Large language models (LLMs) offer a new empirical setting in which long-standing theories of linguistic meaning can be examined. This paper contrasts two broad approaches: social constructivist accounts associated with language games, and a mathematically oriented framework we call Semantic Field Theory. Building on earlier work by the author, we formalize the notions of lexical fields (Lexfelder) and linguistic fields (Lingofelder) as interacting structures in a continuous semantic space. We then analyze how core properties of transformer architectures-such as distributed representations, attention mechanisms, and geometric regularities in embedding spaces-relate to these concepts. We argue that the success of LLMs in capturing semantic regularities supports the view that language exhibits an underlying mathematical structure, while their persistent limitations in pragmatic reasoning and context sensitivity are consistent with the importance of social grounding emphasized in philosophical accounts of language use. On this basis, we suggest that mathematical structure and language games can be understood as complementary rather than competing perspectives. The resulting framework clarifies the scope and limits of purely statistical models of language and motivates new directions for theoretically informed AI architectures.

翻译：大型语言模型（LLMs）为检验长期存在的语言意义理论提供了新的实证场域。本文对比了两种宏观研究路径：与语言游戏相关的社会建构主义解释，以及我们称为语义场理论的数学导向框架。基于作者先前的工作，我们将词汇场（Lexfelder）与语言场（Lingofelder）形式化为连续语义空间中相互作用的数学结构。随后，我们分析了Transformer架构的核心特性——如分布式表征、注意力机制以及嵌入空间中的几何规律性——与这些概念的关联。我们认为，LLMs在捕捉语义规律性方面的成功，支持了语言具有底层数学结构的观点；而它们在语用推理与语境敏感性方面持续存在的局限，则与哲学语言使用理论所强调的社会基础的重要性相吻合。在此基础上，我们提出数学结构与语言游戏可被理解为互补而非对立的视角。由此建立的框架阐明了纯统计语言模型的适用范围与局限，并为融合理论洞见的AI架构设计提供了新的研究方向。