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Formal ethics is a
formal logical system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A form ...
for describing and evaluating the "form" as opposed to the "content" of
ethical Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and wrong behavior".''Internet Encyclopedia of Philosophy'' The field of ethics, along with aesthetics, concerns ma ...
principles. Formal ethics was introduced by Harry J. Gensler, in part in his 1990 logic textbook ''Symbolic Logic: Classical and Advanced Systems'', but was more fully developed and justified in his 1996 book '' Formal Ethics''. Formal ethics is related to ethical formalism in that its focus is the forms of moral judgments, but the exposition in ''Formal Ethics'' makes it clear that Gensler, unlike previous ethical formalists, does not consider formal ethics to be a complete ethical theory (such that the correct form would be necessary and sufficient for an ethical principle to be "correct"). In fact, the theorems of formal ethics could be seen as a largest common subset of most widely recognized ethical theories, in that none of its axioms (with the possible exception of ''rationality'') is controversial among philosophers of ethics.


Symbolic representation

The axioms and theorems of formal ethics can be represented with the standard notation of
predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...
(but with a
grammar In linguistics, the grammar of a natural language is its set of structural constraints on speakers' or writers' composition of clauses, phrases, and words. The term can also refer to the study of such constraints, a field that includes doma ...
closer to
higher-order logic mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more express ...
s), augmented with imperative,
deontic In moral philosophy, deontological ethics or deontology (from Greek: + ) is the normative ethical theory that the morality of an action should be based on whether that action itself is right or wrong under a series of rules and principles, ...
,
belief A belief is an attitude that something is the case, or that some proposition is true. In epistemology, philosophers use the term "belief" to refer to attitudes about the world which can be either true or false. To believe something is to tak ...
, and
modal logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend ot ...
symbols. Formal logic uses an underlined symbol (e.g. \underline) to represent an imperative. If the same symbol is used without an underline, then the plain symbol is an
indicative A realis mood ( abbreviated ) is a grammatical mood which is used principally to indicate that something is a statement of fact; in other words, to express what the speaker considers to be a known state of affairs, as in declarative sentences. Mos ...
and the underlined symbol is an imperative version of the same proposition. For example, if we take the symbol A to mean the indicative "You eat an apple", then \underline means the imperative "Eat an apple". When a proposition is given as a
predicate Predicate or predication may refer to: * Predicate (grammar), in linguistics * Predication (philosophy) * several closely related uses in mathematics and formal logic: **Predicate (mathematical logic) **Propositional function **Finitary relation, o ...
with one or more of the arguments representing agents, the agent to which the imperative applies is underlined. For example, if Dux means "You give a dollar to x" then D\underlinex is the correct way to express "Give a dollar to x". 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). With this interpretation, the negation of an imperative (e.g. \neg \underline) is taken to mean "Don't do A", not "You may omit A". To express demands, an imperative modal operator M (for ''may'') is defined, so that M \underline = "You may do A" and \neg M \neg \underline = "You may not omit doing A" = "You must do A". Note that M is different from the deontic R "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"). Following Castañeda's approach, the deontic operators O (for ''ought'') and R (for ''all right'', represented P for ''permissible'' in some deontic logic notations) are applied to imperatives. This is opposed to many deontic logics which apply the deontic operators to indicatives. Doing so avoids a difficulty of many deontic logics to express conditional imperatives. An often given example is ''If you smoke, then you ought to use an ashtray''. If the deontic operators O and R only attach to indicatives, then it is not clear that either of the following representations is adequate: :O(\mathrm \to \mathrm) :\mathrm \to O(\mathrm) However, by attaching the deontic operators to imperatives, we have unambiguously :O(\mathrm \to \underline) Belief logic symbols, when combined with imperative logic, allow
belief A belief is an attitude that something is the case, or that some proposition is true. In epistemology, philosophers use the term "belief" to refer to attitudes about the world which can be either true or false. To believe something is to tak ...
s and desires to be expressed. The notation u:A is used for beliefs ("You believe A") and u:\underline for desires ("You desire A"). In formal ethics, ''desire'' is taken in a strong sense when the agent of the belief is the same as the agent of the imperative. The following table shows the different interpretations for i:\underline 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". It does not, however, preclude "I want to get out of bed (right now), but I don't get out of bed". Perhaps I act to get out of bed (make my best effort), but can't for some reason (e.g. I am tied down, my legs are broken, etc.). Beliefs may be indicative, as above, or imperative (e.g. \underline : A "Believe A", \underline : \underline "Desire A"). They may also be combined with the deontic operators. For example, if G means "God exists", then O(\underline:G) is "You ought to believe that God exists", and (x)O(\underline:G) is "Everyone ought to believe that God exists". The modal operators \square and \diamond 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 \underset and \underset. In addition, an operator \blacksquare 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 \square. For example, :\blacksquare(O\underline \to \underline) means "In every actual or hypothetical case, if you ought to do A, do A" whereas :\square(O\underline \to \underline) 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. F\underline = "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: * W, where W\underline means "Act A is wrong" (evaluative) * G, where G\underline means "Act A angers God" (proper name) "God" is a proper name if, for example, it is defined as "the god of Christianity". If "God" is defined in another way, G might not reference a proper name. However, G might still not be a universal property if the definition of "God" is evaluative, for example, "the morally perfect being". If the definition of "God" is nonevaluative (e.g. "the creator of the universe"), then G is a universal property. Perhaps a less contentionous example would be T, where T \underline means "Act A angers Terry". * I, where I\underline 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. B, where B \underline 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 G \ast \underline is used to mean "G is a complete description of A in universal terms". Put another way, G is a logical conjunction of all universal properties that \underline has. The G \ast \underline 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
axiom An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or ...
s 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: * P (Prescriptivity) — "Practice what you preach" * U (Universalizability) — "Make similar evaluations about similar cases" * R (Rationality) — "Be consistent" * E (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''. {{ISBN, 0-415-13066-2 Ethics Modal logic Formal systems