Implicit premise is central to argumentative coherence and faithfulness, yet remain elusive in traditional single-pass computational models. We introduce a multi-agent framework that casts implicit premise recovery as a dialogic reasoning task between two LLM agents. Through structured rounds of debate, agents critically evaluate competing premises and converge on the most contextually appropriate interpretation. Evaluated on a controlled binary classification benchmark for premise selection, our approach achieves state-of-the-art accuracy, outperforming both neural baselines and single-agent LLMs. We find that accuracy gains stem not from repeated generation, but from agents refining their predictions in response to opposing views. Moreover, we show that forcing models to defend assigned stances degrades performance—engendering rhetorical rigidity to flawed reasoning. These results underscore the value of interactive debate in revealing pragmatic components of argument structure.