We show that the c.e. Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degrees are not an upper semilattice. We prove that if M is an r-maximal set, A is an arbitrary set and M≡Q1,NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M \equiv{}_ {Q_{1,N}}A}$$\end{document}, then M≤mA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M\leq{}_{m} A}$$\end{document}. Also, if M1 and M2 are r-maximal sets, A and B are major subsets of M1 and M2, respectively, and M1\A≡Q1,NM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus} A\equiv{}_{Q_{1,N}}M_{2}{\setminus} B}$$\end{document}, then M1\A≡mM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus}A\equiv{}_{m}M_{2}{\setminus} B}$$\end{document}. If M1 and M2 are r-maximal sets and M10,M11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0},\,M_{1}^{1}}$$\end{document} and M20,M21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{2}^{0},\,M_{2}^{1}}$$\end{document} are nontrivial splittings of M1 and M2, respectively, then M10≡Q1,NM20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{Q_{1,N}}M_{2}^{0}}$$\end{document} if and only if M10≡1M20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{1}M_{2}^{0}}$$\end{document}. From this result follows that if A and B are Friedberg splitting of an r-maximal set, then the Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degree of A contains only one c.e. 1-degree. (shrink)

Ethics; philosophy; civilization, modern.

Let A be an infinite Δ₂⁰ set and let K be creative: we show that K≤Q A if and only if K≤Q₁ A. (Here ≤Q denotes Q-reducibility, and ≤Q₁ is the subreducibility of ≤Q obtained by requesting that Q-reducibility be provided by a computable function f such that Wf(x)∩ Wf(y)=∅, if x \not= y.) Using this result we prove that A is hyperhyperimmune if and only if no Δ⁰₂ subset B of A is s-complete, i.e., there is no Δ⁰₂ subset (...) B of A such that \overline{K}≤s B, where ≤s denotes s-reducibility, and \overline{K} denotes the complement of K. (shrink)

We investigate strong versions of enumeration reducibility, the most important one being s-reducibility. We prove that every countable distributive lattice is embeddable into the local structure $L(\mathfrak D_s)$ of the s-degrees. However, $L(\mathfrak D_s)$ is not distributive. We show that on $\Delta^{0}_{2}$ sets s-reducibility coincides with its finite branch version; the same holds of e-reducibility. We prove some density results for $L(\mathfrak D_s)$ . In particular $L(\mathfrak D_s)$ is upwards dense. Among the results about reducibilities that are stronger than s-reducibility, (...) we show that the structure of the $\Delta^{0}_{2}$ bs-degrees is dense. Many of these results on s-reducibility yield interesting corollaries for Q-reducibility as well. (shrink)

In this paper we study structural properties of n-c. e. Q-degrees. Two theorems contain results on the distribution of incomparable Q-degrees. In another theorem we prove that every incomplete Q-degree forms a minimal pair in the c. e. degrees with a Q-degree. In a further theorem it is proved that there exists a c. e. Q-degree that is not half of a minimal pair in the c. e. Q-degrees.

We show that the Q-degree of a hyperhypersimple set includes an infinite collection of Q1-degrees linearly ordered under \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\leq_{Q_1}}$$\end{document} with order type of the integers and consisting entirely of hyperhypersimple sets. Also, we prove that the c.e. Q1-degrees are not an upper semilattice. The main result of this paper is that the Q1-degree of a hemimaximal set contains only one c.e. 1-degree. Analogous results are valid for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...) \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^0}$$\end{document}s1-degrees. (shrink)

We use certain strong Q-reducibilities, and their corresponding strong positive reducibilities, to characterize the hyperimmune sets and the hyperhyperimmune sets: if A is any infinite set then A is hyperimmune (respectively, hyperhyperimmune) if and only if for every infinite subset B of A, one has \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}\not\le_{\rm ss} B}$$\end{document} (respectively, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}\not\le_{\overline{\rm s}} B}$$\end{document}): here \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\le_{\overline{\rm (...) s}}}$$\end{document} is the finite-branch version of s-reducibility, ≤ss is the computably bounded version of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\le_{\overline{\rm s}}}$$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}}$$\end{document} is the complement of the halting set. Restriction to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^0_2}$$\end{document} sets provides a similar characterization of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^0_2}$$\end{document} hyperhyperimmune sets in terms of s-reducibility. We also show that no \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \geq_{\overline{\rm s}}\overline{K}}$$\end{document} is hyperhyperimmune. As a consequence, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\deg_{\rm s}(\overline{K})}$$\end{document} is hyperhyperimmune-free, showing that the hyperhyperimmune s-degrees are not upwards closed. (shrink)

