We introduce the Easton collapse and show that the two-stage iteration of Easton collapses gives a model in which the successor of a regular cardinal carries a strongly saturated filter. This allows one to get a model in which many successor cardinals carry saturated filters just by iterating Easton collapses.

In his “A new argument for evidentialism” (Shah, Philos Q 56(225): 481–498, 2006 ), Nishi Shah argues that the best explanation of a feature of deliberation whether to believe that p which he calls transparency entails that only evidence can be reason to believe that p. I show that his argument fails because a crucial lemma that his argument appeals to cannot be supported without assuming evidentialism to be true in the first place.

One prominent feature of belief is that a belief cannot be formed at will. This paper argues that the best explanation of this fact is that belief formation is a process that takes aim at the truth. Taking aim at the truth is to be understood as causal responsiveness of the processes constituting belief formation to what facilitates achieving true beliefs. The requirement for this responsiveness precludes the possibility of belief formation responding to intentions in a way that would count (...) as forming a belief at will. (shrink)

We give an extender characterization of a very strong elementary embedding between transitive models of set theory, whose existence is known as the axiom I2. As an application, we show that the positive solution of a partition problem raised by Magidor would refute it.

In this paper, we present a categorical model for Multiplicative Additive Polarized Linear Logic , which is the linear fragment of Olivier Laurent’s Polarized Linear Logic. Our model is based on an adjunction between reflective/coreflective full subcategories / of an ambient *-autonomous category . Similar structures were first introduced by M. Barr in the late 1970’s in abstract duality theory and more recently in work on game semantics for linear logic. The paper has two goals: to discuss concrete models and (...) to present various completeness theorems.As concrete examples, we present a hypercoherence model, using Ehrhard’s hereditary/anti-hereditary objects, a Chu-space model, a double gluing model over our categorical framework, and a model based on iterated double gluing over a *-autonomous category.For the multiplicative fragment of. (shrink)

There are three main points of the paper. 1. There are straightforward ways of manipulating expected gains and losses that result in a divergence between fair betting odds and credence. Such manipulations are familiar from tools of finance. One can easily see that the Sleeping Beauty case is structured in such a way as to result in a divergence between fair betting odds and credence. 2. The inspection of credences and betting odds in certain betting situations shows that the two (...) main extant positions, Elga's and Lewis's, are both mistaken. 3. My proposal may seem to require a revision of probability theory but it does not. The Sleeping Beauty case merely calls attention to a constraint on partitioning of possibility space that is usually satisfied as a matter of course but can in fact be violated. (shrink)

Determining the relationship between the entire brain structure and individual differences is important in extending healthy life expectancy, which can be affected by brain atrophy. The entire brain structure has been gradually known to be correlated not only with age but also with individual differences, such as quality of life, general intelligence, and lifestyle. However, little attention has been paid to the relationship between the entire brain structure and personal traits. We herein focused on one personal trait, namely spiritual growth, (...) and examined its relationship with the entire brain structure using two neuroimaging-derived measures, namely the gray matter Brain Healthcare Quotient, a measure of GM volume, and the fractional anisotropy Brain Healthcare Quotient, a measure of white matter integrity, in 229 healthy participants. The results indicated no significant relationship between the GM-BHQ and spiritual growth, but there was a significant positive correlation between the FA-BHQ and spiritual growth after controlling for age, sex, and body mass index with partial correlation analysis. Furthermore, multiple regression analysis revealed a significant positive correlation between the FA-BHQ and spiritual growth after controlling for physical characteristics, such as age, sex, and BMI, as well as other variables related to lifestyle that were collected using the Health-Promoting Lifestyle Profile. These results support the idea that there is a relationship between the entire WM brain structure and spiritual growth. Further studies are required to clarify the causal relationship between the entire WM brain structure and spiritual growth with some interventions to improve spiritual growth. Such studies will help extend healthy life expectancy from a new perspective of personal trait. (shrink)

閉塞した現在の政治を担う主体を構想できるのか。世界秩序が揺れ動き、従来の国民概念・市民概念が変革を迫られる今、新たな理論的地平を切り開く。.

