Migration and refugeeism have become widespread phenomena in the contemporary world. They affect both the migrants’ countries of origin, as well as transit and target countries. The contemporary migrant crisis is becoming a challenge not only for politicians, diplomats and economists, but also for sociologists, demographers and philosophers. It is also a challenge for the Catholic Church because it affects millions of Christians to whose countries migrants and refugees are coming. The purpose of this article is to explain the social (...) teaching of the Church in this regard. It contains examples of statements made by the Second Vatican Council and the Popes: John Paul II, Benedict XVI and Francis. (shrink)

Unfounded—conspiracy and health—beliefs about COVID-19 have accompanied the pandemic worldwide. Here, we examined cross-nationally the structure and correlates of these beliefs with an 8-item scale, using a multigroup confirmatory factor analysis. We obtained a two-factor model of unfounded (conspiracy and health) beliefs with good internal structure (average CFI = 0.98, RMSEA = 0.05, SRMR = 0.04), but a high correlation between the two factors (average latent factor correlation = 0.57). This model was replicable across 50 countries (total N = 13,579), (...) as evidenced by metric invariance between countries (CFI = 0.96, RMSEA = 0.06, SRMS = 0.07) as well as scalar invariance across genders (CFI = 0.98, RMSEA = 0.04, SRMS = 0.03) and educational levels (CFI = 0.98, RMSEA = 0.04, SRMS = 0.03). Also, lower levels of education, more fear of COVID-19, and more cynicism were weakly associated with stronger conspiracy and health beliefs. The study contributes to knowledge about the structure of unfounded beliefs, and reveals the potential relevance of affective (i.e., fear of COVID-19) and cognitive (i.e., cynicism) factors along with demographics, in endorsing such beliefs. In summary, we obtained cross-cultural evidence for the distinctiveness of unfounded conspiracy and health beliefs about COVID-19 in terms of their structure and correlates. (shrink)

Unfounded—conspiracy and health—beliefs about COVID-19 have accompanied the pandemic worldwide. Here, we examined cross-nationally the structure and correlates of these beliefs with an 8-item scale, using a multigroup confirmatory factor analysis. We obtained a two-factor model of unfounded (conspiracy and health) beliefs with good internal structure (average CFI = 0.98, RMSEA = 0.05, SRMR = 0.04), but a high correlation between the two factors (average latent factor correlation = 0.57). This model was replicable across 50 countries (total N = 13,579), (...) as evidenced by metric invariance between countries (CFI = 0.96, RMSEA = 0.06, SRMS = 0.07) as well as scalar invariance across genders (CFI = 0.98, RMSEA = 0.04, SRMS = 0.03) and educational levels (CFI = 0.98, RMSEA = 0.04, SRMS = 0.03). Also, lower levels of education, more fear of COVID-19, and more cynicism were weakly associated with stronger conspiracy and health beliefs. The study contributes to knowledge about the structure of unfounded beliefs, and reveals the potential relevance of affective (i.e., fear of COVID-19) and cognitive (i.e., cynicism) factors along with demographics, in endorsing such beliefs. In summary, we obtained cross-cultural evidence for the distinctiveness of unfounded conspiracy and health beliefs about COVID-19 in terms of their structure and correlates. (shrink)

We prove that compactness is equivalent to the amalgamation property, provided the occurrence number of the logic is smaller than the first uncountable measurable cardinal. We also relate compactness to the existence of certain regular ultrafilters related to the logic and develop a general theory of compactness and its consequences. We also prove some combinatorial results of independent interest.

This study was designed to determine the quality of service through the evaluation of hospitalized patients. An analysis of hospitalized patients’ subjective feelings towards service quality was carried out, in the context of the application of the SERVQUAL method. The pilot study was conducted in a Silesian hospital in a group of 29 young patients diagnosed with kidney disease. The study used a standard sheet of 22 SERVQUAL statements and an analysis of the significance of the 5 areas of quality (...) material important for the patient. According to the respondents, the most important of the 5 features that influence the quality of life is the ability of the ward staff to provide adequate medical services The least important were the aesthetics and ergonomics of rooms. Service quality gaps were seen in all the five dimensions as well as in the overall service quality. Hence, the following conclusions could be made: 1. The SERVQUAL method helps to identify discrepancies between perceptions of patients’ expectations in all the dimensions of quality of medical services. 2. For patients, the least important is the material dimension, whereas the one most affecting them is the dimension associated with the reliability of medical services. 3. An improvement of the level of satisfaction with the quality of medical services requires proper planning and effectiveness of implementation of health care services. 4. Research should be conducted on a larger population of patients. (shrink)

Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates. We study graph polynomials from a model theoretic point of view. In this paper we distinguish between the graph theoretic (semantic) and the algebraic (syntactic) meaning of graph polynomials. Graph polynomials appear in the literature either as generating functions, as generalized chromatic polynomials, or as polynomials derived via determinants of adjacency or Laplacian matrices. We show that these (...) forms are mutually incomparable, and propose a unified framework based on definability in Second Order Logic. We show that this comprises virtually all examples of graph polynomials with a fixed finite set of indeterminates. Finally we show that the location of zeros and stability of graph polynomials is not a semantic property. The paper emphasizes a model theoretic view. It gives a unified exposition of classical results in algebraic combinatorics together with new and some of our previously obtained results scattered in the graph theoretic literature. (shrink)

The classical Feferman–Vaught Theorem for First Order Logic explains how to compute the truth value of a first order sentence in a generalized product of first order structures by reducing this computation to the computation of truth values of other first order sentences in the factors and evaluation of a monadic second order sentence in the index structure. This technique was later extended by Läuchli, Shelah and Gurevich to monadic second order logic. The technique has wide applications in decidability and (...) definability theory. Here we give a unified presentation, including some new results, of how to use the Feferman–Vaught Theorem, and some new variations thereof, algorithmically in the case of Monadic Second Order Logic MSOL . We then extend the technique to graph polynomials where the range of the summation of the monomials is definable in MSOL . Here the Feferman–Vaught Theorem for these polynomials generalizes well known splitting theorems for graph polynomials. Again, these can be used algorithmically. Finally, we discuss extensions of MSOL for which the Feferman–Vaught Theorem holds as well. (shrink)

We investigate the expressive power of second-order logic over finite structures, when two limitations are imposed. Let SAA ) be the set of second-order formulas such that the arity of the relation variables is bounded by k and the number of alternations of second-order quantification is bounded by n . We show that this imposes a proper hierarchy on second-order logic, i.e. for every k , n there are problems not definable in AA but definable in AA for some c (...) 1 , d 1 . The method to show this is to introduce the set AUTOSAT of formulas in F which satisfy themselves. We study the complexity of this set for various fragments of second-order loeic. For first-order logic FOL with unbounded alternation of quantifiers AUTOSAT is PSpace complete. For first-order logic FOL n with alternation of quantifiers bounded by n , AUTOSAT is definable in AA . AUTOSAT) is definable in AA for some c 1 , d 1. (shrink)

This paper presents a dual intention model (DIM) of demonstrations as actions to show the agentive nature of demonstrations. According to the DIM, demonstrations are complex actions that contain as components at least three elements: an abductive intention, a deictic intention, and a basic ostensive act of indication. This paper unpacks these three components and discusses their roles from the viewpoint of the philosophy of action and the philosophy of language. It also shows how the DIM applies in selected practical (...) examples and explains the merits of the model in the context of other views on demonstrations and demonstratives. (shrink)

The epidemiological situation resulting from the SARS-CoV-2 pandemic caused the Polish universities to fully switch to distance education in March 2020. Medical e-learning has not yet been broadly implemented into the education process. Therefore, examples of successful e-learning implementations or the organization of the process of medical e-learning offer a valuable source of knowledge today, which is needed immediately. The article presents e-learning practices at the Polish medical universities during the SARS-CoV-2 epidemic during the period from March to September 2020, (...) covering seven universities in Poland that offer medical and health studies. The organization and implementation of e-learning classes is presented, including knowledge evaluation practices, providing example decisions issued by university rectors, on which the teaching process was based. A detailed presentation of the schools’ organizational units or workgroups that played an important role in the process of coordination of measures supporting e-education is also included. The article also presents a description of the software applications, utilities, and services used at the schools in the course of the process of online education. Below are some examples of specific such implementations in selected university courses. (shrink)

We study the effects of Vopěnka's principle on properties of model theoretic logics. We show that Vopěnka's principle is equivalent to the assumption that every finitely generated logic has a compact cardinal. We show also that it is equivalent to the assumption that every such logic has a global Hanf number.

