We prove that a Spector‐like ultrapower extension ???? of a countable Solovay model ???? (where all sets of reals are Lebesgue measurable) is equal to the set of all sets constructible from reals in a generic extension ????[a], where a is a random real over ????. The proof involves the Solovay almost everywhere uniformization technique.

A new method is presented for constructing models of set theory, using a technique of forming pseudo-ultrapowers. In the presence of the axiom of choice, the traditional ultrapower construction has proven to be extremely powerful in set theory and model theory; if the axiom of choice is not assumed, the fundamental theorem of ultrapowers may fail, causing the ultrapower to lose almost all of its utility. The pseudo-ultrapower is designed so that the fundamental theorem holds even if choice (...) fails; this is arranged by means of an application of the omitting types theorem. The general theory of pseudo-ultrapowers is developed. Following that, we study supercompactness in the absence of choice, and we analyze pseudo-ultrapowers of models of the axiom of determinateness and various infinite exponent partition relations. Relationships between pseudo-ultrapowers and forcing are also discussed. (shrink)

We study smooth classes without the algebraic closure property. For such smooth classes we investigate the simplicity of the class of generic structures, in the context of Robinson theories.

We generalize the ultrapower in a way suitable for choiceless set theory. Given an ultrafilter, forcing is used to construct an extended ultrapower of the universe, designed so that the fundamental theorem of ultrapowers holds even in the absence of the axiom of choice. If, in addition, we assume DC, then an extended ultrapower of the universe by a countably complete ultrafilter must be well-founded. As an application, we prove the Vopěnka-Hrbáček theorem from ZF + DC only (the proof (...) of Vopěnka and Hrbáček used the full axiom of choice): if there exists a strongly compact cardinal, then the universe is not constructible from a set. The same method shows that, in L[ 2 ω ], there cannot exist a θ-compact cardinal less than θ (where θ is the least cardinal onto which the continuum cannot be mapped); a similar result can be proven for other models of the form L[ A ]. The result for L[ 2 ω ] is of particular interest in connection with the axiom of determinacy. The extended ultrapower construction of this paper is an improved version of the author's earlier pseudo-ultrapower method, making use of forcing rather than the omitting types theorem. (shrink)

We associate with any abstract logic L a family F(L) consisting, intuitively, of the limit ultrapowers which are complete extensions in the sense of L. For every countably generated [ω, ω]-compact logic L, our main applications are: (i) Elementary classes of L can be characterized in terms of $\equiv_L$ only. (ii) If U and B are countable models of a countable superstable theory without the finite cover property, then $\mathfrak{U} \equiv_L \mathfrak{B}$ . (iii) There exists the "largest" logic (...) M such that complete extensions in the sense of M and L are the same; moreover M is still [ω,ω]-compact and satisfies an interpolation property stronger than unrelativized ▵-closure. (iv) If L = L ωω(Q α ) , then $\operatorname{cf}(\omega_\alpha) > \omega$ and $\lambda^\omega for all $\lambda . We also prove that no proper extension of L ωω generated by monadic quantifiers is compact. This strengthens a theorem of Makowsky and Shelah. We solve a problem of Makowsky concerning L κλ -compact cardinals. We partially solve a problem of Makowsky and Shelah concerning the union of compact logics. (shrink)

Working in ZF + DC with no additional use of the axiom of choice, we show how to iterate the extended ultrapower construction of Spector . This generalizes the technique of iterated ultrapowers to choiceless set theory. As an application, we prove the following theorem: Assume V = LU[κ] + “κ is λ-supercompact with normal ultrafilter U” + DC. Then for every sufficiently large regular cardinal ρ, there exists a set-generic extension V[G] of the universe in which there exists (...) for some σ a set S ρ for which one can define an elementary embedding j mapping V to LD[S], where D is the filter in V[G] generated by the closed unbounded filter on ρ. Moreover, we have j = ρ, j = σ, j) = S according to LD[S]), and j = D ∩ LD[S] i s a normal ultrafilter in LD[S] on ρ. (shrink)

We prove that if is a model of size at most [kappa], λ[kappa] = λ, and a game sentence of length 2λ is true in a 2λ-saturated model ≡ , then player has a winning strategy for a related game in some ultrapower ΠD of . The moves in the new game are taken in the cartesian power λA, and the ultrafilter D over λ must be chosen after the game is played. By taking advantage of the expressive power of (...) game sentences, we obtain several applications showing the existence of ultrapowers with certain properties. In each case, it was previously known that such ultrapowers exist under the assumption of the GCH, and we get them without the GCH. Article O. (shrink)

We show that the theory, consisting of the usual axioms of but with the power set axiom removed—specifically axiomatized by extensionality, foundation, pairing, union, infinity, separation, replacement and the assertion that every set can be well‐ordered—is weaker than commonly supposed and is inadequate to establish several basic facts often desired in its context. For example, there are models of in which ω1 is singular, in which every set of reals is countable, yet ω1 exists, in which there are sets of (...) reals of every size, but none of size, and therefore, in which the collection axiom fails; there are models of for which the Łoś theorem fails, even when the ultrapower is well‐founded and the measure exists inside the model; there are models of for which the Gaifman theorem fails, in that there is an embedding of models that is Σ1‐elementary and cofinal, but not elementary; there are elementary embeddings of models whose cofinal restriction is not elementary. Moreover, the collection of formulas that are provably equivalent in to a Σ1‐formula or a Π1‐formula is not closed under bounded quantification. Nevertheless, these deficits of are completely repaired by strengthening it to the theory, obtained by using collection rather than replacement in the axiomatization above. These results extend prior work of Zarach. (shrink)

Để xem bóng đá và phát sóng video trực tiếp tốc độ cao, Xoilac là trang web lý tưởng. Đặc biệt, Xoilac không có bất cứ quảng cáo nào, vì vậy người xem vẫn thoải mái thưởng thức trận bóng đá mà không lo bị phân tâm vì bất cứ vấn đề gì. Ngoài ra, Xoilac có đội ngũ dày dặn chuyên môn, luôn đưa ra những nhận định chuẩn xác cho từng trận đấu bóng đá. Với đồ hoạ sinh (...) động, âm thanh lôi cuốn và sống động, Xoilac sẽ lưu lại dấu ấn sâu đậm trong tâm trí người xem bóng đá. (shrink)

The following article discusses an edition of Hugo Grotius’s De jure belli ac pacis, issued without a place of publication or publisher in 1719. The article focuses on the claim first advanc...

