Wittgenstein, Turing and testing intelligence

Intro to a session with the TUM Think Tank reading group

The Turing Sidestep and the Wittgensteinian Counter: Two Views on Machine Intelligence

In the history of philosophical debates about artificial intelligence, few encounters are as intellectually charged as the implicit disagreement between Alan Turing and Ludwig Wittgenstein on the question of machine thinking. While these two Cambridge figures did meet historically—Turing attended several of Wittgenstein’s lectures on the foundations of mathematics—their disagreement about machine intelligence represents a fundamental divide in how we approach the question: Can machines think?

The historical meetings between Turing and Wittgenstein were marked by violent disagreement about mathematical foundations. Turing believed mathematical truths were discovered, treating mathematics as the language in which nature is written. Wittgenstein, conversely, viewed mathematics as constructed—like a piece of art where contradictions were aesthetic flaws rather than logical impossibilities. This fundamental disagreement about the nature of truth would echo in their divergent approaches to machine intelligence.

The Turing Sidestep

Turing’s seminal 1950 paper “Computing Machinery and Intelligence” remains remarkably fresh and engaging even today. The paper’s liveliness and clarity make it feel as though it could have been written recently, a testament to its enduring relevance. But beneath its accessible style lies a series of sophisticated philosophical moves that continue to shape debates about artificial intelligence.

Turing’s first philosophical move is to reject what was then known as the linguistic turn in philosophy. When he poses the question “Can machines think?”, he immediately dismisses the classical philosophical approach of analyzing what we mean by “machine” and “think.” This approach, heavily influenced by Wittgenstein and dominant in Cambridge and Oxford at the time, sought understanding through examining how terms are used in language. Turing dismisses this as merely “putting it to a majority vote”—a statistical survey that cannot capture what truly matters about thinking.

Instead, Turing makes what we might call the “Turing sidestep”—his most fundamental and interesting move. Rather than asking what thinking means, he replaces the question entirely:

The new form of the problem can be described in terms of a game which we will call the imitation game. It is played with three people, a man, a woman and an interrogator who may be of either sex. The interrogator stays in a room apart from the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman.

He then asks: “What happens when a machine takes the place of part A in this game? Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman?” These questions, Turing declares, replace our original “can machines think?”

This move appears surprisingly Wittgensteinian on its surface. After all, Wittgenstein famously declared in paragraph 43 of the Philosophical Investigations: “For a large class of cases, though not for all, in which we employ the word meaning, it can be defined thus: the meaning of a word is its use in language.” Turing seems to be doing exactly this—looking at when we would use the term “thinking” rather than what it means. Moreover, Wittgenstein was centrally concerned with language games, making Turing’s game-based approach seem perfectly aligned with Wittgensteinian philosophy.

The Wittgensteinian Response

But would Wittgenstein actually agree? This is where Chapter Four of Part II of the Philosophical Investigations becomes crucial. Though only a single page, this “chapter” contains a devastating critique of the kind of move Turing makes.

Wittgenstein begins with a curious meditation:

I believe that he is suffering. Do I also believe that he isn’t an automaton? It would go against the grain to use the word in both connections. Or is it like this? I believe that he is suffering, but I’m certain that he is not an automaton. Nonsense.

In Wittgenstein’s characteristic style, these rhetorical questions are not seeking answers but exposing confusions. He’s suggesting that believing someone thinks is not like believing other empirical facts. We don’t believe someone thinks based on evidence or impressions—it’s not something we sense in another.

The key distinction emerges when Wittgenstein writes: “My attitude to him is an attitude towards a soul. I’m not of the opinion that he has a soul.” The difference between an attitude (Einstellung) and an opinion (Meinung) is crucial. The term Einstellung carries connotations from Gestalt psychology—it’s like a setting on a machine, suggesting we’re “rigged” to have this attitude towards souls.

This suggests that statements about thinking might be what Wittgenstein later called “hinge propositions”—statements exempt from doubt that enable other doubts to make sense. We don’t test for thinking; we’re embedded in a form of life where we have an attitude towards souls. When we meet something human or human-like, we simply assume it thinks.

Wittgenstein’s argument culminates in one of his most famous statements: “The human body is the best picture of the human soul.” This has been interpreted by AI researchers as requiring embodiment for true artificial intelligence, but the implications are broader. Thinking happens in bodies embedded in forms of life. To say something thinks is to say it’s human, and to be human is to have a body embedded in our communities.

The Philosophical Standoff

Wittgenstein’s position amounts to a rejection of the Turing sidestep. Either meaning isn’t use in this case, or Turing has cherry-picked such a narrow use case that it cannot carry the conceptual weight of “thinking.” The imitation game represents too thin a slice of use to explore the grammar of the complex, embedded world of thinking. Alternatively, the imitation game might simply be an invalid move in the language game of thinking—there are no criteria for ascribing thinking because it’s a hinge proposition.

Turing, however, has counter-moves. His paper anticipates objections with characteristic wit. To the theological objection that only souls can think, he cheekily responds: who are we to doubt God’s power to make machines think? The “heads in the sand” objection—that thinking machines sound horrible—receives his blunt response: that’s just how it is. The mathematical objection involving Gödel’s theorem gets a somewhat weaker response, with Turing questioning whether humans can really solve problems that formal systems cannot.

But Turing’s most powerful counter-move comes at the beginning of his objections section: “I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted.”

This prediction has largely come true. We routinely say “the machine thinks,” “the chatbot said,” “ChatGPT told me.” Our language has changed, which means our form of life has changed. Wittgenstein allows for language to change—there’s no universally fixed grammar throughout history. Turing’s final riposte to Wittgenstein might be: you were right then, but I’m right now. Language has changed so much that we can test for thinking in ways you thought impossible in the 1950s.

Contemporary Implications

This tension between Turing and Wittgenstein continues to reverberate through contemporary philosophy and AI research. Daniel Dennett’s intentional stance represents one attempt to synthesize these positions, arguing that we treat systems as intentional when it’s cognitively economical to do so—a weaker claim than either Turing or Wittgenstein makes.

The proliferation of tests, evaluations, and benchmarks in AI raises urgent questions. The slide from “game” to “test” in discussions of the Turing Test might reflect something deeper in artificial intelligence’s history—perhaps connected to its origins at Stanford, where John McCarthy worked in the same environment as Lewis Terman, author of the Stanford-Binet intelligence test. Early AI conceptualized intelligence as what IQ tests measure.

But what can we legitimately test AI for? Mathematical problem-solving? Certainly. Thinking? Perhaps not. Is there a difference between engineering benchmarks and philosophical tests? When should tests be incorporated into legislation or serve as the basis for rights? The almost hyperbolic “Humanity’s Last Exam”—a test that supposedly shows when machines have surpassed all human competence—makes the kind of grand philosophical claim that Wittgenstein would have dismissed as linguistic confusion.

The debate between Turing and Wittgenstein ultimately concerns not just whether machines can think, but how we should approach such questions. Do we create operational tests that sidestep meaning, or do we examine the grammar of our concepts embedded in forms of life? As artificial intelligence advances and our language evolves, this philosophical standoff remains as relevant as ever—perhaps more so, as we increasingly rely on machines whose “thinking” we must somehow evaluate, regulate, and understand.