Consider the argument over abortion. The two sides may argue over how the legality of abortion affects family structure, illicit sexual relations, and the crime rates in society. These disagreements can, at least in theory, be settled by investigation of facts. Enough research might be able to show the literal effects of abortion, such as whether women who have abortions have a higher chance of contracting mental illnesses, for example.
However, the disagreement is about more than just facts. There may be situations where people on both sides of the issue agree completely on the facts of the matter, may even have perfect knowledge of the facts, yet still disagree on whether abortion should be legal. One side may believe that the woman's bodily autonomy trumps all other considerations, while the other may believe that the right to life of the unborn trumps all other considerations. This is not a disagreement over the facts of the matter, but over which considerations trump which other considerations. It is a disagreement over value, and these values cannot be verified or even perceived by sense experience.
There are two fallacies that accompany this distinction. The first is the naturalistic fallacy. People commit the naturalistic fallacy when they derive a value from a fact. Consider the following argument:
(1) Sam is a human
(2) Humans feel pain if you hit them
(3) You should not hit Sam
This is a fallacious argument. The conclusion (3) simply does not follow from the premises. And you can add all the facts you want, such as:
(3) Pain is a form of suffering
(4) Sam does not want to suffer
(6) If Sam suffers, it will not prevent the worst possible misery for everyone
and still never be able to entail the conclusion. You need to add a "should" or "ought" statement in order to entail that conclusion.
The other fallacy is the moralistic fallacy. Consider the following argument:
(7) Women and men should have equal rights
(8) Women and men have equal abilities
(9) No one should live in poverty
(10) Social programs ought to keep people out of poverty
(11) Social programs do keep people out of poverty
As the opposite of the naturalistic fallacy, it starts with "ought" statements, and concludes with an "is" statement. Again, no amount of additional "ought" premises will give us an "is" conclusion. Feminist groups commit the moralist fallacy all the time. As Daniel Miessler notes:
Up until around 50 years ago–i.e. for the last tens of thousands of years–women have been considered “things”, and men have been considered “those who get things”. The fact that this ancient reality has not been eradicated in the eye-blink of the social equality movement should fail to surprise anyone. . .Here is the problem: if naturalism (the cosmos is all there is, was, or ever will be) is correct, then the only facts of the matter are the "is" statements about space, time, fields, particles, and energy. All facts of the matter are reducible to these facts. Values simply are not objective. Many Internet atheists will bite the bullet at this point and state that the values we have, such as "murder is wrong" are not really objective facts about reality, but are something else.
Slavery is natural. Racism is natural. And so is sexism. We are primates pretending not to be, and every step on the ascent up Mt. Moral will be taxed by the gravity of our animal selves. The fact that these things are natural doesn’t mean we stop working against them, but it does mean we can stop looking for less obvious reasons for their existence. Alas, no additional actors are required.
So I join you in opposing sexism wherever it emerges, but not in assuming it’s some recently contrived tool devised by evil men. We are still the animals we used to be, and unnecessary mystery greets us whenever we forget this.
Theists, on the other hand, believe in the existence of a perfect being. In God, fact and value, is and ought, are one and the same. Fact = value. Is = ought. That is what it means to be a perfect being. If such a being exists, then we have a bridge between fact and value, and between is and ought.
The real kicker: consider an argument you had in the past over which religion is correct, or whether or not God exists. There is a good chance that even if you and your opponent agreed on all the facts of the matter, you might still come to different conclusions. Why? Because you have different criteria for what counts as a successful argument for or against your position. People of different positions disagree all the time over criteria, such as who has the burden of proof. Are these criteria facts or values? We just established that two people can agree on all the facts and yet disagree based on criteria, so criteria are values.
If there are no objective values, then there are no objective criteria by which one ought to judge arguments for anything. Yet, all arguments presuppose that there are such criteria, or else there would be no point in making the argument! An appeal to pragmatism will not get you out of the problem, because what is or is not practical is subjective.
Imagine that there are two routes you could take home from work. The highway will get your to your destination 10 minutes faster, but the back roads will give you a less stressful drive. Which one is more practical? It depends on whether you value a shorter trip or a less stressful one. It is subjective, and therefore cannot rescue objective value from this problem.
Without a perfect being, there can be no objective, factual criteria by which one ought to judge arguments for or against such a perfect being. In short, if there are any objective criteria by which one ought to evaluate arguments in the first place, then it follows with logical necessity that God exists.
For a more complicated and rigorous version of the argument, see Roger Wasson's version on the Ultimate Object website.