Alan Turing
| Alan Turing | |
|---|---|
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Alan Turing at age 16
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| Identity | |
| Lifespan | 1912–1954 |
| Nationality | British |
| Epistemic Position | |
| Tradition | Analytic philosophy, Mathematical logic, Early computer science |
| Methodology | Formalism, Logic, Structuralism |
| Fields | Logic, Mathematics, Computation, Cryptanalysis, Philosophy of Mind |
| Conceptual Payload | |
| Core Concepts | Turing machine, Computability, Entscheidungsproblem, Universal machine, Artificial intelligence
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| Associated Concepts | Symbolic logic, Algorithm, Formalization, Automaton, Code, Information |
| Key Works | On Computable Numbers, with an Application to the Entscheidungsproblem (1936); Computing Machinery and Intelligence (1950); Systems of Logic Based on Ordinals (1939) |
| Theoretical Cluster | Language, Logic, Subjectivity, Symbolization |
| Psychoanalytic Relation | |
| Turing’s formalization of computation and the limits of algorithmic symbolization provided a structural paradigm for understanding the unconscious as a system governed by rules yet marked by undecidability. Lacan’s engagement with logic, automata, and the notion of the subject as a “speaking being” is deeply indebted to Turing’s demonstration of the constitutive gap in any system of signification. | |
| To Lacan | Lacan explicitly references Turing’s work on the machine and the undecidable in his seminars, integrating the Turing machine as a model for the symbolic order and the logic of the unconscious. |
| To Freud | Freud’s metapsychology prefigures the notion of psychic apparatus, but Turing’s formalization of the limits of mechanization reframes the Freudian unconscious as structurally akin to a logical automaton with inherent gaps. |
| Referenced By | Jacques Lacan, Jean Laplanche, Jacques-Alain Miller, Alain Badiou, Slavoj Žižek
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| Lineage | |
| Influences | Bertrand Russell, Kurt Gödel, Ludwig Wittgenstein, David Hilbert
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| Influenced | Jacques Lacan, Jean Laplanche, Alain Badiou, Cognitive science, Artificial intelligence
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Alan Mathison Turing (1912–1954) was a British mathematician, logician, and foundational theorist of computation whose work on the formalization of algorithmic processes, the limits of mechanical reasoning, and the architecture of symbolic systems profoundly influenced the conceptualization of the unconscious in psychoanalysis, especially in the work of Jacques Lacan. Turing’s demonstration of the undecidable within formal systems and his invention of the universal machine provided a new paradigm for thinking the subject, language, and the logic of desire as structurally determined yet marked by constitutive gaps, a legacy that continues to shape psychoanalytic theory.
Intellectual Context and Biography
Turing’s intellectual trajectory unfolded at the intersection of mathematical logic, philosophy, and the nascent field of computation, in a period marked by foundational crises in mathematics and the emergence of structuralist thought.
Early Formation
Educated at King’s College, Cambridge, Turing was deeply influenced by the work of Bertrand Russell and Ludwig Wittgenstein, as well as the formalist program of David Hilbert. The intellectual climate of 1930s Britain was shaped by the aftermath of Kurt Gödel’s incompleteness theorems, which demonstrated the inherent limitations of formal systems. Turing’s early work was animated by the question of what it means for a function to be “effectively calculable,” a problem at the heart of the Entscheidungsproblem (decision problem) posed by Hilbert.[1]
Major Turning Points
In 1936, Turing published On Computable Numbers, with an Application to the Entscheidungsproblem, introducing the concept of the Turing machine—a hypothetical device capable of simulating any algorithmic process.[2] This work not only resolved Hilbert’s problem in the negative but also inaugurated the field of computer science. During World War II, Turing’s cryptanalytic work at Bletchley Park further demonstrated the practical and theoretical power of formal systems and automata. In his later years, Turing turned to questions of artificial intelligence and the philosophy of mind, most notably in his 1950 paper Computing Machinery and Intelligence.[3]
Core Concepts
Turing Machine
The Turing machine is a formal model of computation that abstracts the process of symbol manipulation into a finite set of rules operating on an infinite tape. This model provides a rigorous definition of algorithmic procedure and computability, establishing the limits of what can be mechanically calculated.[4] The Turing machine is not merely a technical device but a conceptual apparatus for thinking the relation between rules, repetition, and the possibility of error or undecidability.
Computability and the Entscheidungsproblem
Turing’s solution to the Entscheidungsproblem demonstrated that there exist well-formed mathematical statements whose truth or falsity cannot be decided by any algorithmic procedure.[5] This result, parallel to Gödel’s incompleteness theorems, established the existence of undecidable propositions within any sufficiently powerful formal system. The concept of computability thus marks a structural limit to formalization, with profound implications for the theory of language, meaning, and subjectivity.
Universal Machine
The universal Turing machine is a device capable of simulating any other Turing machine, thereby formalizing the principle of universality in computation.[6] This concept anticipates later developments in computer science and cybernetics, but also provides a model for thinking the symbolic order as a system capable of generating its own rules and transformations—a theme central to structuralist and psychoanalytic theory.
Artificial Intelligence and the Imitation Game
In Computing Machinery and Intelligence, Turing introduced the imitation game (now known as the Turing Test) as a criterion for machine intelligence.[7] The test foregrounds the role of language, symbolization, and the Other in the constitution of subjectivity, raising questions about the boundaries between human and machine, mind and automaton.
