Lexicon of Arguments

 

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

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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⁾
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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.