Kierstead showed that every computable marriage problem has a computable matching under the assumption of computable expanding Hall condition and computable local finiteness for boys and girls. The strength of the marriage theorem reaches or if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem is maintained in even if local finiteness for boys is completely removed. Using these conditions, we classify the strength of variants of marriage theorems in (...) the context of reverse mathematics. Furthermore, we introduce another condition that also makes the marriage theorem provable in, and investigate the sequential and Weihrauch strength of marriage theorems under that condition. (shrink)

It is crucial for indigenous people living in the Arctic to harvest animals by hunting in a traditional manner, as is the case with such peoples in other parts of the world. Given the nutritional, economic, and cultural importance of hunting for aboriginal people, it seems reasonable to say that they have the moral right to hunt animals. On the other hand, non-aboriginal people are occasionally prohibited from hunting a particular species of animal in many societies. The question then arises: (...) why can aboriginal people, unlike other citizens, have special hunting rights? If indigenous people are to have the right to hunt a particular species that other citizens are denied, then it presents a significant challenge to philosophers to explore the moral grounds that justify such a special right. This exploration is the subject of the current paper. (shrink)

Within a weak subsystem of second-order arithmetic , that is -conservative over , we reformulate Kreisel's proof of the Second Incompleteness Theorem and Boolos' proof of the First Incompleteness Theorem.

The study aimed to identify the relationship between correcting the deviations in the measurement of performance and achieving the objectives of control and the performance of the job at the Islamic University in the Gaza Strip. To achieve the objectives of the research, the researchers used the descriptive analytical approach to collect information. The questionnaire consisted of (20) statements distributed to three categories of employees of the Islamic University (senior management, faculty members, their assistants and members of the administrative board). (...) A random sample of 314 employees was selected and 276 responses were retrieved with a recovery rate of 88.1%. The Statistical Analysis Program (SPSS) was used to enter, process, and analyze the data. The results of the study showed a positive relationship between correcting deviations in performance measurement and achieving the control objectives represented by the functional performance in the Islamic University from the point of view of the members (senior management, faculty and their assistants, and the administrative board), where the relative weight of all the paragraphs was (74.25%). The study recommended the need to ensure that the actual performance of the planned performance is matched and decisions are taken to correct the serious deviations and take the necessary measures in terms of retraining and change in regulations, wages and bonuses and punishment of the culprit, neglect and negligence by mistake. (shrink)

We provide a fine‐grained analysis on the relation between König's lemma, weak König's lemma, and the decidable fan theorem in the context of constructive reverse mathematics. In particular, we show that double negated variants of König's lemma and weak König's lemma are equivalent to double negated variants of the general decidable fan theorem and the binary decidable fan theorem, respectively, over a nearly intuitionistic system containing a weak countable choice only. This implies that the general decidable fan theorem is not (...) equivalent to the binary decidable fan theorem in the absence of a strong countable choice. In addition, we introduce a principle which fills the gap between König's lemma and weak König's lemma, and show that König's lemma is equivalent to weak König's lemma plus this principle. We also solve several problems arising from the investigation. (shrink)

Abe Kobo (1924-1993) was one of Japan's greatest postwar writers, widely recognized for his imaginative science fiction and plays of the absurd. However, he also wrote theoretical criticism for which he is lesser known, merging literary, historical, and philosophical perspectives into keen reflections on the nature of creativity, the evolution of the human species, and an impressive range of other subjects. Abe Kobo tackled contemporary social issues and literary theory with the depth and facility of a visionary thinker. Featuring twelve (...) essays from his prolific career--including "Poetry and Poets (Consciousness and the Unconscious)," written in 1944, and "The Frontier Within, Part II," written in 1969--this anthology introduces English-speaking readers to Abe Kobo as critic and intellectual for the first time. Demonstrating the importance of his theoretical work to a broader understanding of his fiction--and a richer portrait of Japan's postwar imagination--Richard F. Calichman provides an incisive introduction to Abe Kobo's achievements and situates his essays historically and intellectually. (shrink)