Yemeni writer Ahmed Qāsim al-Arīqī, in addition to his profession as a pharmacist, is a writer who has made a name for himself in the country's literary field, especially in the last fifteen years. A prolific writer, al-Arīqī is the author of poetry collections as well as stories and novels that emphasise awareness of the traditional issues of the Yemeni people. He has published "Maḳāmāt al-'Arīḳī" (2006), "Ġalṭṭetu Ḳalem" (2012), "Qurāt al-S̱-S̱elj" (2017), "Ta'riyya" (2018), "Zurbet al-Yumnā" (2018), "Da'wat al-Ḥuḳūl" (2019), (...) "Zuhr al-Ġarām" and "Sīret al-Kūbī" (2022). His novel "Yawma Māta al-Shaytan" (The Day Satan Died) was published electronically by Hindāwī Publishing House in 2022. The novel, which is approximately 120 pages, is written in six chapters. There are eleven passages in the first and fourth chapters, thirteen in the second and sixth chapters, twelve in the third chapter, and eight in the fifth chapter. The novel is about the adventures of a member of the army named Marwan Naji, who was wounded in the war between the Houthi militia and the Yemeni army, and after nine months in a coma, opens his eyes in a perfect world dominated by biological and technological advances. Symbolising the treatment of selfishness and various narcissisms with advanced vaccines through the death of Satan, the author describes Marwan's adventures in his world, which he sometimes describes as the realm of the jinn, in a very simple language, while not failing to criticise reality in its various political, social and religious dimensions. In fact, Marwan's world of imagination and fantasy is the main story of the novel, but not the only one. The author also includes the stories of family members in Marwan's world of turmoil, destruction, massacre, war and victory, giving the reader the opportunity to compare both worlds. While his mother Gusoun, his wife Hamide and his daughter Fatma, who later got engaged in time after being widowed, are the female characters of his real world, Professor Mari and Mariana, one of his seven wives, are the other important characters of his imaginary world. Gusûn is a devoted mother who does not leave the bedside of her comatose son, prays for him day and night and tries to do everything she can for his recovery. Gusûn, who is listened to at home to a certain extent, scolds her grandchildren to prevent the breakup of her son's home because of inheritance, defends that the existing wealth still belongs to her son and reminds them that she will not hesitate to spend money for his recovery. Gusûn's daughter-in-law Hamide also takes care of her husband, who shows no signs of recovery. Hamide, who is not as patient as her mother-in-law, is also a jealous woman. On the other hand, although both of them display false religious tendencies that have no relation with real life, Gusûn is more prone to the superstitious approaches put forward and adopted in the name of religion. Fatma is also a widow who, although she has the will to take care of her children and live her life alone, has been engaged for a long time to her uncle's son Münir, who, like her, took part in anti-regime demonstrations and whose love she believes in. Fatma, who is more conscious than her grandmother and mother, is not alien to the issues that society complains about and often participates in women's movements organised against the government. Professor Mari, one of the two important characters belonging to Marwan's imaginary world, is a psychologist and the chief physician of a large hospital who treats jealousy, anger, lying and selfishness, which are considered dangerous viruses, with vaccines developed by scientists. Professor Mari, who is personally involved in Marwan's treatment, also chairs the committee that records his memory and projects all his memories on a giant screen. Mariana, on the other hand, monitors Marwan's behaviour and thoughts through a biological chip to control the effect of the vaccines given to him, criticises him through the tragic images projected on the screen and provides information that will facilitate his adaptation to his new world. In the article, in which the author's main published works are briefly introduced along with a broad summary of the novel, the social messages that an author, who is not indifferent to the realities of the geography he lives in, tries to give directly and indirectly with a language far from locality, are tried to be determined through the mentioned female characters. It is seen that the desire to become a single nation by making; love, brotherhood, friendship and peace dominant lies behind the author's novelisation of the dream of an ideal world symbolised by the death of Satan. (shrink)

Philosophical study of revelation in religion, chiefly in Islam.

The most prominent arguments for scepticism in modern epistemology employ closure principles of some kind. To begin my discussion of such arguments, consider Simple Knowledge Closure (SKC): (SKC) (Kxt[p] ∧ (p → q)) → Kxt[q].1 Assuming its truth for the time being, the sceptic can use (SKC) to reason from the two assumptions that, firstly, we don’t know ¬sh and that, secondly, op entails ¬sh to the conclusion that we don’t know op, where ‘op’ and ‘sh’ are shorthand for ‘ordinary (...) proposition’ and ‘sceptical hypothesis’ respectively. (SKC), however, fails for familiar reasons: since knowledge entails belief (KB), we can derive the falsity (F) from (SKC) by hypothetical syllogism, and thus reduce (SKC) to absurdity: (KB) Kxt[p] → Bxt[p]. (F) (Kxt[p] ∧ (p → q)) → Bxt[q]. (shrink)

