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.

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".

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)

In the naturalism and evolutionism context, the ultimate objective and function of cognitive faculties is adaptation, survival and reproduction. Our cognitive faculties are not developed to generate true beliefs, therefore, but to have adapt behavior. Alvin Planatinga is not at ease with naturalism idea. To him, the problem with naturalism is the non-existence of proper understanding on the manner by which the belief and behavior are interrelated, thus, he concludes that the reliability of cognitive faculties are founded on low naturalistic (...) evolutionism; because any alleged argument against these faculties, first, requires reliable perceptual faculties and next, if we realize lack of reliability in these faculties we developed self-defeating belief, consequently, in both the cases naturalism face criticism. Plantiga’s criticism on naturalism view as to reliability of cognitive faculties has made some philosophers encounter problems like: 1) high probability of interrelating casual belief and behavior, 2) argument based on personal incredulity, 3) lack of distinction between reflective and non-reflective knowledge, 4) finding independent evidence for reliability as to escape self-defeating, 5) the external status of mental states and 6) the problem of circle. To the authors here, except the problem of circle, Plantiga has been able to find proper answer for the rest of five problems. The objective here is to analyze, complete, expand and criticize Plantiga’s notion in rejecting the atheistic naturalism through the ability to secure cognitive faculties to unveil consistency of the new scientific findings with religious beliefs. (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)

The Global Media and Information Literacy Week commemorates the progress in achieving “MIL for all” by aggregating various MIL-related local and international events and actions across different disciplines around the world.The MIL Global Week 2018, 24 to 31 October, was marked by the United Nations Educational, Scientific and Cultural Organization in collaboration with various organizations including the UN Alliance of Civilizations, the Global Alliance for Partnership on MIL, the International Federation of Library Associations, the International Association of School Libraries, and (...) the UNESCO-UNAOC University Cooperation Programme on Media and Information Literacy and Intercultural Dialogue. (shrink)

Kripke frames (and models) provide a suitable semantics for sub-classical logics; for example, intuitionistic logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive Kripke frames (with persistent satisfaction relations), and the basic logic (of Visser) axiomatizes transitive Kripke frames (with persistent satisfaction relations). Here, we investigate whether Kripke frames/models could provide a semantics for fuzzy logics. For each axiom of the basic fuzzy logic, necessary and sufficient conditions are sought for Kripke frames/models which satisfy them. It turns out that (...) the only fuzzy logics (logics containing the basic fuzzy logic) which are sound and complete with respect to a class of Kripke frames/models are the extensions of the Gödel logic (or the super-intuitionistic logic of Dummett); indeed this logic is sound and strongly complete with respect to reflexive, transitive and connected (linear) Kripke frames (with persistent satisfaction relations). This provides a semantic characterization for the Gödel logic among (propositional) fuzzy logics. (shrink)

The dissemination of information in times of crisis or emergency is distinctive since the affected individuals may take, process, and act on information differently. As the Centers for Disease Control and Prevention noted “the right message at the right time from the right person can save lives.” This study elaborates on the principles of crisis and emergency risk communication (CERC) in the realistic narrative, and notes that a successful CERC should be prompt, accurate, veracious, empathetic, respectful, and promote meaningful action. (...) Since pandemics are not only biomedical but also social, political, economic, and cultural incidents, critical communication in the time of a pandemic is of crucial significance. Hence, the Coronavirus (COVID-19) pandemic is assessed as a recent and important case study. This pandemic had four chief challenges; including that since the disease is caused by the novel SARS-CoV-2 virus the assumptions about the disease have been revised numerously and rapidly. In addition, the cumulative scale and scope of COVID-19 which is in excess of 627 million confirmed cases, and approximately 6.58 million deaths worldwide remained a strain. Another concern was the overwhelming uncertainty and evolving trajectory of the pandemic about how and when it ends or enters the endemic stage of the outbreak. Finally, the overabundance of amplification and dissemination of both accurate and inaccurate information led to an infodemic. Long before the COVID-19 pandemic, many individuals used the internet as an important resource for seeking health-related information. However, the infodemic and the other aforementioned challenges made distinguishing up-to-date accurate information a more arduous task, and CERC and pandemic-related communication are even more crucial. Hence, a multi-dimensional set of skills is required to overcome these challenges whether amidst or after the pandemic. Therefore, a multi-stakeholder approach towards an overarching and comprehensive metaliteracy that “provides an integrated and inclusive framework to cultivate critical thinking and proficiency in comprehending data, information, visuals and the media” is essential. This study recommends and elaborates on how to incorporate metaliteracy into crisis and risk communication at governmental, organizational, and individual levels. (shrink)

