There are three basic areas of moral philosophy: applied ethics, normative ethics, and metaethics.
Applied ethics are defined as:
attempts to deal with specific realms of human action and to craft criteria for discussing issues that might arise within those realms.
Normative ethics are defined as:
determining the content of our moral behavior.
Metaethics are defined as:
the nature of ethics and moral reasoning.
Based upon these definitions, Slim would be defined as following the moral philosophy associated with applied ethics. Given that he does not come across as a great thinker (he is more of a common sense type of person), Slim's moral philosophy would align with the applied ethics given he simply examines what is right and wrong. Applied ethics encompasses the issues which arise within social interactions and the problems associated with differing points of view.
For example, Slim shows his adherence to applied ethics through his support of Carlson's desire to put Candy's dog down. Slim realizes the dog is past its prime, offers no vlaue to the men as a whole, and is, most likely, suffering. He thinks about the "rights and wrongs" associated with the dog.