This paper identifies and criticizes a common line of argument for the negative conclusion that Large Language Models (LLMs) cannot think, or for the closely related conclusions that they cannot understand or that their outputs are meaningless. This line of argument can be found in several recent papers. We begin by discussing a representative example--Stoljar and Zhang's (2024) "argument from rationality"---and present three objections to it: first, it renders the successful performance of LLMs on a wide range of tasks miraculous; second, it does not give sufficient weight to the possibility that LLMs could be extracting information about the world from patterns of word co-occurrence; and third, it overgeneralizes, leading to the conclusion that human inferences could only ever be based on premises about proximal stimulus patterns in the brain. We then discuss recent arguments by Hattiangadi and Schoubye (forthcoming) and Titus (2024), explain how our objections extend to them and identify the underlying reason that makes these sorts of arguments tempting. We finish by drawing a general lesson for debates surrounding thinking in LLMs.