It is proposed that the physical structure of an observer in quantum mechanics is constituted by a pattern of elementary localized switching events. A key preliminary step in giving mathematical expression to this proposal is the introduction of an equivalence relation on sequences of spacetime sets which relates a sequence to any other sequence to which it can be deformed without change of causal arrangement. This allows an individual observer to be associated with a finite structure. The identification of (...) suitable switching events in the human brain is discussed. A definition is given for the sets of sequences of quantum states which such an observer could occupy. Finally, by providing an a priori probability for such sets, the definitions are incorporated into a complete mathematical framework for a many-worlds interpretation. At a less ambitious level, the paper can be read as an exploration of some of the technical and conceptual difficulties involved in constructing such a framework. (shrink)

Thomas Mann (1875-1955), was a leading figure in the 20th century and is writer who has been widely mentioned in world litetarure. He is known not only as the writer of milestone novels but also as the master of oppositions. The Buddenbrook’s Family (1901), The Death in Venice (1912), and The Magıc Mountain (1924) in particular are inspiring the same emotions in the readers of today as the day they were written. While these masterpieces have been the subject of literature (...) research and psychoanalysis, they have also been of interest in the realm of philosophy. In particular, from the perspective of philosophy, The Magic Mountain, was the main concern of this study. This study will indicate both the modern aspects of the story as well as try to show how this work was a mirror for its time. The story takes place in a sanatorium where people who suffering from tuberculosis are sent to recover. This is an illness without remedy in its time and which was widespread through the 19th century. Switzerland, with its lofty mountains, was chosen as a location for tuberculosis senatoriums which offered fresh air, good nutrition, and light exercise. While the hospitals of Davos village tried to treat the patients’ lung spots, they also forced them to follow a life of dicipline. The fact that the “spotted” people went to the senatorium, with no intention of going back to their previous life is the main concern of this study. The most interesting fact here is the chain of events that connected earth to the mystical mountains of this town. The main issue will be the question of why people perceived this earthly place in such a different way. (shrink)

In this paper, we consider certain cardinals in ZF (set theory without AC, the axiom of choice). In ZFC (set theory with AC), given any cardinals C and D, either C ≤ D or D ≤ C. However, in ZF this is no longer so. For a given infinite set A consider $\operatorname{seq}^{1 - 1}(A)$ , the set of all sequences of A without repetition. We compare $|\operatorname{seq}^{1 - 1}(A)|$ , the cardinality of this set, to |P(A)|, the (...) cardinality of the power set of A. What is provable about these two cardinals in ZF? The main result of this paper is that $ZF \vdash \forall A(|\operatorname{seq}^{1 - 1}(A)| \neq|\mathscr{P}(\mathscr{A})|)$ , and we show that this is the best possible result. Furthermore, it is provable in ZF that if B is an infinite set, then $|\operatorname{fin}(B)| <|\mathscr{P}(B)|$ even though the existence for some infinite set B* of a function f from $\operatorname{fin}(B^\ast)$ onto P(B*) is consistent with ZF. (shrink)

Let DO denote the principle: Every infinite set has a dense linear ordering. DO is compared to other ordering principles such as O, the Linear Ordering principle, KW, the Kinna-Wagner Principle, and PI, the Prime Ideal Theorem, in ZF, Zermelo-Fraenkel set theory without AC, the Axiom of Choice. The main result is: Theorem. $AC \Longrightarrow KW \Longrightarrow DO \Longrightarrow O$ , and none of the implications is reversible in ZF + PI. The first and third implications and their irreversibilities (...) were known. The middle one is new. Along the way other results of interest are established. O, while not quite implying DO, does imply that every set differs finitely from a densely ordered set. The independence result for ZF is reduced to one for Fraenkel-Mostowski models by showing that DO falls into two of the known classes of statements automatically transferable from Fraenkel-Mostowski to ZF models. Finally, the proof of PI in the Fraenkel-Mostowski model leads naturally to versions of the Ramsey and Ehrenfeucht-Mostowski theorems involving sets that are both ordered and colored. (shrink)

Consider the regularity thesis that each possible event has non-zero probability. Hájek challenges this in two ways: there can be nonmeasurable events that have no probability at all and on a large enough sample space, some probabilities will have to be zero. But arguments for the existence of nonmeasurable events depend on the axiom of choice. We shall show that the existence of anything like regular probabilities is by itself enough to imply a weak version of AC sufficient to prove (...) the Banach–Tarski Paradox on the decomposition of a ball into two equally sized balls, and hence to show the existence of nonmeasurable events. This provides a powerful argument against unrestricted orthodox Bayesianism that works even without AC. A corollary of our formal result is that if every partial order extends to a total preorder while maintaining strict comparisons, then the Banach–Tarski Paradox holds. This yields an argument that incommensurability cannot be avoided in ambitious versions of decision theory. (shrink)

We will prove in Zermelo-Fraenkel set theory without axiom of choice that the transitive hull R* of a relation R is not much “bigger” than R itself. As a measure for the size of a relation we introduce the notion of κ+-narrowness using surjective Hartogs numbers rather than the usul injective Hartogs values. The main theorem of this paper states that the transitive hull of a κ+-narrow relation is κ+-narrow. As an immediate corollary we obtain that, for every infinite (...) cardinal κ, the class HCκ of all κ-hereditary sets is a set with von Neumann rank ϱ(HCκ) ≤ κ+. Moreover, ϱ(HCκ) = κ+ if and only if κ is singular, otherwise ϱ(HCκ) = κ. The statements of the corollary are well known in the presence of the axiom of choice (AC). To prove them without AC - as carried through here - is, however, much harder. A special case of the corollary (κ = ω1, i.e., the class HCω1 of all hereditarily countable sets) has been treated independently by T. JECH. (shrink)

In set theory without the axiom of choice (AC), we study the relative strength of the principle “No decreasing sequence of cardinals,” that is, “There is no function f on ω such that |f(n+1)|<|f(n)| for all n∈ω” (NDS) with regard to its position in the hierarchy of weak choice principles. We establish the following results: (1) The Boolean prime ideal theorem plus countable choice does not imply NDS in ZF; (2) “Every non-well-orderable set has a well-orderable partition into denumerable (...) sets” (Dℵ0) plus the axiom of choice for well-ordered families of nonempty finite sets does not imply NDS ∨ “The axiom of choice for countable families of nonempty countable sets” in ZFA; and (3) The axiom of choice for well-ordered families of nonempty sets, each of cardinality not greater than or equal to 2ℵ0, does not imply NDS ∨ “countable union theorem” in ZFA. The above results answer corresponding questions left open in works by Howard and Rubin (1998) and Howard and Tachtsis (2016). We also show the following: (4) “Every non-well-orderable set has a well-orderable partition into infinite well-orderable sets” (Dw) is strictly weaker than D ℵ0 in ZFA. This resolves an open problem from Keremedis and Tachtsis (2003). (shrink)

In set theory without the Axiom of Choice, we investigate the set-theoretic strength of the principle NDS which states that there is no function f on the set ω of natural numbers such that for everyn ∈ ω, f ≺ f, where for sets x and y, x ≺ y means that there is a one-to-one map g : x → y, but no one-to-one map h : y → x. It is a long standing open problem whether NDS (...) implies AC. In this paper, among other results, we show that NDS is a strong axiom by establishing that ACLO ↛ NDS in ZFA set theory. The latter result provides a strongly negative answer to the question of whether “every Dedekind-finite set is finite” implies NDS addressed in G. H. Moore “Zermelo’s Axiom of Choice. Its Origins, Development, and Influence” and in P. Howard–J. E. Rubin “Consequences of the Axiom of Choice”. We also prove that ACWO ↛ NDS in ZF and that “for all infinite cardinals m, m + m = m” ↛ NDS in ZFA. (shrink)

In set theory without the Axiom of Choice ( $\mathsf {AC}$ ), we investigate the open problem of the deductive strength of statements which concern the existence of almost disjoint and maximal almost disjoint (MAD) families of infinite-dimensional subspaces of a given infinite-dimensional vector space, as well as the extension of almost disjoint families in infinite-dimensional vector spaces to MAD families.

