Mathematicians have built axiomatic systems since Euclid that have become more and more extensive and sophisticated. But Kurt Gödel performed a great service when he showed that there is much more truth to mathematics than could ever be formalized in an axiomatic system. Mathematicians gave up looking for a complete theory, except within limited domains such as first order logic.
Scientists still have the illusion that a complete theory is possible. It is common to think not only that science is true but that all truth about a subject can and should come through science. This is despite the awareness that science as generally practiced is limited to “natural” sources and methods. Let’s step back and look at this.
Consider a subject, say biology, and ask, What is the truth about this subject? If we ask most people that question, they will likely point to the science of biology as the answer to the question. But there is a difference between the science of biology and the truth about biology, even if we grant that the science of biology is true as far as it goes.
The point is that a science, any science, is limited by its sources and methods. In effect, scientists are saying, Let’s look within this box for the truth about biology, and that box contains only natural sources and methods. So before an investigation gets underway, inquiry is limited to a subdomain. Science doesn’t study biology but the subdomain of natural sources and methods in biology.
This has been pointed out by others but then what should we do about it? Some try to expand science to include other sources and methods. This may help but it will still be limited in some way. Better to acknowledge that science is incomplete and its conclusions are partial. Sciences need to be placed within a larger search for truth that does not limit sources and methods. The conclusions of science need to be input into a wider process of vetting and feedback.
But this is heresy to scientific organizations, which boost the status of science and the definitiveness of scientific conclusions. Scientists today lecture others; they are not open to input by others. After all, they are experts and are considered to have the pinnacle of knowledge.
So we go around in circles: science is incomplete but the public status of science precludes acknowledging this and doing something about it. What is lost is a genuine search for truth wherever and however it may be found. At least the mathematicians have it right.