GPT-4 was released in March 2023 to wide acclaim, marking a very substantial improvement across the board over GPT-3.5 (OpenAI's previously best model, which had powered the initial release of ChatGPT). Despite the genuinely impressive improvement, however, there are good reasons to be highly skeptical of GPT-4's ability to reason. This position paper discusses the nature of reasoning; criticizes the current formulation of reasoning problems in the NLP community and the way in which the reasoning performance of LLMs is currently evaluated; introduces a collection of 21 diverse reasoning problems; and performs a detailed qualitative analysis of GPT-4's performance on these problems. Based on the results of this analysis, the paper argues that, despite the occasional flashes of analytical brilliance, GPT-4 at present is utterly incapable of reasoning.