When Mathematicians, Historians, and Scientists Say That They Have Explained Something, Are They Using the Word Ð''explain' in the Same Way?

When mathematicians, historians, and scientists say that they have explained something, are they using the word Ð''explain' in the same way?

Marcel Wallace

IB #001089

TOK #1(Final Draft)

Word Count:

We all have ways of acquiring information about the complex world in which we live. Mathematicians, historians, and scientists each have their own respective procedure of determining truths and justifying their judgments. Each uses their own Area of Knowledge to present findings and explain occurrences. But, since they are coming from various Areas of Knowledge, are their methods of explanation different, even though we accept their work as truths all the same? Mathematicians, historians, and scientists explain things using varying types of evidence exclusive to their field, but there is still some overlapping between the methods of explanation.

Even though we see differences between the methods of explanation in the various Ways of Knowing, there often times that the process in each way of knowing begins with perception. Perception is the awareness of an entity by use of the senses. It combines different sensory stimuli over time into a single unified whole. The result is the awareness of things and ideas. Mathematicians, historians, and scientists acquire raw information about the world around us through perception. They can then take that information and try to understand it. All knowledge still though, is derived from this common root. Often times in these disciplines there is overlapping of fields: scientists use math to figure out a problem or predict results, and historians will sometimes use science to explain or prove their assumptions.

The word 'explanation' is used in a wide variety of ways in the English language. We speak of explaining the meaning of a word, explaining the background to philosophical theories of explanation, explaining how to bake a pie, explaining why one made a certain decision, explaining irregular occurrences and so on. We can distinguish between two basic kinds of explanations, inductive and deductive. Induction is usually described as moving from the specific premise to the general conclusion, while deduction begins with the general premise and ends with the specific conclusion. Explanations based on experience or observations are best expressed inductively, while arguments based on laws, rules, or other widely accepted principles are best expressed deductively. For example, Carlos says: "I've noticed previously that every time I kick a ball up, it comes back down, so I guess this next time when I kick it up, it will come back down, too". Tadahito says: "That is Newton's Law. Everything that goes up must come down. And if you kick the ball up, it must come down". Carlos is using inductive reasoning, arguing from observation, while Tadahito is using deductive reasoning, arguing from the law of gravity. This theme is clearly evident in the ways of Knowing. Mathematicians and scientists have certain laws and rules they must abide by in their respective areas so deduction is more often their method of explanation. The historian however has more freedom to induct or deduct to explain historical events.

A mathematician is some one whose primary area of expertise is the study and research of the Area of Knowledge, mathematics. In addition, a mathematician contributes new knowledge to the field of mathematics, such theorems or postulates. Mathematics is a unique Area of Knowledge because it is closed system of knowledge with its own set of rules and regulations that must be followed. Like other scientists, mathematicians usually start with hunches and then conduct symbolic or computational tests, involving strictly numbers, to test them. Unlike in the sciences however, fundamental explanations in much of mathematics do not consist of performing experiments. Rather, mathematics is about problem solving, where truths are deduced from other known or accepted truths.

The term 'science' refers to the an analytical and logical systems of acquiring knowledge or the organized body of knowledge humans have gained based on empiricism, experimentation, and methodological naturalism- assumption that perceivable events in nature are explained only by natural not super natural causes. A scientist is an expert, who uses