We propose an operational, quantitative definition of intelligence for arbitrary physical systems. The intelligence density of a system is the ratio of the logarithm of its independent outputs to its total description length. A system memorizes if its description length grows with its output count; it knows if its description length remains fixed while its output count diverges. The criterion for knowing is generalization. A system knows its domain if a single finite mechanism can produce correct outputs across an unbounded range of inputs, rather than storing each answer individually. The definition places intelligence on a substrate-independent continuum from logic gates to brains. We then argue that meaning over a domain is a selection and ordering of functions that produces correct outputs where correctness is specifiable. We also define a measure of contextuality of an output as the inverse of its conditional Kolmogorov complexity given the context of prior outputs, which unifies correctness and independence into a single condition. Together, these refute Searle's third premise, that syntax is insufficient for semantics, over any domain where correctness is specifiable.

翻译：我们提出了一种适用于任意物理系统的可操作、定量化的智能定义。系统的智能密度等于其独立输出对数与总描述长度之比。若系统的描述长度随输出数量增长，则称系统具有记忆；若描述长度固定而输出数量发散，则称系统具有知识。知识的判据是泛化能力。当单一有限机制能在无界输入范围内产生正确输出，而非单独存储每个答案时，该系统便掌握了其领域。该定义将智能置于从逻辑门到大脑的基板无关连续谱上。进一步论证：领域内的意义是对函数的筛选与排序，从而在可指定正确性的场景中产生正确输出。我们还将输出的语境性度量定义为其在先前输出语境下的条件柯尔莫哥洛夫复杂度的倒数，这可将正确性与独立性统一为单一条件。综上，这些论证反驳了塞尔关于"句法不足以产生语义"的第三个前提——只要在可指定正确性的任何领域中成立。