We apply the technique of generic ultrapowers to study the splitting problem of stationary subsets of P K λ . We present some conditions which guarantee the splitting of stationary subsets of P K λ.

We prove that if λ is a strong limit singular cardinal and κ a regular uncountable cardinal < λ, then NSκλ, the non-stationary ideal over [Formula: see text], is nowhere precipitous. We also show that under the same hypothesis every stationary subset of [Formula: see text] can be partitioned into λκ disjoint stationary sets.

We show that if κ is an inaccessible cardinal then P κ λ splits into $\lambda^{ many disjoint stationary subsets. We also show that if P κ λ carries a strongly saturated ideal then the nonstationary ideal cannot be λ + -saturated.

In this paper we will present a simple condition for an ideal to be nowhere precipitous. Through this condition we show nowhere precipitousness of fundamental ideals onPkλ, in particular the non-stationary idealNSkλunder cardinal arithmetic assumptions.In this sectionIdenotes a non-principal ideal on an infinite setA. LetI+=PA/I(ordered by inclusion as a forcing notion) andI∣X= {Y⊂A:Y⋂X∈I}, which is also an ideal onAforX∈I+. We refer the reader to [8, Section 35] for the general theory of generic ultrapowers associated with an ideal. We recallIis said (...) to be precipitous if ⊨I+“Ult(V, Ġ) is well-founded” [9].The central notion of this paper is a strong negation of precipitousness [1]:Definition.Iis nowhere precipitous ifI∣Xis not precipitous for everyX∈ I+i.e., ⊨I+“Ult(V, Ġ) is ill-founded.”It is useful to characterize nowhere precipitousness in terms of infinite games (see [11, Section 27]). Consider the following gameG(I) between two players, Nonempty and Empty [5]. Nonempty and Empty alternately chooseXn∈I+andYn∈I+respectively so thatXn⊃Yn⊃n+1. After ω moves, Empty wins the game if⋂n<ωXn=⋂n<ωYn= Ø.See [5, Theorem 2] for a proof of the following characterization.Proposition.I is nowhere precipitous if and only if Empty has a winning strategy in G(I). (shrink)

We introduce the notion of skinniness for subsets of $\mathcal{P}_\kappa \lambda$ and its variants, namely skinnier and skinniest. We show that under some cardinal arithmetical assumptions, precipitousness or $2^\lambda$-saturation of $\mathrm{NS}_{\kappa\lambda}\mid X$, where $\mathrm{NS}_{\kappa\lambda}$ denotes the non-stationary ideal over $\mathcal{P}_\kappa \lambda$, implies the existence of a skinny stationary subset of $X$. We also show that if $\lambda$ is a singular cardinal, then there is no skinnier stationary subset of $\mathcal{P}_\kappa \lambda$. Furthermore, if $\lambda$ is a strong limit singular cardinal, there (...) is no skinny stationary subset of $\mathcal{P}_\kappa \lambda$. Combining these results, we show that if $\lambda$ is a strong limit singular cardinal, then $\mathrm{NS}_{\kappa\lambda}\mid X$ can satisfy neither precipitousness nor $2^\lambda$-saturation for every stationary $X \subseteq \mathcal{P}_\kappa \lambda$. We also indicate that $\diamondsuit_\lambda(E^{\lambda}_{<\kappa})$, where $E^{\lambda}_{<\kappa} \stackrel{\mathrm{def}}{=} \{\alpha < \lambda \mid \mathrm{cf}(\alpha) < \kappa\}$, is equivalent to the existence of a skinnier (or skinniest) stationary subset of $\mathcal{P}_\kappa \lambda$ under some cardinal arithmetical hypotheses. (shrink)

We show that if $\kappa$ is an inaccessible cardinal then $P_\kappa\lambda$ splits into $\lambda^{<\kappa}$ many disjoint stationary subsets. We also show that if $P_\kappa\lambda$ carries a strongly saturated ideal then the nonstationary ideal cannot be $\lambda^+$-saturated.

A collection of essays discussing the philosophy and foundations of quantum gravity. Written by leading philosophers and physicists in the field, chapters cover the important conceptual questions in the search for a quantum theory of gravity, and the current state of understanding among philosophers and physicists.

String theory promises to be able to provide us with a working theory of quantum gravity and a unified description of all fundamental forces. In string theory there are so called ‘dualities’; i.e. different theoretical formulations that are physically equivalent. In this article these dualities are investigated from a philosophical point of view. Semantic and epistemic questions relating to the problem of underdetermination of theories by data and the debate on realism concerning scientific theories are discussed. Depending on ones views (...) on semantic issues and realism different interpretations are possible of the dualities. (shrink)

String theory has been the dominating research field in theoretical physics during the last decades. Despite the considerable time elapse, no new testable predictions have been derived by string theorists and it is understandable that doubts have been voiced. Some people have argued that it is time to give up since testability is wanting. But the majority has not been convinced and they continue to believe that string theory is the right way to go. This situation is interesting for philosophy (...) of science since it highlights several of our central issues. In this paper we will discuss string theory from a number of different perspectives in general methodology. We will also relate the realism/antirealism debate to the current status of string theory. Our goal is two-fold; both to take a look at string theory from philosophical perspectives and to use string theory as a test case for some philosophical issues. (shrink)

