Can we know something that has not yet been proven true?

Let us start with early man. He was a master of practical knowledge, as there were usually only two possible outcomes- danger and safety. His daily life depended on his practical knowledge to ensure survival. Theoretical knowledge had no real use, so if an early tribe believed that the sun rose and set every morning because a large dung beetle rolled it up into the sky and down again, it would not in any way affect the way that they led their lives. Early tribes handed down their knowledge from generation to generation, teaching the young to accept the doctrine of their ancestors as the absolute and unquestionable truth, making these unproven conceptions seem infallible. John Tomkinson says that “when an ethnologist asked the aboriginal Arunta of Australia why they performed certain ceremonies, they would always reply: “Because the ancestors commanded it”.” However, this approach to the question is flawed, as the question asks if we can know something that has not yet been proven true, and these conceptions of the world have since been proven untrue. For better examples, we must move further forward in history, to the leaders in logical and rational thought- the Greeks.

Over a thousand years before Galileo and Copernicus (at around 310 to 230 B.C.), Aristarchus of Samos suggested that the earth revolved around the sun, instead of vice versa. His line of argument was based on reasoning, not proof. According to Dr. David Stern of NASA, Aristarchus’ theory started when he observed a lunar eclipse, when the moon moves through the earth’s shadow. He noticed that the width of the shadow was about two times the width of the moon, and made various calculations involving angles and proportionate sizes to come to the conclusion that as the earth is smaller than the sun, it would be unlikely that the larger body would revolve around the smaller one. This may seem crude and inaccurate when compared to the advanced astronomical technology today, but the fact that Aristarchus knew that the Earth revolved around the Sun without any substantial proof shows the point that I have been trying to make.

There is also the example of proof that was not accepted at the time. This can be seen in the works of William Harvey in the sixteenth century, who discovered the workings of the mammalian circulatory system. Through detailed dissection and theoretical calculations based on the amount of blood pumped through the body on a daily basis, he showed that the heart, and not the lungs, pumped the blood through the body, and that blood was not manufactured and absorbed by the organs, but circulated through the body and returned to the heart. Although he had this substantial proof, his work was not accepted by many authorities at the time, as the previous writings on the circulatory system, by Galen of Pergamum, were thought to be the absolute truth. Some fellow doctors even denounced Harvey’s proof as invalid, saying that according to their (incorrect) calculations of the amount of blood in the body, Galen’s theory still stood. So, just because something is proven to be true doesn’t necessarily mean that it is known and accepted.

Moving away from the tangible truths of science, a fascinating example of knowing something that has not yet been proven true is found in the realm of pure mathematics. One thing that has to be noted is that mathematics is in no way a science. A researcher in a field of science’s goal is to find the truth. Even though he may use mathematics to reach this end, mathematics itself is not aimed at discovering the truth, but seeing if the conclusions reached are the “necessary logical consequences of the initial assumptions”.  Bertrand Russell even says, “pure mathematics is the subject in which we do not know what we are talking about, or whether what we are saying is true”.

The very basis for mathematical theorems lies in axioms. As Aristotle said, “it is not everything that can be proved, otherwise the chain of proof would be endless. You must begin somewhere, and you start with things admitted but indemonstrable. Theses are the first principles common to all sciences which are called axioms or common opinions”. An example of an axiom in mathematics is that a straight line can be drawn between any two points.

Kurt Gödel elaborates on the dubiousness of axioms in his famous theorem. In the early twentieth century, many mathematicians were trying to “put the theory of elementary arithmetic onto a sound formal footing”, finding a definite proof for all aspects of mathematics. What Gödel showed in his theorem that the “consistency of elementary arithmetic could not be proved from within the theory itself”, i.e. from the axioms, undermining any attempts to provide this solid basis of proof.

Having used only science and mathematics to support my claims, I could be accused of oversimplifying the question. However, I have chosen to remain in these bounds for a reason- tangibility. Science and mathematics are subjects in which proof is seen as being irrefutable, based on a long experience of experiments and research or through centuries of detailed calculations. Other areas of knowledge aren’t as clear-cut, and their proofs could easily come under fire for their vagueness and fragility.  Also, science is firmly rooted in the ‘real world’, and pure mathematics is completely theoretical, giving two contrasting areas to examine.

It is at this point that I must return to the definition of knowledge as “justified, true belief”. The examples that I have presented here show that in some cases justification is not found in proof. In the Ancient Greek model, it is found through rational thought and logic, and analysis of the surrounding world, and in mathematics it is found in the unquestionable (and unprovable) axioms that we are left with after stripping mathematics to its core. Even in the flawed example of early man’s dogmatic tradition some support can be found, as the ancestors’ word was considered to be the only justification necessary for something to be known. In the case of William Harvey, the only example where genuine proof was proffered, the use of proof as justification did not mean that his theory was known and accepted, as Galen’s age-old theory was justified by its authorship and centuries of belief.  It is therefore possible to say that something that has not yet been proven true can be known, even though the standard TOK definition of knowledge seems to refute it.