This is a great topic. Specific clarification is going to be needed in certain elements should there be further exploration in it, but I think that it is a wonderful topic. If we are going to argue that Slim is a utilitarian in terms of working towards the end for the greatest good for the greatest number, we can look at the two deaths of Candy's dog and Lennie as examples of how Slim acts with the idea of ensuring that the greatest good for the greatest number is evident. Candy's dog being put down represents the consensus of the majority. Slim does not act in any way against this. He does not advocate for the dog's interests as he recognizes that Carlson's point about the dog "being no good" for anyone and that most everyone in the quarters agrees with the assessment represents a utilitarian element in Slim's character. At the same time, I think that we see the same entity in Slim's reaction to George after he kills Lennie. It becomes evident that Slim justifies what George did as something that he "had to do." I would say that this instance represents a utilitarian philosophy in that Slim understands that George killing Lennie was something that represented the greatest good for the greatest number.