1. Logical and Mathematical Truths
As Dr. Craig points out, science presupposes the existence of logical and mathematical truths so that to try to use science to explain them would be to argue in a circle. Anything that science presupposes cannot itself be explained by the scientific method, or else you will be guilty of this logical fallacy.
2. Metaphysical Truths
The example that Dr. Craig gave was the truth that the earth was not created 5 minutes ago with the appearance of age. Again, the scientific method makes metaphysical assumptions and therefore cannot be used to prove or disprove these assumptions.
3. Ethical Truths
The scientific method cannot be used to account for ethical truths. In fact, this is a dangerous place to go with the scientific method, since allowing science to make our ethical judgments leads to all sorts of horrendous, immoral acts. Dr. Craig rightly points out that the scientific method cannot prove whether the Nazi regime was wrong or right in committing its atrocities.
4. Aesthetic Judgments
The scientific method cannot tell me whether a painting is beautiful or ugly. It cannot tell me whether the night sky is a thing of beauty or a thing of horror.
5. Science Itself
Dr. Craig points out that science itself is full of assumptions that cannot be proven. Again, any assumption made by science cannot be proven by science without arguing in a circle.
After hearing this speech today and being reminded of this debate, I would like to add on to Dr. Craig's list. Here are some more truths that cannot be proven by the scientific method.
6. Historical Truths
Historical truths cannot be proven by the scientific method. The scientific method requires the observance of phenomena. None of us can go back and observe Abraham Lincoln's inauguration, for example. None of us can experiment with him by placing him in the White House, and then removing him to see what happens, and then replacing him again. Thus, historical truths lie outside the realm of science.
7. Archaeological Truths
Science cannot verify that the archaeological finds made today are actually from, say, a trade route between two major cities in the Middle East. This is merely an interpretation based on assumptions made about a particular find. Archaeological truths cannot be tested by experimentation, and these experiences cannot be repeated. Thus, while some may consider archaeology a science (and many do not), archaeological truths are not derived from the scientific method.
8. Epistemological Truths
Epistemological truths are truths about how we know the truth. Can science prove how we know the truth? Not if it assumes that it can know the truth by the scientific method. In other words, epistemological truths cannot be proven by the scientific method, since epistemological truths are assumed by the scientific method.
9. Legal Truths
Legal truths cannot be proven by the scientific method. Science cannot tell me whether one law or the other would be the better law to pass. Science also cannot tell me whether it is better for a person to be sentenced to life in prison or to the death penalty. These are judgments made based on other assumptions.
10. Moral Truths
While this may appear to be the same thing as ethical truths, there is a distinction between moral and ethical. Ethics has to do with societal standards of right and wrong. Morals, on the other hand, has to do with belief in whether something is good or evil. This may be illustrated by pointing out that someone who follows every ethical standard of his or her practice may not demonstrate any morals at all. Moral truths are inaccessible by the scientific method, and therefore cannot be proven by them.
11. Anthropological Truths
Anthropology has to do with the development of human beings throughout history. These cannot be directly observed, and therefore rely on assumptions made by branches outside of science. That is, when you discover that bone, was this indicative of how everyone looked at this time, or did this individual have a deformation? We cannot go back and observe this. Thus, assumptions beyond the scope of the scientific method must be made to address this issue.
12. Absolute Certainty
The scientific method cannot establish absolute truth. The scientific method is, by definition, an inductive method. An inductive method, by definition, cannot establish absolute certainty for anything that it touches. Only deductions and mathematical proofs can establish such certainty.
The scientific method is a useful tool for discovering truth. However, we need to realize that it, like every discipline, has its limits. We need to recognize these limits and not overstate the effectiveness of any one branch of study.