Set Theory and Logic

1905 Submissions

[23] viXra:1905.0358 [pdf] submitted on 2019-05-20 01:17:30

Proposal of Replacing Classical Logic with Free Logic for Reasoning with Non-Referring Names in Ordinary Discourse

Authors: Bornali Paul
Comments: 9 Pages.

Reasoning carried out in ordinary language, can not avoid using non-referring names if occasion arises. Semantics of classical logic does not fit well for dealing with sentences with non-referring names of the language. The principle of bivalence does not allow any third truth-value, it does not allow truth-value gap also. The outcome is an ad hoc stipulation that no names should be referentless. The aim of this paper is to evaluate how far free logic with supervaluational semantics is appropriate for dealing with the problems of non-referring names used in sentences of ordinary language, at the cost of validity of some of the classical logical theses/ principles.
Category: Set Theory and Logic

[22] viXra:1905.0310 [pdf] replaced on 2019-05-19 22:47:28

Refutation of Tarski’s Geometric Axioms and Betweenness

Authors: Colin James III
Comments: 3 Pages.

Of 13 equations evaluated, five are tautologous and eight are non tautologous. This refutes Tarski’s geometric axioms and betweenness which form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[21] viXra:1905.0276 [pdf] submitted on 2019-05-17 09:44:55

Refutation of Counterpart Theory Via Modal Logic

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.

Of seven examples for counterpart theory, none is tautologous. In fact, a translation is not tautologous in the counterpart model or in QMT, but rather shares the same truth table result. Two definitions of intensionality are also not tautologous and hence refuted. Therefore counterpart theory forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[20] viXra:1905.0275 [pdf] submitted on 2019-05-17 10:56:36

Programming Primitive Recursive Functions and Beyond

Authors: Hannes Hutzelmeyer
Comments: 17 Pages. The details given here relate to document viXra: 1905.0221

In addition to the publication 'The Snark, a counterexample for Church's thesis?' examples and details are offered in the form of two appendices C6 and C7 that allow for better understanding of the general method and the particular problem related to Church's thesis. The author has developed an approach to logics that comprises, but also goes beyond predicate logic. The FUME method contains two tiers of precise languages: object-language Funcish and metalanguage Mencish. It allows for a very wide application in mathematics from recursion theory and axiomatic set theory with first-order logic, to higher-order logic theory of real numbers etc. The most usual approach to calculative (effectively calculable) functions is done by register machines or similar storage-based computers like the Abacus or Turing machines. Another usual approach to computable functions is to start with primitive recursive functions. However, one has to find a way to put this into a form that does not rely on a pre-knowledge about functions and higher logic. The concrete calcule LAMBDA of decimal pinitive arithmetic allows for such an access. It is based on a machine that is completely different from the storage-based machines: the PINITOR does not use storages but rather many microprocessors, one for each appearance of a command in the code of primitive recursive functior. the codes are decimal numbers, called pinons , where only the characters 0 1 2 8 9 appear. There are four kind of commands only: 0 nullification, 1 succession, 2 straight recursion and 8 composition. The PINITOR is a calculator which means that there is no halting problem. Computers have halting problems, per defintion calculators do not. Appendix C6 gives the programming of the codes of most of the usual primitive function and goes even farther, e.g. it introduces generator technique that allows for the straight-forward calculation of so-called processive function, that are not primitive recursive. The most famous examples of Ackermann and other hyperexponential functions are programmed. Appendix C7 turns to the Boojum-function and the Snark-function that have been introduced as calculative functions in the above publication in connection with Church's thesis. A list is provided that gives the lowest values for these functions and gives some more insight into these functions.
Category: Set Theory and Logic

[19] viXra:1905.0254 [pdf] submitted on 2019-05-16 08:59:09

Refutation of Forcing to Change Large Cardinal Strength

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 theorem of the dissertation states a cardinal is greatly inaccessible if and only if it is Mahlo. Three non trivial equations of the proof are not tautologous, thereby refuting theorems derived therefrom. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[18] viXra:1905.0231 [pdf] submitted on 2019-05-15 08:39:24

A Methodology for Urban Sustainability Indicator Design

Authors: Ricardo Alvira
Comments: 19 Pages.

