Why is “an invalid argument, the conclusion of which is a tautology” not possible?

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.

Can an invalid argument have a tautology as a conclusion?

Therefore, if the premises of a propositionally valid argument are tautologies, then its conclusion must be a tautology as well.



No propositionally valid argument can have a contradiction as a conclusion.

P (P∧¬P) ¬(P→P)
T F F
F F F


What is an invalid argument with a true conclusion?

The conclusion is actually true but this fact does NOT follow from the claim that the premises are true. We can imagine a fantasy in which the premises are true but the conclusion is still false.

Is a valid argument always a tautology?

It is not originally defined in the context of premise-conclusion as you said. However, it can be proven that tautological sentences as defined previously is always the ‘true conclusion’ of any argument regardless of truth of the premises. Therefore, tautology is always valid.

Why is the conclusion valid or invalid it is invalid?

A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.

Can a 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 every argument with a tautological conclusion sound?

No. A valid argument may have a true conclusion even if not all its premises are true. For instance: (Premise) All cats are flying creatures.

What is a tautological argument?

A tautological argument is otherwise known as a circular argument, that is, one that begins by assuming the very thing that is meant to be proven by the argument itself.

What is tautological reasoning?

Tautological reasoning is logic that uses the premise as the conclusions, or is too obvious as to be necessary. For example, saying, “When we get a pet we will either get a dog or some other animal” is tautological, as every pet is necessarily either a dog or not a dog.

Are all tautologies logical truths?

Note that every tautology is also a logical truth, and every logical truth is also a TW-necessity. But the converse is not true: some logical truths are not tautologies, and some TW-necessities are not logical truths.

Why does every proposition imply a tautology?

It follows from the definition that if a proposition p is a contradiction then p tautologically implies every proposition, because there is no truth valuation that causes p to be true and so the definition of tautological implication is trivially satisfied.

What is the difference between tautology and logical truth?

A “tautology” refers to a sentence of truth-functional logic where every valuation, every row of a complete truth table, evaluates to true. A “logical truth” is a sentence in first order logic where every interpretation is true.