This paper introduces a systems engineering framework for understanding the fundamental principles of counting and the nature of natural numbers, arguing that traditional axiomatic approaches overlook the essential functional and computational components. We define counting as a Wittgensteinian "counting game" in which an agent, the Counter, must employ robust perception and classification capabilities within a given environment. Central to this approach is the claim that counting is a stateful …
Read moreThis paper introduces a systems engineering framework for understanding the fundamental principles of counting and the nature of natural numbers, arguing that traditional axiomatic approaches overlook the essential functional and computational components. We define counting as a Wittgensteinian "counting game" in which an agent, the Counter, must employ robust perception and classification capabilities within a given environment. Central to this approach is the claim that counting is a stateful computational activity that requires memory, leading to the definition of a natural number as the unique state of a counting system stored in that memory. We examine the role of symbolic representation, identifying numerals as efficient encoding schemes for these numerical states, and argue that this analysis contributes to improving symbolic features in Artificial Intelligence (AI) systems. Furthermore, our model contributes to a long-standing philosophical debate, suggesting that ordinals come first rather than cardinals due to practical memory storage limitations.
