Using a graph representation of classical logic, the paper shows that the
liar or Yablo pattern occurs in every semantic paradox. The core graph
theoretic result generalizes theorem of Richardson, showing solvability of
finite graphs without odd cycles, to arbitrary graphs which are proven solvable
when no odd cycles nor patterns generalizing Yablo's occur. This follows from
an earlier result by a new compactness-like theorem, holding for infinitary
logic and utilizing the graph representation.Comment: 7 pages, submitted to a journa