This paper analyzes human-machine interrelation concerning artificial neuronal networks (ANNs) from a teleological point of view. The paper argues that AI cannot be understood adequately in terms of subjectivity or objectivity but rather as a new kind of teleological relationship that holds between human and artificial performances of intelligence. Thereby, AI is understood as an enactivist extension of human agency, both in instrumental and moral terms. This hybrid account will be distinguished from four alternative accounts of human-machine relations: (i) the simulation account, according to which AI simulates human rationality; (ii) the instrumentalist account, according to which AI is just a tool; (iii) the anthropomorphic account, according to which AI is human-like; and (iv) the indifference account, according to which AI will merge with human rationality due to technological progress. Against these four accounts, the paper argues for a teleological account of AI as extended human agency that is part of the human lifeworld. By focusing on the teleological interrelation of socially grounded databases and algorithms, the paper finally develops an account of responsible AI that considers its specific relatedness with human actions, purposes, and intentions by means of language. Understanding human-machine relations in terms of extended agency finally allows to tackle the question of how to avoid the problems of AI bias and opacity.