Set Theory and Logic

1906 Submissions

[25] viXra:1906.0366 [pdf] submitted on 2019-06-19 10:31:01

Confirmation of Perez’ Definition of the Conceivable Statement

Authors: Colin James III
Comments: 4 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

Of the 16 equations evaluated, 15 are not tautologous. Elsewhere we correctly proved and confirmed most of the conjectures of the author such as refutations of ZFC, Cantor, and Gödel. The definition of a conceivable statement is confirmed as a theorem, with the other equations forming a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[24] viXra:1906.0356 [pdf] submitted on 2019-06-19 14:06:44

The Continued Fractions and the Real Numbers

Authors: Antoine Balan
Comments: 1 page, written in english

We give a new definition of the real numbers by mean of the continued fractions.
Category: Set Theory and Logic

[23] viXra:1906.0334 [pdf] submitted on 2019-06-19 00:26:41

Refutation of Predicative Collapse and Arithmetical Comprehension

Authors: Colin James III
Comments: 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

The four equations evaluated are not tautologous, hence refuting predicative collapsing principles such as arithmetical comprehension. Therefore these form a tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[22] viXra:1906.0319 [pdf] submitted on 2019-06-17 16:18:42

Refutation of the Hol/isabelle Rejection of E.j. Lowe’s Modal Ontological Argument

Authors: Colin James III
Comments: 5 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

Of 20 equations evaluated, 16 are not tautologous. This effectively refutes Lowe’s proof, as rendered by the authors. This also invalidates the authors’ rejection of Lowe’s proof due to incompleteness (six of Lowe’s conclusions are dismissed without evaluation) and due to an interactive, trial by error approach to reconstruct Lowe. Therefore an ideal showcase for the computer-assisted interpretive method using HOL/Isabelle failed. These results form another non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[21] viXra:1906.0305 [pdf] submitted on 2019-06-16 12:31:23

Refutation of the Axiomatic Translation Principle for Modal Logic Via Resolution Decision Procedure

Authors: Colin James III
Comments: 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

The basis of the axiomatic translation principle is that “no resolution decision procedures are known for decidable first-order logic fragments relevant to modal logics that include the formula ∀xyz(R(x,y)∧R(x,z)→R(y,z)) to express the Euclideanness of a relation R”. We prove a decision procedure for that equation, and hence refute the axiomatic translation principle on which the conjecture is based. Therefore, the axiomatic translation principle is a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[20] viXra:1906.0279 [pdf] submitted on 2019-06-15 22:06:36

Rejection of the Quantified Modal Logic Theorem Proving (QMLTP) Library

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

We evaluate five equations from the quantified modal logic theorem proving (QMLTP) library. None is tautologous for the status of the claimed conjecture, rejecting the approach and library. Other objections include: clarity such as not all problems are in English descriptions; skewed coverage such as about 50% the equations are assumed for Gödel’s embedding; and usability such as the utility tool, to translate QMLTP scripts for pre-selected provers, in Prolog source code which is not compiled into executables for major hardware/OS platforms. Based on these results, the QMLTP approach and library forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[19] viXra:1906.0267 [pdf] submitted on 2019-06-14 08:33:02

Refutation of Inquisitive Modal Logic Via Flatness Grade

Authors: Colin James III
Comments: 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

We evaluate two seminal definitions for flatness grade with neither tautologous. This refutes inquisitive modal logic and relegates it to a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[18] viXra:1906.0266 [pdf] submitted on 2019-06-14 08:34:23

Refutation of Category Theory by Lattice Identity, and Graph-Theoretic / Set-of-Blocks in Partitions

Authors: Colin James III
Comments: 3 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

We evaluate a definition and two models of a method in graph theory to define any Boolean operation. The definition is not tautologous, refuting that only partition tautologies using only the lattice operations correspond to general lattice-theoretic identities. Defined models of graph-theoretic and set-of-blocks do not produce a common edge, but rather show the graph-theoretic definition implies the set-of-blocks definition. This refutes the graph-theoretic model as defining any Boolean operation on lattice partitions of category theory. What follows is that general lattice theory is also refuted via partitions. Therefore the conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[17] viXra:1906.0196 [pdf] submitted on 2019-06-11 07:05:52

The Proof is in the Pudding: an Outline of New Proof of the Existence of God

Authors: Victor Christianto, Robert Neil Boyd
Comments: 6 Pages. This paper has been submitted to a journal. Comments are welcome

Starting with a review of few known arguments to prove the existence of God, we discuss our argument i.e. Nature's order, Pascal's void and Arrow of Time as Neutrosophic triadic to prove the existence of God. The most convincing one is what we call : the proof is in the pudding, i.e. how direct experience with God is the only way to fill everyone's inner void (cf. Pascal). To write shortly, our spiritual inner void can be filled by direct experience with God. This is what we suggest: the proof is in the pudding.
Category: Set Theory and Logic

[16] viXra:1906.0190 [pdf] submitted on 2019-06-11 15:04:27

Понятие множества и его элементов

Authors: Анатолий Вайчунас
Comments: 2 Pages.

