Set Theory and Logic

1906 Submissions

[41] viXra:1906.0556 [pdf] submitted on 2019-06-30 02:57:53

Confirmation of VŁ4 as Sound

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.

Logic VŁ4 is defined as a bivalent classical logic that maps tautology correctly and hence is sound. Because paraconsistent, non bivalent, vector logics cannot map non tautology correctly, they are defined as non tautologous fragments of VŁ4 as a universal logic.
Category: Set Theory and Logic

[40] viXra:1906.0543 [pdf] submitted on 2019-06-28 12:10:06

Refutation of Scott’s Existence Axiom in Sheaf Theory

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.

In two non-tautologous equations we refute Scott’s existence axiom in sheaf theory. Therefore it does not follow that automating free logic is supported by using “modern proof assistants and theorem provers for classical higher-order logic”, such as the showcased tools Isabelle/HOL, Sledgehammer, and Nitpik. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[39] viXra:1906.0536 [pdf] submitted on 2019-06-29 05:45:03

Refutation of the Boone-Rogers Theorem

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 Boone-Rogers theorem states that the uniform word problem for the class of all finitely presented groups with solvable word problem is unsolvable. We show that is not tautologous. We further show that a universal, solvable word problem group is tautologous. The former forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[38] viXra:1906.0523 [pdf] submitted on 2019-06-26 09:01:51

An Explicit Mapping of the Real Numbers to the Set of Natural Numbers

Authors: James Edwin Rock
Comments: 1 Page.

By showing that Cantor’s diagonal technique that lists the real numbers does not even work to show the proper cardinality of the rational numbers, we refute his proof technique. To explicitly reference them the real numbers are represented as the limit of partial decimal sums. We show that the real numbers are a denumerable set. We create a new (Level Set Theory), where all infinite sets have the same cardinality as the set of natural numbers.
Category: Set Theory and Logic

[37] viXra:1906.0517 [pdf] submitted on 2019-06-26 11:09:09

Refutation of Hamkins’ Theorem

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.

Hamkins’ theorem claims “every countable model … of set theory embeds into its own constructible universe … x∈y ↔ j(x)∈j(y)”, which is not tautologous, forming a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[36] viXra:1906.0516 [pdf] submitted on 2019-06-26 11:10:14

Refutation of Keisler’s Ultraproduct Construction

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.

The ultraproduct construction of Keisler is based on definitions for proper filter in six equations and for ultrafilter in two equations. The definitions are not tautologous. This refutes the ultraproduct construction as “a uniform method of building models of first order theories which has applications in many areas of mathematics.” Claims by other writers to extend Keisler’s construction similarly fail, to form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[35] viXra:1906.0511 [pdf] submitted on 2019-06-26 23:53:01

Refutation of First-Order Proofs Without Syntax

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.

Proof examples (3) in the introduction, modal combinatorial proofs (1), and rules in Gentzen’s classical sequent calculus (3) are not tautologous. This refutes the conjecture and approach of first-order proofs without syntax, to form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[34] viXra:1906.0499 [pdf] submitted on 2019-06-27 08:02:39

The Existence of Equilibrium States in Dynamic Systems with Attractive Interaction

Authors: Elizabeth Lemeshko
Comments: 4 Pages. Text in Ukrainian. Mohyla Mathematical Journal, Vol 1 (2018) http://mmj.ukma.edu.ua/article/view/152602

Nowadays, science is characterized by needs of the study of various complex processes and phenomena’s. Today’s research of complex and dynamical systems is one of the most advanced ways of research and evolution of the modern world. Models of biology and ecology, physical models, various economic and social models are typical examples of dynamic systems. The concept of an interactive complex system in modern science is a main tool for construction of mathematical models for solving modern civilization problems and development. The dynamical systems approach to conflict is relatively new, but it has beginning in different research fields. Theory of dynamic systems helps us to understand the experiments, build the mathematical model of iterations and examine behavior and relations between opponents, like distribution of resources and territory, population growing etc. This is a challenging problem of finding and achieving a compromise state for opponents on a common territory has different options to define the task and to choose conflict interaction. In 2016, the monograph by V. Koshmanenko where was introduced new approach for dynamic system of conflict that based on interactions of the opponents in the form probability distribution in the disputed area was published. In particular, presented the concept of a complex dynamic system with attractive interaction. The relevance of this research is improving new dynamical system and researching for a new application of abstract models in everyday life. In this paper briefly fundamentals of the theory of dynamical systems described and the theorem on the existence of a equilibrium state in a the new, perspective for research, dynamical system with attractive interaction in terms of probability distributions (measures) and their densities, formulated and proved.
Category: Set Theory and Logic

[33] viXra:1906.0496 [pdf] submitted on 2019-06-27 12:23:34

Refutation of Unification Nets (Canonical Proof Net Quantifiers)

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.

Using the drinker’s paradox, as rendered in two equations, we evaluate the unification net, in two equations, as not tautologous. To extend the unification net to additives is similarly defective, forming a non tautologous fragment of the universal logic VŁ4. We also supply analysis of Smullyan’s drinking principle.
Category: Set Theory and Logic

[32] viXra:1906.0491 [pdf] submitted on 2019-06-25 08:05:42

Refutation of Computer-Simulation Model Theory

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.

