Mathematics as a domain of meaning is also a reflection of the fundamental definitions of the world. The similarities between the world and mathematics make it possible to solve scientific problems. This similarity did not arise overnight. Mathematics is a result of the evolution of meaning from the order of the universe up to the reflection of this order in the minds of people. On the scale of millions and billions of years, the difference between Turing and Wittgenstein disappears: “Turing thought of mathematics as something that was essentially discovered, something like a science of the abstract. Wittgenstein insisted that mathematics was essentially something invented, following out a set of rules we have chosen—more like an art than a science” (Grim 2017, p. 151). In fact, both mathematics and logic in general are the result of cultural evolution that occurs through selection and choice. It could be, that the logical contradiction between meanings expresses the historical and practical discrepancy of meanings in relation to the environment and the subject, and the resolution of such a contradiction reflects the overcoming of this discrepancy.
The simplicity of early meanings did not only concern making. Thinking and communicating were just as simple, relying on crude motions of body and mind. Primitive making has left us its direct results: stones, bones, etc. Unfortunately, the direct products of communicating or thinking no longer exist, so we can only judge them indirectly. In the process of social and then cultural learning, as the norm of first learned and then rational reaction expanded and cultural selection turned into traditional choice, the complexity of meanings and of the culture-society as a whole increased, as did the number of figurae and meanings.
The gradual complication of meanings becomes clear, for example, when we consider the evolution of stone tools: from the simplest Paleolithic choppers to the polished and drilled Neolithic axes, which are characterized by a much higher level of workmanship. Cultural evolution consists in the division of meanings, that is, in the emergence of ever new types of actions and their results. By dividing their activity and knowledge, people specialized in those types of actions in which they had a competitive advantage due to the characteristics of the environment or their active power. Hunting and gathering divided into farming, herding, crafts, trade. Not only the complexity of making grew, but also of communicating and thinking. Languages were more complex. Learned actions became a more important part of self-reproduction relative to instinctive behaviors, rational actions grew more vital relative to learning.
