John Foxal was an English Franciscan active primarily in Italy in the latter half of the fifteenth century. His philosophical and theological positions were Scotist, and in his works he comments upon various texts of John Duns Scotus with reference to the Scotist school of thought active in the early fourteenth century. In this article we supplement the list of extant manuscripts, provide a revised list of Foxal’s treatises and offer an edition of one of these, the Tractatus de propositione (...) per se nota. (shrink)

The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on finitely complete and cocomplete categories. As an instance of this result, we build the final coalgebra for the powerclass functor, in the context of a Heyting pretopos with a class of small maps. This is then proved to provide models for various non-well-founded set theories, depending on the chosen axiomatisation (...) for the class of small maps. (shrink)

We introduce constructive and classical systems for nonstandard arithmetic and show how variants of the functional interpretations due to Gödel and Shoenfield can be used to rewrite proofs performed in these systems into standard ones. These functional interpretations show in particular that our nonstandard systems are conservative extensions of E-HAω and E-PAω, strengthening earlier results by Moerdijk and Palmgren, and Avigad and Helzner. We will also indicate how our rewriting algorithm can be used for term extraction purposes. To conclude the (...) paper, we will point out some open problems and directions for future research, including some initial results on saturation principles. (shrink)

Though the Christian faith has in recent years increasingly shown itself to be a truly African religion, a variety of African authors such as Kä Mana, George Kinoti, Hannah Kinoti, August Shutte and Efoé Julien Penoukou have noted that sub-Saharan Africa is facing a moral crisis. This article explores this crisis in as far as it is caused by difficulties in the reception of the Christian ethic by African Christian communities. It points out that this crisis is visible in double (...) morality, immorality and legalism. It shows that it is both caused by rapid social change in contemporary Africa and by the way the Christian ethic was introduced with a lack of attention for the relationship between worldview and ethics, the social impact of changing cultural practices and the importance of virtue ethics. In this way it also points to the shape Christian moral education for present-day Africa should take. (shrink)

In earlier work we introduced two systems for nonstandard analysis, one based on classical and one based on intuitionistic logic; these systems were conservative extensions of first-order Peano and Heyting arithmetic, respectively. In this paper we study how adding the principle of countable saturation to these systems affects their proof-theoretic strength. We will show that adding countable saturation to our intuitionistic system does not increase its proof-theoretic strength, while adding it to the classical system increases the strength from first- to (...) full second-order arithmetic. (shrink)

We show that Martin Hyland's effective topos can be exhibited as the homotopy category of a path category EFF. Path categories are categories of fibrant objects in the sense of Brown satisfying two additional properties and as such provide a context in which one can interpret many notions from homotopy theory and Homotopy Type Theory. Within the path category EFF one can identify a class of discrete fibrations which is closed under push forward along arbitrary fibrations (in other words, this (...) class is polymorphic or closed under impredicative quantification) and satisfies propositional resizing. This class does not have a univalent representation, but if one restricts to those discrete fibrations whose fibres are propositions in the sense of Homotopy Type Theory, then it does. This means that, modulo the usual coherence problems, it can be seen as a model of the Calculus of Constructions with a univalent type of propositions. We will also build a more complicated path category in which the class of discrete fibrations whose fibres are sets in the sense of Homotopy Type Theory has a univalent representation, which means that this will be a model of the Calculus of Constructions with a univalent type of sets. (shrink)

This is the first in a series of papers on Predicative Algebraic Set Theory, where we lay the necessary groundwork for the subsequent parts, one on realizability [B. van den Berg, I. Moerdijk, Aspects of predicative algebraic set theory II: Realizability, Theoret. Comput. Sci. . Available from: arXiv:0801.2305, 2008], and the other on sheaves [B. van den Berg, I. Moerdijk, Aspects of predicative algebraic set theory III: Sheaf models, 2008 ]. We introduce the notion of a predicative category with small (...) maps and show that it provides a sound and complete semantics for constructive set theories like IZF and CZF. The main technical contribution of this paper is that it shows in detail that such categories can always be conservatively embedded in categories that are exact. These exactness properties play a crucial rôle in showing that predicative categories with small maps contain models of set theory and that they are closed under sheaves and realizability. We will prove the former statement in this paper as well, leaving a proof of the closure properties to the papers on realizability and sheaves as mentioned above. (shrink)

The science and faith debate is dominated by Western voices. In order to enrich this debate, the authors study the discourses of different groups of Christian academics and master's students in francophone Africa. This article describes the process of reconstructing and analyzing the discourse of a group of master's students from Abidjan (Ivory Coast) with the help of group model building and focus groups. Three characteristic features that emerge from this discourse include the foundational position of faith, the central role (...) of truth, and the ambiguous connotations of the term “science” in this context. The reconstructed discourse is then brought into conversation with the North Atlantic debate, with a special focus on the concept of scientism. (shrink)

Using the theory of exact completions, I construct a certain class of pretoposes, consisting of what one might call “predicative realizability toposes”, that can act as categorical models of certain predicative type theories, including Martin-Löf Type Theory.