We consider a question of T. Jech and K. Prikry that asks if the existence of a precipitous filter implies the existence of a normal precipitous filter. The aim of this paper is to improve a result of Gitik (Israel J Math, 175:191–219, 2010) and to show that measurable cardinals of a higher order rather than just measurable cardinals are necessary in order to have a model with a precipitous filter but without a normal one.

This paper is a contribution to the study of equality-free logic, that is, first-order logic without equality. We mainly devote ourselves to the study of algebraic characterizations of its relation of elementary equivalence by providing some Keisler-Shelah type ultrapower theorems and an Ehrenfeucht-Fraïssé type theorem. We also give characterizations of elementary classes in equality-free logic. As a by-product we characterize the sentences that are logically equivalent to an equality-free one.

We work in set-theory without choice ZF. A set is Countable if it is finite or equipotent with ${\Bbb N}$ . Given a closed subset F of [0, 1] I which is a bounded subset of $\ell ^{1}(I)$ (resp. such that $F\subseteq c_{0}(I)$ ), we show that the countable axiom of choice for finite sets, (resp. the countable axiom of choice AC N ) implies that F is compact. This enhances previous results where AC N (resp. the axiom of (...) Dependent Choices) was required. If I is linearly orderable (for example $I={\Bbb R}$ ), then, in ZF, the closed unit ball of the Hilbert space $\ell ^{2}(I)$ is (Loeb-)compact in the weak topology. However, the weak compactness of the closed unit ball of $\ell ^{2}(\scr{P}({\Bbb R}))$ is not provable in ZF. (shrink)

We examine combinatorial aspects and consistency strength properties of almost Ramsey cardinals. Without the Axiom of Choice, successor cardinals may be almost Ramsey. From fairly mild supercompactness assumptions, we construct a model of ZF + ${\neg {\rm AC}_\omega}$ in which every infinite cardinal is almost Ramsey. Core model arguments show that strong assumptions are necessary. Without successors of singular cardinals, we can weaken this to an equiconsistency of the following theories: “ZFC + There is a proper class of (...) regular almost Ramsey cardinals”, and “ZF + DC + All infinite cardinals except possibly successors of singular cardinals are almost Ramsey”. (shrink)

Aristóteles foi o primeiro pensador que articulou uma taxonomia do conheci-mento científico: os quatros livros dos Segundos Analíticos descrevem os critérios que uma disciplina qualquer deve respeitar e satisfazer para legitimamente receber a designação de ciência teorética. Mas Aristóteles é mesmo o criador das “ciências particulares”, ou seja, a biologia, a psicologia, a zoologia e, em geral, as ciências naturais. Trata-se de uma questão já clássica saber se o modo pelo qual Aristóteles desenvolve sua ciência dos animais con-forma-se aos padrões (...) normativos estipulados pela teoria da ciência nos Analíticos. Na men-talidade de muitos intérpretes ficou a convicção de que as obras biológicas de Aristóteles conformam-se a um padrão que utiliza apenas dados empíricos, ao passo que o conheci-mento nos Analíticos é estabelecido a partir de premissas primeiras e imediatas. Agora, nos Segundos Analíticos, encontramos exemplos provenientes da meteorologia, da botânica, da zoologia ao lado de exemplos matemáticos. Fica a pergunta: a metodologia axiomática de estilo matemático que o Estagirita propõe nos Analíticos é totalmente independente e ina-dequada para o estudo da biologia? Se for assim, Aristóteles não teria conseguido encaixar as ciências naturais nos padrões normativos expostos nos Segundos Analíticos. No presente estudo, pretendemos, pelo contrário, ressaltar o fato de que é razoável tomar os textos aristotélicos como orbitando em torno de uma mesma e grande pesquisa, a pesquisa cientí-fica, que inclui os Analíticos, assim como os tratados naturais.Aristotle was the first Greek thinker to articulate a taxonomy of scientific pursuits: the four books of the Analytics present a theory of scientific knowledge with a rigorous ac-count of what a body of propositions must be like in order to count as a theoretical science. But Aristotle was also the originator of “special sciences”. A longstanding problem about Aristotle’s philosophy of science is to understand if there is a conflict between the account of scientific explanation in the Posterior Analytics and the investigations reported in treatises such as the History of Animals, Parts of Animals, Generation of Animals 1. The Analytics restricts knowledge to what has been demonstrated from self-evident first principles. The sciences of nature seem to secure their results without such demonstrations: there are not axioms, nor theorems or proofs, nor definitions. Yet many of the examples in the Posterior Analytics are drawn from meteorology, botany and zoology, and are discussed side by side with mathe-matical examples. It is curious that a philosopher as systematic as Aristotle could formulate the first rigorous theory of scientific inquiry and demonstration, pepper the treatise in which he does so with biological examples, and not aim to structure his science of animals in ac-cordance with that theory. In this investigation I want to show that there is a relation betwe-en Aristotle’s official account of the definition in Posterior Analytics and the nature and the role assigned to definition in the Natural Treatises. (shrink)

Daniel Sennert is one of the more neglected big figures of that seventeenth-century process that goes by the shorthand name of Scientific Revolution. Born in Breslau/wroclaw in 1572, he was professor of medicine at the University of Wittenberg from 1602 until his death in 1637. However, his fame and importance were not due to his classroom teaching but to his writings, which were reprinted throughout the century in Germany, France, England, Italy, and the Netherlands, and partially translated into English. His (...) reputation among both his contemporaries and today’s historians of science has to do with the highly innovative synthesis of natural philosophy, medicine, and chymistry, which he presented notably in the two editions of his De chymicorum cum Aristotelicis et Galenicis consensu ac dissensu and in his late Hypomnemata physica, both of which relied on a novel type of atomistic matter theory. His influence, generally underestimated in today’s scholarship, was felt throughout the century and, as William R. Newman has demonstrated, is particularly important in the case of Robert Boyle, who was “plundering Sennert’s œuvre for proofs of the corpuscularian hypothesis,” albeit without acknowledging his source. (shrink)

Maybe they have been made, but I missed them because I don’t read and listen enough, as most of my energies are focused elsewhere. Apologies if this is all old hat. Don’t feel you have to read on. In case others are interested, I shall put this on my web site at http://www.cs.bham.ac.uk/˜axs/gov/ My main point is that it is just silly to talk so much about universities and top-up fees without putting universities in the context of a complete (...) policy on post-school education. What I am offering is not a detailed policy, but a framework for thinking about the problem. Perhaps someone has already done this but I have never heard it mentioned in any of the public debates. I suspect that’s because this top-up fees issue is not part of a coherent policy but just a sort of religious commitment to a “new way”, like other things done by this government. I start with some comments on the fees issue, then go on to talk about how to think about post-school education, distinguishing several categories that need to be separated and funded differently as part of a joined-up system. (shrink)

seem to be a kind of corruption of the elements and not a mixture. Again, if the substantial form of a mixed body is the act of matter without presupposing the forms of simple bodies, then the simple bodies of the elements will lose their definition (rationem). For an element is that of which something is primarily composed, and exists in it and is indivisible ac-.

