Sābūr ibn Sahl's al-Aqrābādhīn al-saghīr is the earliest Arabic pharmacopoeia known to have survived. Finding fragments of Sābūr's pharmacopoeia in the Cairo Genizah shows that it was used by the medical practitioners of the Jewish community of Cairo, possibly long after it is supposed to have been superceded by other works. We present here a synoptic edition of two Arabic fragments, T-S Ar. 40.5 and Ar. 41.90. These fragments overlap to a large extent, but are not exactly the same. We (...) suggest that one may be the work of a professional scribe, while the other was copied by a practitioner for his personal use. (shrink)

Arabian Drugs in Early Medieval Mediterranean Medicine. By Zohar Amar and Efraim Lev. Edinburgh Studies in Classical Islamic History and Culture. Edinburgh: Edinburgh University Press, 2017. Pp. xiv + 290, ills. $125, £80.

Sovereign Wealth Funds have attracted significant attention over the past few years, as a result of their increasing role in the global economy and their controversial minority investments in distressed financial and infrastructure companies in Western economies. Although SWFs provide important benefits to home, host and global markets, they have been perceived by the Western mind as a growing threat to economic supremacy and national security. While the current legal scholarship provides an incomplete policy response, by either selectively referring to (...) specific legal instruments within the international law framework or proposing an entirely new legal regime, this Article attempts to address this crucial lacuna by providing an original and comprehensive legal analysis of the SWF phenomenon and its interaction with the preexisting framework of international law. The various abovementioned concerns have prompted various Western attempts to block SWF cross-border investments through legislative reforms or ad hoc protectionism of the executive branch. These governmental policies frequently violate international commitments in the international economic law arena and call for a closer look at the nature of such commitments and their respective implementation in the SWF environment. The Article looks at recent practices in Western countries aimed at blocking SWF investments, especially in the context of iconic brands and national champions. It then reviews various relevant provisions in international legal instruments, which are applicable to these potential investments, and examines the question of their violation by capital-importing countries. A proposed innovative adaptation to this new reality is provided. I argue that the existing framework of international investment law can provide adequate solutions to investment protectionism against SWFs. Regarding regulation of SWFs’ investments, since recent experience has underlined that SWFs function largely like any other commercial entities, there is a need to shift the discussion and terminology towards regulation of sovereign activity rather than sovereign funds. Finally, the Article explores the broad consequences of investment law and corporate governance reforms following the debate around SWF investments on maintaining healthy and productive cross-border economic relations in a globalized world. (shrink)

Niche Construction Theory has been gaining acceptance as an explanatory framework for processes in biological and human evolution. Human cultural niche construction, in particular, is suggested as a basis for understanding many phenomena that involve human genetic and cultural evolution. Herein I assess the ability of the cultural niche construction framework to meet this explanatory role by looking into several NCT-inspired accounts that have been offered for two important episodes of human evolution, and by examining the contribution of NCT to (...) the elucidation of two “primary examples” mentioned often in the NCT literature. The result, I claim, is rather disappointing: While NCT may serve as a descriptive framework for these phenomena, it cannot be said to explain them in any substantive sense. Especially disturbing is NCT’s failure to account for differing developments in very similar situations, and to facilitate evaluation and discrimination between divergent and contradictory causal accounts of particular phenomena. I argue that these problems are inherent, and they render NCT unsuitable to serve as an explanatory framework for human phenomena. NCT’s value, at least as related to human phenomena, is therefore descriptive and heuristic rather than explanatory. In conclusion, I discuss and reject comparisons made between NCT and the theory of natural selection, and examine several potential sources of NCT’s explanatory weakness. (shrink)

