Given a regular infinite cardinal κ and a cardinal λ > κ, we study fine ideals H on Pκ that satisfy the square brackets partition relation equation image, where μ is a cardinal ≥2.

Let τ : F → N be a type of a variety V . Every partition Pof the set F determines a so-called P-compatible variety. We consider thevarieties GnP defined by so-called P-compatible identities of Abelian groupswith exponent n. Besides, we study a connection between the lattice of allpartitions of the set F and the lattice of all subvarieties of the variety definedby some kind of P-compatible identities — externally compatible identitiessatisfied in the class of all Abelian groups with exponent (...) n. (shrink)

_ Source: _Volume 7, Issue 1, pp 26 - 52 This is an explication and defense of P. F. Strawson’s naturalist theory of free will and moral responsibility. I respond to a set of criticisms of the view by free will skeptics, compatibilists, and libertarians who adopt the _core assumption_: Strawson thinks that our reactive attitudes provide the basis for a rational justification of our blaming and praising practices. My primary aim is to explain and defend Strawson’s naturalism in light (...) of criticisms based on the core assumption. Strawson’s critiques of incompatibilism and free will skepticism are not intended to provide rational justifications for either compatibilism or the claim that some persons have free will. Hence, the charge that Strawson’s “arguments” are faulty is misplaced. The core assumption resting behind such critiques is mistaken. (shrink)

In [12], P. Scowcroft and L. van den Dries proved a cell decomposition theorem for p-adically closed fields. We work here with the notion of P-minimal fields defined by D. Haskell and D. Macpherson in [6]. We prove that a P-minimal field K admits cell decomposition if and only if K has definable selection. A preprint version in French of this result appeared as a prepublication [8].

We show that if κ is an infinite successor cardinal, and λ > κ a cardinal of cofinality less than κ satisfying certain conditions, then no ideal on Pκ is weakly λ+-saturated. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The p value is the probability under the null hypothesis of obtaining an experimental result that is at least as extreme as the one that we have actually obtained. That probability plays a crucial role in frequentist statistical inferences. But if we take the word ‘extreme’ to mean ‘improbable’, then we can show that this type of inference can be very problematic. In this paper, I argue that it is a mistake to make such an interpretation. Under minimal assumptions about (...) the alternative hypothesis, I explain why ‘extreme’ means ‘outside the most precise predicted range of experimental outcomes for a given upper bound probability of error’. Doing so, I rebut recent formulations of recurrent criticisms against the frequentist approach in statistics and underscore the importance of random variables. (shrink)

Huey P. Newton, founder of the Black Panther Party, is perhaps one of the most interesting and intriguing American intellectuals from the last half of the 20th century. Newton’s genius rested in his ability to amalgamate and synthesize others’ thinking, and then reinterpreting and making it relevant to the situation that existed in the United States in his time, particularly for African-Americans in the densely populated urban centers in the North and West. Newton saw himself continuing the Marxist-Leninist tradition and (...) one of the most important aspects of his thought was his reinterpretation of Marxist class structure. This paper presents Newton’s position that it is the urban poor—who Newton identifies with the lumpenproletariat—that act as the revolutionary class that will bring about a change in the socio-economic order. To that end, there is first a discussion of Newton’s view of the lumpenproletariat and how it differs from the traditional Marxist understanding. Then there is an explanation of the role of the vanguard and its relationship to the lumpenproletariat. The paper concludes with a comparison of Frantz Fanon’s and Newton’s understanding of the lumpenproletariat, and responds to the “problem of lumpenization” in the Black Panther Party. (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 introduce a very weak language L M on p-adic fields K, which is just rich enough to have exactly the same definable subsets of the line K that one has using the ring language. (In our context, definable always means definable with parameters.) We prove that the only definable functions in the language L M are trivial functions. We also give a definitional expansion $L\begin{array}{*{20}{c}} ' \\ M \\ \end{array} $ of L M in which K has quantifier elimination, (...) and we obtain a cell decomposition result for L M -definable sets. Our language L M can serve as a p-adic analogue of the very weak language (<) on the real numbers, to define a notion of minimality on the field of p-adic numbers and on related valued fields. These fields are not necessarily Henselian and may have positive characteristic. (shrink)

This paper is a detailed examination of some parts of J. P. Moreland's book on "the argument from consciousness". (There is a companion article that discusses the parts of the book not taken up in this critical notice.).

