Philosophy Lexicon of Arguments

 
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.

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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 Item Excerpt Meta data

 
Books on Amazon
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 unlike anything - makes unicorns and Pegasi not comparable because it has no elements).
I 63 ~
empty set / Prior: solution: to say that there is exactly one null class, is simply: for a f: nothing f-ts and for each f and y, nothing f-ts and nothing y-ts - then whatever y-ts,f-ts and whatever y-ts, f-ts - related: relation-in-extension.


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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.

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 Prior

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Ed. Martin Schulz, access date 2017-09-22