Man is a remarkable creature perhaps unique in the universe. We think and rationalize and dream. We have a joy of living that drives us to create literature and art. We are endowed with a sense of curiosity concerning the natural world fostering the invention of mathematics and science.
But despite our technological prowess, it is ironic that as our libraries fill to overflowing, we are confronted with an ever greater list of that which is yet to be explored. Every discovery suggests not one but a multitude of new questions. And at the root of it all is a struggle to distinguish between those things we can know and those which are forever forbidden us. That there are logical limits to knowledge in both religion and science is unfortunate but undeniable. We will explore a few of these constraints which if nothing else provides a beneficial brake on our hubris as we take our measure as masters of the cosmos.
To begin, our sources of knowledge are several and self-evident. One categorization might be as follows.
1. Sensory Data. Most immediately we have the direct evidence of our senses. We can perceive the world around us filled with its wondrous sights and sounds. We can smell and taste and feel the warmth of the sun and the cold of the night. We can reach out to touch and know whether a surface is rough or smooth. Our senses allow us to take the measure of the world.
2. Self Awareness. We have thoughts and thereby know we exist as succinctly expressed in Rene Descartes’ phrase “cogito ergo sum” [I think therefore (I know) I am]. We can remember the past. We can extrapolate from experience and imagine things that might happen in the future. We can dream of what never happened and even of what could never happen. Unlike all inanimate matter, our sense of ourselves enables a free will allowing us to act in ways not strictly governed by natural law. And so our every conscious choice has a touch of the supernatural, or that which is “above or beyond nature.”
4. Logic. The human mind can reason and compare the relative merits of abstract ideas. This is the basis of geometry and symbolic logic and indeed all mathematical pursuits. Our minds can construct and manipulate perfect forms unattainable in the natural world.
4. Innate Morality. Every human being has at least to some degree a conscience which acts to govern selfish needs and desires. Every child seems to know the difference between right and wrong. And while we all have survival instincts, this inner voice sometimes, in an unnatural way, acts contrary to reason and even our instinct for survival. Societies universally eulogize those who give their lives to save unrelated individuals.
5. Communication. Others tell us of their experience and beyond that their hopes and fears and discoveries. With the advent of the written record, we have access to the collected thoughts and perceptions even of those long since passed.
6. Sacred Scripture. This refers to a revealed truth from a supernatural deity and is, of course, controversial in that unlike the other entries, it presupposes that which is not immediately obvious. We include it because the existence of the supernatural is a recurring theme throughout human history that cannot be easily dismissed. Indeed any honest reflection reveals a perhaps surprising rational foundation.
But one could not be faulted for professing a healthy skepticism. Miracles in anyone’s experience must be, by definition, rare occurrences. And all societies are perhaps unavoidably beset with charlatans and demagogues who prey on the unfortunate and weak minded. Like modern day democrats, politicians and witch doctors invent dangerous and often imaginary scenarios and appoint themselves saviors. They make promises they cannot keep, and usually have no intention of keeping, to gain personal prestige and power and wealth. They excuse inevitable failure by blaming enemies and sowing hatred and distrust. Nor is this easily corrected as, for instance, excessive subsidies for poverty and dependency tend to swell the ranks of those in need and across generations. The net result is an unfortunate but stable power base.
On the other hand, there is a single unique example of which we might take note. It remains difficult to discount the testimony of the Apostles, who spread the Christian message independently and consistently across the globe. These stalwarts literally gave their lives to affirm a truth of which they apparently had no personal doubts. Indeed Christ and his immediate followers were the textbook example of “testimony contrary to interest” which is generally afforded unusual legal weight. That is, unlike others, they sought no personal gain. That this message so resonates in the hearts of each generation down through the millennia is yet another recommendation. One might be excused for thinking that truth calls to truth.
We would claim that this somewhat tedious list is exhaustive and complete. And we would discount other suggestions to include the following.
1. We have a homeostasis or our self regulating body chemistry as well as our involuntary autonomic reflexes whose results we can sense but in the same qualitative manner as external stimuli.
2. We have an almost instinctive kinesthetic awareness of our surroundings and our position in it. This provides a muscle memory allowing us to walk and run, to hit a baseball, and to play the piano with more ease than might otherwise be the case.
3. Many have an instinctive fear of falling or of snakes or of lightening but again this is triggered by a sense of our surroundings and our imaging the danger.
4. If we are passionate about observing people and well enough practiced, we may almost subconsciously form snap judgments of another’s thoughts or intent.
5. We tend to learn from our own mistakes albeit in a often haphazard and inconsistent fashion.
6. In a similar fashion we may make an almost involuntary connection between various ideas and experience a flash of insight.
In every case these latter items are derived and not fundamental sources different from those previously described. In addition the information they convey to our conscious mind are of a constructed and secondary quality
WHAT IS TRUE (“Justified belief”)
(We make assumptions, develop and simplify axioms, derive logical corollaries, and then test results.)
LIMITS OF KNOWLEDGE
LIMITS OF ARISTOTELIAN LOGIC
QUESTIONS OF SYMBOLIC LOGIC
LIMITS OF PREDICTIBILITY
QUALITIES OF SCIENCE
(Examples of Ptolemy, Copernicus, Kepler, Planck, Schrödinger, Einstein, Feynman)
UNREASONABLE EFFECTIVENESS OF MATHEMATICS