Pese a la estricta contextualización de lomágico como demoníaco en el tejido dela narrativa de El asno dorado de Apuleyo,una corriente que se ha descuidado enla academia moderna explora su legadopagano –r et i ene el al cance par a unahi pót esi s fact i bl e en l a forma de unacoalición paradigmática entre su progeniei nevi tabl e, l as bruj as desesperadas aligual que una comunidad distinguida detaumaturgos, los teúrgos, cuya identidaden el discurso intelectual proporciona elejemplo (...) más fino de las formas politeistasde adivinación. En Sobre los misterios deJamblico, se clarifica la representación deotra tipología de magia, la natural, queavala un notable paralelo en una premisacompartida –los niveles de motivación.Deseo proponer, que en tanto arroja luzsobre una clasificación dual de la magiac omo demoní ac a y nat ur al , t ambi énrefleja de manera fascinante los grados deunidad entre las brujas desesperadas ylos teúrgos en cuestión –las operacionesde l os pri meros a menudo sust ent ans us pl a n t e a mi e n t o s pa r a o c ul t a r e lconocimiento y su potencial no es inferiora l as preocupaci ones el evadas de l ossegundos.Despite the strict contextualization ofmagic as demonic within the fabric ofnar r at i ve i n Aput ei us ’ Go l de n As s , aneglected current in modern academia itspagan legacy - retains scope for a feasiblehypothesis in the form of a paradigmaticcoalition between its inevitable progeny,desperate witches as well as a distinguishedc o mmu n i t y o f t h a u ma t a u r g o i , t h etheurgist, whose identity in intellectualdi scour se, chi ef l y t he f i nest possi bl ee x e mpl um of pol yt he i s t i c f or ms ofdi vi nat i on I ambl i chus’ De Myst eri es,clarify their representation of anothertypology of magic, natural, endorsinga striking parallel in a shared premise -levels of motivation. I wish to propose,that in as much as it throws light on twofold classification of magic as demonic andnatural it also fascinatingly reflects degreesof unity, though not without reserve insome areas, between the desperate witchesand theurgists in question - the formerwhose operations often underpin theirclaims to occult knowledge and whosepotential is no less inferior to the elevatedconcerns of the latter. (shrink)

The object of our investigation is expressing necessary conditions in natural language, particularly in a certain kind of conditional sentences, the so-called Anankastic Conditionals 2, a topic brought into the linguistic discussion by the seminal papers and. A typical AC is the following sentence, Sæbø’s standard example: If you want to go to Harlem, you have to take the A train. Sæbø analyses the sentence by means of the modal theory in, according to which a modal has two contextual parameters, (...) a modal base f and an ordering source g. The modal base contains relevant facts and the ordering source contains an ideal like wishes, moral laws and the like. Normally, the antecedent of a necessity-conditional is added to the modal base. Sæbø’s new proposal for the analysis of the AC is that the antecedent without the information ‘you want’, called inner antecedent, is added to the ordering source. (shrink)

One result of this note is about the nonconstructivity of countably infinite lotteries: even if we impose very weak conditions on the assignment of probabilities to subsets of natural numbers we cannot prove the existence of such assignments constructively, i.e., without something such as the axiom of choice. This is a corollary to a more general theorem about large-small filters, a concept that extends the concept of free ultrafilters. The main theorem is that proving the existence of large-small filters (...) requires a nonconstructive axiom like AC. (shrink)

The article follows on from Sadziński and is his “provocative” antithetical sequel. Ac cording to an internet research, sentences with even occasionally have no chronological order.The analysis carried out has shown that the sentence structures without time series mentioned often do ot understand themselves as temporal sentences. They are the result of de facto contamination with colloquially marked causal clauses.

This article examines Grotius’ lifelong support for Dutch expansion overseas. As noted in other publications of mine, Grotius cooperated closely with the directors of the Dutch East India Company (VOC) in the years 1604–1615. Right up to his arrest for high treason in August 1618, he contributed towards Dutch government discussions about the establishment of a West India Company (WIC). Three years of imprisonment at Loevestein Castle and, following his escape, long years of exile could not weaken his dedication to (...) the cause. His relatives in Holland, in particular his brother Willem de Groot and his brother-in-law Nicolaas van Reigersberch, kept him up-to-date on the fortunes of the VOC and WIC. His expertise on maritime affairs was in high demand. For example, Cardinal Richelieu invited him in November 1626 to become actively involved in the establishment of a French East India Company. As itinerant ideologue of empire, Grotius sought to further his own career and those of his nearest family members, without damaging the interests of the United Provinces. Through Willem de Groot and Nicolaas van Reigersberch, he provided informal advice on Dutch imperial policy to the VOC directors and government officials in The Hague. He was rewarded with the appointment of his brother and his second son, Pieter de Groot, as VOC lawyers (ordinaris advocaten) in 1639 and 1644, respectively. They served as his proxies in diplomatic disputes involving the VOC, the States General and the Portuguese ambassador in autumn 1644, when Pieter and Willem de Groot wrote a defense of VOC claims to the cinnamon-producing areas of Ceylon (modern-day Sri Lanka), liberally citing De Jure Belli ac Pacis. Grotius’ vision of empire hardly changed in the course of 40 years. In his view, the Dutch had gone to the Indies as merchants, not conquerors, and should regulate themselves according to natural law and the law of nations. Thus he contributed to the creation of two political orders, one for Europe and one for the Indies. European diplomatic relations counted for little beyond the Line. VOC and WIC officials could act as judges and executioners in their own cause, without reference to indigenous rulers, other colonial powers, or even the political authorities back home. (shrink)

