Is the sentence 'this statement is false' true or false?

Liar's Paradox: "This statement is false." is known as a liar's paradox. It is an illustration of inherent flaws in logic. Another example of a liar's paradox is: "The next statement is false.

The previous statement is true." Why it is a paradox It is contradictory. If we say the statement is true, then this statement would have to be false since it was true.

If we say it the statement is false, it will make the statement itself true, as that is false. Example in Popular Culture The liar's paradox can be found in an episode of Star Trek where Captain Kirk defeats a "superior" computer by introducing a logic loop similar to the question's liar paradox. (Kirk: "Everything Mudd says is a lie."

Harry Mudd : "I am lying.") Language In semantics there is the issue of truth condition, where the meaning of a sentence is conveyed if the truth conditions for the sentence are understood. A truth condition is what makes for the truth of a statement in an inductive definition of truth. The semantic theory of truth was developed from the work of a Polish logician named Alfred Tarski who attempted to formulate a new theory of truth in order to solve the liars paradox.

In doing so, Tarski developed the indefinability theorem, similar to Godel's incompleteness theorem. The Theory that the concept of truth for the sentences of language cannot be consistently defined within that language means that such paradoxes as "This statement is false" do not reveal the truth or falsity of the sentence by the words that have been used. Solution to the paradox Let us consider "This statement is false."

This quotation could also be read as "This, which is a statement, is false," which could by extent be read as "This is a statement and it is false." Let's call this quotation P. The statement that P is a statement will be called Q.

If S, then R and S equals R; therefore, if Q, then P equals not-P (since it equals Q and not-P). Since P cannot equal not-P, we know that Q is false. Since Q is false, P is not a statement.

Since P says that it is a statement, which is false, P itself is false. Note that being false does not make P a statement; all things that are statements are true or false, but it is not necessarily true that all things that are true or false are statements. In summary: "this statement is false" is false because it says it's a statement but it isn't.

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