This article examines the effect of material evidence upon historiographic hypotheses. Through a series of successive Bayesian conditionalizations, I analyze the extended competition among several hypotheses that offered different accounts of the transition between the Bronze Age and the Iron Age in Palestine and in particular to the “emergence of Israel”. The model reconstructs, with low sensitivity to initial assumptions, the actual outcomes including a complete alteration of the scientific consensus. Several known issues of Bayesian confirmation, including the problem of (...) old evidence, the introduction and confirmation of novel theories and the sensitivity of convergence to uncertain and disputed evidence are discussed in relation to the model’s result and the actual historical process. The most important result is that convergence of probabilities and of scientific opinion is indeed possible when advocates of rival hypotheses hold similar judgment about the factual content of evidence, even if they differ sharply in their historiographic interpretation. This speaks against the contention that understanding of present remains is so irrevocably biased by theoretical and cultural presumptions as to make an objective assessment impossible. (shrink)

Inferences from the absence of evidence to something are common in ordinary speech, but when used in scientific argumentations are usually considered deficient or outright false. Yet, as demonstrated here with the help of various examples, archaeologists frequently use inferences and reasoning from absence, often allowing it a status on par with inferences from tangible evidence. This discrepancy has not been examined so far. The article analyses it drawing on philosophical discussions concerning the validity of inference from absence, using probabilistic (...) models that were originally developed to show that such inferences are weak and inconclusive. The analysis reveals that inference from absence can indeed be justified in many important situations of archaeological research, such as excavations carried out to explore the past existence and time-span of sedentary human habitation. The justification is closely related to the fact that archaeology explores the human past via its material remains. The same analysis points to instances where inference from absence can have comparable validity in other historical sciences, and to research questions in which archaeological inference from absence will be problematic or totally unwarranted. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 63.4 (2002) 717-733 [Access article in PDF] The Voice of Poetry in the Thought of Michael Oakeshott Efraim Podoksik The British philosopher Michael Oakeshott (1901-1990) is mostly known as a political thinker of conservative persuasion, and his general philosophy is usually analyzed only in connection with the social and political aspects of his thought, with most attention being paid to his discussion (...) of practical wisdom, rationalism, and tradition. 1 Yet social theory and politics were by no means Oakeshott's only preoccupation. Among the subjects of his books and essays are philosophies of history, science, and aesthetics. 2 A close look at these writings exposes a different Oakeshott, not a conservative defender of the importance of practice and tradition but a radical thinker familiar with the trends of his own time and deeply influenced by them.Among those philosophies aesthetics is perhaps the most obscure one. Indeed, the significance of aesthetics for Oakeshott is readily recognized by commentators. His thought is often portrayed as having a strong aesthetic dimension. Thus, the influence of the Renaissance and Romanticism on his worldview is emphasized, he is sometimes compared with European existentialists, and one commentator even described his life as "poetic, not prosaic." 3 But, there [End Page 717] are relatively few studies outlining the development of Oakeshott's aesthetic theory. 4 These are usually found in short chapters in general surveys of Oakeshott's philosophy. Thus, W. H. Greenleaf analyzes Oakeshott's theory of aesthetics in the context of the idealistic tradition exemplified by Hegel, Croce, and Collingwood; Robert Grant discusses and rejects what he sees as the deceptive parallels between Oakeshott and the Bloomsbury group, and Andrew Sullivan argues that an aesthetic dimension is present in Oakeshott's concepts of practice and politics. 5Reasons for this neglect may lie in the fact that Oakeshott wrote little about aesthetics and that he was very ambiguous in his views on the character of this form of human experience. He formulated his views on science and history relatively early and never departed from them afterwards. These are first presented in the philosophical treatise Experience and Its Modes (1933).By contrast, it took him a long time to elaborate a coherent theory of aesthetics. It appears only in the essay "The Voice of Poetry in the Conversation of Mankind," first published in 1959. This theory, however, occupies a central place in Oakeshott's mature philosophy as he radically defends "poetry" as one of the independent worldviews which constitute the character of modern experience. The purpose of this paper is to present the development of Oakeshott's view of the autonomy of aesthetic experience within its intellectual context.Oakeshott's interest in art is visible in his early publications in which he tends to recognize the independent character of aesthetic experience. He makes clear the attitude towards art he is defending in his first student article which discusses the character of Shylock in Shakespeare's drama. Oakeshott is attracted by Shakespeare's ability to describe a villain as a character and by his capacity for sympathy for a personality, some of whose traits he may have loathed. That such sympathy does not imply any absolute moral standard makes Shakespeare's description more profound, for "life is more complex than to foster heroes and villains of the conventional type." 6Oakeshott is opposed to the vulgar moralization of art and argues that the artist is able to present a deeper and more complex view of life whereall characters "have some intrinsic value of their own." 7 In the inter-war period in [End Page 718] which artists were often demanded to serve one or another social cause this position was not as commonplace as it is now. Oakeshott aligned himself with thetrend usually called "aestheticism" in England or l'art pour l'art in France, which had been at the peak of its influence at the end of the nineteenth and the beginning of the twentieth century and, while still quite popular in the twenties, was being... (shrink)

