The aim of this paper is to present two arguments for an approach that does not radically differentiate the methodology of mathematics from the methodology of other sciences (especially empirical ones), and that may be more effective or natural for mathematical practice.

A the beginning, the approach of Halina Mortimer [1], [2], one of the representatives of the Lviv-Warsaw School, who was concerned with the logic of induction, i.e. the methodology for developing the theory of empirical sciences, is presented,. Although Mortimer appreciated some of the solutions of Carnap and Hintikka in this area [3], [4], [5], she was of the opinion that they were too idealised. As an alternative, she proposed the solution of Henry Kyburg [6], who pointed out the connection between the system of inductive logic and a given empirical theory through mathematical probability. This proposal did not allow logic and mathematics to be treated as a priori theories explaining the reality described by the empirical sciences, but rather as tools for specifying and ordering these theories.

We will try to apply the above position to the analysis of two questions. First, we will comparatively analyse the methodology of Dedekind [7], [8], [9], [10], who constructed some mathematical models, and the methodology of Cantor [11], [12], [13], who used the genetic-deductive method. This may have been due to Cantor’s idealised Platonic assumptions about mathematics. This sometimes led to errors in his work, which were corrected by later communities of mathematicians. Dedekind, approached mathematics in a more empirical way. He also produced more effective solutions.

We also note the scientific environments that might have influenced the mathematicians. Dedekind’s early environment included mathematicians such as Gauss and Dirichlet, while Cantor’s included Weierstrass and Kronecker. Gauss was also known as an experimental physicist, while Weierstrass devoted himself exclusively to detailed work on mathematical problems [14].

Secondly, we will analyse for comparative purposes the mathematical model that Dedekind built in the Foundations of Mathematics (N) and the modern flow model for a social network [15], [16]. We will pay attention to common and different aspects that could (or might) accompany the creation or recreation of these models.

For this purpose, we will present a proposal for a general cognitive scheme for building a mathematical model in individual mathematical practice. Based on the definition of the model [17], we will use the proposal of Giaquinto [18], [19], who, following Kosslyn, shows how a structure can be “grasped” visually.

The conclusions of these considerations point to the need to pay more attention to the individual and social context of scientific discovery. This would allow us to show more generally that mathematical knowledge, as a product of individual and social practice, is not necessarily developed in a continuous way, where continuity is ensured by the use of the genetic-deductive method. New theoretical structures can also be constructed in relation to - broadly understood - experience, and not only in strict relation to current theory.