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  "id": "article:formal-logic-to-computation",
  "slug": "formal-logic-to-computation",
  "title": "From Formal Logic to Computation: The Mathematical Road to AI",
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  "thesis": "Modern computing and AI became thinkable partly because humans developed formal symbol systems, logic, computability, switching circuits, information theory, and feedback concepts that turned reasoning into something machines could represent and execute.",
  "status": "published",
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  "publishedAt": "2026-06-20",
  "updatedAt": "2026-06-20",
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  "topics": [
    "long-human-road-to-ai",
    "formal-logic",
    "computability",
    "information-theory",
    "cybernetics"
  ],
  "series": {
    "slug": "long-human-road-to-ai",
    "title": "The Long Human Road to AI",
    "season": "Season 1",
    "order": 2,
    "role": "chapter"
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      "claim": "Algebraic and symbolic treatments of logic helped make reasoning inspectable and manipulable as formal symbol systems.",
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          "snippet": "Boole's 1854 Laws of Thought treats logical relations algebraically, making them writable and transformable as symbols.",
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          "snippet": "SEP's Frege entry describes the move toward modern quantificational logic and the contested history of attribution.",
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        }
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      "counterevidence": [
        {
          "summary": "Formal logic alone did not create computation or AI; engineering, institutions, and other intellectual traditions were also required.",
          "assessedAt": "2026-06-20"
        }
      ]
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      "id": "claim-003",
      "claim": "The formalist ambition around mathematical foundations and decision procedures created the problem setting in which computability could be made precise.",
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          "sourceId": "source-hilbert-problems",
          "snippet": "Hilbert's 1900 address frames the formalist ambition of putting mathematics on firm foundations.",
          "supports": "background",
          "assessedAt": "2026-06-20"
        },
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          "sourceId": "source-church-turing",
          "snippet": "SEP's Church-Turing entry explains how the Entscheidungsproblem motivated precise definitions of effective method.",
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          "assessedAt": "2026-06-20"
        },
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          "snippet": "SEP's Church entry connects lambda calculus and the negative result for the Entscheidungsproblem.",
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          "assessedAt": "2026-06-20"
        },
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          "sourceId": "source-principia-archive",
          "snippet": "Principia Mathematica demonstrates the broader formal-system ambition of building mathematics from explicit logical foundations.",
          "supports": "background",
          "assessedAt": "2026-06-20"
        }
      ],
      "counterevidence": [
        {
          "summary": "Hilbert's 1900 problem list is not identical to the later Entscheidungsproblem, and other programs such as logicism and intuitionism also shaped the question.",
          "assessedAt": "2026-06-20"
        }
      ]
    },
    {
      "id": "claim-004",
      "claim": "Gödel's incompleteness theorems showed that consistent formal systems strong enough for arithmetic have intrinsic limits, complicating the dream of complete formal foundations.",
      "confidence": "high",
      "status": "landscape",
      "evidence": [
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          "sourceId": "source-godel",
          "snippet": "SEP's Gödel entry states that any consistent, effectively axiomatized formal system strong enough for arithmetic is incomplete.",
          "supports": "direct",
          "assessedAt": "2026-06-20"
        },
        {
          "sourceId": "source-turing-1936",
          "snippet": "Turing's 1936-1937 paper invokes Gödel's results while applying computability to the Entscheidungsproblem.",
          "supports": "background",
          "assessedAt": "2026-06-20"
        }
      ],
      "counterevidence": [
        {
          "summary": "Incompleteness applies to specific formal systems containing arithmetic; it does not imply that machines, minds, or AI are generally impossible.",
          "assessedAt": "2026-06-20"
        }
      ]
    },
    {
      "id": "claim-005",
      "claim": "Church, Turing, and Post offered different formalizations of effective procedure, helping turn computation into a mathematical subject before modern computers were common.",
      "confidence": "high",
      "status": "core",
      "evidence": [
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          "sourceId": "source-turing-1936",
          "snippet": "Turing's 1936-1937 paper introduces the abstract machine model and applies it to the Entscheidungsproblem.",
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        },
        {
          "sourceId": "source-post-1936",
          "snippet": "Post's 1936 Finite Combinatory Processes offers an independent formulation of symbol manipulation.",
          "supports": "direct",
          "assessedAt": "2026-06-20"
        },
        {
          "sourceId": "source-church",
          "snippet": "Church's lambda calculus and the negative result for the Entscheidungsproblem provide a function-based route to computability.",
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        }
      ],
      "counterevidence": [
        {
          "summary": "These models idealize rule-following and ignore physical costs, memory limits, hardware faults, and engineering constraints.",
          "assessedAt": "2026-06-20"
        }
      ]
    },
    {
      "id": "claim-006",
      "claim": "The Church-Turing thesis concerns effective methods and is often misunderstood when treated as a claim about all physical machines or minds.",
      "confidence": "high",
      "status": "framing",
      "evidence": [
        {
          "sourceId": "source-church-turing",
          "snippet": "SEP's Church-Turing entry distinguishes the thesis about effective methods from physical or psychological overextensions.",
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          "assessedAt": "2026-06-20"
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          "sourceId": "source-turing-1936",
          "snippet": "Turing's paper frames computability in terms of what a human computer following a mechanical procedure can do.",
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          "assessedAt": "2026-06-20"
        }
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      "counterevidence": [
        {
          "summary": "The thesis is informal insofar as effective method is not formally defined; proposed hypercomputational and physical models challenge wider interpretations.",
          "assessedAt": "2026-06-20"
        }
      ]
    },
    {
      "id": "claim-007",
      "claim": "Shannon's switching-circuit work connected Boolean algebra to relay and switching circuit design, helping make logic part of digital engineering.",
      "confidence": "high",
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          "sourceId": "source-shannon-switching",
          "snippet": "Shannon's 1938 paper applies Boolean algebra to relay and switching circuit design.",
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          "snippet": "The Computer History Museum overview describes how Boolean logic became part of digital circuit engineering.",
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          "summary": "Switching logic had prior engineering practice, and logic gates implement operations without understanding propositions.",
          "assessedAt": "2026-06-20"
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    {
      "id": "claim-008",
      "claim": "Shannon's communication theory provided a mathematical treatment of messages, channels, noise, and information, but it is not a theory of semantic meaning.",
      "confidence": "high",
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          "snippet": "The public scan supports the same entropy, information, channel, and noise claims.",
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          "snippet": "Wiener's 1948 Cybernetics treats communication and control, providing a contrasting context that highlights Shannon's focus on signal rather than meaning.",
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      "id": "the-problem",
      "title": "The problem: reasoning is hard to share"
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