Several scholars observed that narratives about the human past are evaluated comparatively. Few attempts have been made, however, to explore how such evaluations are actually done. Here I look at a lengthy “contest” among several historiographic narratives, all constructed to make sense of another one—the biblical story of the conquest of Canaan. I conclude that the preference of such narratives can be construed as a rational choice. In particular, an easily comprehensible and emotionally evocative narrative will give way to a (...) complex and mundane one, when the latter provides a more coherent account of the consensually accepted body of evidence. This points to a fundamental difference between historiographic narratives and fiction, contrary to some influential opinions in the philosophy of historiography. Such historiographic narratives have similarities with hypotheses and narrative explanations in natural science. (shrink)

This treatise covers the history, now more than 170 years long, of researches and debates concerning the biblical city of Ai. This archetypical chapter in the evolution of biblical archaeology and historiography was never presented in full. I use the historical data as a case study to explore a number of epistemological issues, such as the creation and revision of scientific knowledge, the formation and change of consensus, the Kuhnian model of paradigm shift, several models of discrimination between hypotheses about (...) the past, the interplay between scientists' values and their epistemic beliefs, and the truth-bearing of historiographic reconstruction. I show, in particular, that when scientists share common epistemic values they can modify their beliefs even when such changes go against deeply entrenched biases and preconceptions. Considerations of coherence usually constrain such modifications, and when sufficient data is available the result can be a profound change of beliefs. Several episodes of the "Ai debates" demonstrate, however, that similar change of beliefs will not occur when non-epistemic values take precedence. (shrink)

It is often assumed that European thought contained several conceptually distinct and equally influential notions of liberty. The article challenges this perception, arguing that European history was dominated by one concept of liberty. It attempts to show that the tendency to dismiss the idea of one concept of liberty is premature. Such an attitude is caused either by misplaced interpretations of ancient texts, by exaggerated historicism, or by an anachronistic reading of early modern political thought. The article suggests that the (...) paradigm change is in order, and that the time is ripe for composing a history of one concept of liberty. (shrink)

Past entities, events, and circumstances are neither observable nor manipulatable. Several philosophers argued that this inaccessibility precludes a realistic conception of the past. I survey versions of antirealism and agnosticism about the past formulated by Michael Dummett, Leon Goldstein, and Derek Turner. These accounts differ in their motivations and reasoning, but they share the opinion that the reality of at least large swathes of the past is unknowable. Consequently, they consider statements about them as referring, at most, to present constructs. (...) These antirealists about the past are not, however, antirealists or skeptics about time or chronology. They accept, among other things, that present traces can be dated and statements about their temporal provenances are referring and truth-apt.I posit that an antirealist who accepts that at least some of the present traces can be truth-aptly dated while holding that these traces do not support knowledge about past events and circumstances commits herself to a radically skeptic stance. Otherwise, she would be diluting her position so that it will be hardly distinguishable from realism. This problem could be avoided if antirealists about the past would extend their antirealism to estimates of the age of present traces. Such a position, however, would imply a very drastic form of scientific antirealism. I conclude that the past’s inaccessibility is insufficient to support antirealism about the past, either as a part of moderate scientific antirealism or as a stand-alone position. (shrink)