In this paper we present two types of logics and \ ) where certain p-adic functions are associated to propositional formulas. Logics of the former type are p-adic valued probability logics. In each of these logics we use probability formulas K r,ρ α and D ρ α,β which enable us to make sentences of the form “the probability of α belongs to the p-adic ball with the center r and the radius ρ”, and “the p-adic distance between the probabilities of (...) α and β is less than or equal to ρ”, respectively. Logics of the later type formalize processes of thinking where information are coded by p-adic numbers. We use the same operators as above, but in this formalism K r,ρ α means “the p-adic code of the information α belongs to the p-adic ball with the center r and the radius ρ”, while D ρ α,β means “the p-adic distance between codes of α and β are less than or equal to ρ”. The corresponding strongly complete axiom systems are presented and decidability of the satisfiability problem for each logic is proved. (shrink)

In the same year, 1961, Peter D. Mitchell and Robert R.J.P. Williams both put forward hypotheses for the mechanism of oxidative phosphorylation in mitochondria and photophosphorylation in chloroplasts. Mitchell's proposal was ultimately adopted and became known as the chemiosmotic theory. Both hypotheses were based on protons and differed markedly from the then prevailing chemical theory originally proposed by E.C. Slater in 1953, which by 1961 was failing to account for a number of experimental observations. Immediately following the publication of Williams (...) 's hypothesis and before his own was published, Mitchell initiated a correspondence. Examination of the letters shows the development of a dispute based on the validity of the proposals, who should have priority and particularly whether Mitchell had drawn on Williams 's work without acknowledgement. We have concluded that Mitchell's proposals were original although it is evident that prior to the correspondence Williams had considered and rejected a proposition similar to Mitchell's theory. However, a major cause of the dispute was the difference in disciplinary backgrounds of Mitchell, a microbial biochemist and Williams, a chemist. (shrink)

In this article we present a p-adic valued probabilistic logic equation image which is a complete and decidable extension of classical propositional logic. The key feature of equation image lies in ability to formally express boundaries of probability values of classical formulas in the field equation image of p-adic numbers via classical connectives and modal-like operators of the form Kr, ρ. Namely, equation image is designed in such a way that the elementary probability sentences Kr, ρα actually do have their (...) intended meaning—the probability of propositional formula α is in the equation image-ball with the center r and the radius ρ. Due to modal nature of the operators Kr, ρ, it was natural to use the probability Kripke like models as equation image-structures, provided that probability functions range over equation image instead of equation image or equation image. (shrink)

Given a regular uncountable cardinal κ and a cardinal λ > κ of cofinality ω, we show that the restriction of the non-stationary ideal on Pκ to the set of all a with equation image is not λ++-saturated . We actually prove the stronger result that there is equation image with |Q| = λ++ such that A∩B is a non-cofinal subset of Pκ for any two distinct members A, B of Q, where NGκ, λ denotes the game ideal on Pκ. (...) We also remark that for κ > ω1, adding λ+3 Cohen subsets of ω1 to equation image makes NGκ, λ λ+3-saturated. (shrink)

_ Source: _Page Count 27 This is an explication and defense of P. F. Strawson’s naturalist theory of free will and moral responsibility. I respond to a set of criticisms of the view by free will skeptics, compatibilists, and libertarians who adopt the _core assumption_: Strawson thinks that our reactive attitudes provide the basis for a rational justification of our blaming and praising practices. My primary aim is to explain and defend Strawson’s naturalism in light of criticisms based on the (...) core assumption. Strawson’s critiques of incompatibilism and free will skepticism are not intended to provide rational justifications for either compatibilism or the claim that some persons have free will. Hence, the charge that Strawson’s “arguments” are faulty is misplaced. The core assumption resting behind such critiques is mistaken. (shrink)

This is a study of the Ugandan poet and cultural critic Okot p'Bitek. In his poems and critical essays, Okot engages with the oral traditions of his people—the songs, dances, funeral dirges, and so forth—seeing them as manifestations of the people's philosophy of life. Imbo's book aims to make explicit the philosophical questions raised in Okot's work, placing them within the wider picture of contemporary African philosophy as a whole.

