|Terminologies: here, special features of the language use of the individual authors are explained._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
Art: Characteristics to define a mode of symbolization that indicates whether something is a work of art.
1. Syntactic density: where certain minimal differences serve to distinguish symbols - e.g. a scale free thermometer (in contrast to a digital instrument.)
2. Semantic density: where symbols are available for things that differ only by minimal differences from each other, e. g. not only the scale free thermometer mentioned above, but also common German, as long as it is not syntactically dense.
3. Relative fullness: where comparatively many aspects of a symbol are significant, e. g. the drawing of a mountain of Hokusai consisting of a single line, in which every property such as line, thickness, shape, etc. counts. Contrary to the same curve as a depiction of the stock market trend of a day, in which only the height of the values above the basis counts.
4. Exemplification: in which a symbol, whether or not it is denoted, is symbolized by the fact that it serves as a sample of properties which it possesses literally or metaphorically.
5. Multiple and complex reference, where one symbol fulfils several related and interacting reference functions, some direct and others mediated by other symbols.
Definition Symbol scheme: consists of characters
Definition characters are certain classes of utterances or inscriptions. Characteristic of the character in a notation is that its elements can be freely interchanged without any syntactic effects. Class of marks. Score requires character separation. A character in a notation is an abstraction class of character indifference among inscriptions.
Definition Inscriptions: includes statements. An inscription is any brand visually, auditively, etc. that belongs to a character. An inscription is atomic if it does not contain any other inscription, otherwise it is compound. For example, a letter is considered atomic, including spaces. In music, the separation in atomic/together cannot always be recognized immediately, it is more complex. The atoms are best sorted into categories: Key sign, time sign, pitch sign.
Definition mark: individual case of a character in a notation. Includes inscriptions. Actual marks are rarely moved or exchanged. All inscriptions of a given brand are syntactically equivalent. And this is a sufficient condition that they are "genuine copies" or replicas of each other, or are spelled in the same way. No mark may belong to more than one character (disjunctiveness) a mark that is unambiguously an inscription of a single character is still ambiguous, if it has different objects of fulfillment at different times or in different contexts.
Definition type (opposite: use, Peirce): the type is the general or class whose individual cases or elements are the marks. Goodman: I prefer to do without the type altogether and instead name the cases of use of the type replica.
Definition case of use: Replica of a type
Definition Replica: case of use of a type ("genuine copy") There is no degree of similarity necessary or sufficient for replicas.
Definition genuine copy: a genuine copy of a genuine copy of a genuine copy...... must always be a genuine copy of "x". If the relation of being a genuine copy is not being transitive, the whole notation loses its meaning (see below: strictly speaking, a performance may not contain a single wrong note). Score requires character separation.
1. condition is character indifference among the individual cases of each character. Character indifference is a typical equivalence relation: reflexive, symmetrical, transitive. (No inscription belongs to one character to whom the other does not belong).
2. demand to notation: the characters must be differentiated or articulated finally. For every two characters K and K' and every mark m that does not actually belong to both, the provision that either m does not belong to K or m does not belong to K' is theoretically possible.
3. the (first) semantic requirement for notation systems is that they must be unambiguous.
Definition Ambiguity: consists of a multitude of fulfillment classes for one character.
Definition Redundancy: consists of a multitude of characters for one fulfillment class.
Definition syntactically dense: A schema is syntactically dense if it provides an infinite number of characters that are arranged in such a way that there is always a third between two. Such a scheme still has gaps. For example, if the characters are rational numbers that are either less than 1 or not less than 2. In this case, the insertion of a character corresponding to 1 will destroy the density.
Definition consistently dense: If there is no insertion of other characters at their normal positions, the density is destroyed.
Definition ordered syntactically e. g. by alphabet
Definition discreetly not overlapping. Note how absurd the usual notion is that the elements of a notation must be discreet: first, characters of a notation as classes must be rather disjoint! Discretion is a relationship between individuals. Secondly, there is no need for inscriptions of notations to be discreet. And finally, even atomic inscriptions only need to be discreet relative to this notation.
Definition disjunct/disjunctiveness: No mark may belong to more than one character. The disjunctiveness of the characters is therefore somewhat surprising since we do not have neatly separated classes of ordered spheres of inscriptions in the world, but rather a confusing mixture of marks.
Semantic disjunctiveness does not imply the discreetness of the objects of fulfillment, nor do syntactic disjunctiveness of the characters imply the discreetness of the inscriptions.
On the other hand, a schema can consist of only two characters that are not differentiated finally. For example, all marks that are not longer than one centimeter belong to one character, all longer marks belong to the other.
Definition fullness: the symbols in the pictorial schema are relatively full, and fullness is distinguished from both the general public of the symbol and the infinity of a schema. It is in fact completely independent of what a symbol denotes, as well as the number of symbols in a scheme.
Definition "Attenuation". For the opposite of fullness I use attenuation.
Definition density: e.g. real numbers, no point delimitation possible. Opposite: articulated.
Definition articulated: Opposite of dense.
III 232 ff
Syntactic Density - Semantic Density - Syntactic fullness
can be three symptoms of the aesthetic.
Syntactic density is characteristic for non-linguistic systems; sketches differ from scores and scripts.
Semantic density is characteristic of representation, description and expression through which sketches and scripts differ from scores.
Relative syntactic fullness distinguishes the more representational among the semantically dense systems from the diagrammatic ones, the less from the more "schematic" ones.
Density is anything but mysterious and vague and is explicitly defined. It arises from the unsatisfactory desire for precision and keeps it alive._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Catherine Z. Elgin
Reconceptions in Philosophy and Other Arts and Sciences, Indianapolis 1988
Revisionen Frankfurt 1989
Ways of Worldmaking, Indianapolis/Cambridge 1978
Weisen der Welterzeugung Frankfurt 1984
Fact, Fiction and Forecast, New York 1982
Tatsache Fiktion Voraussage Frankfurt 1988
Languages of Art. An Approach to a Theory of Symbols, Indianapolis 1976
Sprachen der Kunst Frankfurt 1997