Ontological pluralism is the view that there are different ways of being. Historically, ways of being are aligned with the ontological categories. This paper is about to investigate why there is such a connection, and how it should be understood. Ontological pluralism suffers from an objection, according to which ontological pluralism collapses into ontological monism, i.e., there is only one way to be. Admitting to ontological categories can save ontological pluralism from this objection if ways of being ground ontological categories. (...) -/- . (shrink)

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.

This paper deals with the question of what the most appropriate semantic theory for theoretical terms would be. Traditionally, in the contemporary literature of philosophy of language, there have been two widely held semantic theories: the descriptivist theory and the causal theory. Comparing theoretical terms with natural kind terms, I attempt to show that the causal theory of reference applies to natural kinds owing to certain ontological and epistemological assumptions of natural kinds realism. I argue that there is no reason (...) to keep these assumptions with respect to theoretical entities. Consequently, the causal theory of reference cannot be applied to theoretical terms. Instead, because of certain ontological and epistemological features of theoretical entities, the rival semantic theory, i.e., the descriptivist theory of reference, properly explains how the referents of these terms get fixed and how these terms find their referents. The paper is structured as follows: the first part deals with the question of how a theoretical entity/kind should be distinguished from non-theoretical ones. The second part facilitates a comparison between theoretical kinds and natural kinds to reveal the ontological and epistemological features of each category. In the third part, I argue why the causal theory of reference fails to be a plausible semantic for theoretical terms, and why its rival theory, i.e., the descriptivist theory, provides an appropriate semantic for such terms. Finally, I raise two potential objections regarding my proposed view and try to show how these objections can be overcome. (shrink)

Ontološki pluralizam je gledište prema kojemu postoje različiti načini postojanja. Povijesno gledano, načini postojanja su usklađeni s ontološkim kategorijama. Ovaj rad istražuje zašto postoji takva veza i kako je treba shvatiti. Ontološki pluralizam pati od prigovora prema kojem se ontološki pluralizam urušava u ontološki monizam, tj. u gledište da postoji samo jedan način postojanja. Priznavanje ontoloških kategorija može spasiti ontološki pluralizam od ovog prigovora ako načini postojanja utemeljuju ontološke kategorije.

We take an argument of Gödel's from his ground‐breaking 1931 paper, generalize it, and examine its validity. The argument in question is this: "the sentence G says about itself that it is not provable, and G is indeed not provable; therefore, G is true".

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)

Eine der grossten Schwierigkeiten eines symmetrischen, wechselseitigen Verstehens und Kooperierens ist die Eigenzentrik des Verstehenskriteriums aufgrund der eigenen Lebensform - mit der hochst bedenklichen Konsequenz des Wittgenstein-Mottos dieses Buches, namlich dass wir uns in den Anderen nicht finden konnen. Korrigiert wird dieser Aspekt des interkulturellen Verstehens durch das Konzept einer von allen Kulturen geteilten, allgemeinen menschlichen Lebensform, die wiederum bei Wittgenstein den Rang eines interkulturellen Verstehens-Aprioris einnimmt und die Funktion hat, Sprachspiele und ihre divergierenden Regeln ineinander zu ubersetzen. Wittgensteins spate (...) Untersuchungen tragen aber auch dem Problem unaufhebbarer Kommunikationsgrenzen Rechnung. Und zwar in ihrer Theorie einer -Grammatik- von Weltbildsatzen, die keinerlei Verstehensbrucken zu Weltbildsatzen fremder Kulturen erlaubt. <BR> Die Aufsatze dieses Sammelbandes, der die Ergebnisse des dritten Wittgenstein-Symposions der Deutschen Ludwig Wittgenstein Gesellschaft e.V. zusammenfasst, sind dieser Problematik gewidmet und versuchen, die unterschiedlichen interkulturellen Verstehensmodelle auszuarbeiten, ihre Schwierigkeiten zu analysieren und angemessene Losungsvorschlage zu entwickeln.". (shrink)

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)

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 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)

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.

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)

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)

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.

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)

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)

The proofs of Gödel (1931), Rosser (1936), Kleene (first 1936 and second 1950), Chaitin (1970), and Boolos (1989) for the first incompleteness theorem are compared with each other, especially from the viewpoint of the second incompleteness theorem. It is shown that Gödel’s (first incompleteness theorem) and Kleene’s first theorems are equivalent with the second incompleteness theorem, Rosser’s and Kleene’s second theorems do deliver the second incompleteness theorem, and Boolos’ theorem is derived from the second incompleteness theorem in the standard way. (...) It is also shown that none of Rosser’s, Kleene’s second or Boolos’ theorems is equivalent with the second incompleteness theorem, and Chaitin’s incompleteness theorem neither delivers nor is derived from the second incompleteness theorem. We compare (the strength of) these six proofs with one another. (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 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.

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 and Intensive Care Unit (...) 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. Also, the intensity of moral distress and the intention to leave the ward 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)

We present axiom systems, and provide soundness and strong completeness theorems, for classes of Kripke models with restricted extension rules among the node structures of the model. As examples we present an axiom system for the class of cofinal extension Kripke models, and an axiom system for the class of end-extension Kripke models. We also show that Heyting arithmetic is strongly complete for its class of end-extension models. Cofinal extension models of HA are models of Peano arithmetic.

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

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)

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)

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

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)

Lajevardi and Salehi, in “There may be many arithmetical Gödel sentences”, argue against the use of the definite article in the expression “the Gödel sentence”, by claiming that any unsound theory has Gödelian sentences with different truth values. We show that their Theorems 1 and 2 are special cases (modulo Löb's theorem and the first incompleteness theorem) of general observations pertaining to fixed points of any formula, and argue that the false sentences of Lajevardi and Salehi are in (...) fact not Gödel sentences. (shrink)

Lajevardi and Salehi, in “There may be many arithmetical Gödel sentences”, argue against the use of the definite article in the expression “the Gödel sentence”, by claiming that any unsound theory has Gödelian sentences with different truth values. We show that their Theorems 1 and 2 are special cases (modulo Löb's theorem and the first incompleteness theorem) of general observations pertaining to fixed points of any formula, and argue that the false sentences of Lajevardi and Salehi are in (...) fact not Gödel sentences. (shrink)

Lajevardi and Salehi, in “There may be many arithmetical Gödel sentences”, argue against the use of the definite article in the expression “the Gödel sentence”, by claiming that any unsound theory has Gödelian sentences with different truth values. We show that their Theorems 1 and 2 are special cases (modulo Löb's theorem and the first incompleteness theorem) of general observations pertaining to fixed points of any formula, and argue that the false sentences of Lajevardi and Salehi are in (...) fact not Gödel sentences. (shrink)