If the fugitive has asymmetric information—e.g., knowing one bridge is structurally weaker or that the pursuer favors the nearest bridge—P2's assumption of equal safety is empirically false and the uniform randomization prescription collapses.

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Asymmetric information(describes the fugitive's advantage over the pursuer): A situation where one person knows important facts that another person doesn't—like when you know a secret but your opponent doesn't.
Empirically false(as used in philosophy and science): Not true in real life when you actually test it or observe it, as opposed to being wrong just in theory.
P2(Provides the truth conditions for proposition (7), identified as proposition (7): George Bush does not exist.): The principle that proposition (7) is true if and only if George Bush does not exist — a modalized instance of the Tarski truth-schema 's is true iff s'.
Uniform randomization(the recommendation that fails when information is unequal): A strategy where you randomly choose between options in a completely equal way—like flipping a fair coin to decide between two choices with no preference.

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