Can a machine understand the meanings of natural language? Recent developments in the generative large language models (LLMs) of artificial intelligence have led to the belief that traditional philosophical assumptions about machine understanding of language need to be revised. This article critically evaluates the prevailing tendency to regard machine language performance as mere syntactic manipulation and the imitations of understanding, which is only partial and very shallow, without sufficient grounding in the world. The article analyses the views on possible ways of grounding as a condition for successful understanding in LLMs and offers an alternative way in view of the prevailing belief that the success of understanding depends mainly on the referential grounding. An alternative conception seeks to show that semantic fragmentism offers a viable account of natural language understanding and explains how LLMs ground the meanings of linguistic expressions. Uncovering how meanings are grounded allows us to also explain why LLMs’ ability to understand is possible and so remarkably successful.