Logical Philosophy

The premises may be any combination of true and false.

Suppose you have an invalid argument with a true conclusion. Given this information, what do you know about the premises of this argument?

It is possible for the conclusion to be false.

Suppose you have an invalid argument with true premises. Given this information, what do you know about the conclusion of this argument?

At least one premise must be false.

Suppose you have a valid argument with a false conclusion. Given this information, what do you know about the truth value of the argument's premises?

The conclusion could be either true or false.

Suppose you have a valid argument with some true premises and some false premises. Given this information, what do you know about the argument's conclusion?

The argument must be unsound.

Suppose you have an argument with a false conclusion. Given this information, what do you know about the soundness of this argument?

The argument must be invalid

Suppose you have an argument with all true premises and a false conclusion. Given this information, what do you know about the validity of this argument?

The argument must be invalid.

Suppose you have an argument with false premises and a true conclusion. What do you know about the validity of this argument?

explanation

If an argument is valid with some true premises and some false premises, the conclusion could be either true or false. From the fact that the argument is valid, all you know is that it is impossible for the premises to be true and the conclusion to be false. But the possibility of having this set of truth values is already eliminated by the false premises (that is, you cannot have all true premises). So the conclusion could be either true or false without affecting the validity of the argument. Thus, if an argument is valid with all false premises, the conclusion could be either true or false.

Yes

Is it possible to have a sound argument that is also valid?

Yes

Is it possible to have a valid argument that is not sound?

The argument is almost sound.

Suppose you have a deductive argument with a true conclusion. Given this information, what do you know about the soundness of this argument?