Large language model (LLM) hallucinations are typically treated as architectural defects requiring technical fixes. We argue instead that hallucinations are a systemic property of the syntactic processing mode, in which a system manipulates symbols without access to their semantic content. Our analysis focuses on base autoregressive architectures; hybrid systems incorporating explicit semantic representations or external verification may partially mitigate the effects we describe, but do not eliminate the underlying syntactic processing mode in the core generation mechanism. This perspective connects Searle's Chinese Room argument with Harnad's symbol grounding problem and empirical findings from cognitive psychology. We demonstrate that humans operating in syntactic mode produce errors that share key properties with LLM hallucinations: high confidence, surface plausibility, and reliance on pattern-matching over verification. In the Wason Selection Task, approximately 10% of subjects arrive at the logically correct answer, yet the majority report high confidence in their incorrect responses, much like LLMs producing false statements with high probability scores. Cheng and Holyoak show that accuracy increases progressively as semantic grounding moves from full abstraction to goal-directed concretization. Cosmides and Tooby extend this gradient to its furthest point: when the same logical task is recast as a social contract, human accuracy jumps to approximately 75%, revealing a capacity for mode-switching that LLMs lack. This reframes the hallucination problem: both humans and LLMs hallucinate when processing symbols without semantic grounding, and it is the processing mode, rather than the agent, that is the source of error.