Question

- Determine whether this argument, taken from Kalish and Montague [KaM064), is valid. If Superman were able and willing to prevent evil, he would do so. If Superman were unable to prevent evil, he would be impotent; if he were unwilling to prevent evil, he would be malevolent. Superman does not prevent evil. If Superman exists, he is nei- ther impotent nor malevolent. Therefore, Superman does not exist.

Please do not use Quantifier statements, just regular P Q R inference rules and logical equivalence, thank you!

Answer 1

Let us express the given aqument as sequence of logically equivalent statement Fox that we way take, P = superman able to prevent evil Q : Superman will beerent eril u: Superman prevents the evil. r R: He is inspotent. C s: He is malevolent T: Superman exists. If "supeensan were able and willing to prevent evil, He would do is equivalent to PAQ » u It superman were conable to prevent evil, he would be impotent. til esp R If he were einwilling to peerent be would be malevolent. - B) peenent evil evil. Superman does not prevent " Capplying conteapositive o n pno u.) su tenu (P no nu ise - in (PAG) .. (@ng (By Modus ponens.)

isu xp na) = opva (Demorgans law) It superman exists, be is beither impotent box malevolent T SRASS by taking contrapositive fore above statement & CuRnus) UT ahR) vnus) - ut RVS T also we have nu exist, and. suspvma) spina upresa exists] case -(1) let cas: a let np exist bossCleone B (modus posens.) is (modus porsens) IR .:RVS (addition) (addition) RVS feom - (1) RVS =257 team - RV3 =) T. RVS RV 3 4 RYS (modus RV3 = T (Modusponens, UT nt From both cases we got st as the conclusion ie, supex man does not exist is valid. up G. feom - A A is p R C leom R popens