Philosophy in Mathematics Education – Mathematica Education

In lectures on mathematics philosophy in this semester, I got a lot of knowledge and benefits from this lecture. Before learning philosophy we often think that philosophy is only for great people. Often people assume that philosophy is a very high science, that if there are people talking there is the word “philosophy”, the other person will immediately respond that “high level language”. Many people will also say that they cannot or are unable to philosophy. We often do not realize that in our lives, we always philosophize only because we do not understand the understanding of philfasat so that we are mistaken in interpreting philosophy.

Literally philosophy, namely philosophyThe term philosophy comes from Greek, philosophyconsists of two words: Philos (love) or philosophy (friendship, interested in) and Shopia (wisdom, wisdom, knowledge, skills, practical experience, intelligence). So etymologically, philosophy means love of wisdom or truth. Plato called Socrates as philosophy (Philosophy) In the sense of lover of wisdom. Philosophy is the view of life of a person or group of people who are the basic concepts of life that are aspired to. Philosophy is also interpreted as an attitude of someone who is aware and mature in thinking about everything in depth and wants to see in terms of broad and comprehensive aspects of all relationships. In the Big Indonesian Dictionary, the word philosophy shows the meaning in question, namely knowledge and investigation with reason about the nature of everything that exists, because of its origin and law.

If you look at the understanding of the above philosophy, we will find that philosophy is very closely related to life. Everything that happens in life can be made as philosophy. From the above understanding it can be concluded that philosophy is the science of human thought. So every human thought is philosophy so that none other than philosophy is ourselves.

Pay attention to from our lives, the things we do from waking up to sleeping soundly, actually the philosophy exists. But often we do not pay attention to that, what we know is only limited to doing and living this life but interpreting what will, is and we have done as a routine. We only remember the incident without taking the meaning or learning of life. All we know is that events are good or bad, fun or sad. We never even know or remember what we have done.

In philosophy there is no base and no end. In philosophy nothing is impossible, in philosophy always talks about what exists and that may exist. As we already know, that philosophy is a science of thought, the study of phenomena that occur in our lives. Philosophy we cannot get from experiments or experiments, because philosophy is pure, not made up, no one is able to make philosophy. Philosophy will come by itself. Philosophy will always penetrate space and time, so that philosophy will be relative, there is no benchmark about everything that happens in our lives. No one can justify and blame all things that are there and that might exist. Everything depends on how we think about it, from what side or aspect we see and think about it. Considering that philosophy talks about what exists and that might exist, no one can limit our minds, so that no one can limit philosophy. Humans have complete dimensions, namely the material, spiritual, formal, and normative dimensions.

Space is limited, an easy dimension is zero dimensions, one dimension, two dimensions, three dimensions, and more difficult, the dimensions of four, which the lay space may not be able to think about it. Mathematics can mention sample space, random space, building space, and so on. Space in philosophy can include normative, formal, material, spiritual, husband and wife, children, lecturers, students, who exist and those that may exist. Then what is called penetrating, for example, we know ourselves in the village have different abilities as a formal to penetrate space and time. What is called time? Imannuel Kant divides time into three, namely sequential, sustainable, and unified time. To understand time we need space. Why is that? In showing time, we usually use the clock, that clock is a space.

Philosophy, especially Western philosophy has appeared in Greece since about the 7th century BC. Philosophy arises when people begin to think about and discuss the state of nature, the world, and the environment around them and do not depend on religion anymore to find answers to these questions. The first Greeks to be given a philosopher were Thales from Mileta, now on the western coast of Türkiye. But the biggest Greek philosophers of course are: Socrates, Plato, and Aristotle. Socrates is Plato’s teacher while Aristotle is a student of Plato. Some even argue that the history of philosophy is nothing but “mere comments from Plato”. This shows Plato’s enormous influence on the history of philosophy.

Western philosophy is a science that is commonly studied academically in universities in Europe and their colonies. This philosophy develops from the tradition of ancient Greeks.

Eastern philosophy is a philosophical tradition that mainly developed in Asia, especially in India, China, and other regions that have been influenced by their culture. A characteristic of Eastern philosophy is the closeness of philosophical relations with religion. Although this is more or less can also be said for Western philosophy, especially in the Middle Ages, but in the Western world philosophy ‘Alone‘Still more prominent than religion.

This Islamic philosophy actually takes a special place. Because judging from history, the philosophers of this tradition can actually be said to be the heirs of the tradition of Western Philosophy (Greece).

The streams in philosophy

1. Rationalism

Rationalism is a philosophy of science that holds that the ratio is the source of all knowledge. Thus, the criteria for truth are based on intellect. The strategy of developing science model rationalism, thus, is to explore ideas with human intellectual abilities. Since the century of enlightenment, rationalism has been associated with the introduction of mathematical methods (continental rationalism). Rationalism figures include Descartes, Leibniz, Socrates, Baruch Spinoza and Spinoza.

2. Empiricism

Empiricism is a philosophical orientation related to the emergence of modern science and scientific methods. Empiricism emphasizes that human science is limited to what can be observed and tested. Therefore, the flow of empiricism has a critical nature of abstraction and speculation in building and gaining knowledge. The main strategy of acquiring knowledge, thus, is carried out by applying scientific methods. British scientists such as John Locke, George Berkeley and David Hume are the main founders of the empiricism tradition.

3. Realism

In philosophical thinking, realism holds that reality is not limited to sensory experience or ideas that are built from within. Thus realism can be said to be a form of rejection of extreme ideas of idealism and empiricism. In building science, realism provides a theory with an empirical induction method. The main idea of ​​realism in the context of acquisition of knowledge is that knowledge is obtained from dual things, namely observation and development of new thoughts from observations made. In this context, scientists can analyze the categories of phenomena that theoretically exist although it cannot be observed directly. The tradition of realism recognizes that abstract entities can become real (reality) with the help of linguistic symbols and human consciousness. This idea is parallel to the modern philosophy from the knowledge approach of the fenomological version of the fenonomology to the structural approach.

4. Idealism

Idealism is a tradition of philosophical thinking that holds that the doctrine about external reality cannot be understood separately from human consciousness. In other words the categories and ideas exist in the space of human consciousness before the sensory experiences. Plato’s view that all concepts exist separately from the material entity can be said to be the source of the radical idealism view. Plato’s work and views provide a clear demarcation line between idealistic thoughts and materialist views. Aritotle became the person who gave the challenges of thought for Plato’s idealistic ideas. Aristotle bases his philosophical thinking based on material and physical.

5. Positivism

Positivism is a doctrine of philosophy and social science that places the central role of experience and empirical evidence as the basis of science and research. The terminology of positivism was introduced by Auguste Comte to reject the subjective value doctrine, replaced by facts that can be observed and the application of this method to build knowledge that is devoted to improving human life. The most influential figures in developing the tradition of positivism are Thomas Kuhn, Paul K. Fyerabend, WVO Quine, and other philosophers. The thoughts of these characters open the way for the use of various methodologies in building knowledge from ethnographic studies to the use of statistical analysis.

6. Pragmatism

Pragmatism is a massive philosophical thinking pioneered by CS Peirce, William James, John Dewey, George Herbert Mead, FCS Schiller and Richard Rorty. The pragmatism tradition arises over the reaction to the dominant idealistic tradition that considers the truth as an abstract, systematic and reflection entity of reality. Pragmatism argues that the philosophy of science must leave transcendental science and replace it with human activities as a source of knowledge. For adherents of pragmatism, science and truth are a journey and not a goal.