We show that the spectrum of a sentence ϕ in Counting Monadic Second Order Logic (CMSOL) using one binary relation symbol and finitely many unary relation symbols, is ultimately periodic, provided all the models of ϕ are of clique width at most k, for some fixed k. We prove a similar statement for arbitrary finite relational vocabularies τ and a variant of clique width for τ-structures. This includes the cases where the models of ϕ are of tree width at most (...) k. For the case of bounded tree-width, the ultimate periodicity is even proved for Guarded Second Order Logic GSOL. We also generalize this result to many-sorted spectra, which can be viewed as an analogue of Parikh's Theorem on context-free languages, and its analogues for context-free graph grammars due to Habel and Courcelle. Our work was inspired by Gurevich and Shelah (2003), who showed ultimate periodicity of the spectrum for sentences of Monadic Second Order Logic where only finitely many unary predicates and one unary function are allowed. This restriction implies that the models are all of tree width at most 2, and hence it follows from our result. (shrink)

We motivate and formalize the idea of sameness by default: two objects are considered the same if they cannot be proved to be different. This idea turns out to be useful for a number of widely different applications, including natural language processing, reasoning with incomplete information, and even philosophical paradoxes. We consider two formalizations of this notion, both of which are based on Reiter’s Default Logic. The first formalization is a new relation of indistinguishability that is introduced by default. We (...) prove that the corresponding default theory has a unique extension, in which every two objects are indistinguishable if and only if their non-equality cannot be proved from the known facts. We show that the indistinguishability relation has some desirable properties: it is reflexive, symmetric, and, while not transitive, it has a transitive “flavor.” The second formalization is an extension (modification) of the ordinary language equality by a similar default: two objects are equal if and only if their non-equality cannot be proved from the known facts. It appears to be less elegant from a formal point of view. In particular, it gives rise to multiple extensions. However, this extended equality is better suited for most of the applications discussed in this paper. (shrink)

We prove that in a locally finite variety that has definable principal congruences , solvable congruences are nilpotent, and strongly solvable congruences are strongly abelian. As a corollary of the arguments we obtain that in a congruence modular variety with DPC, every solvable algebra can be decomposed as a direct product of nilpotent algebras of prime power size.

Are identity criteria grounding principles? The recent debate over this issue seems to indicate a definitively negative answer. Recognising various objections to identity criteria as grounds for identity facts, one may wonder whether the former are capable of playing any salient role in ontology. I argue in this paper that they are, provided that one interprets them not as ontological explanations of identity facts but as ontological specifications thereof. I attempt to elaborate this view in terms of the well-establish distinction (...) between determinables and their determinates, where identity criteria are to play the role of the determinates and the relation of identity is to be their determinable. (shrink)

This paper presents Michael Heller’s notion of “philosophy in science” and re-introduces Michael Heller’s classical text that first presented this concept of philosophy entitled How is “philosophy in science” possible?. The paper discusses the historical context of Heller’s idea as it emerged from the discussions and works of the Krakow philosophical scene and discusses the basic tenants of this philosophy, its analytic character, the role of intellectual tradition in the development of this philosophy, and the critical role played by an (...) interdisciplinary dialogue between philosophy, science, and theology. Despite the idea of philosophy in science having emerged about 40 years ago, this concept still inspires and fuels innovative research. The notion of “philosophy in science” lies at the foundations of the philosophy published in two journals: Philosophical Problems in Science and Philosophy in Science. (shrink)

The paper explores the topic of organizational routines from a philosophical vantage point to see how the philosophy of action may help improve its understanding in organizational research. The main goal is to show the distinctive complexity of the intentional picture of routines. In this respect, the paper clarifies the interrelations between psychological habits and routines and describes similarities and differences between them. It also highlights the special place of mindfulness as a psycho-cognitive mechanism of action meta-control in intentional explanations (...) of routine complexity. (shrink)

Philosophy in technology is a research program that studies the philosophical roots of engineering and technology. Technologists, by virtue of their education, believe that the limits, goals, possibilities, and effects of technology on society and humankind are exclusively technological problems, hence their solutions must lie exclusively in technology. In contrast, philosophy in technology asserts that the resolutions to these problems need to be rooted in an understanding of their philosophical origins. This program paper defines the objectives of philosophy in technology, (...) the kinds of questions it explores, the methods it uses, and how it differs from the philosophy of technology. (shrink)

