Concept Validity Philosophy

T/F: Any argument with false premises and a false conclusion is not a valid argument

False The argument is valid because its form is modus ponens, a valid argument form (and every instance of a valid argument form is a valid argument). But, of course, the argument's premises and conclusion are false. So, it is clearly possible for an argument with false premises and a false conclusion to be valid

T/F: Any argument that has true premises and a true conclusion is a sound argument

False This argument is not sound because it is not valid, and it is not valid because it is possible for its premises to be true while its conclusion is false (incidentally, this argument commits a fallacy called affirming the consequent). Thus, here we have an unsound argument that has true premises and a true conclusion, so it cannot be the case that any argument with true premises and a true conclusion is sound.

T/F A sound argument can have a false conclusion

False To see this, recall that a sound argument is a valid argument all the premises of which are true. Because it's impossible for a valid argument to have true premises and a false conclusion, and sound arguments are valid arguments with true premises, any sound argument must have a true conclusion

T/F: All sound arguments are valid

True For, by definition, a sound argument is a valid argument all the premises of which are true. Since being a valid argument is part of what it is to be a sound argument, all sound arguments are valid.

T/F: It is impossible for there to be a sound argument that is not also a valid argument.

True For, by definition, a sound argument is a valid argument that has no false premises. Thus, necessarily, all sound arguments are valid. In other words, it is impossible for there to be a sound argument that is not also a valid argument.

T/F: Valid arguments are good arguments.

False

T/F: If an argument is valid, then its conclusion is true.

False

T/F: If an argument is valid, then you should believe its conclusion.

False

T/F: Any valid argument has true premises and a true conclusion.

False

T/F: If an argument is unsound, then it has a false premise.

False

T/F: It is possible for an invalid argument to have true premises and a true conclusion.

True

T/F: No argument with false premises and a false conclusion is sound.

True No sound argument has false premises, and no sound argument has a false conclusion. For, a sound argument is, by definition, an argument that is (a) valid and (b) such that all of its premises are true. And given any valid argument with true premises, that argument's conclusion must be true as well, since (by definition) it is impossible for a valid argument to have true premises and a false conclusion. So, necessarily, any sound argument has true premises and a true conclusion. No argument with false premises and a false conclusion could possibly be sound.

T/F: A valid argument can have false premises and a true conclusion.

True The argument is valid because it is an instance of modus ponens, a valid argument form (and given a valid argument form, every instance of that form is a valid argument).

T/F: An unsound argument can have false premises

True The argument is valid, since it is an instance of the valid argument form modus ponens (and every instance of a valid argument form is a valid argument). But even though it is valid, it is unsound; for no sound argument has any false premises, and this argument contains two false premises. Thus, clearly, an unsound argument can have a false premise.

T/F: Given a valid argument, there is absolutely no possible way for its premises to be true and its conclusion false.

True The fact that this statement is true follows directly from the definition of the term "valid": A valid argument is, by definition, an argument such that it's impossible for its premises to be true while its conclusion is false.

T/F: An unsound argument can have true premises and a true conclusion

True This argument has true premises and a true conclusion, but it is unsound because it is invalid. We know that it is invalid because it is possible for its premises to be true and the conclusion false. Indeed, it is an instance of the fallacy of affirming the consequent. In order to be sound, an argument must (a) be a valid argument and (b) have no false premises. The above argument fails to satisfy the first condition.

T/F: Given a valid argument, if you affirm its premises and reject its conclusion, then you have at least one false belief.

True This statement follows from the definition of the term "valid." Given a valid argument, it is impossible for its premises to be true while its conclusion is false. Consider some particular valid argument, call it "A", and suppose that you affirm its premises and reject its conclusion. Now, either all of argument A's premises are true or argument A has at least one false premise. Let us consider what follows from each supposition. First, suppose that all of argument A's premises are true. Then, because argument A is valid, its conclusion must be true. But since you reject A's conclusion, you (wrongly) believe that this conclusion is false. Thus, your belief "A's conclusion is true" is false, and you have at least one false belief. Second, suppose that A has at least one false premise. Then, since you affirm all of A's premises, you have at least one false belief.