There are no objective values.
However, there are objective moral facts.
The claim that there are no objective values means that value does not exist as a property intrinsic to an object of evaluation that, in itself, demands a particular behavioral response. There is no objective goodness that demands that agents protect or create these harbors of goodness, and no objective badness that demands that agents destroy the source and prevent the creation of new sources. Nothing like this exists.
A moral claim that says that this this type of objective badness exists in rape or slavery, for example, would be false.
However, this does not imply that "slavery is bad" or "rape is bad" is false.
There are many types of objectively true statements that are not claims about the intrinsic properties of things. "The earth orbits the sun at an average distance of approximately 150 million kilometers," is an objectively true statement. However, it does not assign an intrinsic property either to the Earth (orbits the sun at an average distance of 150 million kilometers) or the sun (is orbited by the earth at an average distance of 150 million kilometers). Similarly, a statement that something is good or bad can be objectively true in the scientists' sense of the term without being a claim that something contains an intrinsic property of goodness or badness.
The same is true in morality. A moral claim can be objectively true or false even though it is not a claim about an "objective value" in the sense that ethicists often use the term. An objectively true or false claim can describe a relational property - such as the orbital relationship between the earth and the sun.
In the case of value, desirism argues that a value claim is a potentially objectively true claim about a relationship between an object of evaluation and some set of desires. A claim that something is good is a statement that there are some desires (e.g., a desire that P, a desire that Q), and some state of affairs S, where P and Q are true in S, which gives the agents with a desire that P and desire that Q motivating reasons to realize S.
All of the following propositions are objectively true or false using the scientists' concept of "objective" - even though none of them make a claim about objective value in the ethicists' sense.
Albert has a desire that P. P can be any proposition. We can, for example, make P = "Kate is married to Albert." A statement that Albert has a desire is a statement about an organ in the body (the brain), how it is physically structured, and how that structure influences observable events - intentional behavior. It is as objective as the statement, "Jim has a blood pressure of 134/88" - a proposition that any scientist would be comfortable making. It allows us to make predictions about how an agent will behave in certain circumstances. Future observations will help to verify or falsify the claim. Some complex variables might make it difficult to determine if Albert really has this desire. However, difficult-to-know objective facts are still objective facts.
For a particular state of affairs S, P is true in S. This is a simple descriptive claim about S. In our hypothetical case, we are talking about any state of affairs in which Kate is married to Albert. This is no stranger in science than talking about a state in which water is heated to 80 degrees centigrade.
Albert has a motivating reason to realize S. A desire that P is a motivating reason to realize a state of affairs S in which P is true. This is what desires do - they provide motivating reasons. If both of the previous statements are true, then this one is true.
If Albert has a motivating reason to realize S, and giving somebody else a desire that Q will aid in realizing S, then Albert has a motivating reason to give that somebody else a desire that Q. This is nothing more than means-ends rationality. Means-ends rationality can be found in a situation like one in which you want a new car and you need $25,000 to buy a new car. It implies that you have a motivating reason to get $25,000. You might not be able to get the money. There might be other things you want more (e.g., to spend time with friends and family), but you still have a motivating reason to get $25,000. When true, this is objectively true. When false, it is objectively false.
Some desires are malleable. They can be changed through interactions with the environment - particularly interactions that trigger the reward system. Rewards such as praise reinforce certain desires. Punishments such as condemnation reinforce certain aversions. Consequently, a motivating reason to give somebody else a desire that Q is a motivating reason to use the social tools of praise, condemnation, reward, and punishment to mold those desires.
There are some desires and aversions that people generally have many and strong reasons to promote. Desires to help others in times of need, make a contribution to society, promote and defend institutions that allow for peaceful cooperation, are things nearly everybody has reason to promote in others, and others have reason to promote in them. Aversions to lying, killing, breaking promises, taking the property of others, acting in ways that intimately affect others without their consent, and the like are aversions that virtually everybody has reason to promote in others, and others have reason to promote in them.
In any of the cases mentioned above the claim may be false. Perhaps we have many and strong reasons to promote selfishness and to condemn concern for others as the Ayn Rand Objectivists argue. Whatever the case may be, there is a fact of the matter that can be determined by looking at the evidence. This fact is substantially independent of the beliefs or sentiments of any individual person. No person can make it true that people generally have many and strong reasons to promote a desire to help others just by believing it or wanting it to be "true for me". It is true or false as a matter of fact.
The many and strong reasons to promote these desires in others are many and strong reasons to direct social tools such as praise, condemnation, reward, and punishment to promote these desires and aversions. This simply involves using the reward system - which is effective in molding malleable desires - to promote those desires one has reason to promote. It is true in the same sense that having many and strong reasons to change a tire implies having many and strong reasons to get the jack out of the trunk.
Moral terms contain elements of praise and condemnation. We praise certain people by calling them good and virtuous, by calling them heroes, by giving them plaques and honors, and by saying they did the right thing. We condemn them by calling them vicious or evil, calling them liars or bigots or thieves, by shunning or punishing the, and by saying that their actions are wrong. There may be cases in which a person uses moral terms without implying praise or condemnation. However, these are rare.
All of these propositions point to the conclusion that there is an objective rationality to our use of moral terms. This rationality carries through to a large set of activities related to how moral terms are used. For example, it makes sense of the logic of the excuse as a defense against condemnation, explains the possibility of conflicting obligations, links "should" to reasons for action that exists, and does all of this in a way that fits with the natural universe and, in particular, the fact of human evolution.