Originally posted by GregoryWhat about "This statement is false."?
Regarding failing at failing, it depends. If a student tries to fail at a math test and fails, then he has succeeded at failing the math test and failed the math test; no contradiction. If you say he tries to fail in some generic sense, it's a gibberish question. You can't define whether somebody has failed or succeeded unless you have some parameters to measure it by.Well, here's how I see it: we have two statements; we can rephrase it as, "The second part of this statement is true, and the first part of this statement is false"
(2nd true) ^ (1st false)
Assume that this is a true statement; then the second statement is true, the first statement is false, and the second statement is false.
So if (2nd true) ^ (1st false), then (2nd true) ^ -(2nd true).
Statements of the form A ^ -A are false.
So if (2nd true) ^ (1st false) is true, a false statement is also true; therefore it is not true that (2nd true) ^ (1st false), and
"The below sentence is true.
The above sentence is false."
simply describes a situation that is by its nature impossible, like "It is raining and it is not raining." I don't see the problem; so "The below statement is true" and "The above statement is false" are mutually contradictory; that doesn't make it a paradox, it makes it false, in the same way that "It is raining and it is not raining" is false.
I've heard it argued that each statement asserts its own truth. So, "The following statement is true: it is raining" contains exactly the same information as: "It is raining." So "This statement is false" contains the same information as "The following statement is true: this statement is false." Since that contains the assertion and negation of the same statement, it is false.
Originally posted by GregoryBut it has to be true to be false, and if it's false, it's not false, but true...making it false.
I've heard it argued that each statement asserts its own truth. So, "The following statement is true: it is raining" contains exactly the same information as: "It is raining." So "This statement is false" contains the same information as "The following statement is true: this statement is false." Since that contains the assertion and negation of the same statement, it is false.
And it can't be a lie, because that's false, making it true.
If the statement includes both the components, "this statement is false" and "this statement is true" then it is false. No paradox; statements asserting the truth of both something and it's negation (it is raining and it is not raining; this statement is false and this statement is true"😉 are false by there nature.
Originally posted by GregoryOr do you mean the assertion that "This statement is false." is true, is a false assertion? If so, then yeah, that makes sense.
If the statement includes both the components, "this statement is false" and "this statement is true" then it is false. No paradox; statements asserting the truth of both something and it's negation (it is raining and it is not raining; this statement is false and this statement is true"😉 are false by there nature.