Building upon earlier work of Donna Carr, Don Pelletier, Chris Johnson, Shu-Guo Zhang and others, we show that a normal ideal J on Pκ is strongly normal if and only if J+→< 2 for every μ < κ, and we describe the least normal ideal J on Pκ such that J+ →< 2.

The paper examines the claim that significance testing violates the Principle of Total Evidence. I argue that p-values violate PTE for two-sided tests but satisfy PTE for one-sided tests invoking a sufficient test statistic independent of the preferred theory of evidence. While the focus of the paper is to evaluate a particular claim about the relationship of significance testing and PTE, I clarify the reading of this methodological principle along the way.

We classify ultrafilters on ω with respect to sequential contours (see [4].[5]) of different ranks. In this way we obtain an ω1 sequence {Pα}1≤α≤ω1 of disjoint classes. We prove that non-emptiness of Pα for successor α ≥ 2 is equivalent to the existence of P-point. We investigate relations between P-hierarchy and ordinal ultrafilters (introduced by J. E. Baumgartner in [1]), we prove that it is relatively consistent with ZFC that the successor classes (for α ≥ 2) of P-hierarchy and ordinal (...) ultrafilters intersect but are not the same. (shrink)

In the face of continuing assumptions by many scientists and journal editors that p-values provide a gold standard for inference, counter warnings are published periodically. But the core problem is not with p-values, per se. A finding that “p-value is less than α” could merely signal that a critical value has been exceeded. The question is why, when estimating a parameter, we provide a range (a confidence interval), but when testing a hypothesis about a parameter (e.g. µ = x) we (...) proceed as if “=” entails exact equality of the parameter with x. That standard is hard to meet, and is not a standard expected for power calculations, where we are satisfied to reject a null hypothesis H0 if the result is merely “detectably” different from (exact) H0. This paper explores, with resampling (simulation) methods, the impacts on p-values, and alternatives, if the null hypothesis is defined as a thick or thin range of values. It also examines, empirically, the extent to which the p-value may or may not be a good predictor of the probability that H0 is true, given the distribution of the data. (shrink)

_ Source: _Page Count 27 This is an explication and defense of P. F. Strawson’s naturalist theory of free will and moral responsibility. I respond to a set of criticisms of the view by free will skeptics, compatibilists, and libertarians who adopt the _core assumption_: Strawson thinks that our reactive attitudes provide the basis for a rational justification of our blaming and praising practices. My primary aim is to explain and defend Strawson’s naturalism in light of criticisms based on the (...) core assumption. Strawson’s critiques of incompatibilism and free will skepticism are not intended to provide rational justifications for either compatibilism or the claim that some persons have free will. Hence, the charge that Strawson’s “arguments” are faulty is misplaced. The core assumption resting behind such critiques is mistaken. (shrink)

This article is a discussion of the political thought of Huey P. Newton, and by extension, the theory and practice of the Black Panther Party. More specifically, this article will explore a tension that exists between Newton's theory of Intercommunalism and the Black Panther Party Platform. To that end, there is, first, a discussion of the ideological development of the Black Panther Party, which culminated in Newton's theory of Intercommunalism. Second, there is a presentation of what will be broadly construed (...) as the Party Platform, which articulates the basic principles and practices of the Black Panther Party. Finally, there is a discussion of several ways in which there seems to be a conflict between Newton's ideology and his political practice. While some are only apparent contradictions, there does remain a deep conflict between the dialectical basis of Intercommunalism and the foundational basis of the Party Platform. (shrink)

Legal translation has become a principal means to unfold Chinese laws to the world in the global era and the study of it has proved to be of practical significance. Since the proper theory guidance is the key to the quality of LT translation, this paper focuses on the Skopos theory and the strategies applied in the practice of LT. A case study of LT examples from the Criminal Law of the P.R.C. has been made while briefly reviewing the Skopos (...) theory and its principles. Started with short discussion of LT, this paper probes into the applicability of the three principles of Skopos theory, including the Skopos rule, the coherence rule and the fidelity rule, into the legal texts, especially into the translation of the Criminal Law of the P.R.C. and based on the study, the strategies for LT are proposed, with the hope that it can be useful for reference in other legal texts. (shrink)

We prove the following version of Hechler's classical theorem: For each partially ordered set (Q, ≤) with the property that every countable subset of Q has a strict upper bound in Q, there is a ccc forcing notion such that in the generic extension for each tall analytic P-ideal J (coded in the ground model) a cofinal subset of (J, ⊆*) is order isomorphic to (Q, ≤).

