Transreal Explicit Construction of Universal Possible Worlds

Authors

  • Tiago dos Reis Federal Institute of Education Science and Technology of Rio de Janeiro, Rio de Janeiro, 27215-350, Brazil.
  • James Anderson Editor in Chief of Transmathematica
  • Walter Gomide Department of Philosophy, Institute of Humanities and Social Sciences, Federal University of Mato Grosso, 78060-900, Brazil.

DOI:

https://doi.org/10.36285/tm.55

Abstract

In an earlier paper we supplied an indirect proof of the existence of universal possible worlds that have the topological property of being hypercyclic, which means they can access every world in sequences of worlds that approach arbitrarily closely to every possible world. That proof states that there are universal worlds but it does not exhibit such a world explicitly. We now explicitly construct two such universal worlds. A continuous universal world constructs possible worlds with transreal co-ordinates directly. A discrete world provides a binary hypercyclic vector which can be used to create transfloating-point co-ordinates that approximate transreal co-ordinates. We also discuss the philosophical implications of universal worlds for an omniscient observer and human science.

References

J.A.D.W. Anderson. Evolutionary and Revolutionary Effects of Transcom- putation. In 2nd IMA Conference on Mathematics in Defence. 2011.

J.A.D.W. Anderson. Trans-Floating-Point Arithmetic Removes Nine Quadrillion Redundancies From 64-bit IEEE 754 Floating-Point Arith- metic. In Lecture Notes in Engineering and Computer Science: Proceed- ings of The World Congress on Engineering and Computer Science 2014, WCECS 2014, 22-24 October, 2014, San Francisco, USA., volume 1, pages 80–85, 2014.

J.A.D.W. Anderson and T.S. dos Reis. Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics. In Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering and Computer Science 2014, WCECS 2014, 22-24 October, 2014, San Francisco, USA., volume 1, pages 86–91, 2014.

J.A.D.W. Anderson, N. V ̈olker and A.A. Adams. Perspex Machine VIII: Axioms of transreal arithmetic. In Longin Jan Lateki, David M. Mount, and Angela Y. Wu, editors, Vision Geometry XV, volume 6499 of Proceedings of SPIE, pages 2.1–2.12, 2007.

N. Calkin and H.S. Wilf. Recounting the rationals. American Mathematical Monthly, Mathematical Association of America, 107(4):360–363, 2000.

N.C.A. da Costa. The philosophical import of paraconsistent logic. Journal of Non-Classical Logic, 1:1–19, 1982.

J. Floyd. Wittgenstein on philosophy of logic and mathematics. In Stewart Shapiro, editor, Oxford Handbook of Philosophy of Logic and Mathematics, chapter 4, pages 75–128. Oxford University Press, 2005.

W. Gomide, T.S. dos Reis and J.A.D.W. Anderson. Transreal Proof of the Existence of Universal Possible Worlds. South American Journal of Logic, vol. 5, no. 2, pp 231-259, 2019.

P. Hajek. Metamathematics of Fuzzy Logic. Kluwer, 1998.

G. Priest, J.C. Beall and B.A. Gab. The Law of Non-Contradiction. Oxford University Press, 2004.

G. Priest, K. Tanaka and Z. Weber. Paraconsistent logic. The Stanford En- cyclopedia of Philosophy, 2013.

T.S. dos Reis and J.A.D.W. Anderson. Transreal calculus. IAENG In- ternational Journal of Applied Mathematics, 45(1):51–63, 2015.

T.S. dos Reis and J.A.D.W. Anderson. Transreal limits and elementary functions. In Haeng Kon Kim; Mahyar A. Amouzegar; Sio long Ao, editor, Transactions on Engineering Technologies – World Congress on Engineering and Computer Science 2014, pages 209–225. Springer Verlag, 2015.

T.S. dos Reis, W. Gomide and J.A.D.W. Anderson. Construction of the transreal numbers and algebraic transfields. IAENG International Jour- nal of Applied Mathematics, 46(1):11–23, 2016.

S. Rolewicz, On orbits of elements, Studia Math. 32:17–22, 1969.

Y. Shramko and H. Wansing. Entailment relations and truth values. Bul- letin of the Section of Logic, 36:131–143, 2007.

P. Strawson. Identifying reference and truth values. Theoria, 30(2):96– 118, 1964.

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Published

2023-02-03

How to Cite

dos Reis, T., Anderson, J., & Gomide, W. (2023). Transreal Explicit Construction of Universal Possible Worlds. Transmathematica. https://doi.org/10.36285/tm.55

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