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)

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)

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)

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)

. 1. Introduĉão histórica ao pensamento jurídico, épocas medieval e moderna --.

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)

Within the domain of public health, vector-borne diseases are among the most vehemently discussed issues. Recent scientific breakthroughs in genome editing technology provided a solution to this issue in the form of a gene drive that might decrease and even eradicate vector-borne diseases. Gene drives are engineered, and designed genes that can break typical inheritance rules and be passed to almost all of the carrier’s offspring. This genome editing and gene drive technology has become a powerful tool for ecological and (...) environmental engineering, through which man can manipulate his surroundings, adjusting it to himself and directly mastering evolution and the ecosystem. Although the gene drive technology has been perceived as promising in the public health domain, ecological implications of its use are not to be underestimated. The primary aim of this paper is to overcome the ongoing discussion which mostly focuses on whether priority should be given to the environment or to public health, and to find an adequate answer and solution. In this quest to find the proper answer and solution, Pierre Teilhard de Chardin’s thought might be useful, especially his concepts of the biosphere and the noosphere which may provide some clarifications as to why we are at the moment so cautious with gene drive technology and how we need to move towards a better common future on earth. (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)

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

vol. 1. Os intérpretes da filosofia brasileira (3a. ed. revista de O estudo do pensamento filosófico brasileiro) -- vol. 2. As filosofias nacionais (2a ed. rev. e ampliada) -- vol. 3. Etapas iniciais da filosofia brasileira -- vol. 4. A escola eclética (2a ed. rev.) -- vol. 7. A filosofia brasileira contemporânea.

Grice’i algne vahetegemine “‘tähendamise’ naturaalse tähenduse” ja “‘tähendamise’mittenaturaalse tähenduse” vahel osutab loomulikule pingele ‘naturaalse’ ja ‘semantilise’vahel — kui ‘semantilise’ puhul on oluline, et see saab olla väär või ekslik,siis ‘naturaalse’ puhul väärus ja ekslikkus välistatakse. Artikli taotluseks on näidata, et juhul kui naturaalset tõlgendada kui ‘vastavalt füüsikaseadustele’, siis on seevastasseis vältimatu, samas kui tõlgenduse ‘nagu bioloogias’ korral oleneb ebakõlasuurus konkreetsest semantikateooriast, mida ollakse valmis omaks võtma. Viimases punktismööndakse, et kuigi loosung ‘ma suudan eksida’ on immuunne naturalistlikurünnaku vastu kujul ‘sa eksid, (...) kui seda väidad’, saab sellele siiski ette heitaekslikku arusaama ekslikkusest, iseäranis juhul, kui see tugineb ettekujutusele privaatsestkogemusest, nagu antud artiklis. Vastusena tavapärasele kriitikale, nagu eisaaks privaatsed kogemused keeles mingit rolli etendada, esitatakse hüpotees, mis (tuginedes lõdvalt Harry Collinsi eristusele) pakub välja võimaluse, et üksnes interaktiivnekeeleline pädevus ei sõltu privaatsetest kogemustest, samas kui kontributiivne pädevus sõltub. Grice's initial distinction between "natural sense of 'means'" and "nonnatural sense of 'means'" indicates a natural tension between 'natural' and 'semantics'-the former cannot be wrong whereas the latter can. The paper argues that if `natural' is understood as 'according to physics' this opposition is principal, whereas if it is understood as 'like in biology' the degree of discord depends on particular theory of 'semantics' one is ready to adopt. In the last section of the paper it is admitted that, although the slogan 'I am able to be wrong' should be immune to a naturalist refutation of the form 'you are wrong saying this', it may be still criticized for introducing a wrong kind of wrongness, e.g. the one that relies on subject's private episodes (the preferred option in this paper). As a reply to a standard critique against any role of private episodes in language, a preliminary hypothesis is put forward that (relying loosely on Harry Collins' distinction) it is only the interactive linguistic expertise that does not depend on private episodes, whereas the contributive linguistic expertise does. (shrink)