The study of existentially closed closure algebras begins with Lipparini’s 1982 paper. After presenting new nonelementary axioms for algebraically closed and existentially closed closure algebras and showing that these nonelementary classes are different, this paper shows that the classes of finitely generic and infinitely generic closure algebras are closed under finite products and bounded Boolean powers, extends part of Hausdorff’s theory of reducible sets to existentially closed closure algebras, and shows that finitely generic and infinitely generic (...) closure algebras are elementarily inequivalent. Special properties of algebraically closed, existentially closed, finitely generic, and infinitely generic closure algebras are established along the way. (shrink)

We construct a recursive ultrapower F/U such that F/U is a tame 1-model in the sense of [6, §3] and FU is existentially incomplete in the models of II2 arithmetic. This enables us to answer in the negative a question about closure with respect to recursive fibers of certain special semirings Γ of isols termed tame models by Barback. Erik Ellentuck had conjuctured that all such semirings enjoy the closure property in question. Our result is that while many (...) do, some do not. (shrink)

We prove an existential analogue of the Goldblatt‐Thomason Theorem which characterizes modal definability of elementary classes of Kripke frames using closure under model theoretic constructions. The less known version of the Goldblatt‐Thomason Theorem gives general conditions, without the assumption of first‐order definability, but uses non‐standard constructions and algebraic semantics. We present a non‐algebraic proof of this result and we prove an analogous characterization for an alternative notion of modal definability, in which a class is defined by formulas which (...) are satisfiable under any valuation (the so‐called existential validity). Continuing previous work in which model theoretic characterization for this type of definability of elementary classes was proved, we give an analogous general result without the assumption of the first‐order definability. Furthermore, we outline relationships between sets of existentially valid formulas corresponding to several well‐known modal logics. (shrink)

Let Λ denote the semiring of isols. We characterize existential completeness for Nerode subsemirings of Λ, by means of a purely isol-theoretic “Σ1 separation property”. Our characterization is purely isol-theoretic in that it is formulated entirely in terms of the extensions to Λ of the Σ1 subsets of the natural numbers. Advantage is taken of a special kind of isol first conjectured to exist by Ellentuck and first proven to exist by Barback . In addition, we strengthen the negative (...) part of [13] by showing that existential completeness is not secured, for a given Nerode semiring, by either a certain “functional closure” property for the extensions of partial recursive functions or the property of “pulling in” some portion of each partial recursive fiber; these latter results are perhaps a little surprising. (shrink)

This paper explores Simon Stevin’s l’Arithmétique of 1585, where we find a novel understanding of the concept of number. I will discuss the dynamics between his practice and philosophy of mathematics, and put it in the context of his general epistemological attitude. Subsequently, I will take a close look at his justificational concerns, and at how these are reflected in his inductive, a postiori and structuralist approach to investigating the numerical field. I will argue that Stevin’s renewed conceptualisation of the (...) notion of number is a sort of “existential closure” of the numerical domain, founded upon the practice of his predecessors and contemporaries. Accordingly, I want to make clear that l’Aritmetique have to be read not as an ontological analysis or exploration of the numerical field, but as an explication of a mathematical ethos. In this sense, this article also intends to make a specific contribution to the broader issue of the “ethics of geometry.”. (shrink)

A recent popular analysis of English indefinites isthat they involve a choice function mechanism in their semantic interpretation. However,there are diversified views regarding how intermediate scope readings should be dealt withand which level(s) existential closure should apply to. This paper attempts to make acontribution to this debate by examining existential polarity wh-phrases in Chinese. I showthat unlike the behaviors of polarity indefinites in St''át''imcets reported by Matthewson(1999), intermediate scope readings are possible for polarity wh-phrases in Chinese but (...) aresubject to some locality conditions. I suggest that implicit arguments of choice functionsmight have a parametric value the choice of which affects availability of intermediate readings.The findings in this paper thus revive the possibility, rejected by Matthewson (1999), that thechoice function mechanism may vary from language to language or from indefinite NPs in onelanguage to indefinite NPs in another language or even from one type of indefiniteNP to another type of indefinite NP within the same language. (shrink)

