This paper aims to propose a universal definition of intelligence that enables fair and consistent comparison of human and artificial intelligence (AI). With the rapid development of AI technology in recent years, how to compare and evaluate human and AI intelligence has become an important theoretical issue. However, existing definitions of intelligence are anthropocentric and unsuitable for empirical comparison, resulting in a lack of consensus in the research field. This paper first introduces four criteria for evaluating intelligence definitions based on R. Carnap's methodology of conceptual clarification: similarity to explicandum, exactness, fruitfulness, and simplicity. We then examine six representative definitions: IQ testing, complex problem-solving ability, reward optimization, environmental adaptation, learning efficiency, and predictive ability, and clarify their theoretical strengths and limitations. The results show that while definitions based on predictive ability have high explanatory power and empirical feasibility, they suffer from an inability to adequately explain the relationship between predictions and behavior/benefits. This paper proposes the Extended Predictive Hypothesis (EPH), which views intelligence as a combination of the ability to accurately predict the future and the ability to benefit from those predictions. Furthermore, by distinguishing predictive ability into spontaneous and reactive predictions and adding the concept of gainability, we present a unified framework for explaining various aspects of intelligence, such as creativity, learning, and future planning. In conclusion, this paper argues that the EPH is the most satisfactory and universal definition for comparing human and AI intelligence.