PurposeThe unique constraints to everyday life brought about by the COVID-19 pandemic have been suggested to negatively impact those with pre-existing mental health issues such as eating disorders. While individuals with eating disorders or disordered eating behaviors likely represent a vulnerable group to the COVID-19 pandemic, the impact of the pandemic is yet to be fully established.MethodsWe systematically examined the impact of the COVID-19 pandemic on eating disorders and disordered eating behaviors. We searched electronic databases MEDLINE, PsycINFO, CINAHL, and EMBASE (...) for literature published until October 2021. Eligible studies were required to report on individuals with or without a diagnosed eating disorder or disordered eating behaviors who were exposed to the COVID-19 pandemic.FindingsSeventy-two studies met eligibility criteria with the majority reporting an increase in eating disorder or disordered eating behaviors associated with the COVID-19 pandemic. Specifically, it appears children and adolescents and individuals with a diagnosed eating disorder may present vulnerable groups to the impacts of the COVID-19 pandemic.DiscussionThis mixed systematic review provides a timely insight into COVID-19 eating disorder literature and will assist in understanding possible future long-term impacts of the pandemic on eating disorder behaviors. It appears that the role of stress in the development and maintenance of eating disorders may have been intensified to cope with the uncertainty of the COVID-19 pandemic. Future research is needed among understudied and minority groups and to examine the long-term implications of the COVID-19 pandemic on eating disorders and disordered eating behaviors.Systematic review registrationhttps://www.crd.york.ac.uk/prospero/display_record.php?RecordID=284749, PROSPERO [CRD42021284749]. (shrink)

We provide a general criterion for Fraenkel–Mostowski models of $${\textsf{ZFA}}$$ (i.e. Zermelo–Fraenkel set theory weakened to permit the existence of atoms) which implies “every linearly ordered set can be well ordered” ( $${\textsf{LW}}$$ ), and look at six models for $${\textsf{ZFA}}$$ which satisfy this criterion (and thus $${\textsf{LW}}$$ is true in these models) and “every Dedekind finite set is finite” ( $${\textsf{DF}}={\textsf{F}}$$ ) is true, and also consider various forms of choice for well-ordered families of well orderable sets in these (...) models. In Model 1, the axiom of multiple choice for countably infinite families of countably infinite sets ( $${\textsf{MC}}_{\aleph _{0}}^{\aleph _{0}}$$ ) is false. It was the open question of whether or not such a model exists (from Howard and Tachtsis “On metrizability and compactness of certain products without the Axiom of Choice”) that provided the motivation for this paper. In Model 2, which is constructed by first choosing an uncountable regular cardinal in the ground model, a strong form of Dependent choice is true, while the axiom of choice for well-ordered families of finite sets ( $${\textsf{AC}}^{{\textsf{WO}}}_{{\textsf{fin}}}$$ ) is false. Also in this model the axiom of multiple choice for well-ordered families of well orderable sets fails. Model 3 is similar to Model 2 except for the status of $${\textsf{AC}}^{{\textsf{WO}}}_{{\textsf{fin}}}$$ which is unknown. Models 4 and 5 are variations of Model 3. In Model 4 $${\textsf{AC}}_{\textrm{fin}}^{{\textsf{WO}}}$$ is true. The construction of Model 5 begins by choosing a regular successor cardinal in the ground model. Model 6 is the only one in which $$2{\mathfrak {m}} = {\mathfrak {m}}$$ for every infinite cardinal number $${\mathfrak {m}}$$. We show that the union of a well-ordered family of well orderable sets is well orderable in Model 6 and that the axiom of multiple countable choice is false. (shrink)

The present article deals with the power of the axiom of choice within the second-order predicate logic. We investigate the relationship between several variants of AC and some other statements, known as equivalent to AC within the set theory of Zermelo and Fraenkel with atoms, in Henkin models of the one-sorted second-order predicate logic with identity without operation variables. The construction of models follows the ideas of Fraenkel and Mostowski. It is e. g. shown that the well-ordering theorem for (...) unary predicates is independent from AC for binary predicates and from the trichotomy law for unary predicates. Moreover, we show that the AC for binary predicates follows neither from the trichotomy law for unary predicates nor from Zorn's lemma for unary predicates nor from the formalization of the axiom of choice for disjoint families of sets for binary predicates, and that the trichotomy law for unary predicates does not follow from AC for binary predicates. (shrink)

This article examines Grotius’ lifelong support for Dutch expansion overseas. As noted in other publications of mine, Grotius cooperated closely with the directors of the Dutch East India Company (VOC) in the years 1604–1615. Right up to his arrest for high treason in August 1618, he contributed towards Dutch government discussions about the establishment of a West India Company (WIC). Three years of imprisonment at Loevestein Castle and, following his escape, long years of exile could not weaken his dedication to (...) the cause. His relatives in Holland, in particular his brother Willem de Groot and his brother-in-law Nicolaas van Reigersberch, kept him up-to-date on the fortunes of the VOC and WIC. His expertise on maritime affairs was in high demand. For example, Cardinal Richelieu invited him in November 1626 to become actively involved in the establishment of a French East India Company. As itinerant ideologue of empire, Grotius sought to further his own career and those of his nearest family members, without damaging the interests of the United Provinces. Through Willem de Groot and Nicolaas van Reigersberch, he provided informal advice on Dutch imperial policy to the VOC directors and government officials in The Hague. He was rewarded with the appointment of his brother and his second son, Pieter de Groot, as VOC lawyers (ordinaris advocaten) in 1639 and 1644, respectively. They served as his proxies in diplomatic disputes involving the VOC, the States General and the Portuguese ambassador in autumn 1644, when Pieter and Willem de Groot wrote a defense of VOC claims to the cinnamon-producing areas of Ceylon (modern-day Sri Lanka), liberally citing De Jure Belli ac Pacis. Grotius’ vision of empire hardly changed in the course of 40 years. In his view, the Dutch had gone to the Indies as merchants, not conquerors, and should regulate themselves according to natural law and the law of nations. Thus he contributed to the creation of two political orders, one for Europe and one for the Indies. European diplomatic relations counted for little beyond the Line. VOC and WIC officials could act as judges and executioners in their own cause, without reference to indigenous rulers, other colonial powers, or even the political authorities back home. (shrink)

The little francophone community of Port-au-Port Peninsula in Newfoundland is particularly representative of non-standard French spoken in North America. This paper tries to elaborate a grammatical analysis in order to justify the transcriptions of verb forms in the Dictionnaire des régionalismes de Terre-Neuve. In the sentence “I passait les maisons, [bladʒe] ac le monde”, for instance, [bladʒe] could be interpreted as “blaguait” or “blaguer.” In standard French, the same sentence could be translated as “il allait de porte en porte parler (...) avec les gens” or “il allait de porte en porte, parlait avec les gens.” The omission of the subject pronoun seems to allow the transition toward a unmarked verb form either under a short form, limited to the radical of the verb, without any flexional mark like an imperative form, or a full form, like what Remacle calls “infinitif substitut.” The last stade of this evolution is the nominal phrase, whose use is widely spread in popular French, where it often follows a verb phrase. (shrink)

