entities can be considered within mathematical thinking. The relation of mathematical entities to reality can be interpreted as being mediated through signs. The various positions concerning the foundations of mathematics turn out to be based on reductions of the triadic sign-conception to certain dyadic or monadic aspects of it. A development of mathematics from eight signs Dietrich Marsal, University of Stuttgart Summary. Mathematics is embedded in the language of every-day discourse. But every
attempt to define all expressions of that language results in a circle. Thus, there is a
striking difference between the formal rigor of mathematics and the uncertainty of its
sign-theoretic basis. To close this gap, a "Begriffs-Schrift" (concept script)
is presented to reconstruct contemporary mathematics from eight signs that can be
introduced without circularity. After a discussion of the theoretical foundations and of
prerequisite logical notions, central concepts from topics such as sets, relations,
mappings, partial orderings, cardinal numbers, algebras and topological space are
defined.
Syntatics and semantics in arithmetic and the limits of artificial intelligence Pirmin Stekeler-Weithofer, University of Constance Summary. From a mathematical point of view, the difference between syntactics and
formal semantics corresponds to the distinction between effective procedure and general
function. An analysis of this difference reveals principal limits of artificial
intelligence: The output of a procedural system consists essentially in classifying
figures into derivable and non-derivable ones. In non-trivial cases, this output cannot be
studied with purely procedural means nor by a merely empirical investigation of
input-output behavior. Full mathematical intelligence, hence, is far beyond the reach of
computers.
The logic and semiotics of modern day mathematics: the Tractatus of Descartes' "Regulae" Wilhelm F. Niebel, University of Frankfurt am Main Summary. Stimulated by the 350th anniversary of Descartes’ "First Philosophy", this article presents a Cartesian text on the history of mathematics and philosophy that has not yet been considered, namely, Descartes’ early Tractatus of the "Regulae" (1628/29), the second book of which must be considered to be a basic logico-semiotic document for modern mathematical science. By using characters in a non-(or post-)phonetic way, Descartes here introduced the modern "Characteristica" or "term-script" which was to become the formal language of pure mathematics. The significance of this text becomes evident in the fact that, 250 years later, Frege took over the Cartesian mathematical innovations (e.g., the syntactic concept of a function and the operational-constructivist concept of a sign) and applied them to logic in his Begriffsschrift as a Formal Language of Pure Thinking of 1879. Given that Frege is regarded the founder of mathematical logic, the present article advocates considering Descartes the Frege of mathematics. Termini, symbols and signs: the development of algebra and its notation between the 13th and 18th century Hans G. Knapp, University of Graz Summary. As is shown in this contribution, the development of algebra and its notation
between the 13th and 18th centuries corresponds to changes in the conditions of the way of
life and in the ontological assumptions of this period: For the craftsmen, mathematical
thinking consists in the manipulation of "termini", for the merchant in a
mutually compatible ordering of "things", and for the scientist in the
derivation of "ideas". Accordingly, in the transition from predominantly
craft-oriented thinking to commercial and scientific thinking, the "termini" are
first replaced by the symbol aggregates of the "coss" and then by the signs of
modern formal language.
Udo L. Figge, Ruhr-University Bochum Summary. A new branch of semiotics is outlined under the designation "computational semiotics". It seems likely to become an important field of research having interesting applications. Computational semiotics can be regarded as a generalization of computational linguistics. It can draw important ideas from software ergonomics. Its main tasks are the analysis and the systematization of human-computer interaction, giving special consideration to the various manifestations of the inner states of computational systems as well as to the various ways of influencing these inner states by manipulating peripheral devices. Three types of attitudes towards computers are distinguished: taking 1. the computer as a tool, 2. the computer as a partner, 3. the computer as a modeler of reality. Means of interaction mentioned are, above all, formal languages, natural language and graphic techniques. Literary report Katharina Kaspers, University of Munich Summary. When in 1913 Marcel Duchamp declared his Readymades to be art, he questioned the fundamental agreement, that art can be objectively defined by its spiritual substance and relationship to reality or by the employed techniques and intentions. As a consequence, art turned away from portraying the environment and concentrated on representing a spiritual substance which the spectator could no longer comprehend by merely looking at the artistic object. The goal of Concept-Art was to eliminate the object totally. The artists presented their intentions through instructions, which were declared to be art, and left it up to the recipient to construct the object in accordance with them. While the intention to cancel the distance between the artist and the public failed because of the required amount of intellectual effort and capacity of empathy, the documentary value of Concept-Art remains: We understand not only the role that intellect and abstraction play in contemporary art, but also the necessity for visual concreteness, for reverting to a visual language that conforms to the general principles of semiotics. Documentation Gerhard Komar, Munich Summary. In the third stage of its evolution, money as a general means of communication makes use of paper as its sign matter in order to represent the values of a national currency. The relation of monetary signs to their objects is established through numbers and is valid as long as the currency community guarantees the cash value. With regard to the sign matter, the optical, acoustical and tactile properties of money are diligently planned. The introduction of new monetary sign carriers is far from arbitrary, requiring the joint functioning of icons, indices and symbols as well as various security measures. The articles gives a detailed description of the newly issued German bank notes of 1990 and 1991. It emphasizes the difficulty of overcoming habituation to old monetary signs and of guaranteeing long term security against forgery.
Christian Weyers, University of Trier Summary. This contribution discusses the current hypotheses on the origin of the dollar
sign ($). It shows the untenability of the assumptions that the dollar sign developed from
one of the denotations US for "United States", ps for "pesos", lb for
"pounds", ( for "dollars" or 8/ for "8 shillings" and also
rules out as a possible origin the columns of Hercules depicted on Spanish 8-real-pieces
of the 17th century. Instead, arguments are given for the development of the dollar sign
out of the cifrão, a sign used in Portuguese measurement expressions for the separation
of numeral expressions of different denominations.
In hindsight Michael Franz, Academy of Science, Berlin Summary. This contribution gives a survey of the most relevant semiotic developments which occured in the German Democratic Republic during the forty years of its existence. Pointing out the importance of classical authors such as Marx and Hegel as well as Peirce and Morris, the article deals with the controversies about the concepts of function, information and mirror image and discusses the logically oriented semiotics of Georg Klaus, the historically based philosophy of language of Erhard Albrecht, the biosemiotics of Günter Tembrock, the structuralist semiotics of Wolfgang Steinitz and his students Manfred Bierwisch, Ewald Lang, and Wolfdietrich Hartung as well as the semiotics of cultural history developed in the Winckelmann Circle of the Berlin Humboldt University, which included, besides Ewald Lang, Wolfgang Schindler, Christian Kaden, Michael Franz and others. Continuing attention is deserved by the studies on the relationship of syntactic structure, meaning, and function in artefacts of animals and men, on the relation between text and context, on the comparison of the interpretation procedures in the various arts, and on the evolutionary principles of culture. |
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