Do you believe that the statement, “This statement is false” is a valid statement? Either true or false?
It is not. It is an irrational, self-contradicting, statement.
The statement “Every sentence on this page is wrong”, when there is only one statement on the page is the same as the above statement, irrational and self-contradicting, and thus neither true or false, but rather irrational.
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After all of the statements have been written, the rationality of the statements changes because each statement had referred to only the statements that were already written at the time that they each were written, but after all of them are written, each statement encompasses all statements.
That is why I asked to which time you were referring, before all were written or after.
[tab]After they are all written only the last statement, 100th, is self-contradicting and thus irrational (not wrong). For it to be right, all statements have to be wrong including itself. The other statements assert that some of the statements, possibly other than themselves, are false/wrong, but they claim an exact amount of wrong statements.
The statement claiming 99 wrong statements would be either including itself, making it irrational, or including the 100th statement that is irrational. If it includes the 100th, it is wrong for claiming an irrational statement as being wrong. And if the other statements are also wrong, there would be 99 wrong statements with 1 irrational statement. And that would make the 99th statement right because it wasn’t including the irrational statement but rather itself. And then it being right would make it wrong again, and thus actually irrational. So the 99th is either wrong or irrational depending on whether the lesser statements are wrong.
If the 98th statement turned out to be wrong, it would cause the 99th statement to be irrational, but that would make itself irrational and thus turn the 99th to be wrong. And if the 99th is wrong as well as the lesser 97 statements, the 98th would turned out to be right. If the 98th is right, the 99th is definitely wrong (with 98 wrong and 1 irrational).
For the 97th to be right, the 96 lesser statements must be wrong as well as only one of those above it, such as the 99th. But the 98th depends upon the 97th to be wrong, thus if the 97th was right, the 98th would be wrong. And that would make two above the 97th wrong … one too many. And that demands that the 97th be wrong, which returns the 98th to being right.
The 96th requires that all lesser be wrong and only one above it being wrong. But there are already 2 above it that are wrong; 97th and 99th. That makes the 96th wrong already. And it being wrong allows the others above it to remain as they were.
From there on down to the first statement, each will have to be wrong for that same reason - too many above it are wrong and thus it must be wrong also.
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So in the long run, after all of the statements are written, only the 98th can be right in claiming that there are exactly 98 wrong statements (with one irrational).[/tab]