On Formal Definitions

A definition of a concept should pin-point precisely all examples of the concept.

Extensionally, a notion can be defined by providing a set of all examples. Intensionally, a notion can be defined by providing properties that any example should possess, which could take the form of a function that classifies entities as belonging to this concept class or not (or providing a degree of membership).

Some definitions can be denotational in that they specify the literal meaning of a term. For example, defining duty-based deontology in terms of moral theories containing duty statements.

Some definitions can focus on the inferential role of the term, that is, how it’s used in relation to other terms. For example, ethics may be defined in terms of how ethical judgments are used within a society, which could imply that anything fulfilling these roles may be considered as ethics regardless of the precise form.

The SUMO ontology is written in line with the motto: “necessary but not necessarily sufficient”. The logical rules defining terms are not intended to be complete definitions; however, they are meant to be (mostly) correct. This fits the philosophical paradigm of meaning postulates, where each rule captures part of the meaning of a concept; moreover, it is only a postulate that is open to revision and refinement.

Unlike in mathematics, many human-world concepts do not yet have agreed-upon definitions in full analytic rigor. The feasibility of doing so non-trivially can also be debated (see Constructing the World‘s use of a countably infinite scrutability base). Thus, the aim is to provide a web of meaning postulates that capture some core structure of ethics, allowing for greater clarity and understanding in exploring and applying value-based reasoning.

Moreover, it seems valuable to provide clear definitions in English as well as in formal languages because it is, at present, more developed. Nor is it clear that the high-level class hierarchy and ontology of SUMO are optimal for the task. AI developments will likely make porting {English, SUMO} definitions into a more appropriate formal language easier in the near future.

Definitions of Morality

In my ethics worklog, I discuss various meta-ethical considerations concerning the definition of morality: the first of which is whether ethics is descriptively or normatively defined. Yet both of these definitions refer to codes of conduct put forth by some set of people that apply to some set of people, so there should be a common generalization.

My take is that many so-called definitions include additional assumptions or paradigmatic elements: for example, normativity refers to the assumption that certain codes of conduct will be universally put forth by all rational people, and thus context and culture dependence can be dropped. Maybe this can be an additional conjecture and not part of the definition. Also, consider Mill’s definition:

The rules and precepts for human conduct, by the observance of which [a happy existence] might be, to the greatest extent possible, secured.


The core value of a happy existence is built into the definition. Does ‘happiness’ subsume all other human values or do codes of conduct conducive to other human values not fall under the umbrella of morality? I lean toward embracing a plurality of possibly meaningful values.

There are some concise definitions:

Deontology: the branch of ethics concerned with the nature of duty and obligation.

Oxford Reference

This is simple, incredibly vague, and suggests that most definitions of ethics are deontic in nature (as duties/obligations resemble rules or logic, our language for formal precision). Some ethics books explain a concept over multiple pages without giving such a concise definition. I found that discussions of deontology were the worst in this regard whereas virtue ethics was defined more clearly as the philsophical stance that,

An action is right if and only if it is what a virtuous agent would characteristically (i.e., acting in character) do in the circumstances.

On Virtue Ethics

Thus I see the need to focus on the core meaning postulates without aiming for perfect definitions that will stand the test of time against all nuanced debates.