We have done enough work to specifically answer the question of how there can be a science of ethics and the only way this seems plausible is via an reductive naturalist approach, which is consistent with methodological naturalism but does not require metaphysical naturalism.
The Naturalistic Fallacy
There are three versions of the fallacy:
One cannot reduce non-natural properties to natural ones: This approach denies that non-natural properties exist - such as intrinsic prescriptivity - they are fictions. This fallacy is not committed.
One cannot define a basic property: This approach assumes these are no basic properties and so the fallacy is not committed, unless one can show this property is basic which the Open Question Argument fails to, at worst question beggingly assumes this is so and at best is just an appeal to an unsubstantiated subjective intuition that there are two distinct properties but even this does not show that moral properties are basic.
One cannot reduce a moral property to other natural properties: Without question beggingly assuming undefinability and non-naturalness this is contrary to methodological reductionism, the Open Question Argument cannot assume specialness here without question begging and otherwise relies unsubstantiated subjective intuition that there are two distinct properties. This is not a fallacy
Any science of ethics is likely to be taking a similar - if not the same - approach as here and whether you agree with the model proposed or not, the Naturalistic Fallacy is not a block to a science of ethics.
The Fact-Value Distinction
The assumption of fact-value dualism is contrary to the principles of methodological naturalism and is rejected as an unsubstantiated and metaphysical mistake. The challenge is to develop a theory of value as a type of fact, if is not a type of fact it is fiction. The way to do this is to answer:-
The Is-Ought Problem
One can accept the basic point here that
(1) one cannot derive an evaluative conclusion from purely descriptive premises and
(2) that one can drive an evaluative conclusion if there is at least one evaluative premise.
Logically only the second approach is viable and this is the challenge for a reductive naturalism to answer.
The Desire Fulfillment Theory of Value
Biological organisms appear to operate on the world to achieve states of affairs that, if achieved, are conducive to survival and successful reproduction. How can we take this, arguably just, metaphorical and anthropomorphic view of value and make it concrete? If we look at humans the mechanism of operating to produce conducive - to survival and other purposes - states of the world depends on the evolved, biological and neurological capacity of desire. Desires, as a process, are motivational brain states, at the very least and, as a product, can be described as an attitude to make or keep something true. However a desire itself has no value and the states of the world has no value, it is the relation between the two that has value - value is a dynamic relational process. So a state of the world that fulfills a desire is valued, a state of the world that thwarts a desire has is disvalued, the means to achieve valued states of the world are valuable. Both what is valued and what is valuable are dependent on desire. So value is the relation between desire and states of the world (that are the target of the desire). Change the desire or change the state of the world and the valuation of that state of the world can change, since the relation has changed.
Now a desire can be described in terms of its conditions of fulfillment and this is the answer to the Is-Ought problem by taking approach (2). That is the description of such a desire is an evaluative premise from which evaluative conclusions can be drawn.
P1: Person A has a desire that X (evaluative premise)
P2: Action Y is the only way to achieve X (descriptive premise)
C0: A has a reason to Y (evaluative conclusion)
P3: "a reason to" means "ought to" here (descriptive premise)
C1: A ought to Y (evaluative conclusion)
So far this is just a theory of value and not moral value, this ought is generic or practical and not a prudential let alone a moral ought. P3 will be explored more in the next post.
Evaluating Desires as Desires
Well previously an argument was made over the evolutionary basis of certain desires, where evolutionary success was the end and those desires were treated as means to be evaluated against and to answer were they valuable or not for that end? This is a general pattern of how to describe and evaluate desires, by treating them as means according to other ends. So we can reason over desires. And these ends can be the valued state of affairs of other desires. So we can find out the value of a desire by seeing how it is valuable or not with respect to it's effect on the valued state of the world as specified by other desires. That is we turn the fulfilling of the desire in question into a means evaluated against other desires' ends. What that type of value is depends on what other desires are considered.
Descriptive Universal Evaluation of Desires
When a scientist deals wants to investigate complicated real-world phenomenon, they seek to isolate the key factors and either though laboratory experiments or field studies obtain relevant data to analyze and test against. They examine the factor(s) of interest - the independent variable(s) in terms of their effects on the dependent variable(s) and if their research is valid will find some form of predictable relationships to develop further.
The same approach can be used here where the factors of interest are now the desires and their measurements is due to their fulfillments and thwarting. When looking at a specific situation of an interaction of two or more agents, lets look to identify the specific types of desire involved. One can factor out the amount - the number of agents - that hold tokens of those desires and also factor out the confounding factors - fulfilling and thwarting not due to the interactions of agents - and look specifically at the desire-desire interactions. This is analogous, somewhat, to population geneticists looking at populations of gene pools rather than populations of individuals.
Now we have these desire-desire interactions, one can evaluate a single desire, call it the independent desire in terms of it's material effects on all other desires whose fulfillments or thwartings are effected - the dependent desires. The independent desire is treated as a means evaluated to the ends (fulfillments and thwartings) of the dependent desires. How does one vary the independent desire? By comparing the dependent effects of its presence versus its absence. The result is a description of the amount of desire thwarting/fulfilling that the dependent desire has compared to its absence.
Given that value is the relation between a desires and the states of affairs that are the target of those desires, the above descriptive analysis describes the value of an independent desire in terms of the aggregative value of all dependent desires. And this seems to capture the universal sense morality. It is universal in the sense that anyone in the same situation would be responsible for increasing or decreasing global value based on their desires and the actions that result. It is impartial in the sense that it does not matter who the person is, there are no exceptions or double standards. And it takes account everyone who is affected without exception, everyone's interests are considered not just one or a preferred group. Finally it accurately delineates the boundary between harms of all forms (desire thwarting desires) and benefits of all forms (desire fulfilling desires). The conclusion is that the desire fulfillment theory of value applied in contexts can determine the moral value of any desire.
Desire Fulfillment is not the only model of value that has been developed there are others. For example pain/pleasure, categorical imperatives, hedonic happiness, intuition/non-natural properties, eudomonic happiness, desire satisfaction, preference satisfaction, interest/welfare, Randian "life", Divine Command, Karma and so on.
The challenge is to enable them to be used in a similar sort of analysis as above and for them to be as consistent as possible with methodological naturalism. Most fail to be epistemically objective and/or fail to deal with the fact-value distinction and the is-ought problem, leaving, arguably, pain/pleasure, hedonic happiness, eudomonic happiness, desire satisfaction, interest/welfare and preference satisfaction. The current view in moral philosophy is that Preference Satisfaction has dealt with the first three and both incorporates what is correct about them and is superior. We will take that as given here.
Now interest/welfare and desire fulfillment itself (whether of the James Griffin or Alonzo Fyfe variety) can be considered different varieties of Preference Satisfaction. The assertion here is that the Fyfe version of Desire Fulfillment (at least my understanding of it) is superior to other types of Preference Satisfaction as was partly argued for in The Problem with Utilitarianism and the Griffin/Fyfe versions together are superior because they rely only on external empirical states of the world and not internal psychological states of the mind or brain.
The next question is, is if such an evaluation of a desire, which so far is just descriptive, still it is argued a moral value, then how can it be prescriptive? For that we need to change from looking at theory of value to a theory of prescription. There were a couple of hints as to how this is done here but this will be explored fully in the next post.