Friedrich Ludwig Gottlob Frege (b. 1849, d. 1926) was a German philosopher, logician, and mathematician who worked at the University of Jena in Germany. He is regarded as the father of modern mathematics, though his main interests were in geometry, arithmetic, and chemistry. In addition, he worked on methods of calculating the natural logarithm, used as an aid to algebra, and worked on the foundations of mechanics and elliptical mechanics. Among other significant contributions, he made to prove that the simplest things in nature are prime numbers (Gottfried’s formula, geometrical series, etc.). He likewise clarified and proved the existence and uniqueness of prime numbers by the application of arithmetic and algebra.
Frege’s ideas and arguments have exercised their influence even to this day. Analytic philosophers like Bertrand Russell and Oliver Lodge have appreciated and applied some of the ideas of Frege. Moreover, the main work of analytic philosophy was done by Dedekind, who pointed out the influence of Frege’s ideas on developments in set theory. Russell, Lodge, and Charette have also contributed to the development of modern algebra.
According to tradition, a logician thinks of his work as a project, not a product of his own mind. A logician may reject any idea or try to alter any of the basic premises to make the argument more valid. In so doing, he forfeits his claim to be a logician. On the other hand, a logician who accepts an existing truth as a necessary truth and uses it to construct sentences of a different kind, a finite thinker, is a finite thinker.
There are three types of logicians. Inferential logicians use set theory to solve problems of induction. Logical logicians employ syllogistic reasoning to prove truths. Freiberg is perhaps the most important of all finite logicians. He denied the existence of an eternal, absolute, and unchangeable reality. His view was that logic is constructed from sentences that could be analyzed in various ways.
He rejected many of the commonly accepted senses of reality. He used an intuitive way of knowing by means of symbols and pictures rather than by sense experience. According to him, our knowledge can be validated only by reasoning through these pictures. Thus, he denied the existence of the aesthetic sense, the sensual, sensuous, and appetitive.
Freiberg divided all reality into three levels: the physical, metaphysical, and spiritual. The physical world is governed by natural laws, such as gravity and time. Metaphysical principles are those governing the actions of our minds and bodies. Spiritual concepts are beliefs about life, God, and the future. He used intuition to prove that these concepts are real.
Freiberg’s major works include Der Natur und Essien, which covers physical phenomena; Doktor Folds, which studies anatomy and physiology; and Kugelhorn, or Theological contemplation, which explores the connection between theology and aesthetics. According to him, no concept can be understood without using sets. These sets cannot be analyzed by using experience, but only by the use of intuition. For example, the idea of a triangle can be explained by means of a set of points, while sight and touch cannot.
Most of his works are devoted to metaphysics and the relationships between God and nature. Freiberg’s book on Natural Imagination is also an impressive collection of essays and poems. In his last book, Theology, he presents his thoughts on faith, ethics, and morals. Finally, in lectures delivered before the academies, he discusses art, literature, music, science, and sociology.
Like many other naturalists, Freiberg believes that creation is random. However, he rejects the idea that God plays an active role in its development. Instead, he says that God merely anticipates the manner in which things will be, and through this, He ensures that things will work out well for man. Through this, He allows man to lead a satisfactory life. Man must therefore control his inclinations, desires, and opinions. In doing so, he will be able to create a happy existence.
According to Freiberg, reason and intuition are complementary to one another. Reason is capable of arriving at the best answers. On the other hand, intuition is capable of leading us to the most appropriate answers. Reasoning can aid in finding the proper path, but intuition will point us in the right direction. In addition, both can be used to help us learn more about the world.
According to him, knowledge and wisdom are completely necessary to achieve wisdom. He rejected the traditional concept that wisdom comes from the school and from the intellect, as these concepts are contradictory. He instead believed that these concepts go hand in hand. His thoughts attracted a lot of attention during his time, and these days, his theories are still highly respected in Germany and other European countries.