Let ≺ be a primitive recursive well-ordering on the natural numbers and assume that its order-type is greater than or equal to the proof-theoretic ordinal of the theory T. We show that the proof-theoretic strength of T is not increased if we add the negation of the statement which formalizes transfinite induction along ≺.

In [10] Friedman showed that is a conservative extension of <ε0for-sentences wherei= min, i.e.,i= 2, 3, 4 forn= 0, 1, 2 +m. Feferman [5], [7] and Tait [11], [12] reobtained this result forn= 0, 1 and even with instead of. Feferman and Sieg established in [9] the conservativeness of over <ε0for-sentences for alln. In each paper, different methods of proof have been used. In particular, Feferman and Sieg showed how to apply familiar proof-theoretical techniques by passing through languages with Skolem (...) functionals.In this paper we study the same choice principles in the presence of theBar Rule, which permits one to infer the scheme of transfinite induction on a primitive recursive relation ≺ when it has been proved that ≺ is wellfounded. The main result characterizes + as a conservative extension of a system of the autonomously iterated-comprehension axiom for-sentences. Forn= 0 this has been proved by Feferman in the form that + is a conservative extension of <Γ0; this was first done in [8] by use of the Gödel functional interpretation for the stronger systemZω+μ+ + and then more recently by the simpler methods of [9]. Jäger showed how the latter methods could also be used to obtain the general result of Theorem 1 below. (shrink)

Prior studies have shown a general preference among citizens for juries over judges. Researchers, however, have not considered whether race and ethnicity modify this preference. We hypothesized that minorities (African-Americans, Hispanics), who generally express less trust in the legal system, may also express less trust in juries than non-Hispanic whites. We asked a representative sample of 1,465 residents of Texas to state whether they would prefer a jury or a judge to be the decision maker in four hypothetical circumstances. Consistent (...) with expectations, non-Hispanic whites favored juries over judges, particularly if they imagined themselves as a defendant in a criminal trial. By comparison, although African-Americans and some Hispanics generally favored juries, they showed a much weaker set of jury preferences. African Americans had markedly lower support for the civil jury, but support was higher among minorities with prior jury service. Among Hispanics, respondents who took the survey in Spanish typically preferred a judge to make legal decisions. We consider the implications of our findings for trust in the jury system and trust in community members as decision makers. (shrink)

Semantic noise, the effect ensuing from the denotative and thus functional variability exhibited by different terms in different contexts, is a common concern in natural language processing (NLP). While unarguably problematic in specific applications (e.g., certain translation tasks), the main argument of this paper is that failing to observe this linguistic matter of fact as a generative effect rather than as an obstacle, leads to actual obstacles in instances where language model outputs are presented as neutral. Given that a common (...) and long-standing challenge in NLP is the interpretation of ambiguous – i.e., semantically noisy – cases, this article focuses on an exemplar ambiguity-resolution task in NLP: the problem of anaphora in Winograd schemas. The main question considered is: to what extent is the standard approach to disambiguation in NLP subject to a stagnant “image of language”? And, can a transdisciplinary, dynamic approach combining linguistics and philosophy elucidate new perspectives on these possible conceptual shortcomings? In order to answer these questions we explore the term and concept of noise, particularly in its presentation as semantic noise. Owing to its definitional plurality, and sometimes even desirable unspecificity, the term noise is thus used as proof of concept for semantic generativity being an inherent characteristic in linguistic representation, and its concept is used to interrogate assumptions admitted in the resolution of Winograd schemas. The argument is speculative and theoretical in method, and the result is an analysis which provides an account of the fundamentally dialogical and necessarily open-ended effects of semantic noise in natural language. (shrink)

Feferman, S. and G. Jäger, Systems of explicit mathematics with non-constructive μ-operator. Part I, Annals of Pure and Applied Logic 65 243-263. This paper is mainly concerned with the proof-theoretic analysis of systems of explicit mathematics with a non-constructive minimum operator. We start off from a basic theory BON of operators and numbers and add some principles of set and formula induction on the natural numbers as well as axioms for μ. The principal results then state: BON plus set induction (...) is proof-theoretically equivalent to Peano arithmetic PA; BON plus formula induction is proof-theoretically equivalent to the system <0 of second-order arithmetic. (shrink)