Parapsychologists have never been entirely satisfied with their technical vo- cabulary, and occasionally their discontent leads to attempts at terminological reform.1 Recently, a number of prominent parapsychologists, led by Ed May, have regularly abandoned some of parapsychology’s traditional and central categories in favor of some novel alternatives (see, e.g., May, Utts, and Spot- tiswoode, 1995a, 1995b; May, Spottiswood, Utts, and James, 1995). They rec- ommend replacing the term ª ESPº with ª anomalous cognitionº (or AC) and ª psychokinesis (PK)º with (...) ª anomalous perturbationº (or AP). Advocates of these new terms also propose replacing the term ª psiº or ª psi phenomenaº with ª anomalous mental phenomena.º Superf icially at least, these proposals seem merely to be modest extensions of parapsychology’s increasingly fre- quent use of the term ª anomalousº as a substitute for ª paranormal,º a practice which (although controversial) is not without merit, and which Palmer has vigorously defended (1986, 1987, 1992). But in my view, the proposed new terminology creates more problems than it solves. (shrink)

Introduction: The aim of this review was to systematically synthesize the published literature describing the psychological and behavioral correlates of recreational running in adults, defined as running for leisure, with or without a competitive component.Methods: Quantitative research published in peer-reviewed journals until January 2021 were included. Studies were identified through MEDLINE, PsycINFO, SPORTDiscus, and Web of Science and were included in this review if they were aimed at recreational running, included general adult samples, and assessed psychological or behavioral correlates (...) of recreational running.Results: Fifty-six articles reporting 58 studies met the eligibility criteria and were included. There were 27 cross-sectional studies, 12 longitudinal studies, and 19 trials. Twenty-eight studies assessed antecedents of running behavior, and 25 studies used running behavior as treatment or predictor of a given effect or outcome. Four studies examined both predictors and outcomes of running. Thirty-one studies showed poor quality, while 20 had fair and 7 good quality. Motives were the most frequently studied antecedent of running behavior, and results suggest that the highest-ranked or more prevalent motives were physical health, psychological motives, and personal achievement. Additionally, perceived control, attitude toward running, intention and subjective norms, self-efficacy, and social support may have also played a role in the adoption of recreational running. Moreover, improvements in mood and well-being were the most frequently reported positive outcomes of running. Reductions in depression, anxiety, and stress were also reported in included studies.Discussion: To our knowledge, this is the first systematic review on this topic. The identification of behavioral and psychological correlates of recreational running across populations can contribute to inform and guide a public policy agenda, focused on helping people sustain regular physical activity, through a modality they have chosen and appear to enjoy.Systematic Review Registration:https://www.crd.york.ac.uk/prospero/display_record.php?RecordID=68954, identifier: CRD42017068954. (shrink)

Augmentative and alternative communication brain-computer interface systems are intended to offer communication access to people with severe speech and physical impairment without requiring volitional movement. As the field moves toward clinical implementation of AAC-BCI systems, research involving participants with SSPI is essential. Research has demonstrated variability in AAC-BCI system performance across users, and mixed results for comparisons of performance for users with and without disabilities. The aims of this systematic review were to describe study, system, and participant characteristics (...) reported in BCI research, summarize the communication task performance of participants with disabilities using AAC-BCI systems, and explore any differences in performance for participants with and without disabilities. Electronic databases were searched in May, 2018, and March, 2021, identifying 6065 records, of which 73 met inclusion criteria. Non-experimental study designs were common and sample sizes were typically small, with approximately half of studies involving five or fewer participants with disabilities. There was considerable variability in participant characteristics, and in how those characteristics were reported. Over 60% of studies reported an average selection accuracy ≤70% for participants with disabilities in at least one tested condition. However, some studies excluded participants who did not reach a specific system performance criterion, and others did not state whether any participants were excluded based on performance. Twenty-nine studies included participants both with and without disabilities, but few reported statistical analyses comparing performance between the two groups. Results suggest that AAC-BCI systems show promise for supporting communication for people with SSPI, but they remain ineffective for some individuals. The lack of standards in reporting outcome measures makes it difficult to synthesize data across studies. Further research is needed to demonstrate efficacy of AAC-BCI systems for people who experience SSPI of varying etiologies and severity levels, and these individuals should be included in system design and testing. Consensus in terminology and consistent participant, protocol, and performance description will facilitate the exploration of user and system characteristics that positively or negatively affect AAC-BCI use, and support innovations that will make this technology more useful to a broader group of people.Clinical trial registrationhttps://www.crd.york.ac.uk/prospero/display_record.php?ID=CRD42018095345, PROSPERO: CRD42018095345. (shrink)

House of Lords authority in Tesco v Secretary of State for the Environment [1995] 1 WLR 759 has reinforced the well-established principle that judicial review will distinguish between relevant and irrelevant considerations pertaining to the exercise of a power, and leave the weighing of the relevant ones to the decision-maker. It has also problematized the principle by insisting that relevant factors may adequately be taken into account even where the decision-maker allows them no influence (subject to challenge for irrationality). It (...) is difficult to accept that a legislative identification of relevant factors need not influence the decision-maker, and the article begins by observing that this proposition would probably not have been accepted at the time of Roberts v Hopwood [1925] AC 578. It is argued in the article, however, that the proper influence of the relevant can be accommodated within the decision-making process while upholding the Tesco principle. The article therefore charts the activities which are logically implicit in a decision-making process including the consideration and weighing of relevant factors, and locates opportunities for legal challenge. The influence of the expressly relevant must be felt when the decision-maker has to decide whether other factors are impliedly relevant. It will equally be registered when a basis for the assessment of weight is established (weight being impossible to gauge without the prior formulation of criteria of influence). The process of weighing itself is shown to require two separate assessments; the first particular to each factor, the second comparative. This distinction allows explanation of those explanation of those authorities which require substantial weight to be given to certain protected factors, and helps to define the nature of irrationality challenges to absurd weighing. In summary, the article takes a rigorous look at what weight is, how it is assessed, how it differs from relevance, and to what extent a flawed assessment of it can be challenged. (shrink)

There is a Turing functional $\Phi $ taking $A^\prime $ to a theory $T_A$ whose complexity is exactly that of the jump of A, and which has the property that $A \leq _T B$ if and only if $T_A \trianglelefteq T_B$ in Keisler’s order. In fact, by more elaborate means and related theories, we may keep the complexity at the level of A without using the jump.

Ebbhinghaus, H., J. Flum, and W. Thomas. 1984. Mathematical Logic. New York, NY: Springer-Verlag. Forster, T. Typescript. The significance of Yablo’s paradox without self-reference. Available from http://www.dpmms.cam.ac.uk. Gold, M. 1965. Limiting recursion. Journal of Symbolic Logic 30: 28–47. Karp, C. 1964. Languages with Expressions of Infinite Length. Amsterdam.

