Circular reasoning occurs when a definition or argument assumes what it is trying to prove, leading to a lack of independent validation. In the context of the discussion, the phrase "A wave is something satisfying wave equations" is deemed circular if the accompanying definition is "A wave equation is something that describes a wave." This creates a tautological loop where both statements rely on each other without providing external justification. The conversation highlights that while some definitions may appear linear, they can still form a circular chain. An example of circular reasoning is illustrated with a religious text claiming its own truth without external evidence. The discussion also notes that circular reasoning can be treated as axiomatic, allowing for the acceptance of broader implications once the initial circular premise is accepted. Overall, the distinction between circular reasoning and tautology is emphasized, with the former involving presupposed conclusions within the reasoning process.