The modeling of black holes is an important desideratum for any quantum theory of gravity. Not only is a classical black hole metric sought, but also agreement with the laws of black hole thermodynamics. In this paper, we describe how these goals are achieved in string theory. We review black hole thermodynamics, and then explicate the general stringy derivation of classical spacetimes, the construction of a simple black hole solution, and the derivation of its entropy. With that in hand, we (...) address some important philosophical and conceptual questions: the confirmatory value of the derivation, the bearing of the model on recent discussions of the so-called ‘information paradox’, and the implications of the model for the nature of space. (shrink)

This is a nontechnical overview of how various approaches to quantum gravity suggest modifications to the way we conceptualize space and time. A theory of quantum gravity is needed to reconcile quantum physics with general relativity, our best theory for gravity. The most popular approaches to quantum gravity are string theory and loop quantum gravity. So far, no approach has been empirically successful, and there is no commonly accepted theory. Thus, the conclusions presented here are tentative. Many approaches suggest that (...) space and time—or perhaps, it is better to talk about spacetime—might not be fundamental. Various views on how to think about time in quantum gravity are briefly presented. (shrink)

八代将軍吉宗の世、思想界に現れた二つの新興勢力・徂徠学と国学。当時の主流たる朱子学を否定した両「古学派」の進展を考察する。.

Che 1-kwŏn. Kodae-kŭndae sasang -- che 2-kwŏn. Hyŏndae sasang.

Many contemporary physicists suggest that we should take the claim that we live in a multiverse seriously. When doing this they often invoke arguments based on the controversial anthropic principle. Critics argue that this leads to untestable and unscientific theories. In this paper criteria are suggested that need to be satisfied before a multiverse theory should be considered scientifically respectable. One important point is that the multiverse is described in sufficient detail. In some cases, a multiverse theory can be testable; (...) however, to properly test a multiverse theory it is important to distinguish new predictions from explanations based on the multiverse. (shrink)

In this paper, some conceptual issues are addressed in order to make sense of what string theory is supposed to tell us about spacetime. The dualities in string theory are used as a starting point for our argumentation. We explore the consequences of a standard view towards these dualities, namely that the dual descriptions represent the same physical situation. Given this view, one has to understand string theory in a manner such that what counts as physical spacetime is based only (...) on the shared physical content—or common core—of the dual descriptions. In general such a spatiotemporal picture does not have to agree with, or be similar to, any of the ones suggested by naïve readings of the dual descriptions. However, in certain regimes or limits, one or the other of the initial dual descriptions may give a good effective description of physical spacetime. (shrink)

String theory has been very influential within theoretical physics for the past few decades. It is the most popular attempt to solve the problem of formulating a viable theory of quantum gravity. Furthermore, it also unifies the other fundamental forces within one theoretical framework. In string theory, it is assumed that what before was thought to be point particles should really be seen as one-dimensional extended entities, i.e. strings. Different particles are supposed to correspond to various vibrational patterns of the (...) strings.In recent years, much critique has been directed towards string theory, and the fact that it inhabits such a strong position within the theoretical physics community. The main complaint is the complete lack of empirical confirmation of new predictions derived from string theory. The books, criticizing string theory, that have received most attention are the ones written by Smolin (2006), Woit (2006), but there are many more critics some of which express much harsher criticism towards string theory than the above-mentioned authors. (shrink)

The associative theory of creativity states that creativity is associated with differences in the structure of semantic memory, whereas the executive theory of creativity emphasises the role of top-down control for creative thought. For a powerful test of these accounts, individual semantic memory structure was modelled with a novel method based on semantic relatedness judgements and different criteria for network filtering were compared. The executive account was supported by a correlation between creative ability and broad retrieval ability. The associative account (...) was independently supported, when network filtering was based on a relatedness threshold, but not when it was based on a fixed edge number or on the analysis of weighted networks. In the former case, creative ability was associated with shorter average path lengths and higher clustering of the network, suggesting that the semantic networks of creative people show higher small-worldness. (shrink)

001. 王陽明의 철학사상 002. 현대의 시대적 상황 003. 양명학의 형성 배경 004. 기존 학설과 양명학 005. 왕양명의 심즉이론 006. 왕양명의 지행합일체 007. 왕양명의 치량지론 008. 왕양명의 이상사회 사상 009. 왕양명의 군사사상 010. 왕양명의 영향과 전개 011. 동, 서의 양명학 012. 한국의 양명학 013. 양명학의 조선 전래 014. 양명학에 대한 비판 015. 전래 초기의 양명학 수용 016. 조선조 양명학의 태두 정제두 017. 하곡 이후의 양명학 018. 겸곡 박은식의 양명학 019. 애당 정인보의 양명학.

『三太郎の日記』による栄光の後に襲ってきた波乱。同時代の知識人との関係や教育制度から、大正教養派の代表者に迫る社会史的評伝。.