What is Logicism, What Does It Mean?July 2, 2021
Logicism is the understanding that considers logic as the basis of philosophy. Logicism, like Hegel’s teaching, expresses the teachings that consider logic as the basis of philosophy, as well as the teachings of logician mathematicians such as Frege, Russell and Whitehead, who consider logic the basis of mathematics. It was first used by Baldwin to express Hegelianism.
Frederic Rauh also used the term ethical logicism for Kant’s ethics. He also names Edmund Husserl’s understanding of logic as anti-psychological. The contemporary meaning of the phrase expresses the current of logical mathematics. The founder of this understanding, the first traces of which can be found in the Megara School of Antiquity, is the German thinker Leibniz.
However, during these studies, Leibniz found Aristotle’s mistakes and did not publish his works, believing that he had the mistake because he had great respect and trust in him. The English thinker David Hume, with the ideas he found and shaped in the monumental work of the French philosopher Pierre Bayle, Dictionnaire Historique et Criticue (1697), became the basis for today’s various understandings of mathematical logic.
WHAT IS LOGICISM?
According to Hume, who is based on Bayle, our mathematical knowledge is the literal connections that our reason creates only by its own logical operations, without resorting to the external world through the senses. We know mathematics through rational exhibition or rational proof. For example, the proposition “One to one makes two” is a connection that our reason makes through intuition. We arrive at the proposition “The sum of the interior angles of a triangle is 180 degrees” through rational proof by making logical inferences in our minds.
Mathematical facts are actually generalizations of the “red is red” proposition. Our reason arrives at the certainties of these facts by logical analysis. Just as we reject the proposition “red is not red” because it contradicts us, we reject the propositions “added together makes three” or “the sum of the interior angles of a triangle is 200 degrees” because they simply contradict us. Mathematical facts, then, are in fact nothing more than logical propositions. That is why mathematics must be brought back to logic. The basis of various currents of contemporary mathematical logic is the thought of Bayle-Hume. On this intellectual basis, George Boole (1815-1864) established a system of mathematical logic analysis, which he put forward under the name of logic pocket.
This system was developed by Peirce, Schroeder, Poetski etc. It has been followed and developed by logicians such as Another understanding of mathematical logic is an understanding called logical semantics, which was put forward by the German mathematician and logician Gottlob Frege (1848-1925), based on the same foundations. While this understanding was followed and developed in the same direction by Russell and Whitehead, on the other hand, it was drawn into an idealist field under the name of symbolic logic by Carnap and his friends. Aristotle’s formal logic principles lie on the basis of mathematical logic; Accurate knowledge is knowledge that we know its opposite will cause us to contradict.
Although Aristotle’s formal logic takes into account the confirmation of thought by thought, this thought is still connected with the reality in the external world, while symbolic logic is much more formal in that it is separated from formal logic and reality in the outside world; It is not even intellectual connections that matter to him, but only the connections between signs that make up logical formulas. Thus, abstracted symbolic logic is aimed to be opposed to concrete and objective dialectical logic.
All these currents, despite their differences, unite in neo-positivist idealism. As a matter of fact, most of all these understandings of logic are also called logical positivism in a general sense. Logical empiricism also derives from this logical positivism. All these currents are also linguist in form; They argue that philosophy can be reduced to the logical solution of language both in terms of syntax and semantics. In the field of language, for example, they are idealistic enough to argue that with the removal of the word exploitation, the phenomenon of exploitation will “disappear”. On the one hand, the mathematical logic current reduced mathematics to logic, on the other hand, it made logic mathematical.
According to Bertrand Russell, “mathematics and logic are one and the same thing”. In the field of mathematical logic, constructive logic, which argues that formal logic principles such as the principle of impossibility of the third state, cannot be applied to infinite numbers, include necessity, possibility, chance, etc. modal logic, which examines logical modes such as, and the classical two-valued logic derived from it, which is based on the duality of false and true, for example, Lukasiewcz’s three-valued and four-valued logic systems, multi-valued logic that proposes n-valued logic propositions, etc. Many logical understandings have also been derived.
Prepared by: Sociologist Ömer Yıldırım