The proofs of Kleene, Chaitin and Boolos for Gödel's First Incompleteness Theorem are studied from the perspectives of constructivity and the Rosser property. A proof of the incompleteness theorem has the Rosser property when the independence of the true but unprovable sentence can be shown by assuming only the (simple) consistency of the theory. It is known that Gödel's own proof for his incompleteness theorem does not have the Rosser property, and we show that neither do Kleene's or Boolos' proofs. (...) However, we show that a variant of Chaitin's proof can have the Rosser property. The proofs of Gödel, Rosser and Kleene are constructive in the sense that they explicitly construct, by algorithmic ways, the independent sentence(s) from the theory. We show that the proofs of Chaitin and Boolos are not constructive, and they prove only the mere existence of the independent sentences. (shrink)

It is shown that all the provably total functions of Basic Arithmetic BA, a theory introduced by Ruitenburg based on Predicate Basic Calculus, are primitive recursive. Along the proof a new kind of primitive recursive realizability to which BA is sound, is introduced. This realizability is similar to Kleene's recursive realizability, except that recursive functions are restricted to primitive recursives.

Gödel's second incompleteness theorem is proved for Herbrand consistency of some arithmetical theories with bounded induction, by using a technique of logarithmic shrinking the witnesses of bounded formulas, due to Z. Adamowicz [Herbrand consistency and bounded arithmetic, Fundamenta Mathematical vol. 171 (2002), pp. 279-292]. In that paper, it was shown that one cannot always shrink the witness of a bounded formula logarithmically, but in the presence of Herbrand consistency, for theories I∆₀+ Ωm, with m ≥ 2, any witness for any (...) bounded formula can be shortened logarithmically. This immediately implies the unprovability of Herbrand consistency of a theory T ⊇ I∆₀ + Ω₂ in t itself. In this paper, the above results are generalized for I∆₀ + Ω₁. Also after tailoring the definition of Herbrand consistency for I∆₀ we prove the corresponding theorems for I∆₀. Thus the Herbrand version of Gödel's second incompleteness theorem follows for the theories I∆₀ + Ω₁ and I∆₀. (shrink)

Moral distress is a fundamental problem in the nursing profession that affects nurses. Critical care nurses are more susceptible to this problem due to the nature of their work. Moral distress may, in turn, lead to several undesirable consequences. This study aimed to determine the relationship between moral distress and intention to leave the ward among critical care nurses. This descriptive-correlational study was conducted by census method on all eligible nurses who worked in Coronary Care Unit (CCU) and Intensive Care (...) Unit (ICU) of AhVaz hospitals, Iran. Data was collected by Corley’s moral distress questionnaire and a researcher-made questionnaire to investigate the intention to leave the ward. Questionnaires were completed through self-report and data were analyzed using a t-test and Pearson correlation coefficient. The results showed that there was a direct association between moral distress and intension to leave the ward in critical care nurses (P < 0.05). Also, the intensity of moral distress (P = 0.03) and the intention to leave the ward (P = 0.007) were significantly higher in ICU nurses. Given the high exposure of critical care nurses with moral distress and its association with leaving the ward, it seems that devising strategies to reduce or control moral distress and its negative consequences are necessary, particularly in ICU nurses. (shrink)

IntroductionNowadays, biotechnology has a significant influence on different aspects of human life. The applications of biotechnology are so broad, and the advantages so compelling, that virtually every industry is using this technology. Developments are under way in areas as diverse as pharmaceuticals, diagnostics, textiles, aquaculture, forestry, chemicals, household products, environmental cleanup, food processing, and forensics, to name a few. Biotechnology is enabling these industries to make new or better products, often with greater speed, efficiency, and flexibility. Biotechnology is any technological (...) application that uses biological systems, living organisms, or derivatives thereof to make or modify products or processes for specific use. It applies the knowledge of biology to enhance and improve the environment, health, and food supply. Using biotechnology, scientists work to develop environment-friendly alternatives to fossil fuels and plastics; new medicines, vaccines, and. (shrink)

A cornerstone of modern mathematical logic is the diagonal lemma of Gödel and Carnap. It is used in e.g. the classical proofs of the theorems of Gödel, Rosser and Tarski. From its first explication in 1934, just essentially one proof has appeared for the diagonal lemma in the literature; a proof that is so tricky and hard to relate that many authors have tried to avoid the lemma altogether. As a result, some so called diagonal-free proofs have been given for (...) the above mentioned fundamental theorems of logic. In this paper, we provide new proofs for the semantic formulation of the diagonal lemma, and for a weak version of the syntactic formulation of it. (shrink)

