The paraconsistent system CPQ-ZFC/F is defined. It is shown using strong non-finitary methods that the theorems of CPQ-ZFC/F are exactly the theorems of classical ZFC minus foundation. The proof presented in the paper uses the assumption that a strongly inaccessible cardinal exists. It is then shown using strictly finitary methods that CPQ-ZFC/F is non-trivial. CPQ-ZFC/F thus provides a formulation of set theory that has the same deductive power as the corresponding classical system but is more reliable in that non-triviality is (...) provable by strictly finitary methods. This result does not contradict Gödel's incompleteness theorem because the proof of the deductive equivalence of the paraconsistent and classical systemss use non-finitary methods. (shrink)

A new technique for proving realisability results is presented, and is illustrated in detail for the simple case of arithmetic minus induction. CL is a Gentzen formulation of classical logic. CPQ is CL minus the Cut Rule. The basic proof theory and model theory of CPQ and CL is developed. For the semantics presented CPQ is a paraconsistent logic, i.e. there are non-trivial CPQ models in which some sentences are both true and false. Two systems of arithmetic minus induction are (...) introduced, CL-A and CPQ-A based on CL and CPQ, respectively. The realisability theorem for CPQ-A is proved: It is shown constructively that to each theorem A of CPQ-A there is a formula A *, a so-called “realised disjunctive form of A ”, such that variables bound by essentially existential quantifiers in A * can be written as recursive functions of free variables and variables bound by essentially universal quantifiers. Realisability is then applied to prove the consistency of CL-A, making use of certain finite non-trivial inconsistent models of CPQ-A. (shrink)

It is shown that logical contradictions are derivable from natural translations into first order logic of the description and background assumptions of the Soros Game, and of other games and social contexts that exhibit conflict and reflexivity. The logical structure of these contexts is analysed using proof-theoretic and model-theoretic techniques of first order paraconsistent logic. It is shown that all the contradictions that arise contain the knowledge operator K. Thus, the contradictions do not refer purely to material objects, and do (...) not imply the existence of inconsistent, concrete, physical objects, or the inconsistency of direct sensory experience. However, the decision-making of rational self-interested agents is stymied by the appearance of such intensional contradictions. Replacing the rational self-interest axioms with axioms for an appropriate moral framework removes the inconsistencies. Rational moral choice in conflict-reflexive social contexts then becomes possible. (shrink)

This paper is motivated by the search for a natural and deductively powerful extension of classical set theory. A theory of properties U is developed, based on a system of relevant logic related to RQ. In U the set {a, b, c,...} is identified with the property [x: x=a x=b x=c...]. The universe of all sets V, is identified with the property of being a hereditary set. The main result is that relevant implication collapses to material implication for sentences with (...) quantifiers restricted to V. This demonstrates the naturalness of the system. However, an aparent lack of deductive power leads to the conclusion that the best extension of classical set theory is to be found in intensional theories with the unrestricted comprehension schema based on weak relevant logics. The author has obtained similar collapses of to for these systems. (shrink)

The ayn-dayn distinction in Ḥanafī legal thought shapes directly many regulations related to the law of obligations, from the legitimacy conditions of the contracts to the principles of compensation obligation. Three aspects are important in understanding the formative function of this distinction. The first of them is what is the conceptual content of ayn and dayn in Ḥanafī terminology. The second of them is what kind of relationship there is between the qualities of goods and ayn and dayn. The third (...) of them is what kind of differences exist between ayn and dayn in terms of their effects on legal regulations. According to Ḥanafī terminology, in a debt relationship, dayn means goods that have not yet been delivered to the creditor, whether they are in the hands of the debtor or not, in terms of goods (gold, silver and money) that are not suitable for determination by determining. Dayn represents the identical goods that is under the responsibility of the debtor in terms of non-existing identical goods. In terms of existing identical goods, dayn represents the identical goods that exist in clusters but have not yet been determined individually. Non-standard goods are goods that are not suitable for dayn because they are not suitable for abstraction from their material existence. Ayn represents the existing and determined goods in terms of non-standard goods and existing identical goods. Ayn represents the goods received by the creditor in terms of gold, silver, money and identical goods that are in the debtor's obligation from the beginning. What stands out among the differences between ayn and dayn is that although destruction and damage can be considered for ayn, they cannot be considered for dayn. In terms of some legal regulations, establishing a relationship between strict liability and dayn and between fault liability and ayn is a result of this. The other important differences between ayn and dayn are the fact that dayn is only determined by delivery and that postponement and remittance are specific to the dayn. (shrink)

Boarding school is a major educational option for many students (e.g., students living in remote areas, or whose parents are working interstate or overseas, etc.). This study explored the motivation, engagement, and achievement of boarding and day students who are educated in the same classrooms and receive the same syllabus and instruction from the same teachers (thus a powerful research design to enable unique comparisons). Among 2,803 students (boardingn= 481; dayn= 2,322) from 6 Australian high schools and controlling for background (...) attributes and personality, we found predominant parity between boarding and day students in their motivation, engagement, and achievement. We also found that classroom-average motivation, engagement, and achievement was not significantly affected by the number of boarders (relative to day students) in the classroom. In addition, the effects of boarding were generally not moderated by students’ background or personality attributes. We conclude that boarders have academic opportunities and outcomes that are comparable to their day student counterparts. Implications for students, teachers, and parents are discussed. (shrink)

The rights granted to individuals by the legal system are examined with a fundamental distinction as regards their economic value as "property rights" and "personal rights". Property rights, which differ from personal rights in terms of their economic value, are characterized as ‘absolute’ if they can be asserted against everyone and as ‘relative’ if they can only be claimed against the convict on behalf of the debtor. If absolute property rights are based on a tangible (physical) subject, they are referred (...) to as real rights. Real rights and rights of claim that have relative characteristics and can therefore only be used through the act of a specific person constitute two important components of a property. Although various attempts have been made to bring these two types of rights closer together in the historical process, these rights have continued to be considered different in terms of both nature and legal implications. The aforementioned difference arises from the form of dominance over the subject of the right, whether it is direct or indirect, the impact of these rights on the ownership of the property, whether the right is absolute or relative, whether it is continuous or not, and priority/superiority, which will be discussed in detail in the article. The conceptual framework and terms belonging to the Continental European legal system are also found in Islamic legal doctrine in similar or equivalent forms. In this context, the term "milk" has been used in the fiqh literature to encompass all property rights, and terms such as "milk al-ayn," "milk al-manfaa," "milk al-dayn," and "milk al-habs wal-yad" have been developed depending on the nature of the property subject to the right. Real rights and personal rights constitute two important parts of the asset. In some cases where legal interests between people are confronted, it may be necessary to choose between these two types of rights. In such cases, considering the authorities it contains, a kind of priority has been given to real rights over personal rights. One of the cases where this priority is most clearly seen is when a leased property is transferred to third parties while the current lease agreement is in effect. In Islamic law, the authorities granted to the person by the lease contract differ from the Continental European legal system. At this point, the powers granted by the lease contract in Islamic law differ from those in the Continental European legal system. This article argues that the right of the tenant in this regard is considered as real right in Islamic law, unlike in the Continental European legal system. To justify this, the authorities granted to the tenant in Islamic law have been examined in cases where the leased property is transferred to third parties through means that can be interpreted as unlawful acts such as sale, lease, or usurpation during the lease period. In addition, the unique approach of Islamic law on this issue has been expressed by considering both classical and modern fiqh works, and by making comparisons with Turkish law. (shrink)