Suppose you know the premises of an argument are inconsistent. Do you have to do a truth table to know whether it is valid or invalid?


Can an argument be valid if premises are inconsistent?

All arguments with inconsistent premises are valid, as there is no possible world in which the premises are all true.

Can an argument form with inconsistent premises be invalid?

Yes. An argument with inconsistent premises is valid, regardless of what the conclusion is. If an argument has inconsistent premises, then it is impossible for all the premises to be true at the same time; hence it is impossible for all the premises to be true while the conclusion is false.

Can an argument have a counterexample if its premises are inconsistent?

If a set of sentences is inconsistent, and one adds another member to the set, the new set must be inconsistent whatever the new member is. So, if the set of premises of an argument is inconsistent, its counterexample set will be too.

Can an argument with inconsistent premises be sound?

The point of checking for this is that though an inconsistent argument will always be valid, (remember that the definition of invalidity is that it is possible for all the premises to be true and the conclusion to be false–an inconsistent argument will never have all true premises) it can never be sound.

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What does it mean to have consistent premises?

The book defines a set of premises to be consistent if you can’t deduce a contradiction from the set of premises. It also says that a set of premises is consistent if there is some formula P that is not deducible from the set of premises.

Can an argument have true premises and a true conclusion but not be valid?

If an argument has all true premises and a true conclusion, then it is valid. FALSE: It is possible for an argument to have all true premises and a true conclusion but still be invalid.

How do you know if premises are true?

First, one must ask if the premises provide support for the conclusion by examing the form of the argument. If they do, then the argument is valid. Then, one must ask whether the premises are true or false in actuality. Only if an argument passes both these tests is it sound.

Can an argument have one premise?

A premise is a statement in an argument that provides reason or support for the conclusion. There can be one or many premises in a single argument. A conclusion is a statement in an argument that indicates of what the arguer is trying to convince the reader/listener.

Can a conclusion be true if the premises are false?

Validity is a guarantee of a true conclusion when the premises are true but offers no guarantee when the premises are false. False premises can lead to either a true or a false conclusion even in a valid argument. In these examples, luck rather than logic led to the true conclusion.

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What can an argument with false premises not be?

A valid argument can have false premises; and it can have a false conclusion. But if a valid argument has all true premises, then it must have a true conclusion.

What is an argument with false premises and false conclusion?

So, an argument with a mixture of true and false premises is still considered to be an argument with false premises–it is false that all of the premises are true. Nevertheless, in these examples, the conclusion is false. For either example, the logic is invalid and the premises are false. Here the conclusion is false.