Foundations of Arithmetic: A Logical-Mathematical Study on the Concept of Number

The attention of readers is offered the classic work of the outstanding German logic, mathematics and philosopher Gottlob Frege “The Foundation of Arithmetic”. It solves the problem of expression using the proper logical terms of the basic arithmetic concept. Criticizing in this work the previous methods of substantiating numbers - from psychologizing realism to formalism - the German logician bases its study on the specifics of the structure of the concept, considering the number as a reflection of the characteristics of this structure. The number appears as a property of a concept that is far from the psychological association of ideas and from simple operating icons. The reduction of the number to the property of the concept made it possible to consider the methods of reasoning previously considered purely mathematical (for example, the principle of mathematical induction), as a kind of logical method of obtaining consequences. Secondly, this information made it possible to explain the nature of transfinite and complex numbers, the existence of which seemed paradoxical. Thus, arithmetic received such a reliable foundation that she needed, which was attributed to the obviousness of logical knowledge.
The publication is recommended to scientists, teachers, graduate students and students studying mathematical logic, philosophy and the history of mathematics, as well as a wide circle of readers interested in the problems of mathematical logic