|Equivalence class: is obtained from an equivalence relation (reflexive, symmetric, transitive). E.g. from dividing by 3 with remaining 2 2, 5, 8, 11 ... form an equivalence class. E.g. switch positions, e.g. weekdays form equivalence classes modulo 7._____________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. |
Def equivalence relation/W.Salmon: transitive, symmetric and reflexive. - E.g. congruence -
an equivalence relation decomposes a set into a set of equivalence classes with no common elements. - E.g. The relation to have the same number of elements. With respect to this relation all sets that have two elements are equivalent: e.g. a pair of shoes, a team of horses, a couple, a pair of twins - E.g. siblings can be defined as follows: to have the same parents. An equivalence class with respect to this relation is then a number of children who have common parents. - (s)> numerical equality, - "Gleichortigkeit", the definition of number or location. - (s)> partial identity -> "respects", > "regards"._____________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.
Me I Albert Menne Folgerichtig Denken Darmstadt 1988
HH II Hoyningen-Huene Formale Logik, Stuttgart 1998
Re III Stephen Read Philosophie der Logik Hamburg 1997
Sal IV Wesley C. Salmon Logik Stuttgart 1983
Sai V R.M.Sainsbury Paradoxien Stuttgart 2001