This paper considers fair betting odds for certain bets that might be placed in the situation discussed in the so-called Sleeping Beauty Problem. This paper examines what Thirders, Halfers, and Double Halfers must say about the odds as determined by various decision theoretic approaches and argues that Thirders and Halfers have difficulties formulating plausible and coherent positions concerning the relevant betting odds. Double Halfers do not face this problem and that is an important consideration in favor of Double Halfers.

We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall show that Takeuti-Arai's cut-elimination procedure of $(\Pi^{1}_{1}-CA) + BI$ and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game. As a direct corollary the independence result of the Hydra Game follows.

We prove that the full completeness theorem for MLL+Mix holds by the simple interpretation via formulas as objects and proofs as Z-invariant morphisms in the *-autonomous category of topologized vector spaces. We do this by generalizing the recent work of Blute and Scott 101–142) where they used the semantical framework of dinatural transformation introduced by Girard–Scedrov–Scott , Logic from Computer Science, vol. 21, Springer, Berlin, 1992, pp. 217–241). By omitting the use of dinatural transformation, our semantics evidently allows the interpretation (...) of the cut-rule, while the original Blute–Scott's does not. Moreover, our interpretation for proofs is preserved automatically under the cut elimination procedure. In our semantics proofs themselves are characterized by the concrete algebraic notion “Z-invariance”, and our denotational semantics provides the full completeness. Our semantics is naturally extended to the full completeness semantics for CyLL+Mix owing to an elegant method of Blute–Scott 1413–1436) 101–142))). (shrink)

Many cultures have had knowledge imposed from outside, whether by force or for reasons of power, to the detriment of their own endogenous knowledge and the wisdom developed throughout their history. Would Japan’s acquisition of Western knowledge have led but to the development of a lesser know-how, devoid of meaning or sense, or even of knowledge which it might be better to ignore? Far from benefiting from an endogenous development or a modernization respectful of beings and of their environment, the (...) developing countries that superficially adopt this unilateral knowledge undergo a type of ‘self-colonization’. Although concurring with biologist Keiko Nakamura’s theory that scientific attitudes must be studied from within, Masahiro Hamashita considers that knowledge from outside allows for more solid internal reflection. He thus advocates the development of an integrated, hybrid knowledge, where external knowledge is mixed with internal knowledge in a spontaneous, harmonious way, as was the case with the traditional knowledge that Japan acquired from China. (shrink)

Is, or has, democracy a universal value? This is the main question raised by this paper, which distinguishes between two aspects of democracy: political institution in opposition to despotism, and political belief against any kind of slavery and subordination. The role played by intellectuals in the development of contemporary democracy, and the relation of democracy to mass culture and the influence of mass media on a true democratic attitude, are studied within the frame of an overall 'mass aesthetization' which characterizes (...) contemporary societies. (shrink)

We give a model of set theory in which the strongly non‐stationary ideal over is weakly presaturated below some canonical set. Here μ is a regular uncountable cardinal. The model is the forcing extension with the Lévy collapse of a Woodin cardinal to the successor of μ. This improves on results of Goldring and of the first author.

LetKbe an algebraic number field andIKthe ring of algebraic integers inK. *Kand *IKdenote enlargements ofKandIKrespectively. LetxЄ *K–K. In this paper, we are concerned with algebraic extensions ofKwithin *K. For eachxЄ *K–Kand each natural numberd, YKis defined to be the number of algebraic extensions ofKof degreedwithin *K.xЄ *K–Kis called a Hilbertian element ifYK= 0 for alldЄ N,d> 1; in other words,Khas no algebraic extension within *K. In their paper [2], P. C. Gilmore and A. Robinson proved that the existence of a (...) Hilbertian element is equivalent to Hilbert's irreducibility theorem. In a previous paper [9], we gave many Hilbertian elements of nonstandard integers explicitly, for example, for any nonstandard natural numberω, 2ωPωand 2ω are Hilbertian elements in*Q, where pωis theωth prime number. (shrink)