A polynomially bounded recursive realizability, in which the recursive functions used in Kleene's realizability are restricted to polynomially bounded functions, is introduced. It is used to show that provably total functions of Ruitenburg's Basic Arithmetic are polynomially bounded (primitive) recursive functions. This sharpens our earlier result where those functions were proved to be primitive recursive. Also a polynomially bounded schema of Church's Thesis is shown to be polynomially bounded realizable. So the schema is consistent with Basic Arithmetic, whereas it is (...) inconsistent with Heyting Arithmetic. (shrink)

We demonstrate that, in itself and in the absence of extra premises, the following argument scheme is fallacious: The sentence A says about itself that it has a property F, and A does in fact have the property F; therefore A is true. We then examine an argument of this form in the informal introduction of Gödel’s classic (1931) and examine some auxiliary premises which might have been at work in that context. Philosophically significant as it may be, that particular (...) informal argument plays no rôle in Gödel’s technical results. Going deeper into the issue and investigating truth conditions of Gödelian sentences (i.e., those sentences which are provably equivalent to their own unprovability) will provide us with insights regarding the philosophical debate on the truth of Gödelian sentences of systems—a debate which goes back to Dummett (1963). (shrink)

Interesting as they are by themselves in philosophy and mathematics, paradoxes can be made even more fascinating when turned into proofs and theorems. For example, Russell’s paradox, which overthrew Frege’s logical edifice, is now a classical theorem in set theory, to the effect that no set contains all sets. Paradoxes can be used in proofs of some other theorems—thus Liar’s paradox has been used in the classical proof of Tarski’s theorem on the undefinability of truth in sufficiently rich languages. This (...) paradox (as well as Richard’s paradox) appears implicitly in Gödel’s proof of his celebrated first incompleteness theorem. In this paper, we study Yablo’s paradox from the viewpoint of first- and second-order logics. We prove that a formalization of Yablo’s paradox (which is second order in nature) is non-first-orderizable in the sense of George Boolos (1984). (shrink)

Background: Physical restraint is among the commonly used methods for ensuring patient safety in intensive care units. However, nurses usually experience ethical dilemmas over using physical restraint because they need to weigh patient autonomy against patient safety. Aim: The aim of this study was to explore factors behind ethical dilemmas for critical care nurses over using physical restraint for patients. Design: This is a qualitative study using conventional content analysis approach, as suggested by Graneheim and Lundman, to analyze the data. (...) Methods: Seventeen critical care nurses were purposefully recruited from the four intensive care units in Tehran, Iran. Data were collected through in-depth semi-structured interviews and were concurrently analyzed through conventional content analysis as suggested by Graneheim and Lundman. Ethical consideration: This study was approved by the Ethics Committee of Iran University of Medical Sciences, Tehran, Iran with the code: IR.IUMS.REC.1397.795. Before interviews, participants were provided with explanations about the aim of the study, the confidentiality of the data, their freedom to participate, and the right to withdraw the study, and their free access to the study findings. Finally, their consents were obtained, and interviews were started. Results: Factors behind ethical dilemmas for critical care nurses over using physical restraint were categorized into three main categories, namely the outcomes of using physical restraint, the outcomes of not using physical restraint, and emotional distress for nurses. The outcomes of using physical restraint were categorized into the three subcategories of ensuring patient safety, physical damage to patients, and mental damage to the patient. The outcomes of not using physical restraint fell into two subcategories, namely the risks associated with not using physical restraint and legal problems for nurses. Finally, the two subcategories of the emotional distress for nurses main category were nurses’ negative feelings about restraint use and uncertainty over the decision on physical restraint use. Conclusion: Decision-making for restraint use is often associated with ethical dilemmas, because nurses need to weight the outcomes of its use against the outcomes of not using it and also consider patient safety and autonomy. Health authorities are recommended to develop clear evidence-based guidelines for restraint use and develop and implement educational and counseling programs for nurses on the principles of ethical nursing practice, patient rights, physical restraint guidelines and protocols, and management of emotional, ethical, and legal problems associated with physical restraint use. (shrink)