Intuitionistic Propositional Logic is proved to be an infinitely many valued logic by Gödel (Kurt Gödel collected works (Volume I) Publications 1929–1936, Oxford University Press, pp 222–225, 1932), and it is proved by Jaśkowski (Actes du Congrés International de Philosophie Scientifique, VI. Philosophie des Mathématiques, Actualités Scientifiques et Industrielles 393:58–61, 1936) to be a countably many valued logic. In this paper, we provide alternative proofs for these theorems by using models of Kripke (J Symbol Logic 24(1):1–14, 1959). Gödel’s proof gave (...) rise to an intermediate propositional logic (between intuitionistic and classical), that is known nowadays as Gödel or the Gödel-Dummett Logic, and is studied by fuzzy logicians as well. We also provide some results on the inter-definability of propositional connectives in this logic. (shrink)

In Russian Foreign Policy: The Return of Great Power Politics, Jeffrey Mankoff examines the course of Russian foreign policy since the dissolution of the Soviet Union in 1991. He provides a comprehensive over-view of both the continuity and the changes in Russian foreign policy from the end of the Cold War to the Putin era, and analyses Russia’s interactions with major global powers. Throughout the book, the author makes use of various theoretical approaches, including theories of international relations, classical geopolitical (...) theory and Russian geopolitical tradition. (shrink)

It is quite well-known from Kurt G¨odel’s (1931) ground-breaking Incompleteness Theorem that rudimentary relations (i.e., those definable by bounded formulae) are primitive recursive, and that primitive recursive functions are representable in sufficiently strong arithmetical theories. It is also known, though perhaps not as well-known as the former one, that some primitive recursive relations are not rudimentary. We present a simple and elementary proof of this fact in the first part of the paper. In the second part, we review some possible (...) notions of representability of functions studied in the literature, and give a new proof of the equivalence of the weak representability with the (strong) representability of functions in sufficiently strong arithmetical theories. (shrink)

‎A universal schema for diagonalization was popularized by N. S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fit more theorems in the universal‎ ‎schema of diagonalization‎, ‎such as Euclid's proof for the infinitude of the primes and new proofs (...) of G. Boolos (1997) for Cantor's theorem on the non-equinumerosity of a set with its powerset‎. ‎Then‎, ‎in Linear Temporal Logic‎, ‎we show the non-existence of a fixed-point in this logic whose proof resembles the argument of Yablo's paradox (1985‎, ‎1993)‎. ‎Thus‎, ‎Yablo's paradox turns for the first time into a genuine mathematico-logical theorem in the framework of Linear Temporal Logic‎. ‎Again the diagonal schema of the paper is used in this proof; and it is also shown that G. Priest's inclosure schema (1997) can fit in our universal diagonal / fixed-point schema‎. ‎We also show the existence of dominating (Ackermann-like) functions (which dominate a given countable set of functions‎, ‎such as primitive recursive functions) in the schema. (shrink)

By formalizing some classical facts about provably total functions of intuitionistic primitive recursive arithmetic (iPRA), we prove that the set of decidable formulas of iPRA and of iΣ1+ (intuitionistic Σ1-induction in the language of PRA) coincides with the set of its provably ∆1-formulas and coincides with the set of its provably atomic formulas. By the same methods, we shall give another proof of a theorem of Marković and De Jongh: the decidable formulas of HA are its provably ∆1-formulas.

