Computing Truth Values in the Topos of Infinite Peirce’s α-Existential Graphs

Tohmé, Fernando; Caterina, Gianluca; Gangle, Rocco

doi:10.1016/j.amc.2020.125343

Cited by 5 publications

(1 citation statement)

References 29 publications

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“…Before we start a technical consideration, let us mention that a number of papers studying consistency of the new methodology and its connections to the historical panorama of ideas dealing with infinities and infinitesimals have been published (see [21,37,38,41,43,54,59,64]). In particular, in [59], it is stressed that it is not related to non-standard analysis.…”

Section: A New Way Of Countingmentioning

confidence: 99%

Some Paradoxes of Infinity Revisited

Sergeyev

2022

Mediterr. J. Math.

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In this article, some classical paradoxes of infinity such as Galileo’s paradox, Hilbert’s paradox of the Grand Hotel, Thomson’s lamp paradox, and the rectangle paradox of Torricelli are considered. In addition, three paradoxes regarding divergent series and a new paradox dealing with multiplication of elements of an infinite set are also described. It is shown that the surprising counting system of an Amazonian tribe, Pirahã, working with only three numerals (one, two, many) can help us to change our perception of these paradoxes. A recently introduced methodology allowing one to work with finite, infinite, and infinitesimal numbers in a unique computational framework not only theoretically but also numerically is briefly described. This methodology is actively used nowadays in numerous applications in pure and applied mathematics and computer science as well as in teaching. It is shown in the article that this methodology also allows one to consider the paradoxes listed above in a new constructive light.

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