If you see errors in logic or would like to discuss this, please post something in the comments section.
Another note: Discussing philosophy and ethics is much more fun when it’s a multi-agent dialogue. If you wish to have an easier time following along with problems like this, you ought to talk to someone about this.
David Hume was a Scottish empiricist, who believed that all knowledge was derived from sense experience alone. He is perhaps most famous for popularizing the “Problem of Induction”. I’ll address that in a later article. For now, however, we focus on his “Is-Ought problem”. The Is-Ought problem is a problem of how to derive moral judgements, namely, “Ought” statements, from facts of the world, or, “Is” statements.
For instance, it may be said that “One ought to run fast”. But no fact of the world is a valid reason to run fast. It can only be (rationally) said that “One ought to run fast if one wishes to win the race”. The fallacy in this instance then, lies with whether one wishes to win the race. There are several rebuttals to this, and I shall present two.
The first is known as fact-value entanglement, and notably advocated by Hilary Putnam. The issue raised by the entanglement is that, “you cannot explain the activities that conform the task labeled as “describing what the facts are” without introducing a good deal of values in the picture”, Angel M Faerna writes in Moral Disagreement and the Fact Value entanglement. 
A.N. Prior says that from the statement that someone is a sea captain it follows that he ought to do what a sea captain is doing. However, this seems to not be the case. The set or category of “sea captain” only encompasses people who are doing what sea captains do, not those who ought to be doing what sea captains do. The claim that a sea captain should or ought to be doing what a sea captain does seems to me the wrong sort of ought. It follows only in the sense that, “If one is a sea captain and my expectation of a sea captain are correct, he will be doing what a sea captain does.” The ought is a different kind of “ought” and I therefore say that it is a false equivalence.
Immanuel Kant provided perhaps the most famous response to the is-ought problem. The categorical imperative is composed of three maxims. The first is the Formula of Universality, which states, “Act only according to that maxim whereby you can at the same time will that it should become a universal law.” However, this maxim allows for certain immoral actions. A consequence of the universality exemplified by Kant’s Formula of Universality is that no difference can be made from the circumstances of the situation. Lying to protect a child is no more moral under the Formula than lying as a stock swindler, for instance. Most people do not consider lying to protect a child immoral because it protects a child’s life. By protecting the child’s life, it stops a hypothetical murder. This outlines my essential problem with maxim-based systems of morality. Different people under different circumstances will derive different maxims from the same situation. The statement that the person was merely saving a child seems to be no less valid than the claim that they were lying.
James Fieser of University of Tennessee Martin states that this problem is naught, because Kant stated that maxims were to be created from underlying motive. For instance, he gives the example of hitting a pedestrian with a car. Kant would, according to him, use the underlying motive as a maxim. For instance, I may have hit the pedestrian because I hated him. However, this seems to create an infinite regress of motives no better than that created by the Is-Ought problem. What was the motive for hating him, what was the motive for that…etc?
In addition, even if motive could be absolutely defined, that motive may not determine morality. For instance, in Star Wars, the Empire’s motive in destroying Alderaan was to suppress rebellion and maintain order. According to Kant, this is a perfectly fine action because the motive can be made universal while remaining logically consistent.
Kant’s second formulation, The Formula of Humanity, is based on the first formula and the distinction between objective ends. It states that people should not be treated as a means to an end, but as an end themselves. The third maxim is merely an extension of the other two maxims, and states that each will must be universally self-legislating. Things we will must be willed to ourselves as well.
However, again, the second and third are based upon the first, and I disagree with the first. As stated before, moral laws seem to be based upon numbers of examples and counterexamples. Based on an examination of how moral systems are developed, I believe that a maxim is only supported insofar as it produces logically following moral results that are agreeable to the population. See my example of The Surgeon Problem above.
The most interesting, but likely the most complicated response to the is-ought problem is John Searle’s example of lending money. It follows (his revised example): 
P1: Jones uttered the words, ―I hereby promise to pay you, Smith, five dollars.
P2: Jones promised to pay Smith five dollars.
P3: Jones placed himself under (undertook) an obligation to pay Smith five dollars.
P4: Jones is under an obligation to pay Smith five dollars.
P5: As regards his obligation to pay Smith five dollars, Jones ought to pay Smith five dollars.
Essentially, the obligation rests on the idea that facts can be separated into two types—brute facts (facts which are non-reducible), and institutional facts (which are). For instance, the article I cited provides these as examples. “Judith has a million dollars”, and “Raymond won the tennis match” are reducible to the statements “Judith has a lot of paper with green ink on it”, and “Raymond hit the yellow sphere and the person on the other side of the net did not hit it back.”
Essentially, this divide means that within Institutional Facts, ought judgements can be derived. Within the example of lending money for instance, institutionally, a promise is composed of an “ought” (that one ought to pay back the money), so this promise comprises a judgement.
My attempts at a response:
While obviously not a philosopher, and this obviously not being a truly logical response, I will present this as my attempt.
My response follows as such. In saying that it is impossible to derive an ought from an is, Hume makes a perfectly sound logical argument. However, if this argument were true, we would have no reason to believe or accept it. The only way in which we would have an obligation to believe it is if there were some way to find moral judgements, which itself refutes the argument.
If moral reasons are presented without logical support from “is” statements, and can still be considered binding, then this rule could apply to every ought judgement. Without a reason to follow logic, we have no reason to follow logic or even Hume’s own argument. The only world in which in which it is permissible to logically say that we “ought” to follow Hume’s argument is one in which either it is possible to derive an ought from an is, or one where it is logically permissible to assume them without logical support. Of course, this doesn’t logically refute the issue, only points out that it is self-defeating.
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