TOK Journal Post #14

by Michael on March 1, 2019

Article: Maths and Proof no marks

Summary:

  • Math uses rigorous proof, where steps are explicitly laid out, in order to achieve complete certainty in a closed system.
  • Science is more about the degrees of certainty as opposed to being able to achieve complete certainty.
  • It is impossible to achieve complete certainty in ethics, as it is a combination of both emotion and reasoning.
  • Math is based on deductive reasoning, whereas science uses inductive reasoning and does not require rigorous proof.

KQ: As the natural sciences cannot achieve complete certainty, to what extent can we use mathematics to explain scientific phenomena?

Article: Is Maths True?

Summary:

  • Other areas of knowledge can be thought of with debate and contention, whereas mathematics seems like it is ingrained into our minds without question.
  • Numbers don’t really exist in nature, as they are just symbols and aspects of language. Leopold Kronecker said “The natural numbers come from god, everything else is the work of man.” which suggests that numbers do in fact exist in nature, but it is humans who created the symbols and language around it.
  • It could be said that mathematical truth, like beauty, is in the eyes of the beholder, and individuals can pursue truth as they see it.

KQ: To what extent is the mathematics that we learn true?

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