The issue of justice after catastrophe is an enormous challenge to contemporary theories of distributive justice. In the past three decades, the controversy over distributive justice has centered on the ideal of equality. One of intensely debated issues concerns what is often called the “equality of what,” on which there are three primary views: welfarism, resourcism, and the capabilities approach. Another major point of dispute can be termed the “equality or another,” about which three positions debate: egalitarianism, prioritarianism, and sufficientarianism. (...) On these topics of distributive justice, authors are concerned with the current difference between the better-off and the worse-off or the present situation of the badly-off. By contrast, it is essential to take account of the past distribution of well-being as well as the present situation in order to explore questions of post-catastrophe justice. Without looking at the pre-disaster distribution of income, preference satisfaction, or basic capabilities among affected people, no present assessment of the damage caused by the disaster could be correct and no proposed remedy adequate. It is true that luck egalitarians assess the current distribution among people by referring to the decision that each individual made. Yet they pay scant attention to the situation in which each one stayed in the past. Therefore, we can legitimately say that most theorists of distributive justice, including luck egalitarians, have failed to give consideration to the past state of each person. -/- To fill this gap in the literature, the present article explores philosophical questions that arise when we take account of each person’s past and present situations in discussing distributive justice regarding public compensation and assistance to survivors and families of victims of natural and industrial disasters. In addressing these novel questions, I develop and refine various concepts, ideas, and arguments that have been presented in the study of distributive justice in normal settings. I tackle two tasks, the first of which is to explore the foundation and scope of luck egalitarianism. Despite the moral appeal it has in many cases, luck egalitarianism has attracted the so-called harshness objection. Some luck egalitarians attempt to avoid this objection in a pragmatic way by combining the luck egalitarian doctrine with the principle of basic needs satisfaction. However, they do not provide any systematic rationale for this combination. In contrast with such pragmatic responses, I seek to offer a principled argument for holding individuals responsible for their choices only when their basic needs are met, by invoking the ideas of respect for human voluntariness and rescue of human vulnerability. Based on this argument, I propose a form of responsibility-sensitive theory, which considers the pre-disaster distribution of well-being as a default position. The second task I take on is to refine sufficientarianism in the context of post-catastrophe justice. Luck egalitarianism with boundaries set by the basic needs principle seems to indicate the potential for sufficientarianism. But major proponents of this view conceive the welfarist assumption, a considerably high standard of well-being, and the controversial treatment of persons staying below the threshold, all of which seem problematic in the post-disaster situation. I try to construct a new version of sufficientarianism by replacing these current features with more robust ones. (shrink)

: Lately there is more attention paid to technological development in intelligent tutoring systems. This field is becoming an interesting topic to many researchers. In this paper, we are presenting an intelligent tutoring system for teaching DES Information Security Algorithm called DES-Tutor. The DES-Tutor target the students enrolled in cryptography course in the department Information Technology in Al-Azhar University in Gaza. Through DES-Tutor the student will be able to study course material and try the exercises of each lesson. An evaluation (...) of the DES-Tutor was carried out and the results were promising. (shrink)

We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic $\mathsf {PA}$ and intuitionistic arithmetic $\mathsf {HA}$. Using a generalized negative translation, we first provide a structured proof of the fact that $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over $\mathsf {HA} + {\Sigma _k}\text {-}\mathrm {LEM}$ where ${\Sigma _k}\text {-}\mathrm {LEM}$ is the axiom scheme of the law-of-excluded-middle restricted to formulas in $\Sigma _k$. In addition, we show that this conservation theorem is optimal in the (...) sense that for any semi-classical arithmetic T, if $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over T, then ${T}$ proves ${\Sigma _k}\text {-}\mathrm {LEM}$. In the same manner, we also characterize conservation theorems for other well-studied classes of formulas by fragments of classical axioms or rules. This reveals the entire structure of conservation theorems with respect to the arithmetical hierarchy of classical principles. (shrink)

We systematically study several principles and give a principle which is weaker than disjunctive Markov’s principle. We also show that the principle is underivable and strictly weaker than MP∨ in certain extensions of the system EL of elementary analysis.

This article questions the degree to which ecological theory can be used as justification for protection of ‘natural environments’ as well as in determining which portions or features of those envi...