Perceptual experience usually comes with “phenomenal force”, a strong sense that it reflects reality as it is. Some philosophers have argued that it is in virtue of possessing phenomenal force that perceptual experiences are able to non‐inferentially justify beliefs. In this article, I introduce an alternative, inferentialist take on the epistemic role of phenomenal force. Drawing on Bayesian modeling in cognitive science, I argue that the sense of reality that accompanies conscious vision can be viewed as epistemically appraisable in light (...) of its rational etiology. (shrink)

Psychedelic substances elicit powerful, uncanny conscious experiences that are thought to possess therapeutic value. In those who undergo them, these altered states of consciousness often induce shifts in metaphysical beliefs about the fundamental structure of reality. The contents of those beliefs range from contentious to bizarre, especially when considered from the point of view of naturalism. Can chemically induced, radically altered states of consciousness provide reasons for or play some positive epistemic role with respect to metaphysical beliefs? In this paper, (...) I discuss a view that has been underexplored in recent literature. I argue that psychedelic states can be rationally integrated into one’s epistemic life. Consequently, updating one’s metaphysical beliefs based on altered states of consciousness does not have to constitute an instance of epistemic irrationality. (shrink)

In this paper, we consider how an agent may manage a questioning agenda in a situation where multiple information sources are available. We work within the framework of formal dialogue systems with the underpinning of Inferential Erotetic Logic. Firstly, we present the formal dialogue system DL(IEL)mult for managing multi-agent information retrieval. Then, we extend the proposed system so that it is capable of representing group and individual levels for the question decomposition process. We also propose two measures for evaluating information (...) sources: their cooperativeness and success levels; next, we analyse how the choice of agents may influence the way in which a solution for a given problem is reached. (shrink)

_The dynamic development of medical technologies, i.e. the use of medicinal products and medical procedures, requires reflection on the ways to ensure the safety of patients and people using such methods of treatment (medical professionals) in legal and ethical terms. This applies in particular to the currently observed influence of the media on the actions taken in the health care system in Poland as well as individual decisions of patients on the use of the offered drugs and other medical procedures._ (...) _The article presents selected legal provisions defining the conditions for the use of medicinal products (drugs) and experimental medical procedures. The basic element of the considerations is to indicate the legal conditions for this type of use of medical technologies understood in this way, also in a broader context – with the characteristics of ethical conditions for „the media message”, including ensuring its proper quality for the protection of public health._. (shrink)

In this article, apart from a brief review of the relationship between mythos and logos, the author, who has based his study on the Freudian category of the social unconscious and Durkheim’s category of social consciousness, presents the characteristics of three modes of social memory: unconscious memory, interconscious memory and conscious memory. Based on Gilbert Durand’s mytho-analytical tool, the structure of the triad of memory: THE UNCONCIOUS – AWAITING – THE CONSCIOUS is shown as the memory of the Father, Son (...) and Mother. The mythological aspect of elapsing, past, reminiscence, living memory and anticipation is captured on the examples taken from Postmodern (the global society), Modern and even Pre-Modern). In this way, the author concludes that the contemporary transformation of memory into hallucinations means the beginning of anticipation for the End of History. (shrink)

Nietzsche has discovered the origins of Christian metaphysics and identified the dangers caused by its expansion. People have lost the ability to communicate with exterior reality that threatens their culture of well-being, built on metaphysical ideas (the Good, the Beauty, the Truth). In order to avoid nihilism after God's death, humans must regain the ability to communicate with dyonisian reality of sacrum (that is, according to Christian morality, the evil), sacrificed in order to gain Paradise. This is the great task (...) of the "philosophy of the future". The "philosopher of the future" seems to be an overman. Nietzsche and Bataille don't intend to replace the culture of rational entities with the culture of overman. They attempt to repair defects of the human world and restore its lost completion. The main question is: how to recognize the destructive absolute and preserve human identity at the same time? Human as a rational entity perishes while obtaining full knowledge (Nietzsche). The choice is both simple and tragic – to live inside the world of artificial ideas, or to die outside the metaphysical fortress, in the wasteland of full knowledge (sacrum, evil), where there is no God. According to Bataille, inner experience enables temporary reconcilation between the culture of rational entities and the chaos of sacrum. It enables human beings to obtain the full knowledge and survive, for its main "purpose" is to bring into the culture as much sacrum as possible. From this point of view, it appears as a part of the "philosophy of the future" and – in a way – as an appendix to Nietzsche’s lesson of overmanship, for transgressive entity apparently turns out to be a overman. (shrink)

