I have an assignment that asks: Can an argument have false premises and a false conclusion and still be valid? false prem and a true conclusion? true prem and a true conclusion? true prem and a false conclusion?
I responded with:
False premises, False conclusion: A valid argument can have false premises and a false conclusion while still maintaining its validity. The argument "All grass is orange. Bluegrass is a type of grass. Bluegrass must be orange" displays an argument that has false premises and a false conclusion based upon those false premises that still maintains its validity because the conclusion would be a logical consequence IF the premises were actually true.
False premises, True conclusion A valid argument may have false premises and still be a valid argument. In the example "The president of Cuba must be a naturalized US citizen. Fidel Castro is the president of Cuba. Fidel Castro must be a naturalized US citizen" we can see that although the argument has false premises the conclusion would be a logical consequence if the premises were true.
True premises, False conclusion By definition, any argument with true premises and a false conclusion must be considered invalid. This is most commonly found with arguments that state two premises and have a completely unrelated conclusion. For example "Barack Obama is the president. The president is powerful. 1+2 is 7" shows an invalid argument. It can also be found when the conclusion contradicts the premises, for example "The sky is blue. Blue is my favorite color. The sky isn't the same color as my favorite color"
True premises, True conclusion. By definition, any argument is valid if the conclusion must be true in any circumstance in which the premises are true. Therefore, it the premises are true then the conclusion must be a logical consequence of those premises. The argument "Blue is a primary color. My car is blue. The color of my car is one of the three primary colors" shows an argument with true premises and a true conclusion that is valid.