4/9 4. Validity and Soundness Free Online FlashCards

What is an argument?

An argument is a group of statements containing one or more premises and a conclusion; the premises are offered as reasons for accepting the conclusion.

What role do premises play?

The premises provide reasons for accepting the conclusion, which is the statement the argument seeks to establish.

When is a deductive argument valid?

A deductive argument is valid when it is impossible for all its premises to be true while its conclusion is false.

What form is “If $P$, then $Q$; $P$; therefore, $Q$” ?

Modus ponens has the form: If $P$, then $Q$; $P$; therefore, $Q$.

Is “If $P$, then $Q$; $Q$; therefore, $P$” valid?

The form is invalid because the premises can be true while the conclusion is false; another cause may produce $Q$.

What is a counterexample?

A counterexample is a specific case in which the premises are true and the conclusion is false. One counterexample is enough to show that a form is invalid.

What makes a deductive argument sound?

A sound argument is valid and has only true premises. Therefore, a sound argument must have a true conclusion.

Can a valid argument be unsound?

No. A valid argument can be unsound when one or more premises are false, even though the conclusion follows if those premises were true.

Can an invalid argument be sound?

No. An invalid argument cannot be sound because soundness requires validity, even when all its premises and its conclusion happen to be true.

How do validity and soundness differ?

Validity concerns logical structure: whether the conclusion follows. Soundness requires validity plus the actual truth of every premise.

How does a truth table test validity?

A truth table tests validity by checking every row where all premises are true. A single such row with a false conclusion proves invalidity.

What is the main difference between deductive and inductive reasoning?

Deductive reasoning aims to guarantee its conclusion. Inductive reasoning aims to make its conclusion probable or well-supported, not certain.