We argue that Gödel's completeness theorem is equivalent to completability of consistent theories, and Gödel's incompleteness theorem is equivalent to the fact that this completion is not constructive, in the sense that there are some consistent and recursively enumerable theories which cannot be extended to any complete and consistent and recursively enumerable theory. Though any consistent and decidable theory can be extended to a complete and consistent and decidable theory. Thus deduction and consistency are not decidable in logic, and an (...) analogue of Rice's Theorem holds for recursively enumerable theories: all the non-trivial properties of them are undecidable. (shrink)

We formalize the notion of Herbrand Consistency in an appropriate way for bounded arithmetics, and show the existence of a finite fragment of IΔ0 whose Herbrand Consistency is not provable in IΔ0. We also show the existence of an IΔ0-derivable Π1-sentence such that IΔ0 cannot prove its Herbrand Consistency.

We prove the equivalence of the semantic version of Tarski’s theorem on the undefinability of truth with the semantic version of the diagonal lemma and also show the equivalence of a syntactic version of Tarski’s undefinability theorem with a weak syntactic diagonal lemma. We outline two seemingly diagonal-free proofs for these theorems from the literature and show that the syntactic version of Tarski’s theorem can deliver Gödel–Rosser’s incompleteness theorem.

We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel’s First Incompleteness Theorem, one cannot, without impropriety, talk about *the* Gödel sentence of the theory. The reason is that, without violating the requirements of Gödel’s theorem, there could be a true sentence and a false one each of which is provably equivalent to its own unprovability in the theory if the theory is unsound.

BackgroundNurses provide the majority of health-care services and face numerous health challenges during an epidemic. During the COVID-19 epidemic, nurses are subjected to physical, mental, and social disorders that impair their quality of life and hardiness. Therefore, it is important to be aware of the situation of nurses. The current study aimed to compare the compassion satisfaction, compassion fatigue and hardiness among nurses before and during the COVID-19 outbreak.Materials and MethodsThis cross-sectional study included 508 clinical nurses from one public hospital (...) in southern Iran. The subjects were recruited using census sampling methods in 2019–2020. Sampling was performed before and during the COVID-19 with a 1-year interval. Although, the study setting was the same before and during the COVID-19, questionnaires were completed by different nurses before and during the COVID-19. Demographic questionnaire, professional quality of life questionnaire and Occupational Hardiness Questionnaire were used to collect data.ResultsThe scores of compassion satisfaction, compassion fatigue and hardiness did not differ significantly during the COVID-19 compared with before the COVID-19. Before COVID-19, hardiness and work experience predicted 11% of the variance of compassion satisfaction, whereas during COVID-19, hardiness and gender predicted 26% of the variance of compassion satisfaction. Before COVID-19, hardiness and work experience predicted 3% of the variance of compassion fatigue, whereas during COVID-19, hardiness, type of employment and gender predicted 6% of the variance of compassion fatigue.ConclusionThe current study found that compassion satisfaction, compassion fatigue and hardiness did not change during the COVID-19 outbreak compared with before the COVID-19 outbreak. However, during the COVID-19, the hardiness was a significant predictor of compassion satisfaction and compassion fatigue. The study results showed that it was possible to increase the compassion satisfaction and reduce the compassion fatigue by strengthening the hardiness of nurses. However, these results need to be considered in future studies, especially in crises such as COVID-19 disease. (shrink)

We respond to some of the points made by Bennet and Blanck (2022) concerning a previous publication of ours (2021).

To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn Yablo's paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo's paradox comes in several varieties; and he showed in 2004 that there are other versions that are equally paradoxical. Formalizing these versions (...) of Yablo's paradox, we prove some theorems in LTL. This is the first time that Yablo's paradox(es) become new(ly discovered) theorems in mathematics and logic. (shrink)

Effective climate change resilience in local communities must center each community’s unique challenges and essential role in developing climate resilience strategies. This article will discuss recent developments by the federal government that align with a community-centered approach, and how Community Health Workers can influence the outcomes.

Public health laws and policies are uniquely able to mitigate the adverse and inequitable health impacts of climate change. This article summarizes some key considerations in developing such laws and policies and a variety of approaches local public health departments are using to increase climate resilience and health equity.

