|"There is...," philosophy: it is the question whether the talk that "there is" something is synonymous with the assumption of the existence of the said thing. In contrast to that the existential quantification is the attribution of properties to objects. See also everyday language, existence, existential quantification, existence predicate, existence statements, quantification, attribution, properties, schematic letters.|
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|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)
Existence/d'Abro: in Meinong "exist" and "there is" are used synonymously, but they are not synonyms: 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, a proof of existence for a solution is the finding that no contradiction arises from the assumption of a solution, even if the solution is not yet known.