Alan Turing: Computation, Intelligence & Philosophy

Biography

Alan Mathison Turing was born on June 23, 1912, in London, the second son of Julius Mathison Turing, an Indian Civil Service officer, and Ethel Sara Stoney. The boys were raised in England while their parents served in India. Turing showed early gifts — he taught himself to read in three weeks and was fascinated by numbers and chemistry — but his school record at Sherborne was erratic; his headmaster warned that "if he is to stay at Public School, he must aim at becoming educated." He was, in fact, becoming something rarer: a mathematician. He entered King's College, Cambridge, in 1931, and in 1935, at the age of twenty-two, he was elected a fellow of King's on the strength of a dissertation on the central limit theorem of probability.

In 1936 Turing wrote "On Computable Numbers, with an Application to the Entscheidungsproblem," the paper that invented the Turing machine and solved, in the negative, Hilbert's decision problem. He went to Princeton in 1936–38, studied with Alonzo Church, and returned to Cambridge. With the outbreak of war he joined the Government Code and Cypher School at Bletchley Park, where he led the team that broke the German Enigma cipher — work that historians credit with shortening the war and saving hundreds of thousands of lives. After the war he worked on the design of the ACE computer and, in 1950, published "Computing Machinery and Intelligence," the paper that posed the question "Can machines think?" and proposed the imitation game, now the Turing test. His later years were marred by tragedy: prosecuted in 1952 for homosexual acts, he accepted chemical castration rather than imprisonment. He died on June 7, 1954, of cyanide poisoning, officially by suicide, at the age of forty-one. In 2009 the British government apologized; in 2013 he received a posthumous royal pardon; and in 2019 his face appeared on the fifty-pound note.

Historical Background

Turing's 1936 paper was written in response to the Entscheidungsproblem (decision problem) posed by David Hilbert: is there a mechanical procedure to decide, for any first-order formula, whether it is logically valid? Alonzo Church had just answered no, using his lambda calculus. Turing, independently, answered no as well — but his route was more fundamental. Instead of defining "mechanical procedure" by a formal system, he analyzed what a human computer (the word then meant a person) actually does when computing: read symbols, write symbols, and move — operations that could be idealized into a machine with a finite set of states and an infinite tape. The result was the Turing machine, the abstract model of computation.

The paper also connected computation to the limits of mathematics established by Godel: the undecidability of the halting problem (no Turing machine can decide whether an arbitrary Turing machine halts) is the computational form of incompleteness, and the Entscheidungsproblem falls as a corollary. Turing thus unified logic, mathematics, and the notion of an effective procedure into a single theory — the foundation of computer science.

Core Ideas

The Turing machine. A Turing machine consists of an infinite tape divided into squares, a read-write head, a finite set of states, and a table of instructions. At each step it reads a symbol, writes a symbol, moves left or right, and changes state. Despite its simplicity, the machine is universal: one universal machine can simulate any other Turing machine, given its program on the tape. This universality is the theoretical basis of the stored-program computer.

The Church-Turing thesis. Computable functions are exactly the functions computable by a Turing machine (equivalently, by Church's lambda calculus, Godel's general recursive functions, and every other precise notion of effective computation proposed). The thesis is not a theorem but a foundational claim, universally accepted, that fixes the concept of computation: anything that can be computed can be computed by a Turing machine.

The halting problem and undecidability. There is no Turing machine that decides whether an arbitrary Turing machine halts. From this, the Entscheidungsproblem — deciding logical validity in first-order logic — is also undecidable. These results define the boundary of what computation can do.

The Turing test. In "Computing Machinery and Intelligence" (1950), Turing replaced the question "Can machines think?" — meaningless, he argued, because "think" is vague — with the imitation game: if a machine can, in a text-only conversation, deceive a human interrogator as often as a human would, then it should be regarded as thinking. The test operationalized intelligence and set the research agenda of artificial intelligence.

The mind as a computation. Turing's model suggested that mental processes might be computational: a mind is what a machine of the right kind does. This idea — computational functionalism — became the working hypothesis of cognitive science and the philosophy of mind, and the target of John Searle's Chinese Room argument and of a half-century of debate.

Major Works

"On Computable Numbers, with an Application to the Entscheidungsproblem" (1936–37), Proceedings of the London Mathematical Society — the Turing machine, universality, and undecidability.

"Computing Machinery and Intelligence" (1950), Mind — the Turing test and the philosophy of AI.

"Systems of Logic Based on Ordinals" (1939) — Turing machines with oracles, anticipating degrees of unsolvability.

"The Chemical Basis of Morphogenesis" (1952) — the mathematical theory of pattern formation in biology, founding mathematical morphogenesis.

Philosophical Influence

Turing reshaped the philosophy of mind. Before him, the question of whether machines could think was speculation; after him, it was a research program. His functionalism — mental states as computational states — became the default position in the philosophy of mind, defended by Daniel Dennett and contested by John Searle (whose Chinese Room aims to show that syntax is not semantics) and by David Chalmers, who grants computation's role in explaining function but argues it cannot explain consciousness. The debate over the Turing test — whether passing it is sufficient or merely indicative evidence of intelligence — remains central to AI ethics and to the philosophy of mind.

In logic and mathematics, Turing completed the arc from Godel's incompleteness to a general theory of the limits of formal methods: the halting problem, the Entscheidungsproblem, and the arithmetical hierarchy define what no machine can do. His work thus belongs to the theory of logical consequence and to the philosophy of mathematics. And by making "effective procedure" precise, he gave the philosophy of science and of mind the concept of algorithm that organizes modern inquiry.

Related Concepts

Turing's theory of computation defines the limits of logic and formal systems, building on the incompleteness theorems of Godel and the logicism of Russell. His Turing test frames the debate in the philosophy of mind over consciousness and artificial intelligence, and his analysis of computability grounds the modern understanding of reasoning and knowledge. The computational conception of mind is the subject of the philosophy of mind, where his successors and critics — Dennett, Searle, and Chalmers — continue the argument he began.