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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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∙ 10y ago
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is this statement true or false BC?
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How do you find out if a statement is to be true or false?
By knowing your material. If you have kept up with your work, it will be obvious whether a sentence is true or false.
Is the following a statement This statement is false?
The answer depends on your definition of statement, It is a grammatical correct English declarative sentence which may be a statement by one definition. However, in logic, a statement is defined to be a sentence that is either true or false but not both. This sentence is not a statement by this definition.It is neither true nor false, because if is true, since it says it is false, it is false. If it is false. then is true since that is exactly what it says.Please see the related question for more about this famous paradox.
Why is the statement 'This sentence is false' so confusing?
In the logical sense, sentences must be either true or false and not both. "This sentence is false" cannot be true because that would mean that it is false, and it cannot be both. It also cannot be false because that would mean that it is true, and it cannot be both. Therefore, if it is true or false, then it is both true and false. Therefore it is either neither true nor false or both true and false; therefore, in the logical sense, it is not a sentence. However, it says it is a sentence; therefore, it is lying; therefore, it is false.
Are all sentences that are true or false a statement?
Yes, all sentences that can be classified as either true or false are considered statements. Statements are assertions that can be evaluated as either being factually accurate (true) or incorrect (false).
Can a statement be true or false?
Yes, a statement can be true or false but without knowing what the statement is no-one can possibly say whether it is true or it is false.
What does number sentence mean?
A number sentence has a left side (Nominative) the equals (verb) and the right side (predicate). It can be an open sentence with a variable, a false statement or a true statement.
a number when substituded in to an open sentence makes a true statement?
An equation or an inequality that contains at least one variable is called an open sentence. ... When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.
