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One may wonder at this point what would happen if The Convincer were The Wrong Party going into the method, and The Wrong Party were to start expressing why they are supposedly right. In this case, The Wrong Party would express why to form a similar series of small why proofs, and the proofs would also be set up in the unique and special manner, such that if all of The Wrong Party's UP's were correct, then their original P0 claim would also be correct. However, The Wrong Party's original P0 claim is not correct, so it logically follows that not all of their UP's are correct. One or more of The Wrong Party's UP's must be wrong. If an UP is demonstrable, then a demonstrator can easily demonstrate that it is true on command, as this is what it means to be demonstrable. If a demonstrator can easily demonstrate that it's true, then it must be true in order for a demonstrator to be able to do that. Thus, if an UP is demonstrable, then it is true. Wrong UP's are not true, so they are therefore not demonstrable. (It may help the reader to think of the claim, "There is no way to improve at math." Why is there no way? There is no way because there is simply no way, so this claim is an UP. But assuming this were true, a demonstrator could not demonstrate that there is no way, a demonstrator could only demonstrate the way if there was a way.) For this reason, if one or more of The Wrong Party's UP's are wrong, then they are both wrong and non-demonstrable.
If The Right Party accepted all of The Wrong Party's UP's (even though one or more are wrong), then The Right Party would agree with The Wrong Party on the original P0 claim (as a result of the unique and special way that the UP's were generated in relation to the original P0 claim). In that case, The Right Party would be wrong as well. Since The Right Party is not wrong about the original P0, it follows that The Right Party will not accept all of The wrong Party's UP's as true. The Right Party must therefore reject one or more of The Wrong Party's UP's. There are three possible types of UP's:
Demonstrable (And Therefore Right) UP's:
Since any demonstrable UP's are correct, as mentioned above, The Right Party, if they don't already, will accept any of The Wrong Player's
UP's that are demonstrated to them (and therefore proven right to them).
Non-Demonstrable But Right UP's:
If The Right Party disagreed with a right UP, then they wouldn't be right, so it can be concluded that as long as The Right Party is
right on the topic in question, they will agree with any corresponding non-demonstrable but right UP's.
Wrong (And Therefore Non-Demonstrable) UP's:
As shown above, all wrong claims are non-demonstrable. Since The Right Party must reject one or more of The Wrong Party's UP's, and they
accept all correct UP's, both demonstrable and non-demonstrable, then "wrong and non-demonstrable" UP's are all that remain for
The Right Party to reject. For this reason, The Right Party will reject one or more of the wrong and non-demonstrable UP's.
Since The Right Party will reject one or more of the wrong and non-demonstrable UP's, then they will hold the opposite of that UP true. (For instance, they will believe, "It is not 8:00am," if they reject the claim, "It is 8:00am," etc.) If the UP is wrong and non-demonstrable, then The Right Party will hold the UP's opposite, call it (the correct) O, true. As evidenced previously, any (correct) P0 can be why-proven and/or simply demonstrated to be true using small why proofs. So, if (the correct) O is substituted as the new P0 claim, then The Right Party will be able to why-prove and/or simply demonstrate that O is true, except for the rare occurrence, where O is true but non-demonstrable, in which case both parties must accept that neither can know whether the original P0 is true or false, and neither party should hold it true anymore. Assuming the usual case, however, that The Right Party can why-prove and/or simply demonstrate O to be true, The Right Party can prove O to be true, and as a corollary, they have proven its opposite, the UP in question, to be false.
With The Wrong Party's why proofs, The Right Party will typically be able to why-prove or simply demonstrate that one or more of The Wrong Party's UP's are not true. The UP's are the foundation of the why proof chain; when the foundation of the proof is taken out in this manner, and the givens are no longer accepted as true, then whole proof falls apart, because in any two-column proof, the truth of the conclusion depends on the givens being true. These why proofs work the same way: the truth of the proof's conclusion, the original claim P0, depended on the givens (the UP's) being true. When one or more UP's are shown to be false, then the entire proof falls apart, and P0's truth falls apart as well, even for The Wrong Party, who originally held it true. The Right Party proving one single UP wrong has invalidated the entire chain of why proofs that lead The Wrong Party to form their (incorrect) conclusion. The Right Party was able to correct The Wrong Party about their original P0 viewpoint claim, all because of The Wrong Party's why proofs. The Wrong Party expressing why their viewpoint claim was supposedly right allowed The Right Party to be able to correct them about their original viewpoint claim, regardless of what their original viewpoint claim P0 was.
