THE INFINITE

@inproceedings{Relief2007THEI,
  title={THE INFINITE},
  author={Katrina Relief},
  year={2007}
}
Until the 19th century the study of the in nite was an exclusive domain of philosophers and theologians. For mathematicians, while the concept of in nity was crucial in applications of calculus and in nite series, the in nite itself was (to paraphrase Gauss) just \the manner of speaking." Indeed, 18th century mathematics, even with its frequent use of in nite sequences and in nitesimals, had no real need to study the concept of in nity itself. The increasing use of abstract functions of real… Expand
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TLDR
This article reviewing the contributions of some thinkers who argued in favor of the assignment of different sizes to infinite collections of natural numbers and some recent mathematical developments that generalize the part–whole principle to infinite sets in a coherent fashion show how these new developments are important for a proper evaluation of a number of positions in philosophy of mathematics. Expand
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We consider here several versions of finitism or conceptions that try to work around postulating sets of infinite size. Restricting oneself to the so-called potential infinite seems to rest either onExpand
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