Large language models (LLMs) are increasingly used as evaluators for natural language generation, applying human-defined rubrics to assess system outputs. However, human rubrics are often static and misaligned with how models internally represent language quality. We introduce GER-Eval (Generating Evaluation Rubrics for Evaluation) to investigate whether LLMs can design and use their own evaluation rubrics. We evaluate the semantic coherence and scoring reliability of LLM-defined criteria and their alignment with human criteria. LLMs reliably generate interpretable and task-aware evaluation dimensions and apply them within models, but their scoring reliability degrades in factual and knowledge-intensive settings. Closed-source models such as GPT-4o achieve higher agreement and cross-model generalization than open-weight models such as Llama. Our findings position evaluation as a learned linguistic capability of LLMs—consistent within models but fragmented across them—and call for new methods that jointly model human and LLM evaluative language to improve reliability and interpretability.