In recent times we have witnessed proliferation of indicators and models for measuring sustainability. This reveals the lack of common and shared scientific paradigm/common framework from which to confront the issue of quantitatively assessing the sustainability of our society. With the aim of moving forward the definition of such common framework, in this article we explain an easy formal methodology for designing urban sustainability indicators based on Fuzzy Logic / Fuzzy Sets Theory. The interest of this methodology is threefold: Firstly, formal procedures enable easier testing, a most fundamental issue forgotten in many current proposals of sustainability indicators. Secondly, a formal procedure is easily understandable and can become a common language allowing shared use of the indicators and facilitating their continuous improvement. And thirdly, fuzzy logic is widely used in computing and artificial intelligence, thus facilitating the progressive automation of our sustainability monitoring models. To help understand the procedure, the design of two indicators is reviewed.
Category: Set Theory and Logic

[17] viXra:1905.0223 [pdf] submitted on 2019-05-15 18:33:17

Refutation of Jaccard Index

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 definition of the Jaccard index is not tautologous, hence refuting it with derivations and forming a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[16] viXra:1905.0221 [pdf] submitted on 2019-05-16 03:15:48

The Snark, a Counterexample for Church's Thesis ?

Authors: Hannes Hutzelmeyer
Comments: 7 Pages.

In 1936 Alonzo Church put forward his thesis that recursive functions comprise all effectively calculative functions. Whereas recursive functions are precisely defined, effectively calculative functions cannot be defined with a rigor that is requested by mathematicians. There has been a considerable amount of talking about the plausibility of Church's thesis, however, this is not relevant for a strict mathematical analysis. The only way to end the discussion is obtained by a counterexample. The author has developed an approach to logics that comprises, but goes beyond predicate logic. The FUME method contains two tiers of precise languages: object-language Funcish and metalanguage Mencish. It allows for a very wide application in mathematics from recursion theory and axiomatic set theory with first-order logic, to higher-order logic theory of real numbers and so on. The concrete calcule LAMBDA of natural number arithmetic with first-order logic has been defined by the author. It includes straight recursion and composition of functions, it contains a wide range of so-called compinitive functions, with processive functions far beyond primitive recursive functions. All recursive functions can be represented in LAMBDA too. The unary Snark-function is defined by a diagonalization procedure such that it can be calculated in a finite number of steps. However, this calculative function transcends the compinitive functions and presumably the recursive functions. The defenders of Church's thesis are challenged to show that the Snark-function is recursive. Another challenge asks for an example of a recursive function that cannot be expressed as a compinitive function, i.e. without minimization.
Category: Set Theory and Logic

[15] viXra:1905.0215 [pdf] submitted on 2019-05-14 07:54:57

Refutation of Intutionistic Zermelo-Fraenkel Set Theory (Izf), de Jongh’s Theorem, and CZF

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 the nine axioms for intutionistic Zermelo-Fraenkel set theory (IZF). None is tautologous. This refutes IZF and its use in blended models and denies De Jongh’s classical theorem and similar results for constructive ZF (CZF). These segments form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[14] viXra:1905.0195 [pdf] submitted on 2019-05-13 12:10:48

Refutation of Reverse Mathematics and Nets

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 four definitions for reverse mathematics (3) and nets (1). None is tautologous. This refutes reverse mathematics and nets. Therefore these definitions form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[13] viXra:1905.0172 [pdf] submitted on 2019-05-12 23:34:42

Refutation of the Barwise Compactness Theorem Via Sublanguage la

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.

A definition with variant to establish a sublanguage in support of the Barwise compactness theorem is not tautologous. By extension the theorem is also refuted. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[12] viXra:1905.0160 [pdf] submitted on 2019-05-11 19:27:34

Confirmation of VŁ4 as Complete

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 quantifiers to modalities as a tautology making VŁ4 complete. Paraconsistent, non bivalent, vector logics are defined as non tautologous fragments of VŁ4 as a universal logic.
Category: Set Theory and Logic

[11] viXra:1905.0153 [pdf] submitted on 2019-05-10 18:37:20

The Thot-Queen Paradox

Authors: Analytic Birb
Comments: 2 Pages.

