This paper aims to show that Thomas Aquinas consider the problem of evil, not only as a question of evil in itself, but in the much broader context of God’s work of creation and providential government, and thus proves that the existence of evil in the world is not a viable argument against God’s existence. For Thomas Aquinas, evil is not something, some being with its essence and nature, but it is the lack of a good that should by nature (...) be present in a being. Evil has good as its subject, object, and cause, and may ultimately have good as its effect. Such complete immersion and dependence of evil on good says that evil’s ontological status is real, but not absolute. Evil cannot exist from itself, by itself and for itself. It is in every way subordinated to the good. Such a status of evil becomes even more apparent in Aquinas’ view of the relation between evil and the absolute good that is God. God is the one who exists in the absolute sense, and evil exists only in relation to the good that is God’s creation. The decay of things is only a consequence of God creating a good world in which some beings may be deficient in good, which they sometimes are. This means that God does not want evil, but in a way allows it while providentially governing everything to the good that he is. God is so omnipotent that by allowing evil he can accomplish even greater and more numerous goods. In the work of God’s governing over the world, man occupies a special place because he is capable of a personal relationship with God. But man can also voluntarily deviate from the order and rules that lead him to union with his ultimate good which is God. Such an act is called the moral evil of guilt or sin. Thomas Aquinas finds the example and model of the victory of good over evil in the character of the righteous and innocent Job, who, thanks to the experience of a terrible evil, has realised that God infinitely transcends human cognition, being and power, and that any attribution of evil to God would be foolishness, that every denial of God’s existence because of the evil that befell him would be insane. Job realised that God’s righteousness and logos rule everything and that the ultimate victory of good is certain. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that (...) seems to necessitate the addition of sets to V. We argue that, despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We present a method of interpreting extension-talk (V-logic), and show how it captures satisfaction in `ideal' outer models and relates to impredicative class theories. We provide some reasons to regard the technique as philosophically virtuous, and argue that it opens new doors to philosophical and mathematical discussions for the Universist. (shrink)

Moral injury emerged in the healthcare discussion quite recently because of the difficulties and challenges healthcare workers and healthcare systems face in the context of the COVID-19 pandemic. Moral injury involves a deep emotional wound and is unique to those who bear witness to intense human suffering and cruelty. This article aims to synthesise the very limited evidence from empirical studies on moral injury and to discuss a better understanding of the concept of moral injury, its importance in the healthcare (...) context and its relation to the well-known concept of moral distress. A scoping literature review design was used to support the discussion. Systematic literature searches conducted in April 2020 in two electronic databases, PubMed/Medline and PsychInfo, produced 2044 hits but only a handful of empirical papers, from which seven well-focused articles were identified. The concept of moral injury was considered under other concepts as well such as stress of conscience, regrets for ethical situation, moral distress and ethical suffering, guilt without fault, and existential suffering with inflicting pain. Nurses had witnessed these difficult ethical situations when faced with unnecessary patient suffering and a feeling of not doing enough. Some cases of moral distress may turn into moral residue and end in moral injury with time, and in certain circumstances and contexts. The association between these concepts needs further investigation and confirmation through empirical studies; in particular, where to draw the line as to when moral distress turns into moral injury, leading to severe consequences. Given the very limited research on moral injury, discussion of moral injury in the context of the duty to care, for example, in this pandemic settings and similar situations warrants some consideration. (shrink)

This article addresses the question of fundamental entities in set theory. It takes up J. Hamkins’ claim that models of set theory are such fundamental entities and investigates it using the methodology of P. Maddy’s naturalism, Second Philosophy. In accordance with this methodology, I investigate the historical case study of the use of models in the introduction of forcing, compare this case to contemporary practice and give a systematic account of how set-theoretic practice can be said to introduce models as (...) new entities. In conclusion, I argue for a view that takes both sets and models to be fundamental entities in set theory. (shrink)

'Livros com ideias dentro' pretende chamar a atenção para obras que correm o risco de ser preteridas em favor de múltiplas temáticas fúteis que cada vez mais parecem ir ao encontro da procura de grande parte de leitores.

