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In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical...
The infinite is one of the most intriguing, controversial, and elusive ideas in which the human mind has ever engaged. In mathematics, a particularly interesting form of infinity—actual infinity—has gained, over centuries, an extremely precise and rich meaning, to the point that it now lies at the very core of many fundamental fields such as calculus, fractal geometry, and set theory. In this article...
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