Large language models (LLMs) are changing how we interact with computers. As they become capable of generating software dynamically, they invite a fundamental rethinking of the computer's role in human activity. In this conceptual paper, we introduce LLM-mediated computing: a paradigm in which interaction is no longer structured around fixed applications, but emerges in real-time through human intent and LLM interpretation. We make three contributions: (1) we articulate a new interaction metaphor of reflective conversation to guide future design, (2) we use the lens of postphenomenology to understand the human-LLM-computer relation, and (3) we propose a new mode of computing based on co-disclosure, in which the computer is constituted in use. Together, they define a new mode of computing, provide a lens to analyze it, and offer a metaphor to design with.