Formal ethics is a formal logical system for describing and evaluating the "form" as opposed to the "content" of ethical principles.
Formal ethics was introduced by Harry J. Gensler, in part in his 1990 logic textbook Symbolic Logic: Classical and Advanced Systems,[1] but was more fully developed and justified in his 1996 book Formal Ethics.
In fact, the theorems of formal ethics could be seen as a largest common subset of most widely recognized ethical theories,[2]: 11 in that none of its axioms (with the possible exception of rationality) is controversial among philosophers of ethics.
The axioms and theorems of formal ethics can be represented with the standard notation of predicate logic (but with a grammar closer to higher-order logics), augmented with imperative, deontic, belief, and modal logic symbols.
[2]: 166–186 Formal logic uses an underlined symbol (e.g.
to mean the indicative "You eat an apple", then
means the imperative "Eat an apple".
Within the system of formal ethics, an imperative is taken to represent a preference rather than a demand (called "anti-modal" view, because an underline doesn't behave like a modal operator).
To express demands, an imperative modal operator
"all right" operator defined below, as "You must do A" is still an imperative, without any ought judgment (i.e. not the same as "You ought to do A").
for permissible in some deontic logic notations) are applied to imperatives.
Doing so avoids a difficulty of many deontic logics to express conditional imperatives.
only attach to indicatives, then it is not clear that either of the following representations is adequate: However, by attaching the deontic operators to imperatives, we have unambiguously Belief logic symbols, when combined with imperative logic, allow beliefs and desires to be expressed.
depending on the agent and the tense of the imperative: This strong interpretation of desires precludes statements such as "I want to get out of bed (right now), but I don't act to get out of bed".
Perhaps I act to get out of bed (make my best effort), but can't for some reason (e.g.
are used with their normal meanings in modal logic.
In addition, to address the fact that logicians may disagree on what is logically necessary or possible, causal modal operators are separately defined to express that something is causally necessary or possible.
The causal modal operators are represented
is used to mean "in every actual or hypothetic case".
This is used, for example, when expressing deontic and prescriptive counterfactuals, and is weaker than
For example, whereas 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.
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.
is used to mean "G is a complete description of A in universal terms".
is a logical conjunction of all universal properties that
notation is the basis for the definition of exactly similar actions and is used in the definition of relevantly similar actions.
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: 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.