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This statement is false
Is it true or false

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This statement is false

Corit Demus
Student

Usergroup: Members
Joined: May 13, 2008
Location: The Netherlands
Total Topics: 3
Total Posts: 15

Posted 05/14/08 - 06:29 AM:	#26
Consider this. The validity of a statement is defined as whether the things stated in the statement are in fact the truth. So for this example sentence: The chair is red. The validity of the sentence is defined as (using == for boolean comparison): Validity = (Chair Color == Stated Chair Color [Red]) For our sentence however, you can not assign a validity: This sentence is false. Validity = (Validity == Stated Validity [False]) As you can see this is a circle definition. The validity of this sentence is not defined, like the fact that the result of a division by zero is not defined. It's definition contains a error. Any value whose definition is erroneous at some point will be undefined there. It is neither true nor false, it's undefined. EDIT: An important not can be made on the opposite statement: This statement is true. This statement, although it at first glance seems less controversial, is in fact not true, but undefined. It follows the same argument made for the original statement. We do not see this because we assume: - It's says it is true. - This does not contradict it being true. --> It is true. Yet this is incorrect. When we start out with the assumption the statement is false, we could follow a similar argument: - I assume it is false.. - It does not contradict this (it is false that it is true). --> It is false. However, if we look at it's validity like the original, we get: Validity = (Validity == true) Which once again is an error. Conclusion: The validity of both "This statement is false." and "This statement is true." is undefined. Edited by Corit Demus on 05/14/08 - 09:32 AM

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