Philosophy Dictionary of ArgumentsHome
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| Set Theory: set theory is the system of rules and axioms, which regulates the formation of sets. The elements are exclusively numbers. Sets contain individual objects, that is, numbers as elements. Furthermore, sets contain sub-sets, that is, again sets of elements. The set of all sub-sets of a set is called the power set. Each set contains the empty set as a subset, but not as an element. The size of sets is called the cardinality. Sets containing the same elements are identical. See also comprehension, comprehension axiom, selection axiom, infinity axiom, couple set axiom, extensionality principle._____________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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Arthur N. Prior on Set Theory - Dictionary of Arguments
I 165 Nouns/Prior: nouns are no names, no class names. >Names, >Singular Terms, >General Terms, >Terms, >Words, >Word Meaning, >Reference, >Predication, >Naming, >Designation, >Denotation, >Comprehension. Epsilon/Principia Mathematica(1)/Russell: "x ε a": Translation: "A is an element of the class of humans" seems to be a relation between a concrete and an abstract object. >Element relation. Vs: better "x is a": "Russell is a man" - Prior: "is a" is no real verb that makes a sentence of a name, rather a sentence of name and noun - "ε" is not a real predicate. >Predicates, >Predication, >Is, >Type theory. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press._____________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 |
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> Counter arguments against Prior
> Counter arguments in relation to Set Theory
Ed. Martin Schulz, access date 2024-04-28