The apparent contradiction of the status of women as both thots and queens, as expressed by the sentences ‘if she breathes, she’s a thot’ and ‘all women are queens’ is examined. The problem is formalized using the law of the excluded middle and a counterexample to the assertion is provided. The implications of the lack of a paradox are discussed.
Category: Set Theory and Logic

[10] viXra:1905.0116 [pdf] submitted on 2019-05-07 15:52:46

Refutation of Pascal’s Wager

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 antecedent and consequent of the thought experiment of Pascal’s wager are not tautologous. However, to determine gain by one wager or the other is tautologous. This refutes the conjecture of Pascal’s wager as ultimately not allowing reason to determine faith. In other words, the “existence of God is possible to prove by human reason”. What follows furthermore is that the existence of God is more profitable from this thought experiment. Therefore the conjecture forms a tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[9] viXra:1905.0097 [pdf] submitted on 2019-05-06 21:21:49

Refutation of a Fast Algorithm for Network Forecasting Time Series from Definition of Visibility Graph

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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate a definition of the visibility graph as not tautologous to deny a fast algorithm for forecasting time series. Hence the conjecture of a forecasting algorithm is denied. This forms a non tautologous fragment of the universal logic VŁ4. However, we resuscitate the conjecture using the Kanban cell neuron network (KCNN), a linear step-wise function, for the desired conjecture without injected data.
Category: Set Theory and Logic

[8] viXra:1905.0086 [pdf] replaced on 2019-05-13 17:37:50

True Logick

Authors: H. Trismegistus
Comments: 4 Pages.

True Logick is Neohermetic Pythagoreanism for the modern era.
Category: Set Theory and Logic

[7] viXra:1905.0063 [pdf] submitted on 2019-05-04 23:23:21

Refutation of Provability Logic GL and Japaridze’s Derived Polymodal (GLP)

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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate eight equations for provability logic (GL) and the derived polymodal logic of Japaridze (GLB, GLP). None is tautologous, hence refuting provability logic. These form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[6] viXra:1905.0062 [pdf] submitted on 2019-05-04 23:24:52

Refutation of Non Sahlqvist Formulas by Three Counter Examples

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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate three equations as examples of non Sahlqvist formulas. None is tautologous. What follows is that Fine’s theorem and monotonic modal logic are refuted. Therefore those conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[5] viXra:1905.0051 [pdf] submitted on 2019-05-03 10:27:21

Refutation of Isabelle / H O L Prover Assistant

Authors: Colin James III
Comments: Pages.

A meta-rule for structural induction in the prover assistant Isabelle/HOL is not tautologous. This refutes the assistant and denies it can effect a cross-fertilization of computer science and metaphysics. Therefore Isabelle/HOL is a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[4] viXra:1905.0042 [pdf] replaced on 2019-05-19 19:54:43

Recent Advances in the Meth8 Modal Model Checker and VŁ4 Universal Logic [abstract, Tables of Results and Contents]

Authors: Colin James III
Comments: 27 Pages.

We use the Meth8/VŁ4 modal logic model checker to evaluate 494 artifacts in 2841 assertions to refute 2268 as non tautologous (79.1%). This is the results table and table of contents for 814 pages; current document available on request.
Category: Set Theory and Logic

[3] viXra:1905.0038 [pdf] submitted on 2019-05-02 13:39:14

Refutation of the Language of Sets for Model Theory = Universal Algebra + Mathematical Logic

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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

A first order language of sets is proposed, but the first example A⊂B iff (x∈A then x∈B) is not tautologous. This refutes the conjecture of model theory = universal algebra + mathematical logic, which forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[2] viXra:1905.0015 [pdf] submitted on 2019-05-01 11:33:18

Refutation Arrow’s Impossibility 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. (We warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate two versions of Arrow’s impossibility theorem with disjunctive or conjunctive results. Both as rendered are not tautologous. This means Arrow’s framework is refuted, hence coloring the conjecture of Arrow’s theorem before pivotal voters or dictators can be derived. Therefore Arrow’s impossibility theorem forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[1] viXra:1905.0011 [pdf] submitted on 2019-05-01 17:44:36

Refutation of Overlap Algebras Constructively to Prove Complete Boolean Algebras

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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate four equations which are not tautologous, but in fact produce the equivalent logic table values result. This means that the stated problem of applying singletons to the powerset is equivalent to proving singletons are atoms and that every subset satisfying a singleton is also an atom. Hence, overlap algebras do not constructively prove complete Boolean algebras. Therefore that conjecture for intuitionistic logic forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic