If they want proof of the impossibility of their task, they only have to look to Iran.
Dodgson's last work was an elegant, incomplete logical proof of the impossibility of the doctrine of hell.
In many ways, The Vertical Line has become a proof of the impossibility of getting into the caves themselves.
In 1824, while waiting for a royal decree to be issued, he published at his own expense his proof of the impossibility of solving algebraically the general equation of the fifth degree, which he hoped would bring him recognition.
While he draws grand conclusions from such experiments, regarding the non-existence of free will and how we should organize and think about law and ethics, most reasonable peoples' response will inevitably be similar to that of Diogenes the cynic who, when faced with Zeno of Elea's watertight proof of the impossibility of motion, simply got up and walked.
Arrow (1951) has the original proof of this "impossibility" theorem.
William Riker (1920 1993), who inspired the Rochester school in political science, interpreted it as a mathematical proof of the impossibility of populist democracy (e.g., Riker 1982).
If one takes that philosophical stance, then one is inexorably drawn to the foregoing constructive interpretation of the logical connectives and quantifiers: for how could a proof of the impossibility of the non-existence of a certain object x describe a mental construction of x?
Carol Karp remarks (1964, 166), "At the International Congress of Logic, Methodology and the Philosophy of Science at Stanford University in 1960, Dana Scott circulated an outline of a proof of the impossibility of a complete definable formal system for languages with a single two-place predicate symbol in addition to the equality symbol".
Perhaps, a most illuminating proof of the impossibility of a Dirichlet eigenfunction to be simultaneously a Neumann eigenfunction can be based on the third Green identity, which naturally leads to one of the principal topics of this paper.
