Set Theory and Logic

1805 Submissions

[21] viXra:1805.0543 [pdf] submitted on 2018-05-31 13:58:46

Refutation of the Löwenheim–Skolem Theorem © 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.com

Refuted in each segment and in toto.
Category: Set Theory and Logic

[20] viXra:1805.0369 [pdf] submitted on 2018-05-20 23:34:28

Refutation of Gleason's Theorem © 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

"Effectively, the theorem says that any legitimate probability measure on the space of measurement outcomes is generated by some quantum state." The equation as rendered is not tautologous. This means Gleason's theorem is not logically "a mathematical result which shows that the rule one uses to calculate probabilities in quantum physics follows logically [sic] from particular assumptions about how measurements are represented mathematically".
Category: Set Theory and Logic

[19] viXra:1805.0332 [pdf] submitted on 2018-05-19 00:21:07

Set Theory

Authors: Salvatore Gerard Micheal
Comments: 4 Pages.

Objective: to create a precise axiomatic system of exact connected meaningful statements which we can use to build set theory from. The purpose is to make explicit our notion of elements before that notion is used in set equivalence. It is required in a dependency framework. We will find that this system is most economical in terms of repetition and symbol usage. We will state and prove a theorem regarding this.
Category: Set Theory and Logic

[18] viXra:1805.0327 [pdf] submitted on 2018-05-17 13:04:37

On The Mistake That Is Riemann's Prime Zeta Function

Authors: Max Davidović
Comments: 1 Page.

I have succesfully disproved Riemann's hypothesis. It has taken me years of dedicated reseach to realise that such and endeavor is frankly impossible without changing the axioms upon which math is built. The file that I have attached is a shitpost born from my frustration and anger.
Category: Set Theory and Logic

[17] viXra:1805.0302 [pdf] replaced on 2018-05-16 23:04:06

Refutation of Gettier Problem of Justified True/false Belief © 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. info@cec-services dot com

We find justified true belief is not a theorem. We find justified false belief is also not a theorem. This means the Gettier problem as the superset of the justified belief arguments is refuted as a problem and resolved as a non-problem.
Category: Set Theory and Logic

[16] viXra:1805.0266 [pdf] submitted on 2018-05-13 22:32:32

Many Questions and Many Answers © 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.com

If for some questions there are many answers, then for many questions there are some answers, this is a theorem. If for many questions there are some answers, then for some questions there are many answers, this is not a theorem but a truthity.
Category: Set Theory and Logic

[15] viXra:1805.0249 [pdf] submitted on 2018-05-12 13:16:02

Refutation of the Continuum Hypothesis © 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

"The continuum hypothesis states that the set of real numbers has minimal possible cardinality which is greater than the cardinality of the set of integers." That equation is not tautologous, and the briefest known refutation of the continuum hypothesis.
Category: Set Theory and Logic

[14] viXra:1805.0228 [pdf] submitted on 2018-05-11 17:01:14

Refutation of Craig's Interpolation Theorem © 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.com

Craig’s theorem (initially referred to by him as a lemma) is not tautologous, hence refuting itself.
Category: Set Theory and Logic

[13] viXra:1805.0223 [pdf] submitted on 2018-05-12 04:55:58

Refutation of the Molyneux Problem © 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

The equation as rendered is not tautologous. This means the Molyneux problem is resolved as two unrelated states, and hence not a problem.
Category: Set Theory and Logic

[12] viXra:1805.0215 [pdf] submitted on 2018-05-10 23:50:55

Refutation of the Hilbert Grand Hotel Paradox © 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

The equation as rendered is not contradictory but rather falsity. Hence this refutes the Hilbert Grand Hotel paradox. Remark: We could not reduce this paradox to one variable because rooms and guests are distinctly counted.
Category: Set Theory and Logic

[11] viXra:1805.0189 [pdf] submitted on 2018-05-09 12:10:44

Method of Reducing Paradox to not Contradictory and in One Variable © 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. info@cec-services dot com

