This paper begins an analysis of the real line using an inconsistency-tolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistency-reliant inferences; some techniques from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number field, prospects for other non-trivializing contradictions are left open.

The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years, such as relevance logics, paraconsistent logics, fuzzy logics and so on. In this note, we investigate some of these paradoxes and classify them, over minimal logic. We provide proofs of equivalence and semantic models separating the paradoxes where appropriate. A number of equivalent groups arise, all of which collapse with unrestricted use of double negation elimination. Interestingly, the principle ex falso quodlibet, and several (...) weaker principles, turn out to be distinguishable, giving perhaps supporting motivation for adopting minimal logic as the ambient logic for reasoning in the possible presence of inconsistency. (shrink)

We discuss logical difficulties with the naive set theory based on the weak relevant logic DKQ. These are induced by the restrictive nature of the relevant conditional and its interaction with set theory. The paper concludes with some possible ways to mitigate these difficulties.

Editors' Introduction and List of Contributors.

A theorem from Archimedes on the area of a circle is proved in a setting where some inconsistency is permissible, by using paraconsistent reasoning. The new proof emphasizes that the famous method of exhaustion gives approximations of areas closer than any consistent quantity. This is equivalent to the classical theorem in a classical context, but not in a context where it is possible that there are inconsistent innitesimals. The area of the circle is taken 'up to inconsistency'. The fact that (...) the core of Archimedes's proof still works in a weaker logic is evidence that the integral calculus and analysis more generally are still practicable even in the event of inconsistency. (shrink)

We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the Milman-Pettis theorem that uniformly convex Banach spaces are reflexive.

Svoeobrazie drevnerusskoĭ filosofskoĭ mysli -- Osnovnye napravlenii︠a︡ drevnerusskoĭ mysli -- Prilozhenie. Pami︠a︡tniki religiozno-filosofskoĭ mysli Drevneĭ Rusi.

Although transhumanism offers hope for the transcendence of human biological limitations, it generates many intrinsic and consequential ethical concerns. The latter include issues such as the exacerbation of social inequalities and the exponentially increasing technological capacity to cause harm. To mitigate these risks, many thinkers have initiated investigations into the possibility of moral enhancement that could limit the power disparities facilitated by biotechnological enhancement. The arguments often focus on whether moral enhancement is morally permissible, or even obligatory, and remain largely (...) in the realm of the hypothetical. This paper proposes that psilocybin may represent a viable, practical option for moral enhancement and that its further research in the context of moral psychology could comprise the next step in the development of moral transhumanism. (shrink)

This book reveals and discusses the foundations of law and justice. Fifteen leading lawyers and philosophers of law, representing thirteen nations and fifteen different philosophical schools examine the value and purpose of law, and the nature and requirements of law and justice. Some of the world's most learned and provocative legal scholars address the ultimate questions of legal and social philosophy from all angles and the broadest possible perspective, with special reference to the work of Mortimer Newlin Stead Sellers, and (...) the republican, liberal, and analytical schools of legal thought. The conclusions reached here are not fully unanimous, congruent or conclusive, but they represent the pinnacle of legal scholarship as it exists today and furnish the necessary basis for any future study of law, justice, or the ultimate requirements of just, effective and legitimate law and society. (shrink)

Книга предназначена для студентов, преподавателей и научных сотрудников высших учебных заведений, занимающихся вопросами истории мировой культуры.

Impairment of the Self has been described in frontal–temporal dementia but little research has been carried out in patients with Alzheimer’s disease. Objective. The aim of this study was to explore changes in the self in patients with AD. Method. Forty-seven patients with mild to moderate AD were examined using a semi-structured scale designed to assess the self-concept along three dimensions, namely, the Material Self, the Social Self and the Spiritual Self. Results. The majority of patients presented impairment of at (...) least one dimension of the Self. When only one dimension was affected, it was always the Social Self. The severity of impairment of the Self was correlated to the impairment of the semantic autobiographical memory and apathy. The Self is impaired in AD and the Social Self dimension appears to be more vulnerable in AD than other dimensions. (shrink)

A [1983] review, 'Relativity before Einstein' made no mention of the work of Joseph Larmor, whose early derivation of the Lorentz transformation seems to be less well known than those of Lorentz and Poincare. In 1897, Larmor, starting from a first-order transformation similar to Lorentz's first order version, presented the correct form of what is now known as the Lorentz transformation. In his presentation of the theory in 1900 Larmor saw the time dilation effect as a consequence of Maxwell's electromagnetic (...) theory. It was Lorentz who, in 1895, introduced the notion of the relativity of simultaneity (local time), without the time dilation effect. Poincare in 1900 discussed how Lorentz's local time would arise from the procedure of synchronizing moving clocks by exchanging light signals assumed to travel at the same speed in either direction. Lorentz presented the correct version of the transformation in 1899, and discussed the variation of mass with velocity arising from it. In 1902 Lorentz was aware of Larmor's 1897 work but apparently missed its significance. Nevertheless, the credit for the first presentation of the Lorentz transformation including the crucial time dilation belongs to Larmor. (shrink)

This article aims to explore representation of the content knowledge of historical Malay manuscripts by extracting the event features using an event ontology framework. The manuscript used during the testing is Sulalatus Salatin by Abdul Ahmad Samad and it was published at University of Malaya Digital Library database. In aligning to a domain-specific ontology, the Simple Event Model model is adopted and an event-based ontology for historical Malay manuscripts is designed. Information extraction approach is done manually to extract events from (...) the manuscript and mapped into Protégé editor. Competency questions were constructed and submitted to the Protégé editor using SPARQL to check the ontology capability of providing answers as well as to examine its correctness. Event-based ontology model assists in discovering and representing the content knowledge of historical Malay manuscripts and supports organisation of knowledge. All the main concepts are extracted from selected Malay manuscript and 17 concepts used to develop the event-based ontology model. The knowledge was verified by three domain experts in Malay manuscript. In the findings, the interrater reliability for Event and Actor instances is 84%, which means 16% of instances and its type are incorrect and need amendment. For Place, interrater reliability is 95% and 99% for Role. Meanwhile, the experts achieved 100% agreement for Time. In addition, the experts agreed that the concepts, properties and instances for Malay Manuscript Ontology and complied with the criteria of consistency, completeness, conciseness, expandability and ease of use. The development of the event-based model of an ontology-based system with a high level of semantic granularity reflects the various cultural riches and intellectual aspect stored in Malay manuscripts. This will enable systematic research of the knowledge embedded in the manuscripts and make it widely and easily accessible by everyone. (shrink)

The network model of EEG formation has revealed a unified mechanism for disparate EEG phenomena: for various reactions as well as for ontogenetic and phylogenetic differences. EEG rhythmicity was shown to be an external manifestation of the functioning of the intracortical stabilizing system which provides normal informational operations in the cerebral cortex.