The concept of a set and its elements is assumed, in set theory, intuitively known and undetectable to the source. However, it is generalized on the basis of such concepts as the manifold and diversity of mathematical subjects. Понятие множества и его элементов полагается, в теории множеств, интуитивно известным и неопределяемо исходным. Однако, оно является обобщаемым на основе таких понятий как многообразие и разнообразие математических предметов.
Category: Set Theory and Logic

[15] viXra:1906.0179 [pdf] replaced on 2019-06-19 07:09:49

Mapping the Real Numbers to the Set of Natural Numbers

Authors: James Edwin Rock
Comments: 1 Page.

The terminating decimal fractions in the open interval (0, 1) are put in one to one correspondence with the set of positive integers. This shows that attempting to map the set of real numbers to the natural numbers by listing them as infinite decimal fractions is futile. The real numbers are represented as the limit of partial decimal sums. This allows them to be explicitly referenced and makes them into a countable set. We create a new version of set theory (Level Set Theory) in which there is no hierarchy of infinities.
Category: Set Theory and Logic

[14] viXra:1906.0167 [pdf] submitted on 2019-06-11 00:26:19

Refutation of Two Variants of Noncontingency Operator

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

Four axiomatizations of extensions of L(dot-box) over special frames are not tautologous. Those for symmetry and qe&pe are different, but the respective, second-order renditions are equivalent. This refutes the two variants of noncontingency operator. Therefore the conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[13] viXra:1906.0166 [pdf] submitted on 2019-06-11 00:27:28

Refutation of Templates for Converting Counterexamples to Necessitarianism and Into Internalism

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

Five equations of counter-examples for two conjectures are not tautologous. Hence use of templates for metaphysical grounding is refuted in contingentism, externalism, internalism, and necessitarianism. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[12] viXra:1906.0159 [pdf] submitted on 2019-06-09 09:14:14

Refutation of Linear Temporal Logic (LTL)

Authors: Colin James III
Comments: 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

We evaluate two composite modal atoms which turn out to be reductions into single modal operators. This refutes the notion that “new temporal modalities are obtained” and forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[11] viXra:1906.0153 [pdf] submitted on 2019-06-09 12:13:58

Refutation of Temporal Logic Via Instant and Interval/period-Based Models of Time

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

The basic properties in seven equations are not tautologous. This refutes temporal logic via instant- and interval/period-based models of time and forms it as a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[10] viXra:1906.0140 [pdf] submitted on 2019-06-08 07:06:54

The Logical Content of Inequalities

Authors: Ilija Barukčić
Comments: 28 pages. Copyright © 2019 by Ilija Barukčić, Jever, Germany. All rights reserved. Published by:

Objective. From a theoretical point of view, the demarcation between science and (fantastical) pseudoscience is in necessary for both practical and theoretical reasons. One specific nature of pseudoscience in relation to science and other categories of human reasoning is the resistance to the facts. Methods. Several methods are analyzed which may be of use to prevent that belief is masqueraded genuinely as scientific knowledge. Results. Modus ponens, modus tollens and modus conversus are reanalyzed. Modus sine, logically equivalent to modus ponens is developed. Modus inversus and modus juris are described in detail. Conclusions. In our striving for knowledge, there is still much more scientific work to be done on the demarcation between science and pseudoscience. Keywords: non strict inequality, quantum mechanics, science, pseudoscience
Category: Set Theory and Logic

[9] viXra:1906.0130 [pdf] replaced on 2019-06-19 10:49:19

Recent Advances in the Modal Model Checker Meth8 and VŁ4 Universal Logic: Abstract; Table of Results; Table of Contents

Authors: Colin James III
Comments: 29 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

We use the Meth8/VŁ4 modal logic model checker to evaluate 545 artifacts in 3084 assertions to refute 2501 as non tautologous (81.1%). This is the abstract, table of results, and table of contents. The current document in 890-pages includes availability of Meth8/VŁ4 and is available on request from info@ersatz-systems.com.
Category: Set Theory and Logic