We review different conceptions of the set-theoretic multiverse and evaluate their features and strengths. In Sect. 1, we set the stage by briefly discussing the opposition between the ‘universe view’ and the ‘multiverse view’. Furthermore, we propose to classify multiverse conceptions in terms of their adherence to some form of mathematical realism. In Sect. 2, we use this classification to review four major conceptions. Finally, in Sect. 3, we focus on the distinction between actualism and potentialism with regard to the (...) universe of sets, then we discuss the Zermelian view, featuring a ‘vertical’ multiverse, and give special attention to this multiverse conception in light of the hyperuniverse programme introduced in Arrigoni-Friedman :77–96, 2013). We argue that the distinctive feature of the multiverse conception chosen for the hyperuniverse programme is its utility for finding new candidates for axioms of set theory. (shrink)

In this article we show that Morse-Kelley class theory provides us with an adequate framework for class forcing. We give a rigorous definition of class forcing in a model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$$$ \end{document} of MK, the main result being that the Definability Lemma can be proven without restricting the notion of forcing. Furthermore we show under which conditions the axioms are preserved. We conclude by proving that Laver’s Theorem does not hold for (...) class forcings. (shrink)

The consequences of chasm between the rich and the poor vary, depending on whether or not it is suffered by an individual or a larger group of people. Although in the case of various social groups it encompasses a larger area of effect, especially if it amasses as a protest, the consequences can be worse for an individual because the individual feels it stronger. In this paper, considered is the notion of existence in two aspects, socio­economic and philosophical, following examples (...) from the films Parasite and Joker. The focus is placed on the problem of poverty. (shrink)

In the late 1940s and early 1950s, Lorenzen developed his operative logic and mathematics, a form of constructive mathematics. Nowadays this is mostly seen as a precursor of the better-known dialogical logic, and one might assume that the same philosophical motivations were present in both works. However, we want to show that this is not everywhere the case. In particular, we claim that Lorenzen’s well-known rejection of the actual infinite, as stated in Lorenzen, was not a major motivation for operative (...) logic and mathematics. Rather, we argue that a shift happened in Lorenzen’s treatment of the infinite from the early to the late 1950s. His early motivation for the development of operationism is concerned with a critique of the Cantorian notion of set and with related questions about the notions of countability and uncountability; it is only later that his motivation switches to focusing on the concept of infinity and the debate about actual and potential infinity. (shrink)

Many authors have already observed that the Tractatus Theologico-Politicus of Baruch Spinoza was, in its time, the most discussed and most vehemently refuted book. Indeed, at the dawn of the Enlightenment, and almost until the end of the nineteenth century, Spinoza's Theological-Political Treatise was an assertive and powerful appeal to freedom of expression and thought, a bold claim of religious tolerance and freedom of conscience in a Europe that was unaccustomed to the exercise of free thought. But, what is after (...) all the subject of the Theological-Political Treatise, a book maligned for so long and by so many as ultra pestilential and immoral? The present volume, collecting essays by notable European scholars, attempts to address some of the problems created by the broad spectrum of topics included in Spinoza's Theological-Political Treatise. (shrink)

It is often assumed that concepts from the formal sciences, such as mathematics and logic, have to be treated differently from concepts from non-formal sciences. This is especially relevant in cases of concept defectiveness, as in the empirical sciences defectiveness is an essential component of lager disruptive or transformative processes such as concept change or concept fragmentation. However, it is still unclear what role defectiveness plays for concepts in the formal sciences. On the one hand, a common view sees formal (...) concepts to be protected against defects because of their precise and stable nature. On the other, studies going back as far as Lakatos (1963) showcase the changeability of such concepts. -/- In this paper, I will investigate if and how defectiveness based on the occurrence of inconsistencies can appear with formal concepts. To make the case as strong as possible, I employ a strict notion of formal concept that assumes the concept to have a fixed and definite extension. I will show that there are indeed certain types of defectiveness that cannot occur with such concepts; but that there are other types of defectiveness that do occur. This means that while formal concepts have to be treated differently than non-formal concepts, questions about defectiveness---as raised in the conceptual engineering debate and philosophy of science---can still be applied to them. I will highlight this point by showing how formal sciences have special strategies available to them that allow them to resolve defectiveness of their concepts in a flexible and informative manner. (shrink)

