用算法信息论揭示符号接地问题的本质:意义是系统不断突破自身信息极限的开放过程。
An Algorithmic Information-Theoretic Perspective on the Symbol Grounding Problem
- 将符号系统视为通用图灵机,把接地定义为信息压缩行为
- 证明纯符号系统无法接地几乎所有世界,因它们算法随机且不可压缩
- 指出学习新世界的接地行为不可推导,需外部输入新信息
本文通过算法信息论(AIT)为符号接地问题(SGP)提供了一个统一、明确的框架。我们证明,意义的接地本质上受信息论极限约束,从而统一了哥德尔(自指)与无免费午餐(统计)视角。将符号系统建模为通用图灵机,接地被定义为信息压缩行为。首先,纯符号系统无法接地几乎所有的‘世界’(数据串),因为它们算法随机且不可压缩。其次,任何静态接地系统,若专用于压缩特定世界,必然不完整,因可构造一个相对于该系统不可压缩的对抗性世界。第三,适应新世界的‘接地行为’不可推导,因其需要输入新的信息(更短程序),而无法从系统现有代码中推得。最后,利用查坦的不完备性定理,证明任何算法学习过程本身都是有限系统,无法理解或建模其复杂性超出自身的世界。这确立了意义是系统持续尝试突破自身信息论局限的开放过程。
原文摘要 · Abstract (English)
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 Gödelian (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.
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