What definition can we give of 'ought', 'right', and other terms expressing the same fundamental notion? To this I should answer that the notion which these terms have in common is too elementary to admit of any formal definition. (Henry Sidgwick, Methods of Ethics, Book I, Chapter III, Section 3)
Language is a tool - an invention that we may design and build as suits our purpose. If a term does not admit of a formal definition, then this implies nothing more than that our language is poorly designed and constructed, and that some modifications are in order. It is within our power to introduce a new set of formal definitions - those that we think will suit our purpose - and to see how far those definitions can take us.
In many cases, going to the effort of introducing precise definitions for vague and ambiguous terms is not worth the effort. For example, I would not suggest that we go to the effort of standardizing and specifying a definition for the word “game” – because . . . why? It would take a great deal of effort to standardize its use in the language as a whole. There is no corresponding benefit to compensate for that effort.
However, morality is an important subject. Lives hang in the balance. For practical reasons, where we do not have formal definitions of moral terms, we should adopt some.
It is important to note that adopting a set of formal definitions need not alter any of the conclusions that we adopt using those terms. We are choosing a language. A proposition that is true in one set of definitions would be just as true in another set, in the same way that a proposition that is true in English would be just as true in French.
But not all languages are equal. If this were the case, it would not be possible to improve a language – only to change it. We do improve a language – such as when we introduce new terms that allow us to efficiently communicate about things.
In ETHICS: INVENTING RIGHT AND WRONG, J.L. Mackie brought up the fact that we can choose our definitions. If a definition we are using is flawed in some way, we can discard it and bring forth a new definition that suits our purposes.
Specifically, Mackie argued that moral terms contained, as part of their meaning, a claim that its objects of evaluation contained an element of intrinsic prescriptivity - an "ought-to-be-doneness" or "ought-not-to-be-doneness" built into them that provides the reason for doing or forbearing from that action.
These properties do not exist. Therefore, Mackie argued, we should remove this from the meanings of our moral terms, and continue to use those terms with only the remaining parts.
He explained this move by noting that this is exactly what scientists have done with the meaning of "atom". It used to mean, "indivisible particle". When scientists discovered that the smallest bits of an element had parts, they dropped "indivisible" from the meaning of the term "atom". They continued to use it to the smallest parts of an element.
The terms that make up the elements are another set of terms that scientists have redefined in the light of new knowledge. "Gold", "Sulphur", and "Carbon" all got new definitions based on the number of protons in their atomic nucleus. Water became "H2O" and table salt became "NaCl".
Indeed, the practice of redefining terms for pragmatic reasons is rampant in science. In 2006, Pluto ceased to be a planet because astronomers wanted to classify like things with like. The discovery of Pluto-like objects in the Kuyper Belt meant removing Pluto from the "Planet" family and putting it in Kuyper Belt Object family.
If one had done a conceptual analysis of "Planet", it would have shown that Pluto certainly was a planet. All competent users of English counted it as a planet. It would have remained so if conceptual analysis had the deciding vote. Quite obviously, competent English speakers were calling Pluto a "planet" up until 2006. Students told to name the nine known planets would get marked wrong if they did not include Pluto on their list.
However, conceptual analysis did not have the final vote on this issue. The International Astronomical Union had the final vote and they took their vote on September 29, 2006. That is how the issue was settled - by a vote of individuals considering the practical implications of the various options available.
Perhaps moral philosophers could profit from adopting the same sort of system. It could name an international body responsible for the definitions of terms, and can then establish a set of standards for those terms. As those definitions came into conflict with reality or became impractical, the body could convene to vote on modifying those definitions in the light of new information. In the meantime, philosophers would have a standard set of definitions that they could use in their discussion.
There would still be room for debate and discussion - in the same way that astronomers debated and discussed the definition of the term "planet". People would support their candidate definitions - and object to conflicting proposals - on such grounds as whether they described differences that we could identify in the world, the degree to which they were consistent with common use or, instead, were likely to cause confusion and error, or even whether (as was argued in the case with Pluto) it would upset school children.
Even without such a committee, the main point is that when a philosopher reaches a point where a term seems to "admit of no formal definition", we need not accept that verdict. The best option at that point may well be to simply stipulate a formal definition, and see how far one can take it.
If I could - some of the definitions that I would propose would like to propose says:
"Ought" (when applied to intentional action) = "Is such as to fulfill the desires in question."
"Practical Ought" = "The desires in question are those that the agent has or will have."
"Moral Ought" = "The desires in question are those that the agent should have, which are those that people generally practical-ought to promote or inhibit using the social tools of reward, praise, condemnation, and punishment."
"Has a Reason" = "An agent has a reason to perform act A if and only if doing A will serve one or more of the agent's desires." (A modified version of Bernard Williams' proposal.)
"There exists a reason" = "There exists a reason for an agent to do A if and only if there exists one or more desires that would be served by the agent's doing A".
"Obligation" = "An act is obligatory if and only if a person with good desires and lacking bad desires (see 'moral ought') would perform that action."
"Prohibition" = "An act is morally prohibited if and only if a person with good desires and lacking bad desires (see 'moral ought') would not perform that action."
"Non-Obligatory Permission" = "An act is permitted but not required if an agent with good desires or lacking bad desires might or might not perform the action - depending on other interests."
The ultimate point being, the fact that these definitions do not conform to certain linguistic intuitions would not be an objection against them. These definitions may not conform with our sloppy and confused understanding of these terms - but we have no obligation to keep those sloppy and confused definitions. The point is to replace those definitions with something that is useful.