Anthropology in psychology under the title of "personality theories" has been able to be effective in the field of behavioral studies and interpersonal relationships. The need to explain and analyze the true nature of man in the field of "being" - contrary to psychological personality theories that generally identify human nature in the field of "appearance" - caused this article based on Sadra's anthropological opinions and view According to Allport's trait theory, which is one of the pioneers of the trait (...) approach, it should be organized by descriptive-analytical method. The individualistic approach based on traits is the main feature of Allport's and Mulla Sadra's personality theory. The foundation of personality in both theories is based on the most profound characteristics of person; However, in the analysis of Mulla Sadra's philosophical texts, the quality of the appearance of these traits and why they influence the structure of personality and, accordingly, human behavior, have been explained. "Self" or ego, contrary to its abstract concept in Alport's view, is a real and existential thing in Sadrai's system. The dynamism and unity of Alporti's personality can be rationally explained by the rule of "unity of the known and the known" and "intrinsic volitional movement". (shrink)

This is a report on the Doctoral Consortium co-located with the 17th International Conference on Artificial Intelligence and Law in Montreal.

The key stakeholders of the Finnish engineering education collaborated during 2006–09 to reform the system of education, to face the challenges of the changing business environment and to create a national strategy for the Finnish engineering education. The work process was carried out using participatory work methods. Impacts of sustainable development (SD) on engineering education were analysed in one of the subprojects. In addition to participatory workshops, the core part of the work on SD consisted of a research with more (...) than 60 interviews and an extensive literature survey. This paper discusses the results of the research and the work process of the Collaboration Group in the subproject of SD. It is suggested that enhancing systematic dialogue among key stakeholders using participatory work methods is crucial in increasing motivation and commitment in incorporating SD in engineering education. Development of the context of learning is essential for improving skills of engineering graduates in some of the key abilities related to SD: systemic- and life-cycle thinking, ethical understanding, collaborative learning and critical reflection skills. This requires changing of the educational paradigm from teacher-centred to learner-centred applying problem- and project-oriented active learning methods. (shrink)

This work offers a new theory of what it means to be a legal person and suggests that it is best understood as a cluster property. The book explores the origins of legal personhood, the issues afflicting a traditional understanding of the concept, and the numerous debates surrounding the topic.

This is the best general book on philosophy for university students: not just an introduction, but a guide which will serve them throughout their studies. It comprises specially commissioned explanatory surveys of the main areas of philosophy, written by thirteen leading philosophers.

Talking Politics is a philosophical examination of some of the basic concepts of political discourse. Its primary focus is on the ordinary ; on what is said by politicians, in newspapers and by people in pubs, rather than on the works of political theorists. This is a work of , but not on political theory. Talking Politics is: * Invaluable as a source of reference for students, and contains a detailed index * Arranged thematically, around topics such as `Nation'. Each (...) entry has copious cross-references and suggestions for further reading A. W. Sparkes is uniquely qualified to write such a book, combining some thirty years' teaching as a philosopher with wide experience of, and a life-long fascination with, politics. His attitude is that of a critical, but uncynical, observer. (shrink)

This paper describes and defends the view that minimal chemical life essentially involves the chemical integration of three chemical functionalities: containment, metabolism, and program (Rasmussen et al. in Protocells: bridging nonliving and living matter, 2009a ). This view is illustrated and explained with the help of CMP and Rasmussen diagrams (Rasmussen et al. In: Rasmussen et al. (eds.) in Protocells: bridging nonliving and living matter, 71–100, 2009b ), both of which represent the key chemical functional dependencies among containment, metabolism, and (...) program. The CMP model of minimal chemical life gains some support from the broad view of life as open-ended evolution, which I have defended elsewhere (Bedau in The philosophy of artificial life, 1996 ; Bedau in Artificial Life, 4:125–140, 1998 ). Further support comes from the natural way the CMP model resolves the puzzle about whether life is a matter of degree. (shrink)

Multilingual dictionary of philosophical terms.

The use of with the future indicative is admittedly rare in post-Homeric Greek. In the passages concerned many deny the usage completely and either omit the particle or resort to emendation, or dismiss the construction as a mere ana-colouthon. In an instructive article in the Classical Quarterly, xl , Moorhouse argues in favour of retaining many of the readings, and it is only his interpretation that is in question here. His main thesis is that in Homeric Greek, where the usage (...) is common enough, κ or with the future means either ‘in that case’ or ‘probably’ . The latter usage, however, he regards as sometimes assuming a tone of dogmatic certainty , and this ‘emphatic future’ came to be the regular and literal meaning of the later idiom, without any irony being involved. (shrink)

The paper begins with a defence of a new definition of privacy as the absence of undocumented personal knowledge. In the middle section, I criticise alternative accounts of privacy. Finally, I show how my definition can be worked into contemporary American Law.