Owing to the escalating regional rivalries and the conventional arms race, Iran’s post-revolutionary hostilities towards the West, in addition to the crucial geopolitical and economic significance of the region, the complex Iranian nuclear crisis has made the global leaders to brood over the multilateral Iranian negotiations with the P5+1 and the International Atomic Energy Agency, which led to finalization and adoption of the Joint Comprehensive Plan of Action in 2015. The United Kingdom as a permanent member of the United Nations (...) Security Council, a nuclear state, the bridge to the Cross-Atlantic relations, in addition to its noted ‘special relationship’ with the United States, and having over two centuries of political ties with Iran has constantly played a crucial role in all stages of the negotiations and tightening the imposed embargoes. Indeed, ever since the 1979 Revolution the Anglo-Iranian relations have been volatile and have suffered from tension, instability, and upheavals; despite reconciliation in 1998 and some prominent diplomatic accomplishments in nuclear negotiations the sour relations had strained by several incidents in the past two decades. This study addresses the Anglo-Iranian relations and attempts to provide theoretical scrutiny of the UK foreign policy on the Iranian nuclear program and clarify the British approach through the lens of game theories with respect to neorealism, classical realism, neoclassical realism, and liberalism perspectives. (shrink)

The phenomena of terrorism and other politically motivated violence have been assessed across different disciplines from political science and economics to theology and psychology. Whereas the definitions of the concepts of “terrorism” and “terrorist” are disputed and they rather reflect the perspectives of the defining entity, there is a common consensus that terrorism can be classified in terms of its type (such as state-sponsored, dissent, religious, pathological, narco-, cyber-, and bioterrorism), the scale (i.e. domestic vs. international), motives, and objectives. By (...) the same token, the roots and causes of terrorism can be enumerated as internal sources (such as social, economic, political, and cultural indicators) and external sources (such as colonialism and neocolonialism, regional conflicts and historical enmities, failed/failing states and lawless areas, and the penetration of foreign cultures and lifestyles). Although such grounds can be considered as the collective causes, they can merely address how one becomes a potential appropriate recruit for terrorist organizations. Hence, identifying the causes of terrorism is of paramount significance in order to both combat and most importantly prevent terrorism. Given that the first generation of psychological approaches to terrorist violence, chiefly drawing from psychoanalytic theory, has basically run its course, this study takes a systematic approach to evaluate the root causes of terrorism, particularly from social and behavioral perspectives, and attempts to address some key questions such as the progress of and reasons for individuals supporting, joining and leaving terrorist organizations, the relevance of psychopathology to comprehending and preventing terrorism, and the roles of ideology, identity, and belonging in terrorist behavior. (shrink)

From the animosity of the Cold War era, the rapprochement in 1972, normalization of relations in 1979, to rising China and the current trade war, the US-China relationship has emerged and been regarded as an important relationship in global politics, and distinctively significant in the shaping of world order. The United States, a fount of modern think tanks, is home to approximately 30% of the total in the world. These think tanks were gradually embedded into American politics and exercise undoubtedly (...) significant influence in the policymaking process, particularly foreign affairs. Hence, as an emerging global power, China has been the subject of US think tanks debate from different perspectives, such as economy, military, and foreign affairs. This study reviews the post-World War II US-China relations, addresses China’s economic and military rise, its territorial claims and provides policy options for balancing cooperation and conflict in each of these matters. Given that the assimilation of perspectives of American think tanks can foster comprehending the perception of the US regarding China’s rise and Washington-Beijing relations, this internet-mediated research based on foreign policy analysis with the principal focus on agency at institutional level takes a systematic approach to discuss China policy debates among the US think tanks. The objective is to offer an overall review of the China policy debate in the US over the past two decades, whereas the chief focus is dedicated to the perceptions of China in American think tanks about the concepts of “China collapse”, “China threat” and “China responsibilities”; furthermore, providing an assessment of the impact of think tanks on China’s most-favored-nation (MFN) treatment, the legislature on permanent normal trade relations (PNTR), and contemporary trade relations between the two countries. (shrink)