Recently, the second author, Briseid, and Safarik introduced nonstandard Dialectica, a functional interpretation capable of eliminating instances of familiar principles of nonstandard arithmetic—including overspill, underspill, and generalizations to higher types—from proofs. We show that the properties of this interpretation are mirrored by first-order logic in a constructive sheaf model of nonstandard arithmetic due to Moerdijk, later developed by Palmgren, and draw some new connections between nonstandard principles and principles that are rejected by strict constructivism. Furthermore, we introduce a variant of (...) the Diller–Nahm interpretation with two different kinds of quantifiers, similar to Hernest’s light Dialectica interpretation, and show that one can obtain nonstandard Dialectica by weakening the computational content of the existential quantifiers—a process called herbrandization. We also define a constructive sheaf model mirroring this new functional interpretation, and show that the process of herbrandization has a clear meaning in terms of these sheaf models. (shrink)

A nucleus is an operation on the collection of truth values which, like double negation in intuitionistic logic, is monotone, inflationary, idempotent and commutes with conjunction. Any nucleus determines a proof-theoretic translation of intuitionistic logic into itself by applying it to atomic formulas, disjunctions and existentially quantified subformulas, as in the Gödel–Gentzen negative translation. Here we show that there exists a similar translation of intuitionistic logic into itself which is more in the spirit of Kuroda’s negative translation. The key is (...) to apply the nucleus not only to the entire formula and universally quantified subformulas, but to conclusions of implications as well. (shrink)

We study a new proof principle in the context of constructive Zermelo-Fraenkel set theory based on what we will call “non-deterministic inductive definitions”. We give applications to formal topology as well as a predicative justification of this principle.

Non-well-founded trees are used in mathematics and computer science, for modelling non-well-founded sets, as well as non-terminating processes or infinite data structures. Categorically, they arise as final coalgebras for polynomial endofunctors, which we call M-types. We derive existence results for M-types in locally cartesian closed pretoposes with a natural numbers object, using their internal logic. These are then used to prove stability of such categories with M-types under various topos-theoretic constructions; namely, slicing, formation of coalgebras , and sheaves for an (...) internal site. (shrink)

We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Löf's type theory. In addition, it is strong enough to prove the Set Compactness theorem and the results in formal topology which make use of this theorem. Moreover, it is stable under the standard constructions from algebraic set theory, namely exact completion, realizability models, forcing as well as (...) more general sheaf extensions. As a result, methods from our earlier work can be applied to show that this extension satisfies various derived rules, such as a derived compactness rule for Cantor space and a derived continuity rule for Baire space. Finally, we show that this extension is robust in the sense that it is also reflected by the model constructions from algebraic set theory just mentioned. (shrink)

We present a version of arithmetic in all finite types based on a systematic use of an internally definable notion of observational equivalence for dealing with equalities at higher types. For this system both intensional and extensional models are possible, the deduction theorem holds and the soundness of the Dialectica interpretation is provable inside the system itself.

In the post-colonial era, the incarnation has become an important model for cross-cultural missionary presence. Though this model improves on Eurocentric and colonial models, it is deficient because it is unrealistic, potentially paternalistic, inappropriate in the light of globalization and post-modern understandings of culture, and because it doesn’t sufficiently respect the particularity of the incarnation of Christ. This article proposes an alternative model of the role of the cross-cultural missionary as a guest and argues that it is more appropriate on (...) precisely these counts. (shrink)

Analisi critica d'opera, incentrata sulla recezione dell'opera di Tolomeo durante il Medioevo e sul pensiero scientifico-filosofico dell' Età Medievale e Rinascimentale.