[8] viXra:1906.0115 [pdf] submitted on 2019-06-07 09:41:06

Refutation of Self-Referential Sentences and Provability: Antimony of the Liar

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

The seven definitions evaluated are not tautologous. The first four equations refute the author’s abstract that “a sentence cannot be denominated by p and written as p is not true”. The next three refute that “in a system in which q denominates the sentence q is not provable it is not provable that q is true and not provable”. The net result is refutation of the liar’s antimony as a paradox (contradiction) and concludes that self-referential sentences are in fact provable as not tautologous. These findings provide a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[7] viXra:1906.0095 [pdf] submitted on 2019-06-08 04:19:06

Availability of Meth8/VŁ4

Authors: Colin James III
Comments: 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

Manifest of files distributed in current release 2019 June 4 ver 10 (2019.06.04.10)
Category: Set Theory and Logic

[6] viXra:1906.0092 [pdf] submitted on 2019-06-08 05:14:23

Refutation of Conditional Necessitarianism

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

The seminal definition of conditional necessitarianism is not tautologous. The spin-off is to deny the following five conjectures, so based thereon: Truthmaker-dependence (TD); Truthbearer-requirement (TB); Aboutness-requirement (AC); and versions of tf named deflationary and inflationary. Therefore these six conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[5] viXra:1906.0055 [pdf] submitted on 2019-06-04 08:22:22

Refutation of the Predicatively Unprovable Termination of the Ackermannian Goodstein Process

Authors: Colin James III
Comments: 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

We evaluate the Goodstein theorem which is not tautologous. This refutes such follow-on as the Ackermanian Goodstein process and conjecture of its predicatively unprovable termination. Therefore that segment is a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[4] viXra:1906.0052 [pdf] submitted on 2019-06-04 10:05:37

Refutation of the Cabannas Conjecture of Objectivity

Authors: Colin James III
Comments: 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

We evaluate the 13 atomic equations, with none tautologous. This refutes the Cabannas conjecture of objectivity, forming a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[3] viXra:1906.0017 [pdf] submitted on 2019-06-02 16:07:32

The Rebuttal of Colin James III's Refutation of Vidamor Cabannas’ Theory of Objectivity

Authors: Vidamor Cabannas
Comments: 11 Pages. More information and comments on Theory of Objectivity and Author Vidamor Cabannas can be found at www.theoryofobjectivity.com

I analyzed the refutation of the Theory of Objectivity performed by Colin James III in vixra.org/abs/1904.0549 and verified that the applied method as well as the values found were correct. However, there is an error in the conclusion, as it refutes the Theory of Objectivity instead of confirming it. The values found in Colin James III's refutation confirm the exact findings of the Theory of Objectivity. Therefore, as the values that were found confirm those presented by the theory, these values are a confirmation and not a refutation of the theory. In other words, the equation N + 1 = n – 1 is tautological, confirming the existence of a geometric entity that occurred before the onset of the universe, which the Theory of Objectivity calls Nothing. However, Nothing is a geometric entity incompatible with the existence of the universe, which forms a contradiction with non-tautological values at the atomic level. This is because in the era of Nothing, there is no space nor any other element other than the geometrical point known as Nothing. There is no reference. This geometric Nothing does not signify absolute zero and has an informative value. The Theory of Objectivity uses a logical and geometric model to demonstrate how the spherical point called Nothing transformed itself into universal space. Thus, it proves that absolute Nothing does not exist.
Category: Set Theory and Logic

[2] viXra:1906.0015 [pdf] submitted on 2019-06-03 03:35:48

Refutation of the Gödel-Mckinsey-Tarski Translation of Intuitionistic Logic (Ipc)

Authors: Colin James III
Comments: 1 Page. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

We evaluate the Gödel–McKinsey–Tarski [GMT] translation of IPC “by reduction from intuitionistic logic (IPC) using a series of translations”. The equation is not tautologous. This refutes GMT, the method approach using a series of translations, and IPC itself which form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[1] viXra:1906.0014 [pdf] submitted on 2019-06-03 04:37:32

Refutation of Shevenyonov Extension Nary Antropic to Propositional Logic

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

Out of 18 equations evaluated, two were trivial theorems, and 16 were not tautologous. This refutes the Shevenyonov extension nary antropic to propositional logic and relegates it to a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic