Why Does Chatgpt Lack a Proper Understanding of Numbers?——A Preliminary Exploration of Building Agi's Numerical Concepts Through Variable Reasoning

Abstract

As artificial intelligence (AI) becomes increasingly integral to natural sciences, there is a pressing demand for AI systems to comprehend natural numbers and engage in abstract reasoning. However, current mainstream AI models, exemplified by ChatGPT, fail to pass critical tests in developmental psychology such as the number conservation experiment, indicating their deficiency in understanding natural numbers. Further analysis through variable reasoning tests reveals that ChatGPT's shortcomings stem from its inability to comprehend abstract geometric objects, needless to say to represent the holistic properties of sets. In contrast, the AGI project executed via the Non-Axiomatic Reasoning System (NARS) exhibits robust reasoning capabilities aided by multiple reasoning rules, which allow NARS itself to demonstrate proficiency in variable reasoning tasks. Moreover, guided by cognitive theories like mathematical structuralism, NARS constructs meta-sequences of object sets through variable reasoning, facilitating its acquisition of the fundamental concept of natural numbers. This study is intended to elaborate a primitive framework for AGI systems waiting to be developed into a more mathematically capable reasoning system, namely, a system which can apply mathematical principles in varieties of real-time environments.

Keywords: number concept, variable reasoning, quantity conservation, non-axiomatic reasoning system, logical proper name