Set Theory and Logic

1010 Submissions

[2] viXra:1010.0052 [pdf] submitted on 20 Mar 2010

Neutrosophic Degree of a Paradoxicity

Authors: Florentin Smarandache
Comments: 3 pages

A paradox is called a statement <P> which is true and false in the same time. Therefore, if we suppose that statement <P> is true, it results that <P> is false; and reciprocally, if we suppose that <P> is false, it results that <P> is true.
Category: Set Theory and Logic

[1] viXra:1010.0002 [pdf] replaced on 2017-03-23 22:10:04

The Godel's «first Theorem on the Incompleteness of Formal Arithmetic» is not Even a Plausible Hypothesis [«Первая теорема Гёделя о неполноте формальной арифметики» не является даже правдоподобной гипотезой]

Authors: Dmitry Vatolin
Comments: 8 Pages. In Russian

In this paper, we prove that the consistent derivation of the "Gödel formula" possible only in a theory in which it is forbidden to fully discuss the evidence. Gödel's assumptions do not follow from unconditional metamathematical axioms. [В настоящей работе доказано, что непротиворечивый вывод «гёделевой формулы» возможен лишь в теории, в которой запрещено полноценно рассуждать о доказательствах. Гёделевы допущения не вытекают из безусловных метаматематических аксиом.]
Category: Set Theory and Logic