I don't see the simplified ai4 either; just a red, point 7 character box. Chaning ecoding to either of "Chinese Simplified (HZ/GB2312/18030)" options makes no difference to the blank box. I wonder if it has to do with system default language setting.
sl0815---takakoo said:
p: The next sentence is true.
q: The previous sentence is false.
-------Interesting paradoxal sig.
First must be considered who is/are the speaker(s). If p and q were said by two different speakers, they can argue, but there is no inherent paradox as different people can think differently. If they were one person, then it becomes interesting whether any person in his right mind can say two statements that are conradicting one another.
Initially (p, q) has the four possible combinations of truth values (T,T), (T,F), (F,T), (F,F) where T: true, F: false. In this case, statements p, and q are such that a true p will result in a a true q which leads to a false p, hence a contradiction is reached. Similarly, a false p will lead to a false q resulting in a true p, another contradiction.
This confirmation/denial by the first statement resulting in the sustaining/flipping of the next which in turn negates the first was possible only because of symmetry. The symmetry will break down if the degree of certainty had more than the two states of absolute truth or absolute falsehood; in other words, the exclusion of the middle might have caused the fall into the pit.
Therefore, I think (p, q) might not a true paradox, but with an unstated quantification of certainty "I am very certain that..." postulated in each statement, might very well stand together with no clash in logic. CT: certainly true, CF: certainly false, and UT: unsure if true, UF: unsure if false. Hence the original sig and paired truth values can be rewritten;
p': [I am very certain that] p (= thenext sentence is true).
q': [I am very certain that] q (= the previous sentence is false).
T p'=CT p -> T q'=CT q -> F p'=UT p -> UT q'= UT q... After some damping like swinging doors, the result (UT, UT) becomes a stable truth state.
F p'=UT p -> UT q'=UT q -> UF p'=UF p -> UF q'=UF q... The result (UF, UF) is also stable.
So there is no paradox; the single person who seemingly says paradoxical statements is now in the
gray area, where he confesses to his ignorance and does a lot of thinking.
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Firefox was it ? It slows me down too much.
