/PhilosophyOfMath

UC Davis PHI 131

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Philosophy of Mathematics

  • Everyday objects
    • tables, chairs
  • scientific objects
    • strings, electrons
  • mathematical objects
    • numbers, sets, functions, groups, rings

$\Rightarrow$ realism or non-realism

Realists don't have to commit to all the objects.

Realism

  1. object exists independent of us
  2. the way they are in physical, scientific, or mathematical realm fixes truth
    • truth doesn't depend on us
  3. we came to know those objects directly or indirectly (through some experiments)
    1. reason $\implies$ rationalists
    2. senses $\implies$ empiricists

Non-Realism

most are empiricists the senses only give ideas

  1. Idealism
    • I have an idea of ..., but it is in me, not the world.
    • tends to be egnostic about the existence of objects
  2. Nominalism: objects are names
  3. Fictionalism: objects are fictions $\rightarrow$ objects may not be true
  4. Constructionist: construct a proof of the existence of something.
    • a object is true, false, or none/unknown before is is proved.