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume XXIII, Number 2, November 1997, pp. 315-335 Reid: Conception, Representation and Innate Ideas ROGER D. GALLIE Section I of this paper begins with a presentation of Thomas Reid's doctrine of the signification of words, of what words signify or represent. That presentation serves to introduce a problem of interpretation, namely, what Reid thinks the connection is between conceiving something and grasping what a term for it (...) signifies. It is pointed out that even if Reid maintains that what a word signifies is conceived by both speaker and hearer when that word is understood, this is a far cry from the position that he takes the stronger view, whether for all or only for some things, that their being conceived involves the understanding of a term or terms. The position that he does indeed take this stronger, although moderate, view is defended in sections II, III and IV. In sections II and III it is argued that, in Reid's view, for an adequate conception of an individual, real or imaginary, a conception of its attributes is needed. In section IV it is argued that the possession of general conceptions (in distinction from their formation), without which conception of attributes is impossible, requires appropriate understanding of general terms. So since for the conception of an individual a conception of its attributes is needed, and since for the conception of attributes appropriate understanding of general terms is required, we arrive at a textually well-founded position: for the conception of most things, in Reid's view, understanding of terms is indispensable. Roger D. Gallie is at the Department of Philosophy, Nottingham University, University Park, Nottingham NG7 2RD UK. email: [email protected] 316 Roger D. Gallie The remainder of the paper considers the following question: to what extent, if any, Reid is committed to acceptance of nativist views on concept possession? To answer, in section V we consider to what extent Reid's moderate position on the possession of conceptions commits him to accepting Jerry Fodor's representational theory of mind (RTM) for propositional attitudes. It is clear that the view that a propositional attitude state such as belief involves some relation between a person and a representation such as a significant word, phrase or sentence of a natural language such as English can fairly be attributed to Reid. But it is also clear that Reid cannot be an adherent of the view that persons have a functional cum computational relation to Fodorean mental representations, so he cannot be an adherent of any nativism ex- plicitly contained in such a view. But it is to be noted that in his Inquiry, Chapter IV, Reid argues by a different route that in order to acquire a language such as English prior mastery of a system of significant signs is required. In section VI Keith Lehrer's argument in criticism of a reductionist interpretation of a position such as Fodor's is presented: that for a sign to signify something to someone presupposes that that person has a conception of what is signified. It is however pointed out that since there is a case for not viewing Fodor's position as reductionist overall Fodor can accept Lehrer's argument. Lehrer's innatist position, which he both claims to follow easily from this critical argument and to be a correct interpretation of Reid, is then presented: that we must presuppose an innate understanding of some signs to account for our learning the meaning of any signs. The objection that Reid too must accept the alleged innatist implications of Lehrer's critical argument in view of the implications of his moderate position on the possession of conceptions is considered and rebutted. In section VIII argue that while Lehrer makes a respectable case for innate principles of formation of conceptions such as that of hardness, something that Reid clearly endorses in his Inquiry, Chapter V, he does not succeed in making a case for there being any innate possession of conceptions. Finally, in section VIII, Reid's mature views in the Intellectual Powers, Essay VI, on how conceptions come to be possessed are expounded, and are fleshed out with some... (shrink)

It is well-known (due to C. Parsons) that the extension of primitive recursive arithmeticPRA by first-order predicate logic and the rule ofΠ 2 0 -inductionΠ 2 0 -IR isΠ 2 0 -conservative overPRA. We show that this is no longer true in the presence of function quantifiers and quantifier-free choice for numbersAC 0,0-qf. More precisely we show that ℐ :=PRA 2 +Π 2 0 -IR+AC 0,0-qf proves the totality of the Ackermann function, wherePRA 2 is the extension ofPRA by number (...) and function quantifiers andΠ 2 0 -IR may contain function parameters. This is true even forPRA 2 +∑ 1 0 -IR+Π 2 0 -IR −+AC 0,0-qf, whereΠ 2 0 -IR − is the restriction ofΠ 2 0 -IR without function parameters. (shrink)

The modal argument for the existence of a Cartesian human soul proposed by Richard Swinburne more than thirty years ago, if slightly adjusted and interpreted correctly, becomes a plausible argument for anyone who accepts modal arguments. The difficulty consists in a relatively weak justification of the second premise, of the real possibility of a disembodied existence, as a result of which the argument does not provide a real proof. The argument is best understood in the following terms: Special divine action (...) is excluded from the metaphysical possibilities and only the natural possibilities are considered; the “conceivable” possibility of the existence of a person without a body is interpreted as a metaphysical possibility, and inductive support for its reality is provided by apparent first-person-conceivability of a disembodied existence, detailed descriptions of out-of-body and near-death experiences, a priori trust in introspection in psychology and the cognitive sciences, and by the unity of consciousness and the possibility of its extension to peripersonal space; statements about having a soul or being a material substance are excluded from the domain of the premises; and finally, one accepts the Kripkean principle that having a body or a soul is an essential component of a person. If these conditions are met, the argument is valid, and the conclusion is made more plausible by Swinburne’s modal argument than it would be without it.Argumentum modale pro animae humanae “Cartesianae” existentia, quod R. Swinburne ante plures quam 30 annos proposuit, acceptabile reddi potest cuicumque argumenta modalia non generatim respuenti, si paululum emendetur recteque intelligatur. Omnis huius argumenti diffi cultas consistit in iustifi catione debiliore secundae eius praemissae, quo pacto argumentum ineffi cax redditur. Argumentum vero optime intelligetur his quattuor punctis animadversis: Primo, possibilitas metaphysica non nisi possibilitates naturales comprehendere intelligatur, omni speciali Dei ingerentia exclusa. Secundo, personae possibilitas “conceptibilis” sine corpore existendi intelligatur ut realis possibilitas metaphysica. Cui realitati argumenta favent inductiva tum ex possibilitate imaginandi existentiam sine corpore; tum ex minutatim enarratis testimoniis experiendi status “extra corpus” et “prope mortem”; tum ex fi de fundamentali veritatis introspectionis in psychologia scientiis que cognitivis; tum ex unitate conscientiae ac possibilitate eam in spatium extra corpus extendendi. Tertio, e praemissarum congerie assertiones excludantur quibus homo animam habere vel substantiam materialem esse assumeretur. Quarto, principium S. Kripkii accipiatur, scil. corporis vel animae habitum personae essentialem esse debere. His omnibus servatis argumentum Swinburnii validum evadit, conclusionem suam plus credibilem reddens quam secus esset. (shrink)

Recent work on conditional reasoning argues that denying the antecedent [DA] and affirming the consequent [AC] are defeasible but cogent patterns of argument, either because they are effective, rational, albeit heuristic applications of Bayesian probability, or because they are licensed by the principle of total evidence. Against this, we show that on any prevailing interpretation of indicative conditionals the premises of DA and AC arguments do not license their conclusions without additional assumptions. The cogency of DA and AC inferences (...) rather depends on contingent factors extrinsic to, and independent of, what is asserted by DA and AC arguments. arguments do not license their conclusions without additional assumptions. The cogency of DA and AC inferences rather depends on contingent factors extrinsic to, and independent of, what is asserted by DA and AC arguments. (shrink)

