PHI 103 test #1

If an argument is valid and it has false premises, then it must have a false conclusion.

False - A valid argument with false premises may still have a true conclusion. Example: All cats are dogs All poodles are cats All poodles are dogs

If an argument is unsound, then it must have false premises.

False - An argument may be unsound in one of three ways. (1) It may be valid with false premises. (2) It may be invalid with true premises. (3) It may be invalid with false premises. So, some arguments may still be unsound with true premises. These arguments will be invalid. Example: Some poodles are black Some dogs are black . Some dogs are poodles

Counterexamples

Must have true premises and false conclusion

All dogs are animals (counterexamples)

True

All poodles are dogs (counterexamples)

True

Some animals are dogs (counterexamples)

True

The following instance proves that the form is invalid All dogs are animals. No dogs are cats No cats are animals

True

The following instance proves that the form is invalid No dogs are cats Some cats are not poodles ∴Some poodles are not dogs

True

If an argument is valid and has a true conclusion, then it must be sound.

False - A valid argument can have false premises and a true conclusion. Example:All cats are dogs All poodles are cats All poodles are dogs

If an argument is invalid and the premises are both true, then the conclusion must be false.

False - An invalid argument form cannot guarantee that the conclusion is true when the premises are true. An invalid argument can have instances where the premises and conclusion are true. Example: Some poodles are black Some dogs are black . Some dogs are poodles

All arguments with false premises and a false conclusion are valid.

False - Arguments with false premises and a false conclusion can be valid or invalid. Our example is an invalid argument with false premises and a false conclusion. Example: Some cats are mice Some dogs are mice Some dogs are cats

Some valid arguments have true premises and a false conclusion.

False - By definition, a valid argument cannot have even one instance where the premises are true and the conclusion false. All such arguments are invalid.

If an argument is unsound, then it must be invalid.

False - A sound argument has both a valid form and true premises. Unsound arguments can be valid but such arguments will also have false premises. Example: All dogs are cats All mice are dogs All mice are cats

All arguments with true premises and a true conclusion are sound.

False - A sound argument must have both a valid form and true premises. Invalid arguments can have true premises and a true conclusion. But invalid arguments are unsound. Example: Some poodles are black Some dogs are black . Some dogs are poodles

All unsound arguments are invalid.

False - A sound argument must have both a valid form and true premises. Valid arguments can be unsound; but they will have false premises. Example: All dogs are cats All mice are dogs All mice are cats

A valid argument must have a true conclusion.

False - A valid argument can have a false conclusion but only if it also has at least one false premise. Example: All dogs are cats All mice are dogs All mice are cats

If an argument has false premises, then it is invalid.

False - Arguments with false premises and a false conclusion can be valid or invalid. Our example is a valid argument with false premises and a false conclusion. Example: All dogs are cats All mice are dogs All mice are cats

All arguments with false premises and a true conclusion are invalid.

False - Arguments with false premises and a true conclusion may be valid or invalid. Here, we have an example of a valid argument with false premises and a true conclusion. Example: All cats are dogs All poodles are cats All poodles are dogs

If an argument is sound, then it can be invalid.

False - By definition, a sound argument has a valid form and true premises. Thus, a sound argument cannot be invalid.

If an argument is unsound and it has a false conclusion, then it must have false premises.

False - If an argument is unsound and the conclusion is false, the argument may still have true premises. In fact, if we have an argument with true premises and a false conclusion, then we know that the argument is invalid (and unsound). Example: Some cats are black Some dogs are black Some dogs are cats

The following instance proves that the form is invalid All dogs are black All cats are black ∴All cats are black

False

The following instance proves that the form is invalid Some dogs are cats No dogs are poodles ∴Some cats are not poodles

False

The following instance proves that the form is invalid Some dogs are not mice Some cats are not dogs ∴Some cats are not mice

False

No dogs are poodles (counterexamples)

False

Some dogs are not animals (counterexamples)

False

A sound argument must have a true conclusion.

True - A sound argument, by definition, has a valid form and true premises. When a valid argument has true premises, then it must also have a true conclusion.

All sound arguments have a true conclusion.

True - A sound argument has both a valid form and true premises. When a valid argument has true premises, then it must have a true conclusion.

If a valid argument has a false conclusion, then it is unsound.

True - A sound argument must have both a valid form and true premises. When a valid argument has a false conclusion, it must also have at least one false premise. Thus, a valid argument with a false conclusion will also be unsound.

Some arguments with false premises and a true conclusion are invalid.

True - Arguments with false premises and a true conclusion may be valid or invalid. Here, we have an example of an invalid argument with false premises and a true conclusion. Example: Some poodles are cats Some dogs are cats . Some dogs are poodles

All arguments with true premises and a false conclusion are invalid.

True - Since a valid argument cannot have even one instance with true premises and a false conclusion, all such arguments are invalid.

All valid arguments with true premises are sound.

True - The definition of a sound argument is that it has a valid form and true premises. So, all valid arguments with true premises will be sound.