Formal ethics
Encyclopedia
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, 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.
(but with a grammar
closer to higher-order logic
s), augmented with imperative
, deontic
, belief, and modal logic
symbols.
Formal logic uses an underlined symbol (e.g.
) to represent an imperative
. If the same symbol is used without an underline, then the plain symbol is an indicative and the underlined symbol is an imperative version of the same proposition. For example, if we take the symbol
to mean the indicative "You eat an apple", then 
means the imperative "Eat an apple". When a proposition is given as a predicate
with one or more of the arguments representing agents, the agent to which the imperative applies is underlined. For example, if
means "You give a dollar to x" then 
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.
) is taken to mean "Don't do A", not "You may omit A". To express demands, an imperative modal operator 
(for may) is defined, so that 
= "You may do A" and 
= "You may not omit doing A" = "You must do A". Note that 
is different from the deontic 
"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
(for ought) and 
(for all right, represented 
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 
and 
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 belief
s and desires to be expressed. The notation
is used for beliefs ("You believe A") and 
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 
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.
"Believe A", 
"Desire A"). They may also be combined with the deontic operators. For example, if 
means "God exists", then 
is "You ought to believe that God exists", and 
is "Everyone ought to believe that God exists".
The modal operators
and 
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 
and 
. In addition, an operator 
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,
means "In every actual 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:
Requiring a property to be universal, however, is different than 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.
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:
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.
Formal ethics is related to ethical formalism
Ethical formalism
Ethical formalism is a type of ethical theory which defines moral judgements in terms of their logical form rather than their content . The term also often carries critical connotations...
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 logicFirst-order logic
First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...
(but with a grammar
Formal grammar
A formal grammar is a set of formation rules for strings in a formal language. The rules describe how to form strings from the language's alphabet that are valid according to the language's syntax...
closer to higher-order logic
Higher-order logic
In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and a stronger semantics...
s), augmented with imperative
Imperative logic
Imperative logic is the field of logic concerned with arguments containing sentences in the imperative mood. In contrast to sentences in the declarative mood, imperatives are neither true nor false. This leads to a number of logical dilemmas, puzzles, and paradoxes...
, deontic
Deontic logic
Deontic logic is the field of logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts...
, belief, and modal logic
Modal logic
Modal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...
symbols.
Formal logic uses an underlined symbol (e.g.
) to represent an imperativeImperative
Imperative can mean:*Imperative mood, a grammatical mood expressing commands, direct requests, and prohibitions * A morphological item expressing commands, direct requests, and prohibitions...
. If the same symbol is used without an underline, then the plain symbol is an indicative and the underlined symbol is an imperative version of the same proposition. For example, if we take the symbol
to mean the indicative "You eat an apple", then means the imperative "Eat an apple". When a proposition is given as a predicatePredicate (grammar)
There are two competing notions of the predicate in theories of grammar. Traditional grammar tends to view a predicate as one of two main parts of a sentence, the other being the subject, which the predicate modifies. The other understanding of predicates is inspired from work in predicate calculus...
with one or more of the arguments representing agents, the agent to which the imperative applies is underlined. For example, if
means "You give a dollar to x" then 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.
) is taken to mean "Don't do A", not "You may omit A". To express demands, an imperative modal operator (for may) is defined, so that = "You may do A" and = "You may not omit doing A" = "You must do A". Note that is different from the deontic "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
Hector-Neri Castañeda
Héctor-Neri Castañeda was a Guatemalan philosopher and founder of the journal Noûs.Born in San Vicente, Zacapa, Guatemala, he emigrated to the United States in 1948 and studied under Wilfrid Sellars at the University of Minnesota, where he earned a B.A. in 1950 and M.A. in 1952. Castañeda...
's approach, the deontic operators
(for ought) and (for all right, represented 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 and 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 belief
Belief
Belief is the psychological state in which an individual holds a proposition or premise to be true.-Belief, knowledge and epistemology:The terms belief and knowledge are used differently in philosophy....
s and desires to be expressed. The notation
is used for beliefs ("You believe A") and 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 depending on the agent and the tense of the imperative:
 is an imperative for: | Me | Someone else |
|---|---|---|
| Present | I act to do A | I want the person to do A |
| Future | I resolve to do A | |
| Past | I am glad A was done, or I regret that A wasn't done | |
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.
"Believe A", "Desire A"). They may also be combined with the deontic operators. For example, if means "God exists", then is "You ought to believe that God exists", and is "Everyone ought to believe that God exists".The modal operators
and 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 and . In addition, an operator 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, means "In every actual 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 than 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 axiomAxiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
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:
-
(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.