In this article, the life of Göynüklü Ibrāhīm Ḥaḳḳī Efendi will be analyzed. Ibrāhīm Ḥaḳḳī Efen-di was born in Göynük in the middle of 1294/1878 according to the Rūmī calendar. Since his father was a mudarris, he has become familiar with ʿulamāʾ circles since his childhood. He spent the first years of his education life in Göynük, where he was born. He completed the later stages of the education process in Istanbul. He returned to Göynük after completing his mad-rasa education (...) and obtaining his ijāzāt and he undertook various official duties in his hometown until 1946, the date of his death. He served as the Muftī of Göynük for the longest time among the duties he has undertaken. It is known that he had continued this duty in the last period of the Ottoman Empire and the first years of the Turkish Republic. Therefore, Ibrāhīm Ḥaḳḳī Efendi is the last muftī of the Ottoman period and the first muftī of the Republic period in Göynük. Ibrāhīm Ḥaḳḳī Efendi is the subject of this article because we think that his position is important. According to our findings, there has not been any study on Ibrāhīm Ḥaḳḳī Efendi yet. In this respect, the article will enable Ibrāhīm Ḥaḳḳī Efendi to known in the light of archive sources and other available information/documents. The article includes informations about his life, family, education, hodjas, scientific background and the duties he undertook. In order to obtain this information, we first applied to the Istanbul Muftī’s Mashīkhat Archive and to the Religious Affairs Presidency Archive. From the aforementioned archives, the registry files of Ibrāhīm Ḥaḳḳī Efendi were obtained. In addition, other sources that will contribute to the article have been carefully scanned. Ibrāhīm Ḥaḳḳī Efendi took the exam of the lectern sheikhdom and was found successful after his madrasah education. But, since the appointment to the lectern sheikhdom was made ac-cording to a certain hierarchy, his turn did not come. Upon this, Ibrāhīm Ḥaḳḳī Efendi returned from Istanbul to his hometown, Göynük and undertook a number of official duties from this date until his death. Court membership, mudarrisship and muftīship are among his official duties that he undertook. His name was chosen and determined by the local units for the duty of muftī and he was appointed to the post with the approval of Shaykh al-Islām. Ibrāhīm Ḥaḳḳī Efendi had served as the muftī of Göynük between 1912-1946 without any interruption. His long service as a muftī is enoug to reach a positive opinion about his education, scientific knowledge, personal characteristics, and his position in the eyes of administrators and society. Because the fact that a person has held the same post for thirty-four years is at least a sign of trust in him. However, when he was first appointed as muftī, some objections were raised against him. It is possible to list these objections under the headings such as taking sides in favor of Ibrāhīm Ḥaḳḳī Efendi when he was elected as the mufti, ignoring the applications of other candidates and his lack of scientific knowledge. These objections that submitted to the officials were not ignored by the local authorities, on the contrary, they were addressed. Even, these objections were investigated by more than one governmental institution. As a result of the investigations, it was determined that the allegations made against Ibrāhīm Ḥaḳḳī Efendi were unfounded. As a result, this amount of information has been identified for Ibrāhīm Ḥaḳḳī Efendi at least for now. It would be appropriate to state that the contents of the article is open to improvement with the information and documents that are likely to be obtained later. (shrink)

Varlığın mahiyeti meselesi, insanın varlığa hangi açıdan muhatap olduğu ile doğrudan ilgilidir. Felsefe tarihinde ortaya çıkmış olan farklı ekoller arasındaki ayrımı oluşturan da, temelde bu mesele karşısındaki tutumlarıdır. Nicholas of Cusa düşüncesinde varlık, insanın salt epistemik yetileri ile vukufiyet kesp edebileceği bir alan değildir. Bundan dolayı Mutlak Varlık, olduğu haliyle kendi mükemmelliği içerisinde kavranamaz. Bunun için öncelikli olarak gerekli olan, aklın bütün olumlayıcı bilgi iddialarından vazgeçtiği bir tür zihinsel arınmadır. Bu, aslında bir bilinç durumudur ve bu düzeye erişen idrak, varlığı (...) kendi kaynağında temaşa eder. Zıtlığın uyumda, çoğulluğun ise birlikte herhangi bir çelişki olmaksızın göründüğü bu hâl içerisinde, Tanrı artık bir bilgi konusu olmanın ötesinde bir tecrübe konusudur. Cusa’ya göre, insanın iç tecrübesinden hareket eden mistik karakterli bir varlık görüşü ile ancak idrake dayalı yetkin bir bilinç sağlanabilir. Burada artık asıl olan bilme değil, asla bilemeyeceğini bilmedir. Cusa’ya göre, bu idraki seviyeye ulaşmanın yolu ruhsal bir eğitimin yanında Tanrısal lütuftur. The issue of the nature of existence is directly related to the way in which man deals with existence. What makes a difference between the schools in the history of philosophy is their attitudes towards this issue. In the thought of Nicholas of Cusa, existence is not something that a person can realize with purely epistemic abilities. Therefore, Absolute Being cannot be grasped in its own perfection as it is. What is primarily necessary for this is a kind of intellectual purification in which the reason renounces all affirmative claims of knowledge. This actually is a state of consciousness and the intellect that reaches this level contemplates existence at its source. In this state, where opposites appear in harmony and plurality in unity without any contradiction, God is no longer a subject of knowledge but a subject of experience. According to Cusa, only an intellectual comprehension can be achieved with a mystical view of being based on the inner experience of the human being in this way. The main thing is not knowing anymore but knowing that you can never know. According to Cusa, the way to reach this level of understanding is divine grace as well as spiritual education. (shrink)

SummaryGrotius has a rudimentary theory of sociability. Only with hindsight has a remark about appetitus societatis been promoted to the starting point of a theory that flourished in the writings of later natural jurists. In this article, I address the issue of the appearance in Grotius's natural law of sociability [as the 1715/38 English translation of John Morrice renders appetitus societatis, following Barbeyrac's sociabilité]. Writing in the just war tradition, Grotius is first of all interested in finding out the conditions (...) for peace, and although injustice is a condition of war, it is not per se true that injustice is a perversion of society. Apparently, not all societies are perfect and the violence of war and the legal actions of peace are both instruments for achieving a greater modicum of justice in this world. Yet appetitus et custodia societatis is called the foundation of justice. Grotius achieved this context for sociability in phases, through a series of writings from c. 1600 until De iure belli ac pacis of 1625, and its revision of 1631. In this development the notion of fides plays an intriguing role, through which we can obtain a better understanding of the meaning of appetitus societatis in the later work. The present article is a sequel to a previous publication, on fides in De iure praedae. Analysing the genesis of appetitus societatis in De iure belli ac pacis, I argue that Grotius was changing his strategy over the years, without however arriving at a definitive solution to the question of what commits men to the pursuit of justice. (shrink)