Question

Using the imagination test, determine whether the following argument is valid or invalid: Some basketball players are fast. Some basketball players are strong. Therefore, some basketball players are both fast and strong.

invalid

valid

Answer 1

The Imagination Test for Deductive Validity

P1    Some basketball players are fast.

P2    Some basketball players are strong.

C       Therefore, some basketball players are both fast and strong.

To determine whether this argument is valid or invalid, we can first ask whether we can imagine a scenerio where all of the premeses to be true (P1 and P2) and the conclusion (C) is false. If we can imagine such a scenerio, then the argument is invalid. If we cannot imagine such a scenerio, then the argument is valid.

Here, If we can assume: Some basketball players are fast AND Some basketball players are strong, then we can also imagine a scenerio when the conclusion (C) is false: Some basketball players are both fast and strong is false. For example, imagine 10 players. 3 of them fast. 4 of them strong. We can imagine a situation where both 3 fast players to be completely different from 4 strong players. In such a scenerio, the conclusion (C) is false.

Thus,

the argument is:

invalid.