پژوهشگران پدیده تروریسم را از مواضع مختلفی ازجمله سیاسی، اقتصادی، روانشناختی، اجتماعی، فرهنگی و دینی مورد مطالعه قرار دادهاند. علیرغم وجود تعاریف متعدد و غیرواحدی از مفهوم تروریسم و تروریست بیان شده است که به طور کلی بیانگر دیدگاه ارائه دهنده آن است، اجماعی بر دسته بندی تروریسم یراساس نوع (مانند دولتی، مذهبی، پاتولوژیک، سایبری، نارکوتروریسم و بیوتروریسم)، مقیاس (داخلی و بین المللی)، انگیزه ها و اهداف آن وجود دارد. همچنین، ریشه ها و علل تروریسم می تواند منشا داخلی (مانند (...) شاخص های اجتماعی، اقتصادی، سیاسی و فرهنگی) و خارجی (مانند استعمار و پسااستعمار، درگیری های منطقه ای و دشمنی های تاریخی، دولت درمانده و مناطق بی قانون، و نفوذ فرهنگ و سبک زندگی بیگانه) داشته باشد. چنین زمینه هایی می توانند به عنوان علل اشتراکی در نظر گرفته شوند و صرفا بیانگر دلایل احتمالی تبدیل یک فرد به یک عضو بالقوه سازمانهای تروریستی است ولی بهندرت توضیحی درباره چگونگی جذب آن فرد به سازمان های تروریستی ارائه می کنند. از این رو، شناسایی علل ظهور تروریسم و عضویت افراد در سازمانهای تروریستی از اهمیت ویژهای به منظور مبارزه و جلوگیری از آن برخوردار است. با توجه به اینکه نسل اول رویکردهای روانشناختی به خشونت تروریستی اساسا از تئوری روانکاوی نشئت می گرفتند و دیگر توجیه کننده تروریسم مدرن نیستند، این پژوهش با رویکردی سیستماتیک مبنی بر روش پدیدارشناسی به ارزیابی دلایل اصلی تروریسم بهویژه از منظر اجتماعی و رفتاری می پردازد. هدف این پژوهش مطرح کردن و پاسخ دادن به سوالات کلیدی شامل دلایل افراد برای حمایت، عضویت، و ترک سازمان های تروریستی، مناسب بودن علم آسیب شناسی روانی برای درک و جلوگیری از تروریسم، و نقش ایدئولوژی، هویت و تعلق در رفتار تروریستی است. (shrink)

Digitalization and the emergence of the Internet have resulted in escalating access to information and communication. Given the circumstances that soaring access to information amounts to the intensification of misinformation and disinformation, a set of critical skills to navigate and critically assess the information is necessary. This paper outlines the significance of these skills, and provides a perspective on metaliteracy as a supplement to media and information literacy, and argues that the ability to conceptualize, access, comprehend, analyze, and use information (...) is crucial in achieving inclusive, pluralistic, and participatory knowledge societies. (shrink)

Issues including the immigration flows, increased diversity of the society, and alienation of parts of the population are not necessarily new phenomena for the European Union. As an illustration, Frontex, the EU Agency for the Management of Operational Cooperation at the External Borders, was founded in 2004 in the light of the uncontrolled immigration from Africa to control the cooperation between national border guards securing its external borders, or EUROSUR (the European Border Surveillance System) has come to effect since 2013.

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)

Objectives: To explore individuals’ perception of the personal, family and societal educational needs following a spinal cord injury. Methods: Sixty-one patients who sustained a traumatic SCI between March 2015 and June 2016 referred to Brain and Spinal Cord Injury Research Center were included in a cross sectional study and completed an online survey containing open-and closed-ended questions, in Iran. Participants’ responses were analyzed i using a qualitative approach with a thematic analysis. Results: Following a thematic analysis of the patient’s perceived (...) educational needs, 3 themes and 14 subthemes were identified. The 3 themes included personal, family, and societal educational perceived needs. Within personal educational needs, there were 7 subthemes which included personal independence and transportation, financial independence, life skills modification, knowledge about SCI, prevention of SCI complications, relationships and sexual function, and psychological adjustments. Among family educational needs, the 3 subthemes were caregiver skills and communication, first aid and emergency skills, and emotional and psychological support. For societal educational needs, the 4 subthemes described were social integration, interpersonal communication skills, SCI awareness and injury prevention, sympathize while avoiding pity. Conclusion: According to our findings, people with SCI have various needs that need to be addressed. Educational support should be a part of a comprehensive rehabilitation program and geared towards addressing the patients’ personal and family needs, while educating the community about SCI in order to allow for reintegration into society. (shrink)

In this novel work, Paul Chilton expends a considerable amount of effort examining relations between the use of language and political discourse. Many realist linguists in the past century claimed that language should be evaluated as the innate part of a human mind. The scholarly interest in the public use of language is followed by crit-ical theory and the Frankfurt School of social theory and philosophy, which considered language rather as a social phenomenon than a mental phenomenon and intended to (...) validate the crucial relationship between language, politics and culture. (shrink)