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06. the mind as machine

GeorgeMatthews
January 24, 2019
51

06. the mind as machine

philosophy of mind, 2018

GeorgeMatthews

January 24, 2019
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  1. Logic Machines
    a brief history of the idea
    George Matthews
    CC 2018

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  2. Aristotle’s insight
    ! Valid reasoning is a matter of form
    not content.
    ! Cognition is categorization.
    ! The formal structure of categorical
    reasoning can be exhaustively mapped
    out.
    384 – 322 BCE

    View full-size slide

  3. Aristotle’s insight
    ! Valid reasoning is a matter of form
    not content.
    ! Cognition is categorization.
    ! The formal structure of categorical
    reasoning can be exhaustively mapped
    out.
    384 – 322 BCE

    View full-size slide

  4. Aristotle’s insight
    ! Valid reasoning is a matter of form
    not content.
    ! Cognition is categorization.
    ! The formal structure of categorical
    reasoning can be exhaustively mapped
    out.
    384 – 322 BCE

    View full-size slide

  5. Aristotle’s insight
    ! Valid reasoning is a matter of form
    not content.
    ! Cognition is categorization.
    ! The formal structure of categorical
    reasoning can be exhaustively mapped
    out.
    384 – 322 BCE

    View full-size slide

  6. the Aristotelian Square of opposition
    A E
    I O
    subalternation
    contraries
    c o
    n
    t r a
    d
    i c t o
    r i e s
    subalternation
    c o
    n
    t r a
    d
    i c t o
    r i e s
    sub-contraries
    All S are P.
    Some S are P.
    No S are P.
    Some S are not P.

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  7. Lull’s fantasy
    ! All thoughts are combinations of a
    finite set of concepts.
    ! We can mechanically determine all
    possible combinations.
    ! The true nature of reality, God,
    morality can be shown for all to see.
    1232 – 1316

    View full-size slide

  8. Lull’s fantasy
    ! All thoughts are combinations of a
    finite set of concepts.
    ! We can mechanically determine all
    possible combinations.
    ! The true nature of reality, God,
    morality can be shown for all to see.
    1232 – 1316

    View full-size slide

  9. Lull’s fantasy
    ! All thoughts are combinations of a
    finite set of concepts.
    ! We can mechanically determine all
    possible combinations.
    ! The true nature of reality, God,
    morality can be shown for all to see.
    1232 – 1316

    View full-size slide

  10. Lull’s fantasy
    ! All thoughts are combinations of a
    finite set of concepts.
    ! We can mechanically determine all
    possible combinations.
    ! The true nature of reality, God,
    morality can be shown for all to see.
    1232 – 1316

    View full-size slide

  11. Lull’s Art of Finding Truth

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  12. Hobbes’ analysis
    ! Society is made of individuals.
    ! Individuals are made of mechanical
    components.
    ! Thoughts are computations carried
    out by these components. 1588 – 1679

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  13. Hobbes’ analysis
    ! Society is made of individuals.
    ! Individuals are made of mechanical
    components.
    ! Thoughts are computations carried
    out by these components. 1588 – 1679

    View full-size slide

  14. Hobbes’ analysis
    ! Society is made of individuals.
    ! Individuals are made of mechanical
    components.
    ! Thoughts are computations carried
    out by these components. 1588 – 1679

    View full-size slide

  15. Hobbes’ analysis
    ! Society is made of individuals.
    ! Individuals are made of mechanical
    components.
    ! Thoughts are computations carried
    out by these components. 1588 – 1679

    View full-size slide

  16. Hobbes’ Leviathan

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  17. Leibniz’ dream
    ! A perfect language expressing all
    truths is possible.
    ! This language could be encoded in an
    algebra of thought enabling only true
    conclusions to be derived from other
    thoughts.
    ! All questions could be resolved by a
    machine whose workings mirror the
    rules of correct thinking.
    1646 – 1716

    View full-size slide

  18. Leibniz’ dream
    ! A perfect language expressing all
    truths is possible.
    ! This language could be encoded in an
    algebra of thought enabling only true
    conclusions to be derived from other
    thoughts.
    ! All questions could be resolved by a
    machine whose workings mirror the
    rules of correct thinking.
    1646 – 1716