This article argues that such large-scale cases of crowd behavior as the Mexican Wave ( La Ola) constitute forms of shared intentionality which cannot be explained solely with the use of the standard intentionalistic ontology. It claims that such unique forms of collective intentionality require a hybrid explanatory lens in which an account of shared goals, intentions, and other propositional attitudes is combined with an account of the motor psychology of collective agents. The paper describes in detail the intentionalistic ontology (...) of La Ola and discusses the conditions of cooperation it meets. The discussion allows the author to defend the view that large-scale collective intentionality can be based on automaticity to a significant degree: to properly understand such phenomena like La Ola, the idea of probabilistically interpreted decisions and propensities to act should give way to the automatic aspects of behavior. This paves the way for future studies in the philosophy of action to fully recognize the role of automatic performances at the level of collective actions just as they do for individual actions. (shrink)

This paper critically examines and evaluates Yacin Hamami’s reconstruction of the standard view of mathematical rigor. We will argue that the reconstruction offered by Hamami is premised on a strong and controversial epistemological thesis and a strong and controversial thesis in the philosophy of mind. Secondly, we will argue that Hamami’s reconstruction of the standard view robs it of its original philosophical rationale, i.e. making sense of the notion of rigor in mathematical practice.

The paper discusses the thesis of virtual realism presented by David Chalmers in his paper “The Virtual and the Real” (2017). Here, I suggest an even stronger version of the claim that I call “virtual physicalism”. According to this view, virtual objects are not only real but physical as they are identical to the physical states of computers that run VR software. I suggest that virtual objects should have a similar ontological status to toys—they should be treated as models or (...) simplifications of ordinary objects. Just like toys, virtual objects can sometimes be good enough to be used instead of their ordinary counterparts. In these cases, virtual objects start to be treated as instantiations of the same kind. In the last part of the paper, I use Johan Huizinga’s notion of a “magic circle” to suggest how different objects could be successfully “virtualized”, that is, moved into a digital realm while remaining objects of the same kind as their non-virtual counterparts. I suggest this will happen once virtual reality becomes permanent and causally connected with non-virtual reality. I finish the paper by looking at examples of natural kind objects and individuals, which seem to be the hardest cases for successful virtualization. (shrink)

The dialog that has been conducted for a few years between a group of Christian social thinkers and economists on moral aspects of economic activity has led to the creation of a new science discipline called economic personalism. On the one hand it stipulates the need to express economic processes within ethical categories, on the other hand it perceives the necessity to elaborate a strong economic theory. Economic personalists refer to the works of those thinkers who returned to the basic (...) economic inspiration as a field belonging predominantly to moral philosophy. This school is sometimes called the Austrian School or the School of Classical Liberalism. A significant role in the economic personalism development was performed by its forerunners who noticed what was lacking in the previous interpretations of Catholic social thought. Among the there are John Paul II, Michael Novak, Rocco Buttiglione and the Acton Institute. The intellectual sources of economic personalism are mainly related to concept of personalism developed in Poland. Its specific thesis, seen in the maxim that “each person ought to be affirmed for the sake of it itself” also relates to the economic life. Economic personalists formulate principles that are spokesmen in order to promote a free society built on virtues. They are expressed in the following way: pre-eminence of a human being: economy and human dignity; human capital: creation and creativity; dignity of human work: calling for enterprise, integral development of human being, manufacture and personalism, participation, economic common wealth, helpfulness, market restrictions; preferential option for the poor: solidarity and social equity. (shrink)

