Review: Validity

Here's a review of the tricky term "valid" as it refers to deductive arguments:

DEFINED: A deductive argument is valid when the truth of the premises guarantees the truth of the conclusion.

WHAT IT MEANS: Validity focuses on the form or structure of the argument. If an argument is valid, then it has good form – truth preserving form.

Basically, if we assume that all the premises are true, then the conclusion must also be true for an argument to be valid. Notice we are only assuming the truth of the premises, not checking to see whether they are actually true. Again, this makes sense, because we’re truth-preservers: if the premises were true, the conclusion that follows would have to be true.

EXAMPLES:
(1) All humans are mammals.
All mammals have hair.
All humans have hair.

(2) If it snows, then it’s below 32 degrees.
It snows.
It’s below 32 degrees.

(3) All humans are mammals.
All mammals have wings.
All humans have wings.

(4) Either Yao is tall or Spud is tall.
Yao is not tall.
Therefore, Spud is tall.

Even though arguments 3 and 4 are ultimately bad, they are still valid—their form is good. The second premise of argument 3 is false—not all mammals have wings—but it has the same exact structure of argument 1—a valid structure. Same with argument 4: the second premise is false (Yao Ming is about 7 feet tall), but the structure is good (it’s either this or that; it’s not this; therefore, it’s that).

To evaluate validity, then, assume that all the premises are true. Imagine a world in which all the premises are true. In that world, MUST the conclusion also be true? Or can you imagine a scenario in that world in which the premises are true, but the conclusion is still false? If you can imagine this situation, then the argument is not valid. If you cannot, then the argument is truth-preserving (inputting truths guarantees a true output), and thus valid.

IMPORTANT: Individual statements are true or false. Arguments are valid or invalid.