Theories of Mathematical Knowledge

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Theories of Mathematical Knowledge

• By
• Crby cr steussy

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realism

• Mathematical objects are real.
• Their existence is a fact, independent of our
  knowledge of them.
• They are not physical or material
• Mathematicians discover. They do not create.

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Formalism

• There are no mathematical objects.
• Mathematics consists only of formulas and
  strings of symbols.
• It is a creation of the mind.
• When applied to the world it acquires meaning.
• Mathematicians create, they do not discover

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Constructivism

• Constructivism (mathematics) - Wikipedia, the
  free encyclopediaConstructivist mathematics uses
  intuitionistic logic, which is essentially
  classical logic without the law of the excluded
  middle. ...en.wikipedia.org/wiki/Constructivism_(m
  athematics) - 69k - Cached - Similar

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Weekends

• Most mathematicians are realists on weekdays and
  formalists on weekends.
• At work they are convinced they are dealing with
  objective reality, but when challenged to give an
  account of that reality they pretend they dont
  really believe in it.

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Geometry

• How is geometry similar or different from math?
• Some regard geometry as analytic, in other words
  a verbal truth rather than a real one. True by
  its meanings alone.
• Others argue it is synthetic, based on empirical
  evidence.

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Your turn

• Create a problem that has a mathematical
  solution.
• Be prepared to share problem solution with
  class.
• Be prepared to explain the relationship this
  problem has with reality.