logicism

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  • Logic is a direction in the philosophy of mathematics, assuming that its basis can be based on the logic of logic (cf. logic). In particular, it reduces mathematics as a science to a special kind of formal logical theory that implements a set of axioms and derives conclusions based on a set of definitions (cf. formalism (mathematics).)

    Logicism has played a significant role in the founding of modern mathematics. His success owes to Giuseppe Pean's creation of a coherent axiom of natural numbers and the creation of a coherent theory of logical calculus based on the theory of types eliminating the antinomies of self-repudiation classes and other problems that hindered the foundations of mathematics at the beginning of the 20th century by Russell and Alfred Whitehead. However, further development of mathematics has led to the founding of mathematics based on the theory of multiplicity and its association with logic.

    The difference between logic and formalism is that logic does not speak about the meaning of non-logic terms used in the construction of mathematics. Both Hilbert and the creator of the Russell concept had a far different opinion from the modernist views. They emphasized the importance of mathematical concepts and not just their mutual relations. Formalism is in a completely different position by explicitly dividing the axioms into logical and non-logical ones and adding that they are all quite arbitrary.

    Today, logic has been absorbed in the technical layer by formalism which, together with the axiom of set theory, forms a paradigm for the development of the basis of mathematics, at least in terms of knowledge representation and education. It is doubtful whether the mathematicians who form the new theories actually use the axiomatic method. The usual custom in mathematics is the axiomatic formulation of the results of already done work. Leading representatives

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