Prominent thinkers such as Jurgen Habermas and Michael Sandel are warning that biomedical enhancements will undermine fundamental political values. Yet whether biomedical enhancements will undermine such values depends on how biomedical enhancements will function, how they will be administered and to whom. Since only few enhancements are obtainable, it is difficult to tell whether these predictions are sound. Nevertheless, such warnings are extremely valuable. As a society we must, at the very least, be aware of developments that could have harmful (...) consequences. Indeed, if important values were to be jeopardized, we should take appropriate measures to protect them. This paper focuses on four central values: solidarity, personal responsibility, equality and autonomy. It delineates the conditions under which biomedical enhancements would undermine these values. It also details the circumstances under which these values would be unaffected by enhancements as well as those under which they would be promoted. Specifying these conditions is valuable; it would enable society to prepare appropriate ethical guidelines and policy responses in advance. (shrink)

The main focus of the book is the presentation of the 'inertial' view of population growth. This view provides a rather simple model for complex population dynamics, and is achieved at the level of the single species without invoking species interactions. An important part of this account is the maternal effect. Investment of mothers in the quality of their daughters makes the rate of reproduction of the current generation depend not only on the current environment, but also on the environment (...) experienced by the previous generation. (shrink)

Although Oakeshott's philosophy has received considerable attention, the vision which underlies it has been almost completely ignored. This vision, which is rooted in the intellectual debates of his epoch, cements his ideas into a coherent whole and provides a compelling defence of modernity. The main feature of Oakeshott's vision of modernity is seen here as radical plurality resulting from 'fragmentation' of experience and society. On the level of experience, modernity denies the existence of the hierarchical medieval scheme and argues that (...) there exist independent ways of understanding our world, such as science and history, which cannot be reduced to each other. On the level of society, modernity finds expression in liberal doctrine, according to which society is an aggregate of individuals each pursuing his or her own choices. For Oakeshott, to be modern means not only to recognise this condition of radical plurality but also to learn to appreciate and enjoy it. Oakeshott did not think that it was possible to find a comprehensive philosophical justification for modernity, therefore the only way to preserve modern civilisation seemed to be an appeal to sentiment. As a consequence he was a passionate defender of liberal education as the best way to underwrite the 'conversation of mankind.'. (shrink)

This article compares the sections on the qualities desirable in a wife in Abū Ḥāmid al-Ghazālī’s Iḥyāʾ ʿulūm al-dīn and Bar Hebraeus’s Ethicon, which the West Syrian writer modeled on al-Ghazālī’s work. The article first establishes that al-Ghazālī based his profile of the ideal wife on a jurisprudential discussion of the topic by his teacher, Imām al-Ḥaramayn al-Juwaynī, expanding it, however, by adding anecdotes from Sufi literature and reasoned arguments on how “the good wife” will best facilitate her husband’s devotion (...) to God. The article then moves to consider how Bar Hebraeus appropriates, reconfigures, and reframes as Christian teaching al-Ghazālī’s discussion. Finally, the article argues that the similarity between the two texts demonstrates that both carve out a particular notion of male piety intelligible and resonant in their different religious traditions and in the broader monotheistic culture of the premodern Middle East. (shrink)

The Many-Worlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.

This is a philosophical paper in favor of the many-worlds interpretation of quantum theory. The necessity of introducing many worlds is explained by analyzing a neutron interference experiment. The concept of the “measure of existence of a world” is introduced and some difficulties with the issue of probability in the framework of the MWI are resolved.

