re political atheists reference line trimmed ssauyet eagle wesleyan edu scott d sauyet writes first i ll make the assumption that you agree that a murderer is one who has commited murder well i d say that a murderer is one who intentionally committed a murder for instance if you put a bullet into a gun that was thought to contain blanks and someone was killed with such a gun the person who actually performed the action isn t the murderer but i guess this is actually made clear in the below definition i d be interested to see a more reasonable definition what do you mean by reasonable otherwise your inductive definition doesn t bottom out your definition in essence is that murder is the intentional killing of someone who has not commited murder against his will expanding the second occurence of murder in the above we see that yes it is bad to include the word being defined in the definition but even though the series is recursively infinite i think the meaning can still be deduced i assume you can see the problem here to do a correct inductive definition you must define something in terms of a simpler case and you must have one or several bottoming out cases for instance we can define the factorial function the function which assigns to a positive integer the product of the positive integers less than or equal to it on the positive integers inductively as follows math lesson deleted okay let s look at this situation suppose there is a longstanding feud between two families which claim that the other committed some travesty in the distant past each time a member of the one family kills a member of the other the other family thinks that it is justified in killing a that member of the first family now let s suppose that this sequence has occurred an infinite number of times or if you don t like dealing with infinities suppose that one member of the family goes back into time and essentially begins the whole thing that is there is a never ending loop of slayings based on some non existent travesty how do you resolve this well they are all murders now i suppose that this isn t totally applicable to your problem but it still is possible to reduce an uninduced system and in any case the nested murderer in the definition of murder cannot be infintely recursive given the finite existence of humanity and a murder cannot be committed without a killing involved so the first person to intentionally cause someone to get killed is necessarily a murderer is this enough of an induction to solve the apparently unreducable definition see in a totally objective system where all the information is available such a nested definition isn t really a problem keith
