This paper attempts a step in the direction of an integrative perspective. At its centre is the still topical question: what is the difference between human intelligence and so-called artificial intelligence? Or is such a question perhaps meaningless anyway? In detail, the issue is what human intelligence is and what artificial intelligence could be, or what artificial intelligence is and what human intelligence can still be. What is defined as human intelligence is of course decisive for whether at all, and if so to what extent, an AI system can be intelligent. The question whether at all is already answered in the title of this paper: "How intelligent can artificial intelligence be?" concedes that AI already covers areas of intelligence. The only remaining question is to what extent, and above all what is left over as exclusively human intelligence. Never before in the history of humankind have human beings been attacked so directly in this respect – in their self-understanding, in their identity, to which intelligence also belongs – and never before have the sciences been under such pressure to find (or invent) a (new) image of the human being. Philosophers (without this pressure) have always been concerned with cognition, language, knowledge, science, intelligence and so on – Aristotle, Plato, Descartes, Leibniz, Kant, Wittgenstein, to name only a few – and have given us a rich theoretical potential for thinking further in the face of AI. In this spirit I want, on the basis of my interpretation of Ludwig Wittgenstein's Tractatus (1921), to formulate a few thoughts on the intelligence of AI and then to discuss some of them with ChatGPT, in a hybrid mode, so to speak – in search of synergies between human and artificial intelligence. The focus is on the philosophy of language; language is the medium of intelligence, as Liang Wenfeng, CEO and mastermind of DeepSeek, the latest hit on the AI market, also states in an interview: "… we believe that human intelligence might fundamentally be about language – that human thought might simply be a process of language. What you perceive as thinking might just be your brain weaving language."¹