Desirism denies the proposition that you cannot derive "ought" from "is". Actually, given the form of "ought" that desirism uses, there are few who deny that "ought" can be derived from "is". The derivation is straight forward.
• Agent desires that P (for some proposition P) • Doing X will realize P ----------- • Therefore, Agent ought to do X.
This 'ought' can be overriden by stronger concerns elsewhere. This is not an 'all things considered' ought (or an 'all desires considered' ought).
However it is still the case that, in the absence of other concerns, the agent ought to do X. This is a classic hypothetical imperative. It gets this name because the "ought" clause is conditional on what Agent desires. Hypothetically, if Agent's desires change - if he changes from wanting P to wanting Q, and doing X will not realize Q - then what he ought to do changes. It would no longer be the case that he ought to do X.
This derivation of a hypothetical 'ought' from 'is' is not considered a problem. The problem comes from the fact that there seems to be another type of 'ought' - the moral 'ought' - that is not hypothetical. For this type if 'ought', there is no derivation from 'is'. To illustrate this second type of 'ought', if I were to say 'You ought to tell the truth when you are under oath,' this is not generally understood to be a hypothetical imperative. In the moral sense, this does not translate into, 'If the things that you want can be gained by telling the truth under oath, then you ought to tell the truth under oath.' Instead, it says that no matter what the agent wants, the agent ought to tell the truth under oath.
This 'ought' is unconditional. This is the type of 'ought', it is argued, that cannot be derived from 'is'.
Desirism states that the reason this type of 'ought' cannot be derived from 'is' rests on the fact that it does not exist. It is not real. It is a fictitious or mythical 'ought'. Ultimately, desirism does not recognize a distinction between 'is' and 'ought'. It only recognizes a distinction between 'is' and 'is not'. Any 'ought' that cannot be derived from 'is' is an 'ought' that 'is not'.
If we are going to claim that 'moral ought' has any type of influence in the real world - that real-world atoms changed their velocity as a result of the influence of some 'moral ought' - that at some time or some place a moral ought reached out and changed a person's behavior and changed the world - then we need to fix that 'ought' in the real world. It has to be something capable of producing real-world effects. If 'moral ought' has no influence in the real world - if everything that happens in the world is entirely unaffected by 'moral oughts' - then we have no real-world reason to refer to them. They are not real-world reasons to adopt a law or an institution, to perform an action, or to engage in real-world praise and condemnation.
Consequently, desirism states that, where non-hypothetical 'ought' does not exist, we are stuck with hypothetical 'oughts' - the type that are unproblematically derived from 'is'. However, there is a specific set of hypothetical imperatives that functions so much like a moral ought so as to be nearly - if not entirely - indistinguishable from it. On this account, "Ought to do X" implies "People generally have many and strong reasons to praise those who do X." Their reasons for praise have to do with tapping into the reward system of the human brain to promote stronger and more widespread sets of desires that would motivate people to do acts like X. Those reasons for tapping into the reward system in this way have to do with the desires that people have. That this 'ought' relies at its base on desires makes it a type of hypothetical 'ought' that can be derived form 'is'.
On this model, "You ought not to lie under oath" implies "People generally have many reasons to condemn those who lie under oath" because the aversion to lying under oath - made more widespread and stronger through certain acts of praise and condemnation - will tend to help in the fulfillment of many and strong desires.
Among other things, this explains why moral statements include elements of praise and condemnation and why they tend to refer to act-types (or acts relevantly similar to the act in question) rather than to specific acts. It also serves to explain what qualities are relevant in defining the range of an act-type; they are the set of actions that would be influenced by the desires being targeted. It also provides a moral claim with a truth value that does not depend on the sentiments of the speaker, and one that contains emotivist elements of praise and condemnation that serve a real-world purpose relevant to the truth value of the claim.
While the agent can respond that he does not care about what people generally have reason to praise/condemn, it does not change the fact that people generally and genuinely do have reason to praise/condemn such a person - where praise or condemnation is built directly into the moral claim right beside its truth value. It provides a moral claim that makes use of many of our practices. For example, it makes sense of moral counter claims such as an excuse or a charge of negligence. If we take a moral claim to be a claim about what people generally have many and strong reasons to condemn, then an excuse is a claim that refutes the assertion that the act is one that people generally have many and strong reasons to condemn.
Finally, this 'ought' can be derived from 'is' and has a real-world effect on real-world events.