Psychology Dictionary of ArgumentsHome
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| Empty set: an empty set is a set without an element. Notation ∅ or {}. There is only one empty set, since without an existing element there is no way to specify a specification of the set. The empty set can be specified as such that each element of the empty set is not identical with itself {x x unequal x}. Since there is no such object, the set must be empty. The empty set is not the number zero, but zero indicates the cardinality of the empty set._____________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 Empty Set - Dictionary of Arguments
I 63 ~ Empty set/Prior: creates only the logical construction identity between unicorns and Pegasi. - A logical structure is not any sort of entity. ((s) There is only one empty set, so it is unlike anything. - And it makes unicorns and Pegasi not comparable because it has no elements). >Relations, >Objects, >Abstract objects, >Abstractness, >Comparisons, >Comparability. I 63ff Empty set/Prior: solution: to say that there is exactly one null class, is simply: for a φ: nothing φ-s and for each φ and ψ, nothing φ-s and nothing ψ-s. Then whatever ψ-s,φ-s and whatever ψ-s, φ-s - related: relation-in-extension. Relation in Extension/Prior: two digit predicates can be associated in the same way with Relation in Extension. E.g. both: being father and mother of is not the same as both: being greater than and less than. But the corresponding "relations-in-extension" are the same. Because you can say that for an x and a y, if x is both father and mother of y then x is also bigger and smaller than y and vice versa, because both implications are just empty. >Implication._____________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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