Formalization and Symbolic Logic
Turing’s work is characterized by a commitment to formalization, the reduction of reasoning to explicit symbolic manipulation. His engagement with symbolic logic and the architecture of codes prefigures later developments in structural linguistics and the psychoanalytic theory of the signifier.[8]
Relation to Psychoanalysis
Turing’s influence on psychoanalysis is primarily structural and formal, mediated through the transformation of logic, language, and the theory of the subject in the mid-twentieth century.
Freud and the Limits of Mechanization
While Freud’s metapsychology predates Turing, the Freudian model of the psychic apparatus as a system governed by rules, codes, and energetic flows anticipates the logic of automata.[9] Turing’s demonstration that no mechanical system can exhaustively formalize meaning or resolve all contradictions reframes the Freudian unconscious as a site of structural undecidability—a logic that cannot be fully automated.
Lacan and the Logic of the Signifier
Jacques Lacan’s engagement with Turing is explicit and sustained. In his Séminaire XI and subsequent seminars, Lacan invokes the Turing machine as a model for the symbolic order, emphasizing the gap between the rules of the signifier and the emergence of meaning.[10] For Lacan, the subject is constituted in and through the symbolic, yet is always marked by a point of non-knowledge or undecidability—the “real” that escapes symbolization. Turing’s formalization of the undecidable thus becomes a paradigm for the psychoanalytic understanding of the unconscious as a “machine” that both produces and disrupts meaning.[11]
Mediation through Structuralism and Logic
Turing’s influence on psychoanalysis is also mediated by the rise of structuralism and the importation of formal logic into the human sciences. Figures such as Roman Jakobson, Claude Lévi-Strauss, and Jean Laplanche drew on the logic of codes, automata, and information theory to rethink language, myth, and the unconscious.[12] Lacan’s “return to Freud” is inseparable from this structuralist moment, in which Turing’s legacy is omnipresent.
Reception in Psychoanalytic Theory
Turing’s conceptual apparatus has been variously appropriated, debated, and transformed within psychoanalytic theory.
Jacques-Alain Miller, in his commentaries on Lacan, underscores the centrality of the Turing machine for understanding the logic of the signifier and the function of repetition.[13] Alain Badiou, drawing on both Turing and set theory, situates the subject as an effect of the “event” that interrupts the order of the countable.[14] Slavoj Žižek and other contemporary theorists have explored the implications of Turing’s undecidability for the logic of desire, jouissance, and the impossibility of total symbolization.[15]
Debates persist regarding the analogy between machine and subject, the limits of formalization, and the risk of reducing the unconscious to a mere automaton. Some critics argue that the Turing paradigm risks effacing the irreducible singularity of the subject, while others maintain that it illuminates the structural logic of the unconscious.
Key Works
- On Computable Numbers, with an Application to the Entscheidungsproblem (1936): Turing’s foundational paper introducing the Turing machine and demonstrating the existence of undecidable problems, a result that underpins the psychoanalytic notion of the structural gap in the symbolic order.
- Systems of Logic Based on Ordinals (1939): Explores the extension of formal systems beyond the limits identified by Gödel, relevant for thinking the possibility of “supplementary” logics in psychoanalysis.
- Computing Machinery and Intelligence (1950): Introduces the imitation game (Turing Test) and raises questions about language, subjectivity, and the boundaries between human and machine, themes central to Lacanian theory.
- Intelligent Machinery (1948, unpublished in his lifetime): Early exploration of the possibility of artificial intelligence and the architecture of automata, prefiguring later debates on the machinic unconscious.
Influence and Legacy
Turing’s legacy in psychoanalysis is both direct and structural. His formalization of the limits of computation provided a model for thinking the unconscious as a system governed by rules yet marked by undecidability. Lacan’s integration of logic, automata, and the theory of the signifier is unthinkable without Turing’s demonstration of the constitutive gap in any system of symbolization. Beyond psychoanalysis, Turing’s influence extends to structural linguistics, anthropology, philosophy of mind, and contemporary debates on artificial intelligence and the nature of subjectivity. The Turing machine remains a central metaphor for the logic of the unconscious, the function of repetition, and the impossibility of total self-transparency.
See also
References
- ↑ Hodges, Andrew. Alan Turing: The Enigma. Princeton University Press, 1983.
- ↑ Turing, Alan. "On Computable Numbers, with an Application to the Entscheidungsproblem." Proceedings of the London Mathematical Society 2.42 (1936): 230–265.
- ↑ Turing, Alan. "Computing Machinery and Intelligence." Mind 59.236 (1950): 433–460.
- ↑ Turing, Alan. "On Computable Numbers, with an Application to the Entscheidungsproblem."
- ↑ Hodges, Andrew. Alan Turing: The Enigma. Princeton University Press, 1983.
- ↑ Turing, Alan. "On Computable Numbers, with an Application to the Entscheidungsproblem."
- ↑ Turing, Alan. "Computing Machinery and Intelligence."
- ↑ Copeland, B. Jack. Turing: Pioneer of the Information Age. Oxford University Press, 2012.
- ↑ Freud, Sigmund. "The Unconscious." In The Standard Edition of the Complete Psychological Works of Sigmund Freud, Vol. XIV.
- ↑ Seminar XI: The Four Fundamental Concepts of Psychoanalysis (1964)
- ↑ Tomšič, Samo. The Capitalist Unconscious: Marx and Lacan. Verso, 2015.
- ↑ Dosse, François. History of Structuralism. Vol. 1. University of Minnesota Press, 1997.
- ↑ Miller, Jacques-Alain. "Suture (Elements of the Logic of the Signifier)." In Screen 18.4 (1977): 24–34.
- ↑ Badiou, Alain. Being and Event. Continuum, 2005.
- ↑ Žižek, Slavoj. The Parallax View. MIT Press, 2006.