What does Tautologically valid mean?

I would say ‘tautologically valid’ and ‘logically valid’ are close to being synonyms. Maybe you could differentiate ‘tautologically valid’ as being a bare assertion at the level of a judgement: [;\vdash P;], while ‘logically valid’ could mean a proposition that is true under every interpretation. 1.

What is the difference between a valid argument and an invalid argument?

Valid: an argument is valid if and only if it is necessary that if all of the premises are true, then the conclusion is true; if all the premises are true, then the conclusion must be true; it is impossible that all the premises are true and the conclusion is false. If this is possible, the argument is invalid.

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 semantically valid?

An inference is valid if all interpretations that validate the premises validate the conclusion. This is known as semantic validity.

Can two false sentences be logically equivalent?

No two false sentences are logically equivalent. A pair of equivalent sentences must both be false at the same time if they are false at all. Page 43. Focus on exercise sets 1 and 5.

Is the argument generally logically acceptable?

In effect, an argument is valid if the truth of the premises logically guarantees the truth of the conclusion. An argument is valid if the premises and conclusion are related to each other in the right way so that if the premises were true, then the conclusion would have to be true as well.

Is valid argument a tautology?

A valid argument with true premises has a true conclusion. This implies that the conclusion is a tautology. Therefore, if the premises of a propositionally valid argument are tautologies, then its conclusion must be a tautology as well.

Can you have a valid argument with contradictory premises?

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.

What is a semantically valid argument?

An argument is semantically valid iff (i) if it is impossible that its premises be true and its conclusion false; and (ii) this impossibility is grounded in the senses of the extra-logical terms of. the argument.

What is a logically sound argument?

Definition. In deductive reasoning, a sound argument is an argument that is valid and all of its premises are true (and as a consequence its conclusion is true as well). An argument is valid if, assuming its premises are true, the conclusion must be true.

Is a tautologically valid argument necessarily true?

A tautologically valid argument is necessarily true, which is to say a tautology is not possibly not the case. A tautology is not an argument but a type of proposition, which is true in virtue of its structure or meaning of predicates (definitionally true).

What is an a valid argument?

A valid argument means the premises necessarily lead to the conclusion. For instance, “1 = 2, 3 = 1, therefore 2 = 3.”. Notice that this has nothing to do with the truth of the premises only that the conclusion must be true based on the premises.

Is the conclusion of an argument necessarily true?

A logically valid argument’s conclusion is a logical consequence of its premises and therefore necessarily true given the truth of its premises. A statement (not an argument) can either be true or necessarily true. All necessarily true statements are true, but not all true statements are necessarily true.

How do you prove that an argument is sound?

A sound argument is necessarily valid, but a valid argument need not be sound. The argument form that derives every $A$ is a $C$ from the premises every $A$ is a $B$ and every $B$ is a $C$, is valid, so every instance of it is a valid argument. Now take $A$ to be prime number, $B$ to be multiple of $4$, and $C$ to be even number.