Naturalism about value is the philosophical position that value properties (e.g. moral properties, aesthetic properties, etc.) can be reduced to (or identified with) natural properties. For example, a naturalist about value might claim that an action is morally good if and only if the action increases the aggregate amount of human pleasure in the world. That is, the naturalist would try to reduce the moral property of goodness to the natural property of aggregate human pleasure. Alternatively, a naturalist about value might assert that an action is morally good if and only if the action leads to the flourishing of the essentially human capacities (e.g. friendship, intellectual activity, the arts). This latter view is along the lines of Aristotle’s position; the former is akin to the view of utilitarians like Jeremy Bentham. In both cases, what we mean by a ‘natural’ property is (roughly) a property that can be studied by the methods of natural science. Pleasure, for instance, can be thought of as a certain sort of chemical state of the brain, and can be measured with modern scientific tools.
By the beginning of the Twentieth Century, naturalism about value had become among the most important position in the Western moral and ethical thought. The influential work of the British Utilitarian thinkers such as Bentham, J.S. Mill, and Henry Sidgwick had made naturalism a common view among secular, scientifically-minded philosophers of the Nineteenth Century. Yet, with the publishing of G.E. Moore’s Principia Ethica in 1903, naturalism about value faced a stern challenge in the form of Moore’s famous Open-Question argument. The argument is best explained by considering a naturalist S who claims to identify goodness with some natural property P. (Only minor alterations to the following argument suffice to deal with moral terms like 'ought', 'should', and 'right' and other value terms like ‘beautiful’.) If S thinks that "goodness=P" is an analytic identity, i.e. the words 'good' and 'P' mean exactly the same thing, then the words 'good' and 'P' should be interchangeable in a sentence without changing its meaning. Therefore the sentences 'Is goodness good?' and 'Is P good?' should have the same meaning. Yet it is intuitively clear that if P is replaced with the usual candidate natural properties, such as 'maximizing aggregate pleasure' or 'maximizing the flourishing of the essentially human capacities’, then the two questions do not mean the same thing. The first question is 'closed', for there is no way the answer could be negative. The question ‘Is goodness good?’ is a trivial question that barely even makes sense. The second question, ‘Is maximizing aggregate pleasure good?’ is open, for it is not trivially the case that any answer to it must be affirmative. This question makes perfect sense. Many people would answer it in the affirmative, but it is not trivially answered affirmatively in the way that ‘Is goodness good?’ is. So the analytic reduction of 'good' fails.
Suppose the naturalist now tries the other option: a synthetic reduction of goodness. He claims that 'good' and 'P' do not have identical meanings, but that they are coextensive predicates, necessarily picking out the same set of entities. It is here that we invoke Frege's sense-reference distinction in response to the naturalist. If 'good' and 'P' are coextensive but have different meanings, then they agree on reference but not on sense. By hypothesis, the sense of 'P' is some natural property. But what of the sense of 'good'? It can't be a natural property, because then there would be a natural property with the same sense and reference, i.e. the same meaning, as 'good', but that was refuted by the Open-Question argument above. And so the sense of 'good' must be a non-natural property, and so, a fortiori, goodness is a non-natural property. So the naturalist must admit that there are non-natural properties, which contradicts his original position.
There are various ways the naturalist might attempt to extract himself from this Moore-Frege argument. I'll focus on attempts that try to defeat the Moorean arm of the argument. One concern with Moore's Open-Question argument is that it makes a nontrivial assumption about linguistic intuitions. A plausible view of linguistic competence is that one knows the meaning of a word W if one can recognize the correct use of W in various simple, platudinous statements containing it. Knowing a word's meaning need not involve knowing precisely the meaning of every possible sentence containing the word. For instance, someone who knows the meaning of 'chair' must be able to see the falsity of the sentence "A table is a chair". But it need not mean knowing the truth-value, if any, of "A chair-shaped formation of termites is a chair". Similarly, it may not mean knowing the precise meaning of an attempted reduction of chairhood such as "A portable seat for one = a chair", since this reduction sentence is certainly not a common platitude uttered about chairs. Hence, it may not mean knowing whether "Is a portable seat for one a chair?" and "Is a chair a chair?" have the same meaning.
The above response quibbles with Moore's method. A different approach is to accept that Moore's argument works if terms like 'good' have referents, but to deny that this is the case. For example, suppose that emotivism is true, and that saying 'x is good' is just to express a certain emotion felt toward x (equivalent to, say, smiling at x). Then it is no surprise that "Is goodness good?" and "Is P good?" are different questions. The word 'goodness' doesn't refer to a particular property, and so the first question doesn't make proper sense, which explains its apparently triviality. The second question does make sense, as P refers, and is a question about the readers emotional response to P. Hence, since the emotivist does not claim that any predicate has the same referent as 'good', he may be immune to Moore's argument.