al-Mujallad al-awwal. Muqaddimāt al-taḥqīq wa-muqaddimat al-Imām al-Zubaydī lil-Itḥāf -- al-mujallad al-thānī. Kitāb al-ʻIlm ilá nihāyat al-bāb al-thālith -- al-mujallad al-thālith. Tatimmat kitāb al-ʻilm min al-bāb al-rābiʻ ilá ākhir al-kitāb -- al-mujallad al-rābiʻ. Kitāb Qawāʻid al-ʻaqāʼid -- al-mujallad al-khāmis. Kitāb Asrār al-ṭahārah -- al-mujallad al-sādis. Kitāb Asrār al-ṣalāh ilá nihāyat shurūṭ al-jumʻah min al-bāb al-khāmis -- al-mujallad al-sābiʻ. Tatimmat kitāb asrār al-ṣalāh min ādāb al-jumʻah ilá ākhir al-kitāb -- al-mujallad al-thāmin. Kitābā Asrār al-zakāh wa-asrār al-ṣawm -- al-mujallad al- tāsiʻ. Kitāb asrār (...) al-ḥajj -- al-mujallad al-ʻāshir. Kitābā ādāb tilāwat al-Qurʼān wa-al-adhkār wa-al-daʻawāt -- al-mujallad al-ḥādī ʻashar. Kitābā tartīb al-awrād wa-tafḍīl iḥyāʼ al-layl wa-ādāb al-akl -- al-mujalladal-thānī ʻashar. Kitābā ādāb al-Nikāḥ wa-ādāb al-Kasb wa-al-maʻāsh -- al-mujallad al-thālith ʻashar. Kitāb al-Ḥalāl wa-al-ḥarām -- al-mujallad al-rābiʻ ʻashar. Kitāb al-Ulfah wa-al-ukhuwwah -- al-mujallad al-khāmis ʻashar. Kitābā ādāb al-ʻUzlah wa-ādāb al-Safar -- al-mujallad al-sādis ʻashar. Kitābā ādāb al-Samāʻ wa-al-wajd wa-al-Amr bi-al-maʻrūf wa-al-nahy ʻan al-munkar -- al-mujallad al-sābiʻ ʻashar. Kitābā ādāb al-maʻīshah wa-akhlāq al-nubūwah wa-sharḥ ʻajāʼib al-qalb -- al-mujallad al-thāmin ʻashar. Kitābā riyāḍat al-nafs wa-tahdhīb al-akhlāq wa-kasr al-shahwatayn -- al-mujallad al-tāsiʻ ʻashar. Kitābā āfāt al-lisān wa-dhamm al-ghaḍab -- al-mujallad al-ʻishrūn. Kitābā dhamm al-dunyā wa-dhamm al-bukhl -- al-mujallad al-ḥādī wa-al-ʻishrūn. Kitābā dhamm al-jāh wa-dhamm al-kibr wa-al-ʻajab -- al-mujallad al-thānī wa-al-ʻishrūn. Kitābā dhamm al-ghurūr wa-al-tawbah -- al-mujallad al-thālith wa-al-ʻishrūn. Kitābā al-ṣabr wa-al-shukr -- al-mujallad al-rābiʻ wa-al-ʻishrūn. Kitābā al-rajā wa-al-khawf -- al-mujallad al-khāmis wa-al-ʻishrūn. Kitāb al-zuhd wa-al-faqr -- al-mujallad al-sādis wa-al-ʻishrūn. Kitāb al-tawḥīd wa al-tawakkul -- al-mujallad al-sābiʻ wa-al-ʻishrūn. Kitāb al-maḥabbah wa-al-shawq wa-al-uns wa-al-riḍā -- al-mujallad al-thāmin wa-al-ʻishrūn. Kutub al-ikhlāṣ wa-al-nīyah wa-al-murāqabah wa-al-muḥāsabah wa-al-tafakkur -- al-mujallad al- tāsiʻ wa-al-ʻishrūn. Kitāb dhikr al-mawt wa-mā baʻdih ilá nihāyat al-bāb al-thāmin -- al-mujallad al-thalāthūn. Kitāb dhikr al-mawt wa-mā baʻdih ilá ākhar al-kitāb wa-yalīhi maṣādir al-taḥqīq. (shrink)

We show that the e-degree 0'e and the map u ↦ u' are definable in the upper semilattice of all e-degrees. The class of total e-degrees ≥0'e is also definable.

Bakhsh-i avval. Akhlāq-i Islāmī -- Bakhsh-i duvvum. Ādāb-i ijtimāʻī.

A law is one of the basic concepts of the dialectical materialist conception of determinism as a philosophical theory of the objective interrelationship and mutual conditioning of phenomena in the material and mental world. A law establishes a rigorously determined connection among circumstances, i.e., a totality of derivative components and conditions of their actions and results. By overlooking the existence of two different levels—the concept and the objective reality corresponding to it—some philosophers erroneously interpret Marx's theses concerning the approximateness of (...) the realization of the laws of society. Let us take, for example, Marx's thesis that "In general, in capitalist production general laws are realized in a very confused and approximate way, merely as a prevailing tendency, as a kind of average among constant fluctuations that is never solidly established."1 Some investigators see this as an objectively existing social law in itself, attributing to it an "inexactitude" of operation, variation, and approximation, instead of seeing it as a specific application of a particular law. They thus forget that Marx said, in the Foreword to the very first volume of Capital: "The question does not specifically have to do with a greater or lesser degree of development of the social antagonisms that derive from the natural laws of capitalist production, but rather lies in these laws themselves, these trends, which operate and are realized with iron necessity.". (shrink)

al-Juzʼ al-awwal. al-Akhlāq al-fāḍilah -- al-juzʼ al-thānī. al-Akhlāq al-sāfilah.