We answer a question of Cummings and Magidor by proving that the P-ideal dichotomy of Todorčević refutes ${\square}_{\kappa, \omega}$ for any uncountable $\kappa$. We also show that the P-ideal dichotomy implies the failure of ${\square}_{\kappa, < \mathfrak{b}}$ provided that $cf(\kappa) > {\omega}_{1}$.

We study a reduct ${\mathcal{L}_*}$ of the ring language where multiplication is restricted to a neighbourhood of zero. The language is chosen such that for p-adically closed fields K, the ${\mathcal{L}_*}$ -definable subsets of K coincide with the semi-algebraic subsets of K. Hence structures (K, ${\mathcal{L}_*}$ ) can be seen as the p-adic counterpart of the o-minimal structure of semibounded sets. We show that in this language, p-adically closed fields admit cell decomposition, using cells similar to p-adic semi-algebraic cells. From (...) this we can derive quantifier-elimination, and give a characterization of definable functions. In particular, we conclude that multiplication can only be defined on bounded sets, and we consider the existence of definable Skolem functions. (shrink)

Salvo contadas excepciones, el itinerario de Antonio Gramsci en la Argentina es generalmente asociado a los gramscianos argentinos reunidos en la revista Pasado y presente, encabezada por José Aricó, sin atender a su historia previa. Sin embargo, se olvida u omite que la introducción del pensamiento de Gramsci en este país fue realizada por Héctor P. Agosti, quien ejerció una notable influencia en muchos de aquellos jóvenes que luego confluirían en el grupo en torno a Aricó. El objetivo de este (...) trabajo es, más allá de las observaciones que se hacen sobre los detractores de Agosti, contribuir a la difusión, y presentación en algunos casos, del pensamiento de uno de los intelectuales más notables que ha dado el Partido Comunista Argentino . Se pretende profundizar en algunos de los vínculos entre las elaboraciones teóricas de Agosti y las de Gramsci que no han sido suficientemente atendidos, así como incidir en el papel que Agosti tuvo en la inserción del pensador italiano en el debate comunista argentino. (shrink)

p-consequence is intended as a formalization of non-deductive reasoning. So far semantical or general properties have been presented more thoroughly ([2]–[5]). In the present paper we would like to focus on its syntactic properties.

We investigate the partition property of ${\mathcal{P}_{\kappa}\lambda}$ . Main results of this paper are as follows: (1) If λ is the least cardinal greater than κ such that ${\mathcal{P}_{\kappa}\lambda}$ carries a (λ κ , 2)-distributive normal ideal without the partition property, then λ is ${\Pi^1_n}$ -indescribable for all n < ω but not ${\Pi^2_1}$ -indescribable. (2) If cf(λ) ≥ κ, then every ineffable subset of ${\mathcal{P}_{\kappa}\lambda}$ has the partition property. (3) If cf(λ) ≥ κ, then the completely ineffable ideal over (...) ${\mathcal{P}_{\kappa}\lambda}$ has the partition property. (shrink)

Review on Realist conception of Truth, of the W. P. Alston.

Given a regular cardinal κ > ω 1 and a cardinal λ with κ ≤ cf (λ) < λ, we show that NS κ,λ | T is not λ+-saturated, where T is the set of all ${a\in P_\kappa (\lambda)}$ such that ${| a | = | a \cap \kappa|}$ and ${{\rm cf} \big( {\rm sup} (a\cap\kappa)\big) = {\rm cf} \big({\rm sup} (a)\big) = \omega}$.

We prove the existence of p-ideals that are nonmeagre subsets of P(ω) under various set-theoretic assumptions.

For each vertex of a simple polygon P an integer valued weight is given. We consider the path p1, p2, ..., pk in P which is created according to the following strategy: p1 is a designated start vertex s and pi+1 is obtained by choosing the vertex with smallest weight among all vertices visible from pi and different from p1, p2, ..., pi. If there is no such vertex the path is finished. This path is called geometric lexicographic dead end (...) path. We shall prove the problem of determining whether a distinguished vertex t of P is on the geometric lexicographic dead end path or not to be P-complete. (shrink)

We develop a notion of cell decomposition suitable for studying weak p-adic structures definable). As an example, we consider a structure with restricted addition.

