What does it mean to be Tautologically valid?
What does it mean to be Tautologically valid?
What does it mean to be Tautologically valid?
In one hand, by the definition of validity, the conclusion must be true if all of the statements in the argument are true. On the other hand, an argument is tautology when it’s always true, regardless the truth or falseness of its promises. As an instance x=x is tautology, then it’s valid, too.
Is a contradiction valid?
Therefore, this argument is an example of one that is propositionally valid, despite the fact that its conclusion is a contradiction….No propositionally valid argument can have a contradiction as a conclusion.
| P | (P∧¬P) | ¬(P→P) |
|---|---|---|
| T | F | F |
| F | F | F |
Can tautology be invalid?
If an argument is invalid, then there is an interpretation where all the premises are true and the conclusion is false. So If the conclusion is a tautology, the argument must be valid since the conclusion can’t be false under any interpretation. Thank you for your answer.
Is a tautology always true?
A tautology is a formula which is “always true” — that is, it is true for every assignment of truth values to its simple components. You can think of a tautology as a rule of logic. The opposite of a tautology is a contradiction, a formula which is “always false”.
Is an argument with contradictory premises valid?
Well, if the premises are contradictory, then they cannot all be true (that’s just what contradictory means) so they can’t all be true while the conclusion is false (the necessary condition for non-validity). So the argument cannot be non-valid, it must be valid. Thus an argument with contradictory premises is valid.
Why are contradictory premises valid?
But on a classical conception of validity, any argument with contradictory premises counts as valid, since it is impossible for all the premises of an argument with contradictory premises to be true, and so a fortiori impossible for the argument to have true premises and false conclusion.
Is a contradiction an argument?
An argument deals with opposing opinions, ideas, or beliefs. A contradiction deals with opposing statements, phrases, and meanings.
Who discovered tautology?
philosopher Charles Sanders Peirce
The notion of tautology in the propositional calculus was first developed in the early 20th century by the American philosopher Charles Sanders Peirce, the founder of the school of pragmatism and a major logician.
How do you become a Tautologist?
If you are given a statement and want to determine if it is a tautology, then all you need to do is construct a truth table for the statement and look at the truth values in the final column. If all of the values are T (for true), then the statement is a tautology.