This paper examines the psychology of existential guilt with Martin Heidegger and Rollo May’s conceptualizations as the point of departure. The concept of existential guilt describes preconditions for responsibility and accountability in life choices and the relationship to the potential given in the life of a human. It might also be used as a starting point to examine an individual’s relationship to the potential offered in their life and life context and, in this way, the hitherto unlived life (...) of an individual. The following questions are discussed in contexts of identity development, perfectionism, and current cultural shifts in conceptualizations of selfhood: How can humans relate to the fact that only limited parts of who they might be can ever be actualized? Moreover, how can they relate to the fundamental ambiguity and “groundlessness” in the contexts of life where choices are made? There are striking parallels between the role of exploration in the Eriksonian approaches to healthy identity development and the ontological groundlessness that stands out as a premise for existential guilt. There are also parallels between identity fore-closure and normative identity styles and “falling” into das Man in the existential framework. Perfectionistic ideals easily become an objectivization – and closure – of possible alternatives and choices. In contemporary theories of constructions of selfhood, the dangers of alienation from the community on the one hand and escape into what might become totalitarian collectivism on the other is pointed out. The contextualization of personal responsibility offered through the concept of existential guilt might address both dangers. It provides a perspective on how personal responsibility is embedded in contexts of human relationships, relationships to nature, and the finitude, freedom, uncertainties, and suffering that is given through human existence. Existential guilt can wake sorrow and regret over opportunities overlooked and lost. However, most of all, it can be seen as a drive toward repair in the relationship toward both oneself and the other. It takes the form of receptivity, an openness to a life not yet lived, and creative use of imagination. (shrink)

This paper offers an analysis of metalinguistic comparatives such as more dumb than crazy in which they differ from ordinary comparatives in the scale on which they compare: ordinary comparatives use scales lexically determined by particular adjectives, but metalinguistic ones use a generally-available scale of imprecision or ‘pragmatic slack’. To implement this idea, I propose a novel compositional implementation of the Lasersohnian pragmatic-halos account of imprecision—one that represents clusters of similar meanings as Hamblin alternatives. In the theory that results, (...) class='Hi'>existential closure over alternatives mediates between alternative-sets and meanings in which imprecision has been resolved. I then articulate a version of this theory in which the alternatives are not related meanings but rather related utterances, departing significantly from Lasersohn’s original conception. Although such a theory of imprecision is more clearly ‘metalinguistic’, the evidence for it from metalinguistic comparatives in English is surprisingly limited. The overall picture that emerges is one in which the grammatical distinction between ordinary and metalinguistic comparatives tracks the independently motivated distinction between vagueness and imprecision. (shrink)

Various laws and theories in the natural and social sciences are presented with a view to discerning the syntactic and semantic characteristics of many idealizations in science. Three different kinds of idealizations are discussed: ideal conditions, ideal cases, and idealized theories. An ideal condition is a formula in which state variables occur, whose existential closure is false, and for which there is another formula that can be constructed out of the original formula such that the existential (...) class='Hi'>closure of the new formula is true. An ideal case is a statement which is logically equivalent to a universal conditional which has an ideal condition as its antecedent. And an idealized theory is a set of false universal conditional statements. Alternative syntactic and semantic analyses are viewed and criticized. (shrink)

We compare two different notions of generic expansions of countable saturated structures. One kind of genericity is related to existential closure, and another is defined via topological properties and Baire category theory. The second type of genericity was first formulated by Truss for automorphisms. We work with a later generalization, due to Ivanov, to finite tuples of predicates and functions. Let $N$ be a countable saturated model of some complete theory $T$ , and let $(N,\sigma)$ denote an expansion (...) of $N$ to the signature $L_{0}$ which is a model of some universal theory $T_{0}$ . We prove that when all existentially closed models of $T_{0}$ have the same existential theory, $(N,\sigma)$ is Truss generic if and only if $(N,\sigma)$ is an e-atomic model. When $T$ is $\omega$ -categorical and $T_{0}$ has a model companion $T_{\mathrm {mc}}$ , the e-atomic models are simply the atomic models of $T_{\mathrm {mc}}$. (shrink)