It is possible to predict future life forms? In this paper it is argued that the answer to this question may well be positive. As a basis for predictions a rationale is used that is derived from historical data, e.g. from a hierarchical classification that ranks all building block systems, that have evolved so far. This classification is based on specific emergent properties that allow stepwise transitions, from low level building blocks to higher level ones. This paper shows how this (...) hierarchy can be used for predicting future life forms.The extrapolations suggest several future neural network organisms. Major aspects of the structures of these organisms are predicted. The results can be considered of fundamental importance for several reasons. Firstly, assuming that the operator hierarchy is a proper basis for predictions, the result yields insight into the structure of future organisms. Secondly, the predictions are not extrapolations of presently observed trends, but are fully integrated with all historical system transitions in evolution. Thirdly, the extrapolations suggest the structures of intelligences that, one day, will possess more powerful brains than human beings.This study ends with a discussion of possibilities for falsification of the present theory, the implications of the present predictions in relation to recent developments in artificial intelligence and the philosophical implications of the role of humanity in evolution with regard to the creation of future neural network organisms. (shrink)

Jäger, G., Fixed points in Peano arithmetic with ordinals, Annals of Pure and Applied Logic 60 119-132. This paper deals with some proof-theoretic aspects of fixed point theories over Peano arithmetic with ordinals. It studies three such theories which differ in the principles which are available for induction on the natural numbers and ordinals. The main result states that there is a natural theory in this framework which is a conservative extension of Peano arithmeti.

This paper is about the semantic structure of verbal and deverbal noun phrases. The focus is on noun phrases which describe actions, perceptions, sensations and beliefs. It is commonly thought that actions are movements of parts of the agent’s body which we typically describe in terms of their effects, and that perceptions are slices of sensible experience which we typically describe in terms of their causes. And many philosophers hold that sensations and beliefs are states of the central nervous system (...) which we generally describe in terms of their typical causes and effects. For example ‘Brutus’s killing of Caesar’ is thought to describe a movement of a part of Brutus’s body – e.g. the thrust of an arm – in terms of one of its effects, namely, Caesar’s death. And ‘ Hyman ’s visual perception of a table in front of him’ is thought to describe the visual experience I’m having right now in terms of its cause. The object of the paper is to show that these doctrines misrepresent the semantic structure of verbal and deverbal noun phrases. (shrink)

Der Download enthält die penultimative Fassung (noch unter dem vorläufigen Titel "Molina über Vorsehung und Freiheit"). Diese ausführliche Einleitung zu dem Band "Luis de Molina: Göttlicher Plan und menschliche Freiheit", hg. und übersetzt von C. Jäger, H. Kraml und G. Leibold, Hamburg: Meiner 2018, rekonstruiert auf 165 S. Molinas berühmte Theorie der Willensfreiheit und die Frage ihrer Vereinbarkeit mit göttlichem Vorherwissen und göttlicher Vorsehung. Sie zeichnet wesentliche Stationen der Debatte um den theologischen Determinismus nach, wie sie sich von Augustinus und (...) Boethius über Anselm, Thomas von Aquin, Scotus, Ockham und andere bis zu Molina und von dort bis in die jüngste, vor allem analytische Religionsphilosophie hinein entwickelt. (shrink)

An important challenge in bilingualism research is to understand the mechanisms underlying sentence processing in a second language and whether they are comparable to those underlying native processing. Here, we focus on verb-particle constructions (VPCs) that are among the most difficult elements to acquire in L2 English. The verb and the particle form a unit, which often has a non-compositional meaning (e.g., look up or chew out), making the combined structure semantically opaque. However, bilinguals with higher levels of English proficiency (...) can develop a good knowledge of the semantic properties of verb-particle constructions (Blais and Gonnerman, 2013). A second difficulty is that in a sentence context, the particle can be shifted after the direct object of the verb, (e.g., The professor looked it up). The processing is more challenging when the object is long (e.g. The professor looked the student’s last name up.). This shifted structure favors syntactic processing at the expense of VPC semantic processing. We sought to determine whether or not bilinguals’ reading time (RT) patterns would be similar to those observed for native monolinguals (Gonnerman and Hayes, 2005) when reading VPCs in sentential contexts. French-English bilinguals were tested for English language proficiency, working memory and explicit VPC semantic knowledge. During a self-paced reading task, participants read 78 sentences with verb-particle constructions that varied according to parameters that influence native speakers’ reading dynamics: verb-particle transparency, particle adjacency and length of the object noun phrase (NP; 2, 3, or 5 words). RTs in a critical region that included verbs, NPs and particles were measured. Results revealed that RTs were modulated by participants’ English proficiency, with higher proficiency associated with shorter RTs. Examining participants’ explicit semantic knowledge of VPCs and working memory, only readers with more native-like knowledge of VPCs and a high working memory presented RT patterns that were similar to those of monolinguals. Therefore, given the necessary lexical and computational resources, bilingual processing of novel structures at the syntax-semantics interface follows the principles influencing native processing. The findings are in keeping with theories that postulate similar representations and processing in L1 and L2 modulated by processing difficulty. (shrink)