In the late 1940s and early 1950s Lorenzen developed his operative logic and mathematics, a form of constructive mathematics. Nowadays this is mostly seen as the precursor to the more well-known dialogical logic and one could assumed that the same philosophical motivations were present in both works. However we want to show that this is not always the case. In particular, we claim, that Lorenzen’s well-known rejection of the actual infinite as stated in Lorenzen (1957) was not a major motivation (...) for operative logic and mathematics. In this article, we claim that this is in fact not the case. Rather, we argue for a shift that happened in Lorenzen’s treatment of the infinite from the early to the late 1950s. His early motivation for the development of operativism is concerned with a critique of the Cantorian notion of set and related questions about the notion of countability and uncountability; only later, his motivation switches to focusing on the concept of infinity and the debate about actual and potential infinity. (shrink)

We survey recent developments in the theory of class forcing for- malized in the second-order set-theoretic setting.

We review different conceptions of the set-theoretic multiverse and evaluate their features and strengths. In Sect. 1, we set the stage by briefly discussing the opposition between the ‘universe view’ and the ‘multiverse view’. Furthermore, we propose to classify multiverse conceptions in terms of their adherence to some form of mathematical realism. In Sect. 2, we use this classification to review four major conceptions. Finally, in Sect. 3, we focus on the distinction between actualism and potentialism with regard to the (...) universe of sets, then we discuss the Zermelian view, featuring a ‘vertical’ multiverse, and give special attention to this multiverse conception in light of the hyperuniverse programme introduced in Arrigoni and Friedman (2013). We argue that the distinctive feature of the multiverse conception chosen for the hyperuniverse programme is its utility for finding new candidates for axioms of set theory. (shrink)

In this article we introduce and study hyperclass-forcing in the context of an extension of Morse-Kelley class theory, called MK∗∗. We define this forcing by using a symmetry between MK∗∗ models and models of ZFC− plus there exists a strongly inaccessible cardinal. We develop a coding between β-models ℳ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}$$ \end{document} of MK∗∗ and transitive models M+ of SetMK∗∗ which will allow us to go from ℳ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...) \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}$$ \end{document} to M+ and vice versa. So instead of forcing with a hyperclass in MK∗∗ we can force over the corresponding SetMK∗∗ model with a class of conditions. For class-forcing to work in the context of ZFC− we show that the SetMK∗∗ model M+ can be forced to look like Lκ∗[X]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$L_{\kappa ^*}[X]$$ \end{document}, where κ∗ is the height of M+, κ strongly inaccessible in M+ and X ⊆ κ. Over such a model we can apply definable class forcing and we arrive at an extension of M+ from which we can go back to the corresponding β-model of MK∗∗, which will in turn be an extension of the original ℳ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}$$ \end{document}. Our main result combines hyperclass forcing with coding methods of Beller et al. and Friedman to show that every β-model of MK∗∗ can be extended to a minimal such model of MK∗∗ with the same ordinals. A simpler version of the proof also provides a new and analogous minimality result for models of second-order arithmetic. (shrink)

En este artículo se intenta mostrar si se puede aplicar el concepto griego de epiméleia al pensamiento zoroastriano. Más en concreto, se abordan los temas del cuidado del mundo, el cuidado de la palabra y el cuidado del alma. Para ello se analizan algunas categorías fundamentales del mazdeísmo tales como menog, getic, paiman, daena, jorrah o fravarsi. La conclusión que se extrae es que sí es pertinente hablar de cuidado del mundo, cuidado de la palabra y cuidado de sí en (...) el ámbito zoroastra en particular y en el ámbito iranio en general. (shrink)