This article discusses the role of communication research in the Cold War, moving from a US-centered to a comparative-transnational point of view. It examines research on prop-aganda and mass communication in the United States and the Soviet Union, focusing not only on the similarities and differences, but also on mutual perceptions and transnational entanglements. In both countries, communication scientists conducted their research with its benefits for propaganda practitioners and waging the Cold War in mind. It has been suggested that after (...) an initial period of close cooperation between politics and communication science, early expectations of the potential of systematic research for controlling the hearts and minds of people through propaganda started to fade. On both sides of the Iron Curtain, communication research eventually became a ‘normal’ scholarly discipline. (shrink)

If critique does not want to be more than just a ‘passion of the head’ it has to engage in dialogue with the worst-off in society. However, there are several mechanisms that hinder the excluded from giving words to their suffering. Furthermore, there are processes of invisibilization that impede even the perception of the excluded and their critique in the public space. The aim of this article is to conceptually explore the mechanisms of formulating critique by the excluded and of (...) understanding critique in the public space. Therefore, I first provide a brief overview on the meaning of critique before then presenting suffering as a language of critique. In a third step, I explore the multiple mechanisms that hinder suffering from becoming visible and end up discussing some (fragmented) solutions for overcoming these invisibilities. Although the excluded is hindered in formulating public critique in linguistic form, the suffering of the excluded can be understood as the ground for a powerful form of social critique. (shrink)

Public extension services play a key role in the implementation of strategies for rural development based on the sustainable management of natural resources. However, the sector suffers from restricted financial and human resources. Using experiences from participatory action research, a strategy for rural extension in the Amazon was defined to increase the efficiency and the relevance of external support for local resource users. This strategy considered activities initiated and coordinated by local people. Short-term facilitation visits provided continuous external support for (...) the purpose of establishing locally based planning and learning mechanisms. In collaboration with the municipality of Muaná in the Eastern Amazon, the strategy was tested in two traditional communities – Monte Moriat and Boa Esperança. Both communities recognized as most important the need to reduce their dependence on açaí (Euterpe oleracea Mart.), the principal source of food and income. This forest resource has been overexploited, seriously affecting açaí stands and diminishing the forest benefits fundamental for survival. Two local groups decided to raise chickens as a way to reduce nutritional problems and as an alternative source of income. Supported by monthly, short-term planning and evaluation visits, the groups managed to achieve significant progress in their endeavor. The groups identified (1) the control of decision-making and information, and (2) the absence of external obligations to be the greatest advantages of the development initiative. The study confirmed the potential of participatory strategies for public extension in the Amazon. Special attention was given to realistically define the role of forests for local development. However, drastic measures are necessary to smooth the way for real participation in governmental and non-governmental organizations acting in the Brazilian Amazon. (shrink)

In two pre-registered online studies during the COVID-19 pandemic and the early 2020 lockdown (one of which with a UK representative sample) we elicit risk-tolerance for 1,254 UK residents using four of the most widely applied risk-taking tasks in behavioral economics and psychology. Specifically, participants completed the incentive-compatible Balloon Analog Risk Task (BART) and the Binswanger-Eckel-Grossman (BEG) multiple lotteries task, as well as the Domain-Specific Risk-Taking Task (DOSPERT) and the self-reported questions for risk-taking used in the German Socio-economic Panel (SOEP) (...) study. In addition, participants in the UK representative sample answered a range of questions about COVID-19-related risky behaviors selected from the UCL COVID-19 Social Survey and the ICL-YouGov survey on COVID-19 behaviors. Consistently with pre-COVID-19 times, we find that risk tolerance during the UK lockdown (i) was higher in men than in women and (ii) decreased with age. Undocumented in pre-COVID-19 times, we find some evidence for healthier participants displaying significantly higher risk-tolerance for self-reported risk measures. We find no systematic nor robust patterns of association between the COVID-19 risky behaviors and the four risk-taking tasks in our study. Moreover, we find no evidence in support of the so-called “risk compensation” hypothesis. If anything, it appears that participants who took greater risk in real-life COVID-19-relevant risky behaviors (e.g., isolating or taking precautions) also exhibited higher risk-tolerance in our experimental and self-reported risk-taking measures. (shrink)

What is empiricism and what could it be? Bas . van Fraassen, one of the world’s foremost contributors to philosophical logic and the philosophy of science, here undertakes a fresh consideration of these questions and offers a program for renewal of the empiricist tradition. The empiricist tradition is not and could not be defined by common doctrines, but embodies a certain stance in philosophy, van Fraassen says. This stance is displayed first of all in a searing, recurrent critique of metaphysics, (...) and secondly in a focus on experience that requires a voluntarist view of belief and opinion. Van Fraassen focuses on the philosophical problems of scientific and conceptual revolutions and on the not unrelated ruptures between religious and secular ways of seeing or conceiving of ourselves. He explores what it is to be or not be secular and points the way toward a new relationship between secularism and science within philosophy. (shrink)