This paper addresses a proof of incompleteness published by George Boolos. An analysis of this proofs demonstrates that there is an elementary error in the proof; the proof relies on the unproven assumption that the formal system can selfreference its own formulas.

This paper reports on an exploration of Boolos' Curious Inference, using higher-order automated theorem provers (ATPs). Surprisingly, only suitable shorthand notations had to be provided by hand for ATPs find a short proof. The lemmas required constructing proof are automatically discovered the ATPs. Given observations and suggestions in this paper, full automation related examples now seems wi...

Makala haya yanalenga kuangazia mikakati ya kimawasiliano katika matangazo ngono salama. Masuala utangazaji wa mipira ni baadhi mada ambazo mwiko tamaduni nyingi. Hii changamoto inayowakumba wanaoandaa salama ili kukabiliana na hii kitamaduni. Usomi huu ulitathmini Durex mtandao Facebook fan page Kenya. Madhumuni yalikuwa: kuhakiki inayotumiwa Durex. Utafiti uliongozwa nadharia Uchanganuzi Haki...

Reading ‘x̂(Fx)’ as ‘the value-range of the concept F ’, Basic Law V thus states that, for every F and G, the value-range of the concept F is the same as the value-range of the concept G just in case the F s are exactly the Gs. In Frege: Philosophy of Mathematics, Michael Dummett (1991, pp. 217–22) raises the question how the serpent entered Eden, that is, how we should understand the genesis of...

In his famous paper announcing the incompleteness theorem, Gödel remarked that, though his argument is analogous to the Richard and the Liar paradoxes, “Any epistemological antinomy could be used for a similar proof of the existence of undecidable propositions.” ([7] Note 14). It is interesting that, despite the fact that the soundness of arguments like Gödel’s one built on self–reference (or d...

The cover highlights an array of 3D-printed porous microneedles, fabricated by two-photon polymerization as described in the article number 2300161 Esraa Fakeih, Khaled N. Salama, and co-workers. Due to their multiple pores, these microneedles can deliver fluids large areas while still preserving mechanical stability. These be used healthcare applications, such transdermal drug delivery interst...

" The hardest logic puzzle ever " presented by George Boolos became a target for philosophers and logicians who tried to modify it and make it even tougher. I propose further modification of the original puzzle where part of the available information is eliminated but the solution is still possible. The solution also gives interesting ideas on logic behind discovery of unknown language.

Salama M El Darier, Sania A Kamal, Ream I Marzouk and Iman H Nour* Author Affiliations Health Center Romareda Seminar, Spain Received: April 14, 2021 | Published: 21, Corresponding author: Botany Microbiology Department, Faculty of Science, Alexandria University, Egypt DOI: 10.26717/BJSTR.2021.35.005674

In an earlier paper, we proved that Smarandache’s definition of neutrosophic paraconsistent topology is neither a generalization of Çoker’s intuitionistic fuzzy topology nor a generalization of Smarandache’s neutrosophic topology. Recently, Salama and Alblowi proposed a new definition of neutrosophic topology, that generalizes Çoker’s intuitionistic fuzzy topology. Here, we study this new defin...

In this paper, we introduce and study the concepts of correlation and correlation coefficient of neutrosophic data in probability spaces. In the case of finite spaces, these results give the results due to Salama et al. [16, 17, 18] and study some of their properties.