The Personality of Aristotle - Essay Example

February Aristotle established the basic principles of mathematics, distinguishing between the axiom and the postulate. Example: ‘Things equal to the same thing are equal to one another.’ (If 3 x 4 = 6 x 2, and 8 + 4 = 6 x 2, then 3 x 4 = 8 + 4) Abstract The son of a doctor, Aristotle lived and worked at a time when knowledge was starting to branch into different disciplines. Well educated, his fine language skills furnished him with the tools for analysis, calculation, interpretation and reckoning. He defined the basics of logic, upon which the building blocks of science and mathematics have been placed. Aristotelian logic is the mainstay of the methods used to arrive at logical, workable and reasonable conclusions. Born in 384 BC and living until 322 BC, he worked under Alexander the Great at the time when Alexandria in Egypt was a great center of learning. He went on to found his own school, which he named the Lyceum. The Greek philosopher Aristotle (384 - 322 BC) did not confine himself to one subject or discipline. He studied under Alexander the Great and Plato, at a time when knowledge was grouped together, seen as inter-connected: it was only much later that the various disciplines, simply because so much knowledge had been added and there was so much to learn, were separated to the branches we know today and studied in isolation. Here, an attempt will be made to explore the contribution Aristotle made to the branch of knowledge that was even then known as mathematics. Since his father Nicomachus the doctor died young, Aristotle could not inherit his knowledge and his profession. In those days, knowledge was considered mental, and went orally and practically from father to son, rather than than written in books. But Aristotle was only 10, so instead, he had to study under Proxenus who taught him Greek, poetry and rhetoric, and built upon the biological information gained from his father (JOC/EFR 1999). He travelled to Athens when he was 18 and joined Plato’s Academy, where he studied and later taught. Political events meant he had to move on a number of times, which put him in contact with many learned men and great thinkers such as Xenocrates. This was the Hellenistic period, when important discoveries were being studied and built upon what earlier mathematicians and scientists, such as Pythagoras, had taught. Alexander the Great’s school - in Alexandria, Egypt - was the most important in the Mediterranean basin. It remained the center of mathematics for over a thousand years, until the library was raided by the Muslims in about 700 A.D. (Allen 1997). It is important to remember that the Arabs were among the first to find an arithmetical system. Among those carrying out studies connected with this center were Archimedes, whose principles became well-known and indispensible. Greek was the language of scholarship: it was excellent for reasoning, and since Aristotle was well brought up and educated, his language skills furnished him with the tools for analysis, calculation, interpretation and reckoning. The Hellenistic time was when the rules of geometry were nutted out, together with the ideas for formal proof. In this area, Aristotle did a lot of thinking and discussing - which was the method of teaching of the day. Without formal rules for proving and establishing fact, it would be impossible to formalize mathematics or science, so this was an important time in the history of mathematics. Aristotle was fundamental in establishing the ways of thinking necessary to make mathematical calculation possible, against a set of standards. Another factor that made Aristotle important is his recording of things studied, which provided evidence for those who later wrote histories of mathematics. Part of his contribution, therefore, is his perpetuating fact to enable others to read it (Hodgkin 2005). Fauvel and Gray, two mathematicians who did a lot of research into ancient Greek mathematics, give many extracts from Aristotle’s sources (Hodgkin ibid). Aristotle believed that logic must be applied to the sciences and to mathematics. ‘The sciences - at any rate the theoretical sciences - are to be axiomatised,’ he wrote. How people think mathematically is in part due to his works known as ‘Prior and Posterior Analytics’. In a simple way, this can be explained as a way to analyze, which determines the correct order in which things happen. We know today that this avoids circular reasoning (Allen 1997). In his Metaphysics, Aristotle goes into great details about reality, and how all processes are ultimately material. These are not simple concepts for the student to understand, and the prose of these writings - generally translated by wordy scholars - can be quite daunting. However, it is possible to conduct a simple mathematical search, to count the number of times the word ‘mathematics’ occurs in this, one of Aristotle’s most important works. It is an astonishing fact, that for a philosopher - and for one who is generally not though to have made much of a contribution to the discipline of mathematics - the word occurs over 50 times, scattered evenly over the book. This gives the student a lot to consider: if in works such as Metaphysics, Aristotle pays so much attention to the subject of math, he must certainly have given it a great deal of weight in the way conclusions are reached when making any sort of reasoned argument. His axiomatic way of sorting similarities and differences, for example, must have been sorted out mathematically for it to have given him any reassurance that he was right (Aristotle and Lawson-Tancred 2009). It is not hard to imagine the old haughty philosopher, in the Lyceum, a school he instituted as a counterfoil for the Academy, showing students how logic worked by using mathematical examples on a clay tablet, with his stylus, scribbling numbers and shapes. It is not without cause, therefore, that Aristotle had a significant impact on the way mathematics is practiced. In all other sciences, too, Aristotelian logic is the mainstay of the methods used to arrive at logical, workable and reasonable conclusions that can be repeated, proved and debated, and can be shown to give the same results. Mathematics and science need to be reliable in this way. Aristotle was so confident of his math that he wrote a biography of Pythagoras, which must certainly have contained a number of rational arguments about that mathematician’s conclusions. Unfortunately the work has been lost, but few doubt that he was a good candidate to take on such a daunting task (Hodgkin 2005). No one can mention method and logic without mentioning Aristotle: the disciplines of science and math, and the principles they operate under, are largely the legacy of this philosopher who taught the world how to think. Sources cited Aristotle (2009) Metaphysics Translated by Hugh Lawson-Tancred NuVision Publications Allen, Don (1997) The Origins of Greek Mathematics < http://www.math.tamu.edu/ ~dallen/history/greekorg/greekorg.html> Accessed February 26, 2010 JOC/EFR (1999) Aristotle: Biography School of Mathematics and Statistics, University of St Andrews, Scotland Accessed February 26, 2010 Hodgkin, Luke (2005) A History of Mathematics: From Mesopotamia to Modernity Oxford University Press Read More