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Non-existence, philosophy: non-existence is not simply expressible for the classical predicate logic which attributes properties through quantification in the form of (Ex)(Fx) "There is at least one x, with the property F" (in short "There is at least one F"), since existence is not a property. The form "There is at least one x that does not exist" is contradictory. See also existence predicate, "There is", existence, unicorn example, pegasus example, round square, proof of God's existence.
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

Alexius Meinong on Non-Existence - Dictionary of Arguments

A. d'Abro Die Kontroversen über das Wesen der Mathematik 1939 in Kursbuch 8 Mathematik 1967

Non-existence/Meinong/d'Abro: since we can truthfully say "something like a round square does not exist," there must be something like a round square, albeit as a non-existent object. At first Russell had not been able to escape this, but in 1905 he discovered a theory of representation, according to which the round square seems to be mentioned when one says: "A round square does not exist." (Principia Mathematica)(1)
Existence/d'Abro: in Meinong "exists" and "there is" are used synonymously, but they are not synonymous: "exist" in the mathematical sense means to contain no contradiction.
If one takes Meinong seriously, this is evidence of the inability to think clearly, as in the joke: "Where does the light go when it goes out?".
Thus, an existence proof is for a solution the determination that no contradiction arises from the assumption of a solution, even if the solution is not yet known.

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.
Meinong, A.

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