What is the most important reason for using Computer Vision methods in humanities research? In this article, I argue that the use of numerical representation and data analysis methods offers a new language for describing cultural artifacts, experiences and dynamics. The human languages such as English or Russian that developed rather recently in human evolution are not good at capturing analog properties of human sensorial and cultural experiences. These limitations become particularly worrying if we want to compare thousands, millions or (...) billions of artifacts—i.e. to study contemporary media and cultures at their new twenty-first century scale. When we instead use numerical measurements of image properties standard in Computer Vision, we can better capture details of a single artifact as well as visual differences between a number of artifacts–even if they are very small. The examples of visual dimensions that numbers can capture better then languages include color, shape, texture, contours, composition, and visual characteristics of represented faces, bodies and objects. The methods of finding structures and relationships in large numerical datasets developed in statistics and machine learning allow us to extend this analysis to very big datasets of cultural objects. Equally importantly, numerical image features used in Computer Vision also give us a new language to represent gradual and continuous temporal changes—something which natural languages are also bad at. This applies to both single artworks such as a film or a dance piece and also to changes in visual characteristics in millions of artifacts over decades or centuries. (shrink)

Analyzes principal forces that determined the direction of Camus' thought on ethics and political values.

Michael Oakeshott (1901-1990) was one of the leading British philosophers of the twentieth century. He has been influential particularly as a political philosopher, but his work reflects a range of philosophical interests that have more gradually come to be appreciated. In this volume a broad group of scholars offers a comprehensive overview of Oakeshott's philosophy, including his moral and political philosophy, his philosophy of history, science and aesthetics, and his views on the role of education. They analyse Oakeshott's ideas in (...) different intellectual contexts and assess his overall contribution to twentieth-century thought. Accessible and rich with new scholarly material, this volume will be an excellent guide for students and scholars alike. (shrink)

Jacob Talmon and Michael Oakeshott represent two opposite tendencies in the anti-totalitarian world view. Both thinkers share many central features of this broad intellectual trend, such as the equation between the Soviet and Nazi regimes, Anglophilia and the rejection of the utopian quest. Yet this basic agreement should not distract us from significant differences in attitude and temperament. Talmon, like most other critics of totalitarianism, was strongly affected by the atmosphere of a profound intellectual and political crisis in Europe, and (...) he regarded the danger of totalitarianism to be an inherent aspect of modernity itself. His liberalism was that of ‘fear’. By contrast, for Oakeshott, who believed in the strength of liberal, and specifically British, civilisation, totalitarianism was merely a child of resentment, a parasitic force with no positive message of its own. He thus displayed a greater measure of confidence in the fortunes of liberal modernity. (shrink)

It is argued that the many-worlds interpretation is by far the best interpretation of quantum mechanics. The key points of this view are viewing the wave functions of worlds in three dimensions and understanding probability through self-locating uncertainty.

Social network structure has been argued to shape the structure of languages, as well as affect the spread of innovations and the formation of conventions in the community. Specifically, theoretical and computational models of language change predict that sparsely connected communities develop more systematic languages, while tightly knit communities can maintain high levels of linguistic complexity and variability. However, the role of social network structure in the cultural evolution of languages has never been tested experimentally. Here, we present results from (...) a behavioral group communication study, in which we examined the formation of new languages created in the lab by micro‐societies that varied in their network structure. We contrasted three types of social networks: fully connected, small‐world, and scale‐free. We examined the artificial languages created by these different networks with respect to their linguistic structure, communicative success, stability, and convergence. Results did not reveal any effect of network structure for any measure, with all languages becoming similarly more systematic, more accurate, more stable, and more shared over time. At the same time, small‐world networks showed the greatest variation in their convergence, stabilization, and emerging structure patterns, indicating that network structure can influence the community's susceptibility to random linguistic changes (i.e., drift). (shrink)