The present volume collects papers that were presented at the 34th International Wittgenstein Symposium “Epistemology: Contexts, Values, Disagreement” 2011 in Kirchberg. Contributors include: P. Baumann, A. Beckermann, E. Brendel, J. Bromand, G. Brun, M. David, W. Davis, C. Elgin, E. Fischer, W. Freitag, S. Goldberg, J. Greco, E. Harcourt, A. Kemmerling, M. Kober, D. Koppelberg, A. Koritensky, H. Kornblith, M. Kusch, M. Lee, N. Miscevic, K. Munn, B. Niederbacher, E. J. Olsson, C. Piller, R. Raaatzsch, S. Schmoranzer, S. Schroeder, G. (...) Schurz, N. Shackel, M. Solomon, M. Willaschek. (shrink)

(No abstract is available for this citation).

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 20 (2000) 247-248 [Access article in PDF] Christ and Buddha: Weaving a Path for the New Millennium Thomas G. Hand, S.J.Mercy Center, Burlingame, CAThis dialogue conference/retreat was held at Mercy Center, Burlingame, CA, August 10-15, 1999. Well over the stated limit of 150 people joined a faculty of ten in presentations, discussions, sharing, meditation, and rituals. The conference was born primarily out of the personal and social (...) need for dialogue felt by Sandi Peters, who joined the program staff of Mercy Center after three years spent at Insight Meditation East, Barre, Massachusetts.Besides Peters as presider, the faculty members were: representing the Buddhist side--Nigel Edmonds (Mahayana and Christianity), Chris Phillips (Theravada), Ven. Thubten Chodron (Vajrayana), Rev. Heng Sure (Chinese Mahayana), and Patrick Thornton (Theravada and Christianity); representing the Christian side--Thomas G. Hand, S. J. (Catholic), Kevin Hunt, OCSO (Cistercian monk), Roshi Jinne Richardson (Zen and Christianity), and Rev. Shari Young (Episcopal and Zen).In a well-received keynote talk, Thomas Hand offered as the basis for the whole dialogue "The Primacy of Experience" in both traditions. The major themes were: (1st day) "The Challenges of Buddhist-Christian Dialogue," (2nd day) "The Language and Symbols of the Traditions," (4th day) "Weaving a Path for the New Millennium" as a joint venture of the two traditions together. On the third day, participants engaged in "Practice--East and West," including presentations geared toward practice both then and there and in the future.One marked difference between this conference and those that Mercy Center put on from 1985 to 1988 was the quality of the participants. In the earlier conferences, many were seekers and intellectual questioners. This year, besides such qualities, the participants were sincere practitioners. In fact, a great many were practicing in both traditions. They often classified themselves as Buddhist Christians or as Christian-root Buddhists. The greater depth of dialogue that has developed in less than fifteen years was clearly apparent. What is more, the sharing and insights of both Buddhist and Christian presenters seemed to have become increasingly relaxed, articulate, and vital. Their presentations were met with much deeper understanding and enthusiasm by all the participants. [End Page 247]Besides the presentations, participants deeply appreciated the chi kong and tai chi sessions, the daily meditation together, the day of practice, the tea ceremony, and the closing ritual. In a word, the conference was holistic dialogue.Those of dual practice were especially happy to find that they are not alone, that many are coming together to weave a new Path for the new millennium.Tapes are available. Contact Sandi Peters at (650) 340-7486.... (shrink)

This chapter examines various Islamic perspectives on natural theology, and briefly outlines the reasons why the philosophy of Ibn Rusdh does not represent a definition of natural theology in Islam. It then discusses varieties of natural theology and Islam; Kalām texts and revelation; al-Ghazālī's criticism of philosophers; Nizām al-Dīn al-Nīsābūrī's views on the reasoned study of nature; natural theology and religious obligations; Sharī'a and natural law; and reactions to Darwin in the nineteenth- and early twentieth-century Near East.

