Why shouldn't an ought be derived from an Is?

This problem has probably been around ever since people began thinking of ethics but David Hume formulated it in concrete terms in the 18th century. Basically the problem is that you cannot deduce from a set of facts what ought to be. For example, murders occur in this country. That's a fact. But, can we deduce from that fact that murders ought to occur? No. What's especially troubling is that we also cannot deduce that murders ought not to occur. That's the problem.

To illustrate consider this case. You are a student in a writing course and have an assignment to write a 10 page paper. You know the following facts: the professor has a strong policy against plagiarism and being caught with a plagiarized paper means automatic failure of the course, studies show that at least 75% of students claim to cheat in one form or another during their college career, papers are easily available for purchase online that fit your assigned topic, you have a friend who has told you that you can use his paper from last semester.

So, you have a decision to make! You can either decide what must be done and provide a good justification for this decision or ask for more facts first. But, you can only appeal to the facts to make your decision. Looked at in this narrow fashion it seems that the is-ought problem is intractable and that we cannot make any moral judgments.

But, there is a way out. If you stop and think about it, there must be since we make moral judgments all of the time. While some of these are flawed, many are good judgments. How could this be if we cannot make inferences based on facts alone?

The solution involves recognizing that there are moral facts. Are there moral facts? David Hume denied that there were and this denial has carried forward very well and is still a pervasive attitude not only among philosophers but the public at large. After all, there don't seem to be elements to morality that clearly stand out as the facts which tell us that something is right or wrong.

According to James Rachels in his book The Elements of Moral Philosophy, the mistake comes from thinking that there are only two possibilities regarding moral facts. Either they are like the facts of science or any other empirical study or there are no moral facts. But, this ignores an important third alternative. There are moral facts and these are facts of reason. The moral judgments we make are backed up by facts of reason which means that I can provide good, objective grounds for saying that a certain moral judgment is true and a certain other moral judgment is false. In other words, we can derive an ought from an is as long as we include in our facts some moral facts.

One of the reasons we think that this cannot be done is because we look at the most difficult cases, like abortion, find them difficult and from this conclude that proving anything in ethics is impossible. This is the wrong approach. To illustrate let's consider some simpler examples considered by Rachels in The Elements of Moral Philosophy:

“A student says that a test given by a teacher was unfair. This is clearly a moral judgment— fairness is a basic moral value. Can this judgment be proved? The student might point out that the test covered in detail matters that were quite trivial, while ignoring matters the teacher had stressed as important. The test also included questions about some 9 matters that were not covered in either the readings or the class discussions. Moreover, the test was so long that not even the best students could complete it in the time allowed (and it was to be graded on the assumption that it should be completed).

Suppose all this is true. And further suppose that the teacher, when asked to explain, has no defense to offer. In fact, the teacher, who is rather inexperienced, seems muddled about the whole thing and doesn’t seem to have had any very clear idea of what he was doing. Now, hasn’t the student proved the test was unfair? What more in the way of proof could we want?”

Of course you might be saying that this wouldn't convince the teacher. But, there is a distinction between proving an opinion to be correct and persuading someone. The two are different and the fact that someone is not persuaded doesn't mean you haven't proven your case. What we need is a way to evaluate, objectively, whether the evidence we're putting forward is good, relevant, evidence. Certainly in the case cited, the evidence does prove the case. I mean, what else would you have the student do to prove their case?!

We can also illustrate the point with other cases:

“Jones is a bad man. Jones is a habitual liar; he manipulates people; he cheats when he thinks he can get away with it; he is cruel to other people; and so on.
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“Dr. Smith is irresponsible. He bases his diagnoses on superficial considerations; he drinks before performing delicate surgery; he refuses to listen to other doctors’ advice; and so on.
“A certain used‐car dealer is unethical. She conceals defects in her cars; she takes advantage of poor people by pressuring them into paying exorbitant prices for cars she knows to be defective; she runs misleading advertisements in any newspaper that will carry them; and so on. “

In each case, we are deriving a moral claim from a set of facts. And, if we cannot derive these moral claims from a set of facts, we simply cannot make moral claims. After all, the facts are all we have!
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Another take on this which illustrates that we can provide a way out of the is-ought problem is offered by Sam Harris in his TED talk: Science can answer moral questions