The prevalent interpretation of Gödel’s Second Theorem states that a sufficiently adequate and consistent theory does not prove its consistency. It is however not entirely clear how to justify this informal reading, as the formulation of the underlying mathematical theorem depends on several arbitrary formalisation choices. In this paper I examine the theorem’s dependency regarding Gödel numberings. I introducedeviantnumberings, yielding provability predicates satisfying Löb’s conditions, which result in provable consistency sentences. According to the main result of this paper however, these (...) “counterexamples” do not refute the theorem’s prevalent interpretation, since once a natural class ofadmissiblenumberings is singled out, invariance is maintained. (shrink)

In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion of self-reference even for expressively weak languages. The results of this paper suggest that the question whether truly self-referential reasoning can be formalised in arithmetic is more sensitive to the underlying coding apparatus than usually believed. As a case study, we show how this sensitivity affects the formal study (...) of certain principles of self-referential truth. (shrink)

This paper investigates the conditions under which diagonal sentences can be taken to constitute paradigmatic cases of self-reference. We put forward well-motivated constraints on the diagonal operator and the coding apparatus which separate paradigmatic self-referential sentences, for instance obtained via Gödel’s diagonalization method, from accidental diagonal sentences. In particular, we show that these constraints successfully exclude refutable Henkin sentences, as constructed by Kreisel.

INTRODUCTION The search for identity, the attempt to define oneself — the result of the individual's sense of alienation — is not restricted to contemporary ...

There is a well-known gap between metamathematical theorems and their philosophical interpretations. Take Tarski’s Theorem. According to its prevalent interpretation, the collection of all arithmetical truths is not arithmetically definable. However, the underlying metamathematical theorem merely establishes the arithmetical undefinability of a set of specific Gödel codes of certain artefactual entities, such as infix strings, which are true in the standard model. That is, as opposed to its philosophical reading, the metamathematical theorem is formulated (and proved) relative to a specific (...) choice of the Gödel numbering and the notation system. A similar observation applies to Gödel’s and Church’s theorems, which are commonly taken to impose severe limitations on what can be proved and computed using the resources of certain formalisms. The philosophical force of these limitative results heavily relies on the belief that these theorems do not depend on contingencies regarding the underlying formalisation choices. The main aim of this paper is to provide metamathematical facts which support this belief. While employing a fixed notation system, I showed in previous work (_Review of Symbolic Logic_, 2021, 14(1):51–84) how to abstract away from the choice of the Gödel numbering. In the present paper, I extend this work by establishing versions of Tarski’s, Gödel’s and Church’s theorems which are invariant regarding _both_ the notation system and the numbering. This paper thus provides a further step towards absolute versions of metamathematical results which do not rely on contingent formalisation choices. (shrink)

On business ethics of Papuan peoples in Indonesia.

Facial attributes such as race, sex, and age can interact with emotional expressions; however, only a couple of studies have investigated the nature of the interaction between facial age cues and emotional expressions and these have produced inconsistent results. Additionally, these studies have not addressed the mechanism/s driving the influence of facial age cues on emotional expression or vice versa. In the current study, participants categorised young and older adult faces expressing happiness and anger or sadness by their age and (...) their emotional expression. Age cues moderated categorisation of happiness vs. anger and sadness in the absence of an influence of emotional expression on age categorisation times. This asymmetrical interaction suggests that facial age cues are obligatorily processed prior to emotional expressions. Finding a categorisation advantage for happiness expressed on young faces relative to both anger and sadness which are negative in valence but different in their congruence with old age stereotypes or structural overlap with age cues suggests that the observed influence of facial age cues on emotion perception is due to the congruence between relatively positive evaluations of young faces and happy expressions. (shrink)

Persoonlijk verslag van de zoektocht van de beroemde auteur naar de essentie van haar leven.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Religionskritik als Chance und Herausforderung für den christlichen Glauben - Selbstverantwortung und religiöse Mündigkeit - Dialog zwischen Religionen.

Background Advances in artificial intelligence, robotics and wearable computing are creating novel technological opportunities for mitigating the global burden of population ageing and improving the quality of care for older adults with dementia and/or age-related disability. Intelligent assistive technology is the umbrella term defining this ever-evolving spectrum of intelligent applications for the older and disabled population. However, the implementation of IATs has been observed to be sub-optimal due to a number of barriers in the translation of novel applications from the (...) designing labs to the bedside. Furthermore, since these technologies are designed to be used by vulnerable individuals with age- and multi-morbidity-related frailty and cognitive disability, they are perceived to raise important ethical challenges, especially when they involve machine intelligence, collect sensitive data or operate in close proximity to the human body. Thus, the goal of this paper is to explore and assess the ethical issues that professional stakeholders perceive in the development and use of IATs in elderly and dementia care. Methods We conducted a multi-site study involving semi-structured qualitative interviews with researchers and health professionals. We analyzed the interview data using a descriptive thematic analysis to inductively explore relevant ethical challenges. Results Our findings indicate that professional stakeholders find issues of patient autonomy and informed consent, quality of data management, distributive justice and human contact as ethical priorities. Divergences emerged in relation to how these ethical issues are interpreted, how conflicts between different ethical principles are resolved and what solutions should be implemented to overcome current challenges. Conclusions Our findings indicate a general agreement among professional stakeholders on the ethical promises and challenges raised by the use of IATs among older and disabled users. Yet, notable divergences persist regarding how these ethical challenges can be overcome and what strategies should be implemented for the safe and effective implementation of IATs. These findings provide technology developers with useful information about unmet ethical needs. Study results may guide policy makers with firsthand information from relevant stakeholders about possible solutions for ethically-aligned technology governance. (shrink)

In this paper, I set out to argue in favour of a philosophical posthumanist and Nietzschean reading of Ira Levin’s This Perfect Day while demonstrating how transhumanism isunbefitting of being called a Nietzschean theory. I will do this by establishing Chip, the protagonist, as a posthuman and being on the path of the ‘Overhuman’ whereas Wei, the antagonist, will be illustrated as Chip’s intended counterpart the Last Human. Through explaining ‘Transhumansim’ and connecting the field to Wei, I will showcase a (...) new way of reading transhumanist ideology, namely ‘Weiism’. The polar opposite in characters of ‘Overhuman’ and ‘Last Human’ will argue in favour of the Nietzschean paradoxical, as part of philosophical posthumanism. Amor fati and the eternal recurrence become posthumanist narrative tools through their weaving into the posthuman narrative of Chip. My argument is that by making philosophical posthumanism more existentialist in nature, it becomes simpler to argue against nihilistic and totalitarian tendencies of worshipping technology. Finally, it is the spiralling motion forward as a mix between the Nietzschean, eternally cyclical re-inventing of oneself and the posthumanist consideration for the future which makes for a literary combination of the two fields of study. (shrink)