Set Theory and Logic

1803 Submissions

[6] viXra:1803.0318 [pdf] replaced on 2018-03-21 06:51:30

Refutation of Abductive Reasoning © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

Abductive logic of C.S. Peirce is refuted as not tautologous.
Category: Set Theory and Logic

[5] viXra:1803.0202 [pdf] replaced on 2018-03-23 05:35:52

Recent Advances in Refutations and Validations Using Meth8 Modal Logic Model Checker © Copyright 2016-2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 263 Pages. © Copyright 2016-2018 by Colin James III All rights reserved. Abstract updated at: ersatz-systems.com Email: info@cec-services dot com

We evaluate 187 items for 1008 assertions to validate 230 as tautology and 778 as not (77%). We use Meth8 that is a modal logic checker in five models. The Meth8 modal theorem prover implements the logic system variant VŁ4 which corrects the quaternary Ł4 of Łukasiewicz. There are two sets of truth values on the 2-tuple {00, 10, 01, 11} as respectively {False proof for contradiction; Contingent for falsity; Non contingent for truthity; Tautology for proof} and {Unevaluated; Improper; Proper; Evaluated}. The designated proof value is T for tautology and E for evaluated. DRAFT ONLY Abstract updated at: ersatz-systems.com Email: info@cec-services dot com
Category: Set Theory and Logic

[4] viXra:1803.0180 [pdf] replaced on 2018-03-13 17:40:00

Refutation of the Euathlus Paradox: Neither Pay © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 2 Pages. © Copyright 2018 by Colin James III All rights reserved.

Regardless of who wins the lawsuit of Portagoras, Euathlus does not pay. Hence the Euathlus paradox is refuted and resolved by default in favor of Euathlus.
Category: Set Theory and Logic

[3] viXra:1803.0094 [pdf] replaced on 2018-03-07 17:10:19

Refutation of Cantor's Original Continuum Hypothesis Via Injection and Binary Trees © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 1 Page. © Copyright 2018 by Colin James III All rights reserved.

This is the briefest known such refutation of Cantor's continuum conjecture.
Category: Set Theory and Logic

[2] viXra:1803.0088 [pdf] submitted on 2018-03-07 03:33:06

The Continuum Hypothesis

Authors: Chris Pindsle
Comments: 12 Pages.

A proof of the Continuum Hypothesis as originally posed by Georg Cantor in 1878; that an uncountable set of real numbers has the same cardinality as the set of all real numbers. Any set of real numbers can be encoded by the infinite paths of a binary tree. If the binary tree has an uncountable node it must have a descendant with 2 uncountable successors. Each of those will have descendants with 2 uncountable successors, recursively. As a result the infinite paths of an uncountable binary tree will have the same cardinality as the set of all real numbers, as will the uncountable set of real numbers encoded by the tree.
Category: Set Theory and Logic

[1] viXra:1803.0034 [pdf] submitted on 2018-03-02 17:28:55

Meth8/VŁ4 on Complex Numbers (ℂ) © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 1 Page. © Copyright 2018 by Colin James III All rights reserved.

Meth8/VŁ4 maps complex numbers (ℂ) using implication and not equivalence which serves to reason since complex numbers are imaginary and not real.
Category: Set Theory and Logic