or hypothetical case, if you ought to do A, do A" whereas means "You ought to do A logically entails do A" Finally, formal ethics is a higher-order logic in that it allows properties, predicates that apply to other predicates. Properties can only be applied to actions, and the imperative notation is used (e.g. = "action A has property F"). The only types of property that formal ethics admits are universal properties, properties are not evaluative and do not make reference to proper names or pointer words. The following are examples of properties that are not universal properties: , where means "Act A is wrong" (evaluative) , where means "Act A angers God" (proper name) , where mean "Act A is something I do" (pointer word) Requiring a property to be universal, however, is different from requiring it to be morally relevant. , where means "Act A is done by a black person" is a universal property, but would not be considered morally relevant to most acts in most ethical theories. Formal ethics has a definition of relevantly similar actions that imposes certain consistency constraints, but does not have a definition of morally relevant properties. The notation is used to mean "G is a complete description of A in universal terms". Put another way, is a logical conjunction of all universal properties that has. The notation is the basis for the definition of exactly similar actions and is used in the definition of relevantly similar actions. Axioms Formal ethics has four axioms in addition to the axioms of predicate and modal logic. These axioms (with the possible exception of Rationality, see below) are largely uncontroversial within ethical theory. In natural language, the axioms might be given as follows: (Prescriptivity) — "Practice what you preach" (Universalizability) — "Make similar evaluations about similar cases" (Rationality) — "Be consistent" (Ends-Means) — "To achieve an end, do the necessary means" Care must be taken in translating each of these natural language axioms to a symbolic representation, in order to avoid axioms that produce absurd results or contradictions. In particular, the axioms advocated by Gensler avoid "if-then" forms in favor of "don't combine" forms. Notes Further reading Gensler, Harry J. Formal Ethics. Ethics Modal logic Formal systems