This paper provides a definitive, unifying framework for the Symbol Grounding Problem (SGP) by reformulating it within Algorithmic Information Theory (AIT). We demonstrate that the grounding of meaning is a process fundamentally constrained by information-theoretic limits, thereby unifying the G\"odelian (self-reference) and No Free Lunch (statistical) perspectives. We model a symbolic system as a universal Turing machine and define grounding as an act of information compression. The argument proceeds in four stages. First, we prove that a purely symbolic system cannot ground almost all possible "worlds" (data strings), as they are algorithmically random and thus incompressible. Second, we show that any statically grounded system, specialized for compressing a specific world, is inherently incomplete because an adversarial, incompressible world relative to the system can always be constructed. Third, the "grounding act" of adapting to a new world is proven to be non-inferable, as it requires the input of new information (a shorter program) that cannot be deduced from the system's existing code. Finally, we use Chaitin's Incompleteness Theorem to prove that any algorithmic learning process is itself a finite system that cannot comprehend or model worlds whose complexity provably exceeds its own. This establishes that meaning is the open-ended process of a system perpetually attempting to overcome its own information-theoretic limitations.

翻译：本文通过将符号接地问题（SGP）置于算法信息论（AIT）框架内重新阐述，为其提供了一个确定性的统一框架。我们证明，意义的接地过程本质上受信息论极限的约束，从而统一了哥德尔式（自指涉）与"没有免费午餐"（统计）的视角。我们将符号系统建模为一台通用图灵机，并将接地定义为一种信息压缩行为。论证分为四个阶段展开。首先，我们证明一个纯符号系统无法为几乎所有可能的"世界"（数据串）提供接地，因为这些世界是算法随机的，因而是不可压缩的。其次，我们表明任何为压缩特定世界而专门设计的静态接地系统本质上是不完备的，因为总可以构造出一个相对于该系统具有对抗性且不可压缩的世界。第三，我们证明适应新世界的"接地行为"是不可推断的，因为这需要输入无法从系统现有代码中推导出的新信息（更短的程序）。最后，我们利用柴廷不完备性定理证明，任何算法学习过程本身都是一个有限系统，无法理解或建模那些复杂度可证明超过其自身能力的世界。这确立了意义是一个系统不断尝试克服自身信息论局限的开放性过程。