Finitism

Finitism

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the philosophy of mathematics, one of the varieties of finitism is an extreme form of constructivism, according to which a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps. Another form of finitism was pursued by Hilbert and Bernays. In her book Philosophy of Set Theory, Mary Tiles characterized those who allow countably infinite objects as classical finitists, and those who deny even countably infinite objects as strict finitists. Historically, the written history of mathematics was thus classically finitist until Cantor invented the hierarchy of transfinite cardinals in the end of the 19th century. Leopold Kronecker[citation needed] is remembered as Cantor's opponent. God created the natural numbers, all else is the work of man. Finitist constructivism can be seen as a pragmatic attitude in mathematics and in the computerized modern world: whatever can ever be applied (computed) is finite. Thus, the finitist asks, what benefits do the transfinite elements in mathematics bring.show more

Product details

  • Paperback | 124 pages
  • 152 x 229 x 7mm | 191g
  • Lect Publishing
  • United States
  • English
  • 6135825283
  • 9786135825282