06. the mind as machine

philosophy of mind, 2018

Transcript

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 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 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 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 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 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 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 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
    

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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
    

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14. 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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15. 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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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
    

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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 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 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
    

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21. Leibniz’ calculator
    

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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 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 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 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
    

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26. A Boolean circuit
    

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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 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 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 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
    

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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 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 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 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 Slide

36. Turing’s Automatic Computing Engine
    

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