Truth-ε and machine knowledge: from demonstrative rationality to bounded computational convergence

This paper introduces the concept of Truth-ε as a framework for understanding the epistemological status of contemporary artificial intelligence. Modern AI systems increasingly produce reliable and scientifically useful outputs while remaining only partially reconstructible through explicit symbolic reasoning. This raises a central question: how can machine-generated representations count as knowledge if they are neither exact copies of reality nor demonstrative conclusions derived from transparent logical chains? Truth-ε refers to a form of epistemic reliability achieved through convergence under conditions of finite information, uncertainty, and computational limitation. The paper argues that AI does not abolish rationality or reduce truth to mere prediction. Instead, it makes explicit a conception of rationality already embedded in the history of mathematics and science, where knowledge advances through controlled approximation, convergence, and bounded error. From the method of exhaustion and ε–δ analysis to probability theory, information theory, computational complexity, and machine learning, scientific knowledge has evolved by disciplining error rather than eliminating it entirely. Within this framework, AI systems derive epistemic legitimacy through robustness, calibration, generalization, reproducibility, and explicit disclosure of epistemic limits.