This article inquires into a paradoxical position held by the concept of ‘nature’ in Derrida's thought. While a pivotal part of his project of deconstruction is devoted to a critique of the metaphysical privileging of nature over its others (technics, culture, and so on), the same project also aims at dismantling the hierarchical binary opposition of man/animal. Insofar as the term ‘animal’ or ‘animality’ to a large extent overlaps with nature, these two strands of his thought appear to stand in (...) a significant tension with each other. I explore this conceptual tension by re-examining Derrida's early critique of the notion of nature – specifically in his reading of Rousseau – in conjunction with his later engagement with the question of animality. As my reading shows, deviating from his early approach, his later work indicates the way in which animal others (and, by extension, all living and non-living others) are indeed constituted by supplementarity and yet, in their irreplaceable singularity, exceed the very structure of supplementarity. This opens up a new way of conceiving nature, no longer as originary presence nor simply as an effect of supplementary play, but in terms of the aporetic relation between supplementarity and what may be termed ‘the unsupplementable’. (shrink)

Climate change apparently calls for urgent action, but both individuals and governments have been slow to react. This is partly because, in addition to natural science, economics and moral philosop...

This article challenges claims that the Japanese neologism shūkyō lacked an established nature prior to the twentieth century and had little to do with experiences of the urban masses. It accordingly problematizes the term as a largely legal concept, highlighting historical newspapers as underutilized sources that offer insight into Meiji popular discourse and attendant conceptualizations of “religion.” This article endorses a shift in both our chronological understanding of shūkyō’s conceptual history as well as its sociocultural mobility. By expanding the milieu (...) understood as being familiar with debates on a range of “religious” issues, this article thereby offers a counter-narrative in which regular use of shūkyō begins to clearly emerge from the mid-1880s, exponentially increasing with the following decades. (shrink)

We refine the arithmetical hierarchy of various classical principles by finely investigating the derivability relations between these principles over Heyting arithmetic. We mainly investigate some restricted versions of the law of excluded middle, De Morgan's law, the double negation elimination, the collection principle and the constant domain axiom.

We shall prove the second incompleteness theorem via Kolmogorov complexity.

We give a proof of Gödel's first incompleteness theorem based on Berry's paradox, and from it we also derive the second incompleteness theorem model-theoretically.

Abed Azzam offers a fresh interpretation of Nietzsche's engagement with the work of Paul the Apostle, reorienting the relationship between the two thinkers while embedding modern philosophy within early Christian theology. Paying careful attention to Nietzsche's dialectics, Azzam situates the philosopher's thought within the history of Christianity, specifically the Pauline dialectics of law and faith, and reveals how atheism is constructed in relation to Christianity. Countering Heidegger's characterization of Nietzsche as an anti-Platonist, Azzam brings the philosopher closer to Paul through (...) a radical rereading of his entire corpus against Christianity. This approach builds a compelling new history of the West resting on a logic of sublimation, from ancient Greece and early Judaism to the death of God. Azzam discovers in Nietzsche's philosophy a solid, tangible Pauline structure and virtual, fragile Greek content, positioning the thinker as a forerunner of the recent "return to Paul" led by Badiou, Agamben, Žižek, and Breton. By changing the focus of modern philosophical inquiry from "Nietzsche and philosophy" to "Nietzsche and Christianity," Azzam initiates a major challenge to the primacy of Plato in the history of Western philosophy and narrow certainties regarding Nietzsche's relationship to Christian thought. (shrink)

In this paper, I show that the availability of what some authors have called the weak reading and the strong reading of donkey sentences with relative clauses is systematically related to monotonicity properties of the determiner. The correlation is different from what has been observed in the literature in that it concerns not only right monotonicity, but also left monotonicity (persistence/antipersistence). I claim that the reading selected by a donkey sentence with a double monotone determiner is in fact the one (...) that validates inference based on the left monotonicity of the determiner. This accounts for the lack of strong reading in donkey sentences with MON determiners, which have been neglected in the literature. I consider the relevance of other natural forms of inference as well, but also suggest how monotonicity inference might play a central role in the actual process of interpretation. The formal theory is couched in dynamic predicate logic with generalized quantifiers. (shrink)