We characterize some large cardinal properties, such as $\mu$-measurability and $P^2(\kappa)$-measurability, in terms of ultrafilters, and then explore the Rudin-Keisler (RK) relations between these ultrafilters and supercompact measures on $P_\kappa(2^\kappa)$. This leads to the characterization of $2^\kappa$-supercompactness in terms of a measure on measure sequences, and also to the study of a certain natural subset, $\mathrm{Full}_\kappa$, of $P_\kappa(2^\kappa)$, whose elements code measures on cardinals less than $\kappa$. The hypothesis that $\mathrm{Full}_\kappa$ is stationary (a weaker assumption than $2^\kappa$-supercompactness) is equivalent to (...) a higher order Lowenheim-Skolem property, and settles a question about directed versus chain-type unions on $P_\kappa\lambda$. (shrink)

In the present paper we give syntactical and semantical characterization of the class of algebras defined by P-compatible identities of modular ortholattices. We also describe the lattice of some subvarieties of the variety MOL Ex defined by so called externally compatible identities of modular ortholattices.

The article addresses the emerging framework of ‘positioning theory’, which has become influential in educational theory. We will present the central concepts and ideas of ‘positioning theory’ and subsequently how they are being used to contribute to educational theory. We will focus on an article by Svend Brinkmann where he uses ‘positioning theory’ as the foundation for moral education. Seemingly, Brinkmann uses ‘positioning theory’ rather uncritically in an attempt to ‘strengthen’ the educational process by introducing fixed categorisations and concepts to (...) it. Contrary to this approach, we will use the educational theories of Knud Grue-Sørensen and Gert Biesta to emphasise how we instead should recognise what is here defi ned as the ‘weakness’ of educational theory, and how we have to consider both the adaptive element of education as well as the emancipatory element of it. (shrink)

For a regular cardinal κ with κ<κ = κ and κ ≤ λ , we construct generically a subset S of {x ∈ Pκλ : x ∩ κ is a singular ordinal} such that S is stationary in a strong sense but the stationarity of S can be destroyed by a κ+-c. c. forcing ℙ* which does not add any new element of Pκλ . Actually ℙ* can be chosen so that ℙ* is κ-strategically closed. However we show that such (...) ℙ* itself cannot be κ-strategically closed or even <κ-strategically closed if κ is inaccessible. (shrink)

We prove that all infinite Boolean rings have the property P ≠ NP according to the digital nondeterminism.

We study the partition relation $X@>{\rm w}>>[Y]_{p}^{2}$ that is a weakening of the usual partition relation $X\rightarrow [Y]_{p}^{2}$ . Our main result asserts that if κ is an uncountable strongly compact cardinal and $\germ{d}_{\kappa}\leq \lambda ^{<\kappa}$ , then $I_{\kappa,\lambda}^{+}@>{\rm w}>>[I_{\kappa,\lambda}^{+}]_{\lambda <\kappa}^{2}$ does not hold.

This is an encyclopedia entry for William P. Alston.

In this paper, it will be argued that the concept of ‘Bildung’ has a twofold role in pedagogical research. On the one hand, it holds a position for conceptual analysis and discussions of how a pedagogical relation is established between an individual and the world. In this sense, it belongs to theoretical pedagogics. Humboldt concepts of receptivity and self-determination and Klafki’s theory of categorial pedagogy are central contributions to this discussion. On the other hand, the concept of Bildung has a (...) role as a regulative idea due to the ideas and imaginations of various forms of humanity it contains. In this sense, it fulfills an ethical dimension since it is regulative for the pedagogical relationship between individual and world. (shrink)

Evidence that led to the hypothesis of a backwards referral of conscious sensory experiences in time, and the experimental tests of its predictions, is summarized. Criticisms of the data and the conclusion by Churchland that this hypothesis is untenable are analysed and found to be based upon misconceptions and faulty evaluations of facts and theory. Subjective referral in time violates no neurophysiological principles or data and is compatible with the theory of "mental" and "physical" correspondence.

This article shows that Popper’s measure of corroboration is inapplicable if, as Popper argued, the logical probability of synthetic universal statements is zero relative to any evidence that we might possess. It goes on to show that Popper’s definition of degree of testability, in terms of degree of logical content, suffers from a similar problem. 1 The Corroboration Function and P(h|b) 2 Degrees of Testability and P(h|b).