0
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.
Add your answer:
Earn +20 pts
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 paradoxIt 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 CultureThe 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.")LanguageIn 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 paradoxLet 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.
Graph use in a sentence?
The graph on my test was confusing, so I left it blank.
What does one in a half equal to 3?
One in a half = 1/2 and so the given statement is a FALSE statement.
Is x equals 0 a mathematical sentence?
What do you mean by a "mathematical sentence"? In some practice in analysis (Calculus stuff), we call a statement a sentence if it looks like one or any combination of the following: "For all a in set A, condition P(a) is true/false" "There exist some (or unique) a in set A where P(a) is true/false" So in that practice, your statement is NOT a sentence, but if you phrase it "There exist a unique x in our set where x = 0 is true" or simply "There exist a unique element x where x = 0" It would be a sentence. BUT, I am pretty sure what I am talking about is not the same "mathematical sentence" as yours.
What is the converse of the contrapositive of a statement?
Look at the statement If 9 is an odd number, then 9 is divisible by 2. The first part is true and second part is false so logically the statement is false. The contrapositive is: If 9 is not divisible by 2, then 9 is not an odd number. The first part is true, the second part is false so the statement is true. Now the converse of the contrapositive If 9 is not an odd number, then 9 is not divisible by two. The first part is false and the second part is true so it is false. The original statement is if p then q,the contrapositive is if not q then not p and the converse of that is if not p then not q
True or false 1 equals?
The question makes no statement; so as it stands, there's nothing there yet to be true or false.
What is a sentence for coastal plane?
It is not true. So it must be false.
What is the difference between a mathematical sentence and a mathematical statement?
A mathematical sentence is a specific type of mathematical statement that uses mathematical symbols and operations to express a relationship or equation, such as 2 + 3 = 5. A mathematical statement, on the other hand, is a broader term that encompasses any declarative sentence in mathematics, including theorems, definitions, and conjectures. In summary, all mathematical sentences are mathematical statements, but not all mathematical statements are necessarily mathematical sentences.
What is the value of n in 8 equals 12?
8 = 12 is FALSE. So, the value of n, in a false statement can be anything at all.
What is a clearative sentence?
A declarative sentence is one that makes a definite statement. It is considered to be the direct opposite of a question.
What one of these statements about the Job is false?
We don't know the statement you were given so the answer is unknown.
Is a contrapositive statement true?
If a conditional statement is true, then so is its contrapositive. (And if its contrapositive is not true, then the statement is not true).
