Formal Ethics (Gensler)

Origin. Harry J. Gensler, "A formalized ethical theory" in Symbolic Logic: Classical and Advanced Systems (1990), developed fully in Formal Ethics (1996, Routledge). Builds on Castañeda's insistence that deontic operators attach to imperatives, and on Hare's prescriptivism. Gensler is explicit that it is not a complete ethical theory: the theorems are meant to be the largest common subset of the recognized ethical theories, so that no axiom is controversial.

Models. Every deontic logic in this division attaches O to an indicative — O(φ), where φ is a proposition. Gensler attaches it to an imperative. That single change dissolves the conditional-obligation ambiguity that Contrary-to-Duty and Dyadic Deontic Logic exist to work around: if you smoke, you ought to use an ashtray is ambiguous between O(smoke → ashtray) and smoke → O(ashtray) only because O takes a proposition, and it is unambiguous once O takes an imperative.

Formalism.

Imperatives by underlining: A — indicative: "You eat an apple" A̲ — imperative: "Eat an apple" For a predicate with agent arguments, the agent's argument is underlined: Gu̲x = "Give a dollar to x".

The anti-modal reading: An imperative expresses a preference, not a demand — the underline is not a modal operator. ¬A̲ is "Don't do A", not "You may omit A". Demands need a separate imperative modal: MA̲ = "You may do A"; ¬M¬A̲ = "You must do A". "You must do A" is still an imperative and is not "You ought to do A".

Deontic operators on imperatives (Castañeda): OA̲ = "You ought to do A" RA̲ = "It is all right to do A" The ashtray case: O(smoke → ashtray̲) is well formed and unambiguous.

Belief and desire: BA = "You believe A"; DA̲ = "You desire A". Desire is read strongly when the agent of the belief and of the imperative coincide: present → "I act to do A"; future → "I resolve to do A"; past → "I am glad A was done". So "I want to get out of bed now but I don't act to" is ruled out; "but I don't get out of bed" is not.

Modals: □, ◇ standard. ⊡, ⟐ for causal necessity and possibility, kept separate because logicians disagree about what is logically necessary. ⩣ = "in every actual or hypothetical case" — weaker than □, needed for prescriptive counterfactuals: ⩣(OA̲ → A̲) is not O A̲ → A̲ entailed logically.

Higher-order, restricted: Properties apply only to actions: F A̲ = "action A has property F". Only universal properties admitted: non-evaluative, no proper names, no indexicals. Excluded: "A is wrong" (evaluative), "A angers God" (proper name), "A is something I do" (indexical). Universal ≠ morally relevant: "done by a black person" is universal and irrelevant. Gensler defines relevantly similar actions by consistency constraints and does not define moral relevance.

The four axioms (over predicate and modal logic): 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" Each stated in "don't combine" form rather than "if-then", to avoid the absurdities the conditional forms generate.

Symbols.

Symbol	Unicode	Name	Meaning
A̲	—	Imperative	Letter plus U+0332 combining low line; a preference, not a demand
O	—	Ought	Applied to an imperative: OA̲
R	—	All right	RA̲ = "it is all right to do A"
M	—	Imperative may	¬M¬A̲ = "you must"
B	—	Belief	BA = "you believe A"
D	—	Desire	DA̲, read strongly for one's own present acts
□	U+25A1	White square	Logical necessity
◇	U+25C7	White diamond	Logical possibility
⊡	U+22A1	Squared dot operator	Causal necessity, kept apart from □
⟐	U+27D0	White diamond with centred dot	Causal possibility, kept apart from ◇
⩣	U+2A63	Logical or with double underbar	"In every actual or hypothetical case"; weaker than □
¬	U+00AC	Negation	¬A̲ is "don't do A", not "you may omit A"
→	U+2192	Material conditional	O(smoke → ashtray̲)
≠	U+2260	Not equal	Universal ≠ morally relevant
φ	U+03C6	Greek phi	Proposition variable in O(φ)

Metatheory. The Castañeda move — deontic operators on imperatives — is the system's whole contribution and it is a real one: the contrary-to-duty and conditional-obligation paradoxes that dyadic deontic logic was invented to handle are artifacts of attaching O to a proposition, and they do not arise here. The "don't combine" form of the axioms is the second careful move: Prescriptivity as don't combine believing you ought to do A with not acting to do A avoids the detachment problems that "if you believe you ought, then do" generates. Gensler's restriction to universal properties, together with his refusal to define moral relevance, is the system's honest boundary: it delivers consistency constraints and not a decision procedure, which is why he denies it is a complete ethical theory.

Applies to. Deontic logic's foundations, where the imperative reading is the live alternative. The golden rule and universalizability, formalized. Ethical consistency arguments. Applied ethics teaching, which is where Gensler's book is actually used.

Limitations. The system proves consistency constraints and nothing substantive: by design its theorems are what every ethical theory already agrees on, so it settles no moral question and Gensler says so. Universal properties are defined by exclusion — non-evaluative, no names, no indexicals — and the exclusions are not obviously exhaustive or obviously principled. The strong reading of desire is a stipulation that makes "I want to but I won't try" contradictory, which is a substantive psychological claim carried by a semantic clause. And the underline is not a modal operator, so the Kripke apparatus that yields soundness and completeness for KD has no purchase here: the four axioms are defended by the absurdity of what their denial commits one to, not by a frame semantics, and there is correspondingly no frame condition, no decision procedure and no complexity result to state.