This demonstration serves as two examples to confirm the method that a paradox refuted as not contradictory is also reducible to one variable. The examples are the paradox of Zhuangzi known as the butterfly dream and the paradox of Maimonides known as the argument from freewill.
Category: Set Theory and Logic

[10] viXra:1805.0183 [pdf] submitted on 2018-05-09 20:19:28

Refutation of Fredkin Paradox in One Variable © 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

"The more equally attractive two alternatives seem, the harder it can be to choose between them —- no matter that, to the same degree, the choice can only matter less." This is not contradictory, and not tautologous, thereby refuting the Fredkin paradox, and in one variable p as chosen state and alternative state.
Category: Set Theory and Logic

[9] viXra:1805.0158 [pdf] submitted on 2018-05-06 21:33:10

Refutation of Fitch's Paradox of Knowability © 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. info@cec-services dot com

We find the Fitch paradox to be tautologous, that is, not contradictory, and hence a theorem. We state the theorem as "every truth is discernible", and we add, "by the instant modal logic model checker". A subsequent invocation of Gödel incompleteness and with jettison of the knowability rule to generalize and solve the paradox is contradictory, proving nothing.
Category: Set Theory and Logic

[8] viXra:1805.0155 [pdf] submitted on 2018-05-06 23:17:06

Refutation of Drinker's Paradox © 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

The drinker's paradox is not tautologous and also not contradictory. Therefore, the drinker's paradox is refuted as a paradox.
Category: Set Theory and Logic

[7] viXra:1805.0150 [pdf] submitted on 2018-05-07 07:40:33

Refutation of the New Riddle of Induction © 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

Both states of the argument are tautologous, not contradictory, and hence theorems. Therefore the new riddle of induction is refuted as a riddle or paradox.
Category: Set Theory and Logic

[6] viXra:1805.0146 [pdf] submitted on 2018-05-07 10:09:55

Refutation of the Paradox of Epimenides the Cretan © 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

The argument is: "Epimenides the Cretan said that all Cretans were liars, and all other statements made by Cretans were certainly lies. Was this a lie?" It is not tautologous and not contradictory. Therefore the paradox of Epimenides is refuted as a paradox. The answer to the question "Was this a lie" is neither contradiction nor proof.
Category: Set Theory and Logic

[5] viXra:1805.0138 [pdf] replaced on 2018-05-09 04:48:16

Refutation of the Paradox of Moses Maimonides © 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

Does God know or does He not know that a certain individual will be good or bad? If thou sayest 'He knows', then it necessarily follows that the man is compelled to act as God knew beforehand he would to act, otherwise God's knowledge would be imperfect. The question is tautologous. The additional sentence with the first is not tautologous and not contradictory. Therefore the paradox of Maimonides is refuted as a paradox.
Category: Set Theory and Logic

[4] viXra:1805.0124 [pdf] replaced on 2018-05-06 14:30:48

Refutation of the Prisoner Paradox© 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

The three states of the prisoner paradox are not contradictory. This means the prisoner paradox is not a paradox.
Category: Set Theory and Logic

[3] viXra:1805.0110 [pdf] submitted on 2018-05-05 08:48:59

Refutation of Carroll's Tortoise and Achilles as a Paradox © 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

A: "Things that are equal to the same are equal to each other" B: "The two sides of this triangle are things that are equal to the same" Therefore Z: "The two sides of this triangle are equal to each other" The argument as rendered is tautologous and hence a theorem. Because it is not contradictory: this refutes Carroll's tortoise and Achilles as a paradox.
Category: Set Theory and Logic

[2] viXra:1805.0106 [pdf] submitted on 2018-05-05 11:23:45

Refutation of the Paradox of the Concept of an Analysis as Both Correct and Informative © 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

The concept of an analysis as both correct and informative is not a paradox.
Category: Set Theory and Logic

[1] viXra:1805.0105 [pdf] submitted on 2018-05-05 14:58:45

Refutation of the Newcomb Paradox© 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

The two separate states of the Newcomb paradox are not contradictory (and not tautologous), so the paradox is refuted. However interestingly if the states are tested as one system (either or), it is tautologous.
Category: Set Theory and Logic