This article argues that Oakeshott's theory of freedom possesses a greater degree of coherence than is often perceived. Freedom in Oakeshott's philosophy may be defined as `recognized contingency', combining the notions of a genuine choice of action and of an agent's awareness of having such a choice. Oakeshott employs his notion of freedom in two different contexts. One is the context in which freedom is understood as a concept distinguishing what is conceived as `human' from what is conceived as `non-human'. (...) The other context is that of membership in societies, which under certain circumstances can be characterized either by the presence or the lack of freedom. The article argues that, while at first glance Oakeshott's ideas look counter-intuitive, at a deeper level this understanding of freedom is akin to that prevalent in the consciousness of modern liberal societies. (shrink)

We elaborate Weiermann-style phase transitions for well-partial-orderings (wpo) determined by iterated finite sequences under Higman-Friedman style embedding with Gordeev’s symmetric gap condition. For every d-times iterated wpo \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d}\right)}$$\end{document} in question, d > 1, we fix a natural extension of Peano Arithmetic, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T \supseteq \sf{PA}}$$\end{document}, that proves the corresponding second-order sentence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{WPO}\left({\rm (...) S}{\textsc{eq}}^{d}, \trianglelefteq _{d}\right) }$$\end{document}. Having this we consider the following parametrized first-order slow well-partial-ordering sentence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d}, r\right):}$$\end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \forall K > 0 \right) \left( \exists M > 0\right) \left( \forall x_{0},\ldots,x_{M}\in {\rm S}\text{\textsc{eq}}^{d}\right)$$\end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \left( \forall i\leq M\right) \left( \left| x_{i}\right| 1}$$\end{document} then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d},r \right) }$$\end{document} is not provable in T.Moreover, by the well-known proof theoretic equivalences we can just as well replace T by PA or ACA0 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta _{1}^{1}\sf{CA}}$$\end{document}, if d = 2 and d = 3, respectively.In the limit case d → ∞ we replaceEFA-provably computable reals r by EFA-provably computable functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f: \mathbb{N} \rightarrow \mathbb{R}_{+}}$$\end{document} and prove analogous theorems. (In the sequel we denote by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}_{+}}$$\end{document} the set of EFA-provably computable positive reals). In the basic case T = PA we strengthen the basic phase transition result by adding the following static threshold clause\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2}, 1\right)}$$\end{document} is still provable in T = PA (actually in EFA). Furthermore we prove the following dynamic threshold clauses which, loosely speaking are obtained by replacing the static threshold t by slowly growing functions 1α given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${1_{\alpha }\left( i\right)\,{:=}\,1+\frac{1}{H_{\alpha }^{-1}\left(i\right) }, H_{\alpha}}$$\end{document} being the familiar fast growing Hardy function and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H_{\alpha }^{-1}\left( i\right)\,{:=}\,\rm min \left\{ j \mid H_{\alpha } \left ( j\right) \geq i \right\}}$$\end{document} the corresponding slowly growing inversion. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha < \varepsilon _{0}}$$\end{document}, then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2}, 1_{\alpha}\right)}$$\end{document} is provable in T = PA. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left( {\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2},1_{\varepsilon _{0}}\right)}$$\end{document} is not provable in T = PA. We conjecture that this pattern is characteristic for all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T\supseteq \sf{PA}}$$\end{document} under consideration and their proof-theoretical ordinals o (T ), instead of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon _{0}}$$\end{document}. (shrink)

Progressions of iterated reflection principles can be used as a tool for the ordinal analysis of formal systems. We discuss various notions of proof-theoretic ordinals and compare the information obtained by means of the reflection principles with the results obtained by the more usual proof-theoretic techniques. In some cases we obtain sharper results, e.g., we define proof-theoretic ordinals relevant to logical complexity Π1 0 and, similarly, for any class Π n 0 . We provide a more general version of the (...) fine structure relationships for iterated reflection principles (due to U. Schmerl [25]). This allows us, in a uniform manner, to analyze main fragments of arithmetic axiomatized by restricted forms of induction, including IΣ n , IΣ n − , IΠ n − and their combinations. We also obtain new conservation results relating the hierarchies of uniform and local reflection principles. In particular, we show that (for a sufficiently broad class of theories T) the uniform Σ1-reflection principle for T is Σ2-conservative over the corresponding local reflection principle. This bears some corollaries on the hierarchies of restricted induction schemata in arithmetic and provides a key tool for our generalization of Schmerl's theorem. (shrink)