Computer simulation model theory (CSMT), as a substituted extension of mathematical model theory (MMT), is a conjecture that: for a formula φ, construct a computer simulation model S such that 1- φ does not hold in S, and 2- the reasoner I (human being, the one who lives inside the reality) cannot distinguish S from the reality (R), then I cannot prove φ in reality. The conjecture is not tautologous. While we show elsewhere that P=NP is not tautologous (via refutation of the Schaefer theorem), the unprovability of P=NP does not follow from this CSMT approach. This conjecture forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[31] viXra:1906.0479 [pdf] submitted on 2019-06-25 21:05:45

Refutation of Program Verification by Reduction

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 formula for program verification by reduction is not tautologous, thereby refuting such an approach and forming a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[30] viXra:1906.0473 [pdf] submitted on 2019-06-24 07:49:30

Refutation of Kripke Frames from Incompleteness of BAO’s with ◊⊥=⊥

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.

Because Kripke frames require ◊⊥=⊥, not tautologous, they are refuted. What follows is BAOs so defined are also refuted (which we respectively demonstrate elsewhere), namely: Jónsson-Tarski, Lemmon-Scott; Fine-Thomason, van Benthem, Boolos-Sambin, and Lindenbaum-Tarski. These results also make the Blok dichotomy suspicious. Therefore these conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[29] viXra:1906.0456 [pdf] submitted on 2019-06-23 09:18:35

Refutation of Formalization of Axiom of Choice and Equivalent Theorems Using the Coq Tool

Authors: Colin James III
Comments: Pages.

We evaluate two definitions for maximum and minimal set membership, for the nesting of sets, and the equivalence relations of axiom of choice, Tukey’s lemma, Hausdorff maximal principle, maximal principle, Zermelo’s postulate, Zorn’s lemma, well-ordering theorem. None is tautologous, refuting the claims. The authors conclude: “The whole process of formal proof demonstrates that the Coq-based machine proving of mathematics theorem is highly reliable and rigorous. The formal work of this paper is enough for most applications, especially in set theory, topology and algebra.” We refute those assertions based on the non-bivalent performance of the Coq proof assistant. Therefore, these formalizations and methodology render a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[28] viXra:1906.0448 [pdf] submitted on 2019-06-23 12:06:00

Refutation of Free Choice Permission (FCP) in Deontic 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.

The formula for free choice permission (FCP) in deontic logic as P(p\/q)→(Pp/\Pq) (FCP) is not tautologous, not a paradox, and hence not applicable in Hilbert-style classical deontic logic as a guarded version. Therefore FCP forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[27] viXra:1906.0407 [pdf] replaced on 2019-07-17 13:33:25

Visualizing the Distributions and Isosurfaces of Some Traditional and Non-Traditional Quaternion Fractal Sets

Authors: Shawn Halayka
Comments: 18 Pages.

After a concise introduction, the length, displacement, and magnitude distributions and isosurfaces related to some quaternion fractal sets are visualized.
Category: Set Theory and Logic

[26] viXra:1906.0396 [pdf] submitted on 2019-06-21 04:28:02

Refutation of Π1− of Self-Verifying Axioms for Grounding Functions and Relation Predicates

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 Π1− self-verifying axioms defining the grounding functions and the relation predicates as not tautologous. This refutes the approach for weak axiom systems to use subtraction and division primitives, rather than addition and multiplication, to encode formally theorems of arithmetic. Therefore the conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[25] viXra:1906.0380 [pdf] submitted on 2019-06-21 19:35:05

Refutation of Bob Boyer’s Paradox

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.

Bob Boyer’s paradox is as follows. “A question: It is generally granted that 'p implies p', which is to say, 'if p, then p'. So what about this claim: 'If any number is prime, then any number is prime'?” We find the sentences are unrelated. We then rewrite the second sentence as: “If at least one number is prime, then at least one number is prime”; or as “If at least one number is prime, then possibly all numbers are prime”. Both are trivial tautologies, meaning neither is a contraction or paradox, and therefore forming a tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[24] viXra:1906.0375 [pdf] submitted on 2019-06-22 06:21:16

Refutation of Comorphism of Sites

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 complex equation evaluated is not tautologous, hence refuting the conjecture of comorphism of sites as a functor with a covering lifting property. What follows is that the following are also refuted: surjections, inclusions, localic morphisms, hyperconnected morphisms, and equivalences of toposes. This further relegates category theory of Grothendieck to a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[23] 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

[22] 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

[21] 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

[20] 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

[19] 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

[18] 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

[17] 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

[16] 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

[15] 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

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

Понятие множества и его элементов

Authors: Анатолий Вайчунас
Comments: 2 Pages. in Russian. Только e-meil диалог = onli e-meil dialogue

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

[13] 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

[12] 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

[11] 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

[10] 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

[9] viXra:1906.0140 [pdf] replaced on 2019-07-13 09:21:21

The Logical Content of Inequalities

Authors: Ilija Barukčić
Comments: 20 pages. Copyright © 2019 by Ilija Baruk�?ić, Jever, Germany. All rights reserved. Published by: Ilija Baruk�?ić "The Interior Logic of Inequalities" IJMTT, 65 (7) (2019): 146-155. doi: 10.14445/22315373/IJMTT-V65I7P524

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

[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