Physicians in Islamic countries might be requested to participate in the Islamic legal code of qiṣāṣ, in which the victim or family has the right to an eye-for-an-eye retaliation. Qiṣāṣ is only used as a punishment in the case of murder or intentional physical injury. In situations such as throwing acid, the national legal system of some Islamic countries asks for assistance from physicians, because the punishment should be identical to the crime. The perpetrator could not be punished without a (...) physician’s participation, because there is no way to guarantee that the sentence would be carried out without inflicting more injury than the initial victim had suffered. By examining two cases of acid throwing, this paper discusses issues related to physicians’ participation in qiṣāṣ from the perspective of medical ethics and Islamic Shari’a law. From the standpoint of medical ethics, physicians’ participation in qiṣāṣ is not appropriate. First, qiṣāṣ is in sharp contrast to the Hippocratic Oath and other codes of medical ethics. Second, by physicians’ participation in qiṣāṣ, medical practices are being used improperly to carry out government mandates. Third, physician participation in activities that cause intentional harm to people destroys the trust between patients and physicians and may adversely affect the patient–physician relationship more generally. From the standpoint of Shari’a, there is no consensus among Muslim scholars whether qiṣāṣ should be performed on every occasion. We argue that disallowing physician involvement in qiṣāṣ is necessary from the perspectives of both medical ethics and Shari’a law. (shrink)

This paper gives a recursive generalization of a strong notation system of ordinals, which was devellopped by Jäger [3]. The generalized systemT(V′) is based on a hierarchy of Veblen-functions for inaccessible ordinals. The definition ofT(V′) assumes the existence of a weak Mahlo-ordinal. The wellordering ofT(V′) is provable in a formal system of second order arithmetic with the axiom schema ofΠ 2 1 -comprehension in a similar way, as it is proved in [6] for the weaker notation systemT(V′).

There is a surprising amount of philosophy underlying the way we choose to measure poverty, including in the matter of the seemingly uncomplicated task of specifying an income poverty line. The present essay examines some of these issues of fact, value, and reasoning as they apply to the enterprise of assessing magnitudes of, and trends in, global money-metric poverty.

Islamic Financial Institutions have recently witnessed remarkable growth driven by their holistic business model. The key differentiator of IFIs is their Shari’a-based business proposition which often requires some financial sacrifices, e.g. being ethical, responsible and philanthropic. It also requires them to refrain from investments in tobacco, alcohol, pornography or earning interest. For IFIs’ sponsors and managers, however, the key motivational factor for entering the Islamic financial market is not the achievement of Shari’a objectives through the holistic business model, (...) but rather the urge to tap this highly profitable market where customers are inclined to pay a premium for Shari’a compliance. In order for IFIs to be accepted by the market, their financial instruments need to be approved by Shari’a scholars, known for their integrity and expertise in Shari’a. One can therefore expect potential tensions between IFIs’ managers and Shari’a scholars. The purpose of this research is to probe the hidden struggle between managers and Shari’a scholars in pursuit of their respective objectives. The study investigates this phenomenon using grounded theory as a methodological framework based on data collected from three IFIs from two countries. The findings reveal that Shari’a scholars and managers of IFIs have divergent objectives, which creates incongruence of objectives at the strategic level. The findings illustrate the tension and latent struggle for Shari’a compliance, which has been termed as ‘Fatwa Repositioning’ resulting in four possible consequences: deep, reasonable, minimum and superficial Shari’a compliance. Fatwa Repositioning is the core category of this study, which exhibits how managers and Shari’a scholars struggle to position the Shari’a compliance of their institutions so as to best serve their respective objectives. Interestingly, Shari’a scholars are seemingly not always in control of what they are supposed to be controlling, i.e. Shari’a compliance. (shrink)

The comments focus on a presumed circular reasoning in the operator hierarchy and the necessity of understanding life’s origin for defining life. Below it is shown that its layered structure prevents the operator hierarchy from circular definitions. It is argued that the origin of life is an insufficient basis for a definition of life that includes multicellular and neural network organisms.