The significance of the German philosopher and social thinker, Georg Simmel, is only now being recognised by intellectual historians. Through penetrating readings of Simmel's thought, taken as a series of reflections on the essence of modernity and modern civilisation, Efraim Podoksik places his ideas within the context of intellectual life in Germany, and especially Berlin, under the Kaiserreich. Modernity, characterised by the growing differentiation and fragmentation of culture and society, was a fundamental issue during Simmel's life, underpinning central intellectual (...) debates in Imperial Germany. Simmel's thought is depicted here as an attempt at transforming the complexity of these debates into a coherent worldview that can serve as an effective guide to understanding their main parameters. Paying particular attention to the genealogy and usage of the concepts of Bildung, culture and civilisation in Germany, this study offers contextual analyses of Simmel's philosophies of culture, society, art, religion and the feminine, as well as his interpretations of Dante, Kant, Nietzsche, Schopenhauer, Goethe and Rembrandt. (shrink)

Historically, appearance of the quantum theory led to a prevailing view that Nature is indeterministic. The arguments for the indeterminism and proposals for indeterministic and deterministic approaches are reviewed. These include collapse theories, Bohmian Mechanics and the many-worlds interpretation. It is argued that ontic interpretations of the quantum wave function provide simpler and clearer physical explanation and that the many-worlds interpretation is the most attractive since it provides a deterministic and local theory for our physical Universe explaining the illusion of (...) randomness and nonlocality in the world we experience. (shrink)

A well-known result states that, over basic Kalmar elementary arithmetic EA, the induction schema for ∑n formulas is equivalent to the uniform reflection principle for ∑n + 1 formulas . We show that fragments of arithmetic axiomatized by various forms of induction rules admit a precise axiomatization in terms of reflection principles as well. Thus, the closure of EA under the induction rule for ∑n formulas is equivalent to ω times iterated ∑n reflection principle. Moreover, for k < ω, k (...) times iterated ∑n reflection principle over EA precisely corresponds to the extension of EA by k nested applications of ∑n induction rule.The above relationship holds in greater generality than just stated. In fact, we give general formulas characterizing in terms of iterated reflection principles the extension of any given theory by k nested applications of ∑n or Πn induction rules. In particular, the closure of a theory T under just one application of ∑1 induction rule is equivalent to T together with ∑1 reflection principle for each finite Π2 axiomatized subtheory of T.These results have closely parallel ones in the theory of subrecursive function classes. The rules under study correspond, in a canonical way, to natural closure operators on the classes of provably recursive functions. Thus, ∑1 induction rule precisely corresponds to the primitive recursive closure operator, and ∑1 collection rule, introduced below, corresponds to the elementary closure operator. (shrink)

Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopological space. Such spaces are called GLP-spaces whenever they satisfy all the axioms of GLP. We develop some constructions to build nontrivial GLP-spaces and show that GLP is complete w.r.t. the class of all GLP-spaces.

Karl Mannheim's contribution to a conceptual framework towards establishing objective knowledge in the social sciences has been overlooked and neglected. The paper discusses and reevaluates particularly Mannheim's concept of relationism which he used for clarifying the possibility of a "dynamic synthesis of perspectives" as the task of sociology of knowledge. One of the functions of Mannheim's conceptual framework was to narrow the gap between the techno-scientific or empiricist paradigm of knowledge and the humanistic-hermeneutical paradigm by a set of mediations which (...) shifted the emphasis from facts to the way of looking at them through concepts and terms which are never purely experiential, i.e. independent of interpretation. The author stresses the epistemological fertility of the relationist model of truth in view of recent insights of sociology of science. (shrink)