Question

Translate the following argument into symbolic form using the translation key given in parentheses. Then use the first eight rules of inference to derive the conclusion of the argument. Either animals are mere mechanisms or they feel pain. If either animals feel pain or they have souls, then they have a right not to be subjected to needless pain and humans have a duty not to inflict needless pain on them. It is not the case that animals are mere mechanisms. Therefore, animals have a right not to be subjected to needless pain. (M = Animals are mere mechanisms. P = Animals feel pain. S = Animals have souls. R = Animals have a right not to be subjected to needless pain. D = Humans have a duty not to inflict needless pain on animals.)

Answer 1

To translate the argument into symbolic form, we can use the following translation key:

M: Animals are mere mechanisms.

P: Animals feel pain.

S: Animals have souls.

R: Animals have a right not to be subjected to needless pain.

D: Humans have a duty not to inflict needless pain on animals.

The argument can be translated as follows:

1. (M ∨ P) (Either animals are mere mechanisms or they feel pain.)

2. ((P ∨ S) → R) (If either animals feel pain or they have souls, then they have a right not to be subjected to needless pain.)

3. ¬M (It is not the case that animals are mere mechanisms.)

Now, let's use the first eight rules of inference to derive the conclusion of the argument:

4. P ∨ S (Disjunction Elimination, using 1 and 3)

5. R (Modus Ponens, using 4 and 2)

6. ¬R → ¬P (Contrapositive of 2)

7. ¬R (Modus Tollens, using 6 and 3)

8. ¬P (Disjunctive Syllogism, using 4 and 7)

Therefore, we can conclude that animals have a right not to be subjected to needless pain (¬P).