What is intuitionism?

Intuitionism is a mathematical philosophy that claims that mathematics is a purely formal creation of the mind. It came up at the beginning of the twentieth century by the Dutch mathematician L.E.J. Brouwer. Intuitionism assumes that mathematics is an internal process that is empty, and consistent mathematical statements can only be conceived as mental construction. In this sense, intuitionism is contrary to many main principles of classical mathematics, which claims that mathematics is an objective analysis of external existence. In addition, it does not assume that mathematics is a symbolic language that must follow certain fixed rules. Since symbolic characters commonly used in mathematics are considered pure mediation, they are only used to transmit mathematical ideas from the mind of one mathematician to another and in itself does not propose further mathematical evidence. The only two things that assume intuitionism are the awareness of time and existence creating mind.

intuitionism and classical mathematics each assumes different explanations of what it means to call a mathematical statement true. In intuitionism, the truth is not only strictly defined by its demonstrability, but rather the ability of mathematics to intitate the statement and prove it by further clarifying other rationally consistent mental constructions.

intuitionism has serious consequences that contradict some key terms in classical mathematics. Perhaps the most famous of them is the rejection of the law of the excluded center. In the most basic sense, the law of the excluded center says that either "A" or "no and" can be true, but both can be true at the same time. Intuitionists believe that it is possible to prove both "A" and "not" if the mental structures can be built that everyone proves consistently. In this sense, evidence does not deal with intuitionist reasoning by proving whether "and" existenceIt is, but instead defined by whether "a" and "no and" can be coherent and consistently designed as mathematical statements in the mind.

Although intuitionism has never replaced classic mathematics, it still receives great attention to this day. The study of intuitionism was associated with a wide degree of progress in mathematics study because it replaces the concepts of abstract truth concepts on the justification of mathematical structures. It was also treated in other philosophy sectors for its concern about the idealized and Mr.-Subjective Mind Creation, which was compared with the phenomenological concept of Husserl's "transcendental object."