The Physical Numbers

Danny A. J. Gómez Ramírez
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Danny A. J. Gómez Ramírez: Instituto Tecnológico Metropolitano (ITM), Research’s Labs Center Parque i

Chapter Chapter 5 in Artificial Mathematical Intelligence, 2020, pp 67-89 from Springer

Abstract: Abstract A detailed cognitive analysis of the most outstanding forms of “understanding” the natural numbers is presented. In particular, the fundamental formal features and intuitions of this ancient numerical system are classified into physically supported parts and meta-physical (or mental) ones. A new numerical system consisting of the physical numbers is proposed which has an initial and a final element, and is essentially grounded in the physical realm. Semantic foundations and an initial seminal axiomatization for the physical numbers are offered, as well as a canonical correspondence between them and the natural numbers. The classic act of counting numbers is reduced in terms of doing physical partitions in a sequential way. Additionally, a pragmatic ontological clarification of the notion of infinity is presented in terms of the (physical) concept of immensity. Finally, based on the former constructs, a paradigm-shifting (bottom-up) meta-perspective is shown for understanding the causes of the high level of difficulty that the solutions of a large number of problems in classic elementary number theory possess.

Date: 2020
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DOI: 10.1007/978-3-030-50273-7_5

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