Philosophy of Language – The Principles of the Natural World Reliance on Experience

Bayes Theorem is one of several branches of mathematics which are often referred to as “Theories of Learning” (TH). The premise of all TH is that we can construct reasonable deductions from certain prior knowledge. Many a student can recite the classic example, where you use a pencil to prove that (x) is not equal to (y), by making a series of inferences which seem to be reasonably valid because they are derived from other facts. In fact, these seemingly reasonable deductions are not actually so reasonable after all. A student could find out that, although all the premises to their argument are correct, the conclusion they draw from it is false.

Bayesians, then, are those who believe in the power of intuition or “view to self-justification,” as many would say. This school of thought was first put forward a few centuries ago by Jean Bodin, a French mathematician and philosopher. He posed the question, “What is the science?” and hoped that his answer would give birth to a new science. He defined mechanics as “the science of the proper arrangement of the various elements in Nature.”

The discipline was immediately controversial, and each school tried to refine and develop it. The outcome is a body of ideas, methods, and concepts which are still under debate today. One school, known as the rationalists, disagreed with Bodin’s views and rejected the method. Other rationalists argued that the laws of physics could be mathematically proven. Still others thought that knowledge could be gained through sensory experiences.

By attempting to answer the question “what is the law of cause and effect,” the rationalists created a paradox. They claimed that knowledge could be created and established, and thus could in effect be a matter of chance. According to this school of thought, students could learn physical laws and physical reality through experience and thereby derive the knowledge of universal physical laws from the direct experiences they had. To this day, those who subscribe to this school of thought remain relatively divided regarding what the Bayesians actually meant by “causes and effects.”

As it turned out, however, neither logic nor experience was necessary to arrive at knowledge. In fact, the axiom of knowledge was itself a creation of the great philosophers. Descartes, for example, pointed out that all truths could be understood by means of self-consciousness, and that to know a thing is to know its self-awareness, and therefore its relationship to all other things. In his work, he gave great weight to the idea of self-consciousness, arguing that all knowledge is self-knowledge. In his thoughts concerning causation, Cartes made a number of simple arguments against the common view, which has been modified and expanded by subsequent philosophers.

One of the most influential arguments of the school, based on personal experience, is that of the great chain of reasoning. According to this argument, the knowledge of a number of causes and effects can be deduced from the knowledge of the one true principle, namely the law of cause and effect. The argument goes on to state that a law of nature, such as the law of cause and effect, could in reality be a general or particular law, depending on how it is to be perceived by individuals. Therefore, in this way, it is possible to deduce knowledge from experience, as a result of which general or particular laws will then affect each individual as she observes her life.

In order to illustrate the effectiveness of the arguments of the school, it would be useful to take as an example a situation where a thief steals a box of sweets from a shopkeeper. The police come to the scene after the theft, and the shopkeeper claims, on pain of imprisonment to identify the thief. To this end, he uses the language of logic to make sense of the crime, by means of descriptions of what he saw and heard, and by indicating the likely consequences of the theft. In this case, the police evidence points to the identity of the thief, through his testimony, and therefore the validity of the law of cause and effect is therefore confirmed.

The Bayesians therefore argue that we can be justified in accepting, on faith, the existence of a priori concepts of a posteriori nature, such as the proposition that “all truths are probable,” or “the knowledge of all men is reliable.” Through experience, we learn to verify the truth of these concepts, and through reflection, we come to realize that experience proves concepts to be true, while reasoning proves them to be false. In effect, the principle of the contingency of causes and effects, according to the major philosophers, is thus an empirical one, the grounds of which rest on experience and reflection, on the one hand, and on the other hand, reason and the knowledge of mankind.