Akama et al. [1] systematically studied an arithmetical hierarchy of the law of excluded middle and related principles in the context of first-order arithmetic. In that paper, they first provide a prenex normal form theorem as a justification of their semi-classical principles restricted to prenex formulas. However, there are some errors in their proof. In this paper, we provide a simple counterexample of their prenex normal form theorem [1, Theorem 2.7], then modify it in an appropriate way which still serves (...) to largely justify the arithmetical hierarchy. In addition, we characterize a variety of prenex normal form theorems by logical principles in the arithmetical hierarchy. The characterization results reveal that our prenex normal form theorems are optimal. For the characterization results, we establish a new conservation theorem on semi-classical arithmetic. The theorem generalizes a well-known fact that classical arithmetic is $\Pi _2$ -conservative over intuitionistic arithmetic. (shrink)

The uniform continuity theorem states that every pointwise continuous real‐valued function on the unit interval is uniformly continuous. In constructive mathematics, is strictly stronger than the decidable fan theorem, but Loeb [17] has shown that the two principles become equivalent by encoding continuous real‐valued functions as type‐one functions. However, the precise relation between such type‐one functions and continuous real‐valued functions (usually described as type‐two objects) has been unknown. In this paper, we introduce an appropriate notion of continuity for a modulus (...) of a continuous real‐valued function on [0, 1], and show that real‐valued functions with continuous moduli are exactly those functions induced by Loeb's codes. Our characterisation relies on two assumptions: (1) real numbers are represented by regular sequences (equivalently Cauchy sequences with explicitly given moduli); (2) the continuity of a modulus is defined with respect to the product metric on the regular sequences inherited from the Baire space. Our result implies that is equivalent to the statement that every pointwise continuous real‐valued function on [0, 1] with a continuous modulus is uniformly continuous. We also show that is equivalent to a similar principle for real‐valued functions on the Cantor space. These results extend Berger's [2] characterisation of for integer‐valued functions on and unify some characterisations of in terms of functions having continuous moduli. (shrink)

The term ‘sporting integrity’ is widely used in the normative assessment of sports. The term, however, suffers from a lack of conceptual precision. Alfred Archer’s ‘coherence-view’ of sporting integrity goes a long way to help clarify what ‘sporting integrity’ actually means and the specific institutional and individual obligations that it generates. Archer argues that ‘sporting integrity’ essentially means that the constraints athletes face ‘cohere’, in the sense of applying consistent inefficiencies between athletic competitors. For example, those who use performance enhancing (...) drugs are less constrained than those who do not use PEDs, and thus PED use undermines sporting integrity. This paper presents the argument that over and above competitive coherence, sporting integrity means living up to the ‘spirit’ or ‘ethos’ of a game. The implications of this view are that a sport could have ‘coherent’ competitive constraints and still lack sporting integrity; additionally, a sport could have ‘i... (shrink)

We propose a new game to strategically justify the constrained equal awards rule in claims problems. Our game is “procedurally fair” and “multilateral”. In addition, even if claimants cannot reach an agreement in any period, they can renegotiate in the next period. We show that, for each claims problem, the awards vector chosen by the constrained equal awards rule achieved at period 1 is the unique subgame perfect equilibrium outcome of the game.

A minimal formula is a formula which is minimal in provable formulas with respect to the substitution relation. This paper shows the following: (1) A β-normal proof of a minimal formula of depth 2 is unique in NJ. (2) There exists a minimal formula of depth 3 whose βη-normal proof is not unique in NJ. (3) There exists a minimal formula of depth 3 whose βη-normal proof is not unique in NK.

Along the line of Hirst‐Mummert and Dorais, we analyze the relationship between the classical provability of uniform versions Uni(S) of Π2‐statements S with respect to higher order reverse mathematics and the intuitionistic provability of S. Our main theorem states that (in particular) for every Π2‐statement S of some syntactical form, if its uniform version derives the uniform variant of over a classical system of arithmetic in all finite types with weak extensionality, then S is not provable in strong semi‐intuitionistic systems (...) including bar induction in all finite types but also nonconstructive principles such as Kőnig's lemma and uniform weak Kőnig's lemma. Our result is applicable to many mathematical principles whose sequential versions imply. (shrink)

We systematically study the interrelations between all possible variations of \(\Delta ^0_1\) variants of the law of excluded middle and related principles in the context of intuitionistic arithmetic and analysis.