Philosophy of Mathematics
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Questions and Answers

According to Bertrand Russell, what is mathematics the chief source of?

  • Belief in eternal and exact truth (correct)
  • Sensible intelligible world
  • Infallible conclusions
  • Unreasonable effectiveness
  • How did Eugene Wigner feel about the effectiveness of mathematics?

  • Unreasonable
  • Sensible
  • Dumbfounded (correct)
  • Infallible
  • In contrast to Bertrand Russell's view, how did Goethe feel about the conclusions yielded by mathematics?

  • Belief in eternal and exact truth
  • Completely false reputation (correct)
  • Sensible intelligible world
  • Unreasonable effectiveness
  • What analogy is used to describe the position of Mathematics in relation to the Sciences?

    <p>A main trunk and branches of a tree</p> Signup and view all the answers

    What is the almost universal agreement on regarding Mathematics and its role in shaping mankind's thinking?

    <p>Its unique role in shaping mankind's thinking</p> Signup and view all the answers

    What is the main analogy used to describe the relationship between mathematics and physics in the text?

    <p>Trunk and branches</p> Signup and view all the answers

    How is the fabric of mathematical reasoning compared to the format of reasoning in physics?

    <p>Stronger and tougher</p> Signup and view all the answers

    What does the text suggest about the quest for a 'mathematical proof' of a successful physical theory?

    <p>It is not a properly defined exercise</p> Signup and view all the answers

    In 'pure' mathematics, what does the text emphasize about the hypotheses present in a theorem?

    <p>There are no hypotheses other than those present in the statement of a particular theorem</p> Signup and view all the answers

    What example does the text provide to illustrate that a fool-proof mathematical theorem is not necessarily a good physical theory?

    <p>Heisenberg’s theory of turbulence</p> Signup and view all the answers

    What are the four basic operations of mathematics?

    <p>Addition, subtraction, multiplication, and division</p> Signup and view all the answers

    If mathematics is considered as a machine, what are considered to be its tools?

    <p>Addition and subtraction</p> Signup and view all the answers

    What foundational concepts do addition and subtraction represent in mathematics?

    <p>Whole and parts</p> Signup and view all the answers

    How can subtraction be defined in terms of addition?

    <p>Every subtraction problem can be rewritten as an addition problem</p> Signup and view all the answers

    What does subtraction in mathematics involve?

    <p>Taking something away from a group/set or number of things</p> Signup and view all the answers

    Which mathematical operations form the basis for many advanced mathematical theories?

    <p>Addition and multiplication</p> Signup and view all the answers

    What determines the whole in terms of the parts in mathematics?

    <p>Addition</p> Signup and view all the answers

    What does subtraction determine in mathematics?

    <p>A missing part</p> Signup and view all the answers

    What is the relationship between addition and subtraction in mathematics?

    <p>They are inversely related operations</p> Signup and view all the answers

    What does subtraction involve when performed on a group or set of things?

    <p>The group becomes smaller</p> Signup and view all the answers

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