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Note: I don't know how many of you are into propositional logic, but here it is, if only to please myself.









KEY TO MEANINGS OF LETTER SYMBOLS



C: Kirk and Spock are stranded in a cave on an uninhabited planet.



PF: Spock is in pon farr.



~W: There are no women available.



~S: Spock will not get any sex.



D: Spock will die.



L12: Spock has saved Kirk's life a dozen times over.



K: Kirk wants Spock not to die.



K/S: Kirk and Spock will have sex.



~K/S: Kirk and Spock will not have sex.







Given that:







1. C Kirk and Spock are stranded in a cave on an uninhabited planet.



2. PF Spock is in pon farr.



3. L12 Spock has saved Kirk's life a dozen times over.







And that:







4. C =>~W Being stranded in a cave on an uninhabited planet means there are no women available.



5. ~W => [(~K/S) => ~S] If there are no women available, that means that if Kirk doesn't have sex with Spock, Spock will not get any sex.







And also that:







6. PF => (~S => D) If Spock is in pon farr, then if he does not get any sex he will die.



7. L12 => K If Spock has saved Kirk a dozen times over, Kirk wants him not to die.



8. K => [(~K/S => D) => K/S] If Kirk wants Spock not to die, then if Kirk and Spock not having sex implies Spock's death, Kirk will have sex with him.







You can deduce, by the rule of modus ponens, that:






9. ~W (from 1 and 4)



10. ~S => D (from 2 and 6)



11. K (from 3 and 7)







And by the same rule, from those conclusions, that



12. (~K/S) => ~S (from 5 and 9)



13. (~K/S => D) => K/S (from 8 and 11)







and, by the rule of hypothetical syllogism, that:



14. ~K/S => D (from 10 and 12)







and again by modus ponens, that



15. K/S (from 13 and 14).







Another logical argument!







END
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