Buridan's bridge
Contradicting the principle of bivalence, Buridan implies a system of three-valued logic in which there are three truth values—true, false, and some indeterminate third value.
[4] Dr. Dale Jacquette of the University of Bern says that "Plato can either permit Socrates to pass or have him seized and thrown into the river without violating his conditional vow".
Jacquette argues that Plato's conditional promise was given only in regard to Socrates's proposition being clearly and unconditionally either true or false.
To prove his point Jacquette asks, what would Plato have to do if Socrates had said nothing and was "as silent as a Sphinx", or if he uttered something that could not be either proven or "undisproven", something like Goldbach's conjecture.
[3] In his book Paradoxes from A to Z Professor Michael Clark comes to the conclusion that if Plato is an honorable man, Socrates should not get wet under any circumstances.
[5] Dr. Joseph W. Ulatowski believes that since the truth value in Plato's conditional promise and even more so in Socrates's proposition is indeterminate, it means that Plato "ought to err on the side of caution with respect to the future contingency and allow Socrates to cross the bridge".
Sancho summarizes the situation by saying: "the man swears that he is going to die upon the gallows; but if he dies upon it, he has sworn the truth, and by the law enacted deserves to go free and pass over the bridge; but if they don't hang him, then he has sworn falsely, and by the same law deserves to be hanged".
"[6] Sancho comes up with the moral solution:...there is the same reason for this passenger dying as for his living and passing over the bridge; for if the truth saves him the falsehood equally condemns him; and that being the case it is my opinion you should say to the gentlemen who sent you to me that as the arguments for condemning him and for absolving him are exactly balanced, they should let him pass freely, as it is always more praiseworthy to do good than to do evil.