    View full-size slide

  19. Leibniz’ dream
    ! A perfect language expressing all
    truths is possible.
    ! This language could be encoded in an
    algebra of thought enabling only true
    conclusions to be derived from other
    thoughts.
    ! All questions could be resolved by a
    machine whose workings mirror the
    rules of correct thinking.
    1646 – 1716

    View full-size slide

  20. Leibniz’ dream
    ! A perfect language expressing all
    truths is possible.
    ! This language could be encoded in an
    algebra of thought enabling only true
    conclusions to be derived from other
    thoughts.
    ! All questions could be resolved by a
    machine whose workings mirror the
    rules of correct thinking.
    1646 – 1716

    View full-size slide

  21. Leibniz’ calculator

    View full-size slide

  22. Boole’s laws
    ! Logic is a branch of mathematics.
    ! Logical reasoning can be built up from
    the elementary operations OR, AND,
    NOT and the laws governing them.
    ! Thinking is the mechanical
    application of these laws to express
    complex ideas and reasoning.
    1816 – 1864

    View full-size slide

  23. Boole’s laws
    ! Logic is a branch of mathematics.
    ! Logical reasoning can be built up from
    the elementary operations OR, AND,
    NOT and the laws governing them.
    ! Thinking is the mechanical
    application of these laws to express
    complex ideas and reasoning.
    1816 – 1864

    View full-size slide

  24. Boole’s laws
    ! Logic is a branch of mathematics.
    ! Logical reasoning can be built up from
    the elementary operations OR, AND,
    NOT and the laws governing them.
    ! Thinking is the mechanical
    application of these laws to express
    complex ideas and reasoning.
    1816 – 1864

    View full-size slide

  25. Boole’s laws
    ! Logic is a branch of mathematics.
    ! Logical reasoning can be built up from
    the elementary operations OR, AND,
    NOT and the laws governing them.
    ! Thinking is the mechanical
    application of these laws to express
    complex ideas and reasoning.
    1816 – 1864

    View full-size slide

  26. A Boolean circuit

    View full-size slide

  27. Babbage’s ambitions
    ! Complex mathematical operations can
    be broken down into simple mindless
    steps.
    ! A general purpose machine can be
    built to carry out complex
    calculations.
    ! This machine can be programmed to
    perform different operations on
    different inputs.
    1814 – 1871

    View full-size slide

  28. Babbage’s ambitions
    ! Complex mathematical operations can
    be broken down into simple mindless
    steps.
    ! A general purpose machine can be
    built to carry out complex
    calculations.
    ! This machine can be programmed to
    perform different operations on
    different inputs.
    1814 – 1871

    View full-size slide

  29. Babbage’s ambitions
    ! Complex mathematical operations can
    be broken down into simple mindless
    steps.
    ! A general purpose machine can be
    built to carry out complex
    calculations.
    ! This machine can be programmed to
    perform different operations on
    different inputs.
    1814 – 1871

    View full-size slide

  30. Babbage’s ambitions
    ! Complex mathematical operations can
    be broken down into simple mindless
    steps.
    ! A general purpose machine can be
    built to carry out complex
    calculations.
    ! This machine can be programmed to
    perform different operations on
    different inputs.
    1814 – 1871

    View full-size slide

  31. Babbage’s Difference Engine

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  32. Turing’s proof
    ! All computations require only the
    ability to read and write symbols in
    some location in response to
    instructions.
    ! It is possible to construct a machine
    that can imitate all other machines.
    ! Thus a universal machine is possible.
    1912 – 1954

    View full-size slide

  33. Turing’s proof
    ! All computations require only the
    ability to read and write symbols in
    some location in response to
    instructions.
    ! It is possible to construct a machine
    that can imitate all other machines.
    ! Thus a universal machine is possible.
    1912 – 1954

    View full-size slide

  34. Turing’s proof
    ! All computations require only the
    ability to read and write symbols in
    some location in response to
    instructions.
    ! It is possible to construct a machine
    that can imitate all other machines.
    ! Thus a universal machine is possible.
    1912 – 1954

    View full-size slide

  35. Turing’s proof
    ! All computations require only the
    ability to read and write symbols in
    some location in response to
    instructions.
    ! It is possible to construct a machine
    that can imitate all other machines.
    ! Thus a universal machine is possible.
    1912 – 1954

    View full-size slide

  36. Turing’s Automatic Computing Engine

    View full-size slide