# is a tautology always a valid argument? [duplicate]

I'm gonna conclude that a tautology always a valid argument.

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.

Am I right by above argument?

• But `x=x` is not an argument. Do you mean to ask about arguments in which the conclusion is tautological (such as `y, therefore x=x`) or arguments that have a tautological form (such as `x, therefore x`)? Jan 25, 2017 at 6:57
• Valid, but only within a chosen system. Jan 25, 2017 at 8:43
• There's several other questions like this. Is yours identical to or distinct from these? Jan 25, 2017 at 9:57

You are correct about the definition of validity, but actually 'tautological sentence' is defined in the way regardless of premises or conclusions. A 'tautological sentence' is one that is always true regardless of the truth of 'atomic sentences (ex. 'A','B',...)' that consist of the sentence. 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. (In the rigorous manner, 'tautology' usually refers to the logical sentence, not argument. However, it can differ from how the person defines each terminology.)

-I used the terms from Elementary Logic by Benson Mates.

A Tautology isn't an argument.

An argument requires support for an idea where as a tautology is merely a repetition/rephrasing of an idea. If a tautology was posed as an argument it would be an invalid one because it doesn't support the idea any further, not because it is logically incorrect.

The analytic / synthetic divide is interesting and useful, because it allows us to separate out interesting from uninteresting arguments.

Tautologies are analytic statements that are true by way syntax only, so e.g.

• "Either Plato was a Greek or Plato was not a Greek."

Tautologies may not be interesting, but that does not mean they are not useful. e.g., stating them may help us establish that we know and agree upon what a contradiction is, or may help as a means to introduce a term into the discussion.

A tautology is not an argument, but rather a logical proposition. A logical argument may contain tautologies.

To be a valid logical argument (using the traditional rules of predicate logic), not only do all of your statements need to be true, but the argument needs to prove the statement being argued.

If you are making the argument that "the sky is blue if the sky is blue," and your proof is a single logical statement: "the sky is blue if the sky is blue," provided as a tautology, then you have indeed made a valid argument. However, typically such is not the sort of argument that people make. Typically the argument would be a more interesting statement such as "the sky is blue." As part of such an argument, one might use the tautology above. That tautology would be valid, but on its own it would not prove the intended statement "the sky is blue," so the whole argument would not be valid.