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). However, despite the genuinely impressive improvement, 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, as well as the way in which LLM reasoning performance is currently evaluated; introduces a small collection of 21 diverse reasoning problems; and performs a detailed qualitative evaluation of GPT-4's performance on those problems. Based on this analysis, the paper concludes that, despite its occasional flashes of analytical brilliance, GPT-4 at present is utterly incapable of reasoning.