Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939

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  • For
  • several
  • terms
  • at
  • Cambridge
  • in
  • 1939,
  • Ludwig
  • Wittgenstein
  • lectured
  • on
  • the
  • philosophical
  • foundations
  • of
  • mathematics.
  • A
  • lecture
  • class
  • taught
  • by
  • Wittgenstein,
  • however,
  • hardly
  • resembled
  • a
  • lecture.He
  • sat
  • on
  • a
  • chair
  • in
  • the
  • middle
  • of
  • the
  • room,
  • with
  • some
  • of
  • the
  • class
  • sitting
  • in
  • chairs,
  • some
  • on
  • the
  • floor.
  • He
  • never
  • used
  • notes.
  • He
  • paused
  • frequently,
  • sometimes
  • for
  • several
  • minutes,
  • while
  • he
  • puzzled
  • out
  • a
  • problem.
  • He
  • often
  • asked
  • his
  • listeners
  • questions
  • and
  • reacted
  • to
  • their
  • replies.
  • Many
  • meetings
  • were
  • largely
  • conversation.These
  • lectures
  • were
  • attended
  • by,
  • among
  • others,
  • D.
  • A.
  • T.
  • Gasking,
  • J.
  • N.
  • Findlay,
  • Stephen
  • Toulmin,
  • Alan
  • Turing,
  • G.
  • H.
  • von
  • Wright,
  • R.
  • G.
  • Bosanquet,
  • Norman
  • Malcolm,
  • Rush
  • Rhees,
  • and
  • Yorick
  • Smythies.
  • Notes
  • taken
  • by
  • these
  • last
  • four
  • are
  • the
  • basis
  • for
  • the
  • thirty-one
  • lectures
  • in
  • this
  • book.The
  • lectures
  • covered
  • such
  • topics
  • as
  • the
  • nature
  • of
  • mathematics,
  • the
  • distinctions
  • between
  • mathematical
  • and
  • everyday
  • languages,
  • the
  • truth
  • of
  • mathematical
  • propositions,
  • consistency
  • and
  • contradiction
  • in
  • formal
  • systems,
  • the
  • logicism
  • of
  • Frege
  • and
  • Russell,
  • Platonism,
  • identity,
  • negation,
  • and
  • necessary
  • truth.
  • The
  • mathematical
  • examples
  • used
  • are
  • nearly
  • always elementary.
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