The aim of this paper is to study a particular family of non-deterministic semantics for modal logics that has eight truth-values. These eight-valued semantics can be traced back to Omori and Skurt (2016), where a particular member of this family was used to characterize the normal modal logic K. The truth-values in these semantics convey information about a proposition’s truth/falsity, whether the proposition is necessary/not necessary, and whether it is possible/not possible. Each of these triples is represented by a unique (...) value. In this paper we will study which modal logics can be obtained by changing the interpretation of the $$\Box $$ modality, assuming that the interpretation of other connectives stays constant. We will show what axioms are responsible for a particular interpretations of $$\Box $$. Furthermore, we will study subsets of these axioms. We show that some of the combinations of the axioms are equivalent to well-known modal axioms. We apply the level-valuation technique to all of the systems to regain the closure under the rule of necessitation. We also point out that some of the resulting logics are not sublogics of S5 and comment briefly on the corresponding frame conditions that are forced by these axioms. Ultimately, we sketch a proof of meta-completeness for all of these systems. (shrink)

Like most goods‐producing sectors in the West, modern health‐care systems have been profoundly changed by globalization and the neoliberal policies that attend it. Since the 1970s, the role of the welfare state has been considerably reduced; funding and management of health systems have been subjected to wave upon wave of reorganization and assimilated to the private sector. At the same time, neoliberal policy has imposed the notion of patient empowerment, thus turning patients into consumers of health. The literature on nursing (...) has accordingly reported on the significant repercussions on all aspects of the profession, from delivery of care and treatment, through training for new nurses, to legislated policy reforms regarding the role and responsibilities of modern nurses. In light of these developments, this paper analyses and theorizes about the way the injection of neoliberal policy is linked to and affects the practice of nursing. Drawing on a number of Nietzschean arguments, we begin with an exploration of the complex effects of neoliberalism, bureaucratization, and technocratization on the health system and the practice of nursing. Our main theoretical point here is that neoliberal policy engenders and promotes a neoliberal tide, which results in the conversion of the values that drive modern nursing practice. We then examine this tide in the light of Nietzsche's concepts. Starting with an analysis based on the ontology of the will to power, we show that nurses are dominated by neoliberal values embedded in technocratic and bureaucratic ideologies. Finally, we argue that the application of neoliberal policy constitutes a form of domestication from which one might potentially be freed through the Nietzschean concept of transvaluation of values. This transvaluation, as its freeing from some of the neoliberal tide, may be accomplished in accordance with a hierarchy of specific life‐affirming values for nursing culture and practice. (shrink)

In this paper, I use the predictive processing theory of perception to tackle the question of how perceptual states can be rationally involved in cognition by justifying other mental states. I put forward two claims regarding the epistemological implications of PP. First, perceptual states can confer justification on other mental states because the perceptual states are themselves rationally acquired. Second, despite being inferentially justified rather than epistemically basic, perceptual states can still be epistemically responsive to the mind-independent world. My main (...) goal is to elucidate the epistemology of perception already implicit in PP. But I also hope to show how it is possible to peacefully combine central tenets of foundationalist and coherentist accounts of the rational powers of perception while avoiding the well-recognized pitfalls of either. (shrink)

Despite the fact that the notion of internal representation has - at least according to some - a fundamental role to play in the sciences of the mind, not only has its explanatory utility been under attack for a while now, but it also remains unclear what criteria should an explanation of a given cognitive phenomenon meet to count as a representational explanation in the first place. The aim of this article is to propose a solution to this latter problem. (...) I will assume that representational explanations should be construed as a form of mechanistic explanations and proceed by proposing a general sketch of a functional architecture of a representational cognitive mechanism. According to the view on offer here, representational mechanisms are mechanisms that meet four conditions: the structural resemblance condition, the action-guidance condition, the decouplability condition, and the error-detection condition. (shrink)

The Middle Ages takes over from antiquity the perception of memory as primarily a rhetoric skill needed for composing. Both the memory of the canon authors and the memory of mnemotechnics are a testament to the enormous significance that education and science were attached to remembering and reminding themselves. Unfortunately, so far we don't know enough about the great role played by monastic inspiration – deriving from liturgy and meditation – in shaping the culture of memory.

According to the dialetheist argument from the inconsistency of informal mathematics, the informal version of the Gödelian argument leads us to a true contradiction. On one hand, the dialetheist argues, we can prove that there is a mathematical claim that is neither provable nor refutable in informal mathematics. On the other, the proof of its unprovability is given in informal mathematics and proves that very sentence. We argue that the argument fails, because it relies on the unjustified and unlikely assumption (...) that the informal Gödel sentence is informally provable. (shrink)