If supposing that a statement is false gives rise to a paradox, does this prove that the statement is true?

Yes. This is what is known as a proof by contradiction. When you want to prove a statement P implies a statement Q (i.e., you want to prove P⟹Q is true), you always start by assuming P is true. Then, if you want to proceed by contradiction, you suppose Q is false.

How do you prove a statement is false?

A counterexample disproves a statement by giving a situation where the statement is false; in proof by contradiction, you prove a statement by assuming its negation and obtaining a contradiction.

What is the solution to the liars paradox?

Jean Buridan has offered a solution to the Liar Paradox, i.e. to the problem of assigning a truth-value to the sentence ‘What I am saying is false’. It has been argued that either (1) this solution is ad hoc since it would only apply to self-referencing sentences [Read, S. 2002.

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Is a paradox true?

A paradox is a logically self-contradictory statement or a statement that runs contrary to one’s expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.

Is the assertion This statement is false a proposition?

In propositional logic, a proposition is a statement that is either true or false, but not both. In a text I am reading and in many others, “this statement is false” is not considered a proposition.

Is statement always false?

Contradiction: A statement form which is always false.

What do you call if the statement is false?

A false statement is a statement that is not true. Although the word fallacy is sometimes used as a synonym for false statement, that is not how the word is used in philosophy, mathematics, logic and most formal contexts. A false statement need not be a lie.

How is this sentence is a lie a paradox?

If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. In “this sentence is a lie” the paradox is strengthened in order to make it amenable to more rigorous logical analysis.

What are some examples of paradox?

Here are some thought-provoking paradox examples:

  • Save money by spending it.
  • If I know one thing, it’s that I know nothing.
  • This is the beginning of the end.
  • Deep down, you’re really shallow.
  • I’m a compulsive liar.
  • “Men work together whether they work together or apart.” – Robert Frost.

How do you find the paradox?

Paradox is dependent upon two elements: 1) a statement or situation which initially appears contradictory; 2) the statement or situation that appears contradictory must, after consideration, be a logical or well-founded premise.

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Is false a proposition?

This kind of sentences are called propositions. If a proposition is true, then we say it has a truth value of “true”; if a proposition is false, its truth value is “false”. For example, “Grass is green”, and “2 + 5 = 5” are propositions. The first proposition has the truth value of “true” and the second “false”.

Why is this sentence is false not a proposition?

For example, ‘This sentence is false’ is not a proposition, since no truth value can be assigned. For instance, if we assign it the truth value True, then we are saying that ‘This sentence is false’ is a true fact, i.e. the sentence is false.

What is a proposition statement that is always false?

A proposition has only two possible values: it is either true or false. We often abbreviate these values as T and F, respectively. Given a proposition p, we form another proposition by changing its truth value.
2.1: Propositions.

p ¯p
T F
F T

What is a proposition that is always true?

Definitions: A compound proposition that is always true for all possible truth values of the propositions is called a tautology. A compound proposition that is always false is called a contradiction. A proposition that is neither a tautology nor contradiction is called a contingency.

Is a declarative statement which is either true or false?

A proposition is a declarative sentence that is either true or false (but not both). For instance, the following are propositions: “Paris is in France” (true), “London is in Denmark” (false), “2 < 4” (true), “4 = 7 (false)”.

What do you call a proposition that is always true?

A compound proposition that is always true irrespective of the values of its component propositions is called a tautology.

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Is a statement that is either true or false but not both?

A true-false statement is any sentence that is either true or false but not both. A negation of a statement has the opposite meaning of a truth value. A negations is written as ~p.

What is a compound statement that is always false?

A self-contradiction is a compound statement that is always false.