Linear probing of large language model (LLM) hidden states is widely used to claim that models learn distinct representations for different reasoning types. We test this by probing Qwen3-14B on three benchmarks spanning the classical trichotomy: LogiQA 2.0 (deductive), ARC-Challenge (inductive), and $α$NLI (abductive). At layer 32 of 40, linear probes achieve 100\% cross-validated accuracy with well-separated geometry (intrinsic dimensionalities: 20.6, 28.5, 33.6; convex hull contamination $\leq$1.5\%). However, this separation is entirely driven by format confounds. Residualizing source identity, option count, and response length reduces accuracy to chance. Trace-anchor similarity indicates largely shared reasoning across tasks (42.5\% agreement vs.\ 33.3\% chance), and causal steering with random controls ($n=20$) shows no functional link between geometry and reasoning mode ($p=0.286$). Thus, high probe accuracy reflects task format rather than computational structure, motivating routine format deconfounding in mechanistic interpretability.