|Signs: signs are recognizable and definable forms that an observer can assign to two domains. The first domain is the repertoire of available forms that allows a distinction of similarity and dissimilarity within this domain, the second domain is a set of objects which also distinguishes between similarity and dissimilarity between these objects as well as distinguishing the objects of the second domain from the forms of the first domain. There are no signs without observation or interpretation. See also language, words, symbols, icons, systems, image, image theory, pictures, assignment._____________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. |
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Signs: as long as E.g. the plus sign is used only between integers ("a + b"), it only needs to be explained for this purpose. If other objects are to be linked, E.g. "sun" with something else, the plus sign must be redefined.
Frege: Sign: Deputy.
Numeral/Frege: E.g. "2" - saturated - in contrast: functional character - E.g. "sin" (sine) unsaturated.
Sign/Frege: are the requirements for conceptual thinking - they no longer refer to the individual thing, but to what several things have in common.
Sign/FregeVsFormalism: empty signs are only black spots on paper - their use would be a logical error. - Empty signs do not solve any task E.g. x + b = c: if b>c, there is no natural number x that can be inserted - nor to accept the difference (c-b) as an artificial new sign. Sign/Frege: and where a solution is possible, the sign is not the solution, but the meaning of the sign.
FregeVsFormalism: only gives instructions for definitions - no definitions themselves.
E.g. Number i: the meaning of "total" must be re-explained. - FregeVsHilbert: it is not enough just to call for a sense._____________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.
Die Grundlagen der Arithmetik Stuttgart 1987
Funktion, Begriff, Bedeutung Göttingen 1994
Logische Untersuchungen Göttingen 1993