Review: Invalidity

DEFINITION: A deductive argument is invalid when the truth of the premises does NOT guarantee the truth of the conclusion.

WHAT IT MEANS: If an argument isn’t valid, it is invalid. This means that you can’t draw the conclusion from the premises – they don’t naturally follow. Invalid arguments do not preserve truth.

EXAMPLES:
1) All humans are mammals.
All whales are mammals.
All humans are whales.

2) If it snows, then it’s below 32 degrees.
It doesn’t snow.
It’s not below 32 degrees.

3) All humans are mammals.
All BCC students are mammals.
All BCC students are humans.

4) Either Yao is tall or Spud is short.
Yao is tall.
Spud is short.

Even though arguments 3 and 4 have all true premises and a true conclusion, they are still invalid, because their form is bad. Argument 3 has the same exact structure as argument 1—a bad structure (it doesn’t preserve truth).

Even though in the real world the premises and conclusion of argument 3 are true, we can imagine a world in which all the premises of argument 3 are true, yet the conclusion is false. For instance, imagine that BCC starts letting whales take classes. The second premise would still be true, but the conclusion would then be false.

The same for argument 4: even though Spud is short (Spud Webb is around 5 feet tall), this argument doesn’t guarantee this. The structure is bad (it’s either this or that; it’s this; therefore, it’s that, too.). We can imagine a world in which Yao is tall, the first premise is true, and yet Spud is tall, too.