Philosophy Dictionary of ArgumentsHome
| |||
|
| |||
| Element relation, element relationship: the existence of a number within a set. In the broader sense the existence of an object (urelement) within a set. The element relation is to be distinguished from the subset relation. See also sets, classes, subsets, elements, set theory, empty set, universal class, paradoxes._____________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. | |||
| Author | Concept | Summary/Quotes | Sources |
|---|---|---|---|
|
Stanislav Lesniewski on Element Relation - Dictionary of Arguments
Prior I 163 Epsilon/Classes/Individual/LesniewskiVsRussell/Prior: "ε" constant for the relation between classes - Ex "a ε b": "The a is b" or "There is exactly one a and every a is b". In Russell there are of course such forms, but the form "x ε a" has not this meaning! >Principia Mathematica, >"Exactly one". L: "a = b" : "the a is the b" this does not correspond to the Def class identity/Russell: "the a "s coincide with the b "s". >Coextension, >Identity. But identity in Lesniewski is also not quite the same as individual identity in Russell. >Identity/Russell. Prior I 165ff Epsilon/Lesniewski/Prior: also higher-level: "f ε g": e.g. "the unit class-of-classes-of f is contained in the class-of-classes g". >Classes, >Sets, >Set theory, >Inclusion._____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
||
> Counter arguments against Lesniewski
> Counter arguments in relation to Element Relation
Ed. Martin Schulz, access date 2024-04-28