We define notions of homomorphism, submodel, and sandwich of Kripke models, and we define two syntactic operators analogous to universal and existential closure. Then we prove an intuitionistic analogue of the generalized (dual of the) Lyndon-Łoś-Tarski Theorem, which characterizes the sentences preserved under inverse images of homomorphisms of Kripke models, an intuitionistic analogue of the generalized Łoś-Tarski Theorem, which characterizes the sentences preserved under submodels of Kripke models, and an intuitionistic analogue of the generalized Keisler Sandwich Theorem, which (...) characterizes the sentences preserved under sandwiches of Kripke models. We also define several intuitionistic formula hierarchies analogous to the classical formula hierarchies $\forall_n (= \Pi^0_n)$ and $\exists_n (=\Sigma^0_n)$ , and we show how our generalized syntactic preservation theorems specialize to these hierarchies. Each of these theorems implies the corresponding classical theorem in the case where the Kripke models force classical logic. (shrink)

We examine several cases of object movement from various languages, and demonstrate that the syntactic behavior of objects can be derived from certain conditions on LF representations. Conditions on LF relevant to the distribution of arguments are identified as relative scope fixing and type mismatch repair. These two conditions interact with the multiple semantic types that may be assigned to NPs (cf. Partee 1987) to induce movement of certain objects out of the VP, universally by LF and parametrically in the (...) overt syntax. Diesing's (1992b) Mapping Hypothesis combined with the multiple NP types predicts that quantificational NPs in object position will have to undergo movement by LF. This movement is forced by the principles of semantic composition as a mechanism of type mismatch resolution. The existential closure operation over VP is claimed to be genuinely unselective: any NP that introduces a free variable and does not receive an existential interpretation must move out of the scope of existential closure (and thus out of the VP) by LF. Pronouns are variables, limited in semantic type assignment, that by virtue of their definiteness cannot be bound by existential closure and must move out of its scope. In Egyptian Arabic, object pronouns escape from the VP via attachment to a verb that raises to adjoin to an Aspect inflectional head above the VP. The movement of object pronouns and definite/specific NPs in Scandinavian is also associated with verb movement. (shrink)

In my view, meanings are instructions to construct monadic concepts that can be conjoined with others, given a few thematic relations and an operation of existential closure. For example, ‘red ball’ is understood as—and has the semantic property of being—an instruction to fetch and conjoin two concepts that are linked, respectively, to ‘red’ and ‘ball’. Other expressions are more complex. But to a first approximation, ‘I stabbed it violently with this’ is an instruction to construct and existentially close (...) a six-conjunct concept of the form indicated below; AGENT(E, S) & STAB(E) & BEFORE(E, T) & PATIENT(E, 1) & VIOLENT(E) & INSTRUMENT(E, 2) where ‘S’, ‘T’, ‘1’ and ‘2’ stand for concepts of the relevant speaker, time, and things demonstrated. The verb and adverb correspond directly to conjoinable concepts of events. The pronouns correspond to such concepts via certain relational notions, reflected with the tense, preposition, and grammatical relations that ‘stab’ bears to its subject and object. I have argued elsewhere that this neo-Davidsonian conception of semantics is descriptively adequate, and yet. (shrink)

It is shown that counterpart theory and the duplication account of intrinsicality —two key pieces of the Lewisian package—are incompatible. In particular, the duplication account yields the result that certain intuitively extrinsic modal properties are intrinsic. Along the way I consider a potentially more general worry concerning certain existential closures of internal relations. One conclusion is that, unless the Lewisian provides an adequate alternative to the duplication account, the reductive nature of their total theory is in jeopardy.

In biscuit conditionals (BCs) such as If you’re hungry, there’s pizza in the fridge, the if clause appears to apply to the illocutionary act performed in uttering the main clause, rather than to its propositional content. Accordingly, previous analyses of BCs have focused on illocutionary acts, and, this, I argue, leads them to yield incorrect paraphrases. I propose, instead, that BCs involve existential quantification over potential literal acts such as assertions, questions, commands, and exclamations, the semantic objects associated with (...) declarative, interrogative, imperative, and exclamative sentences, respectively. Such an existential interpretation of BCs requires only that we add potential literal acts to our inventory of individuals, and it produces reasonable paraphrases in which if has its normal meaning: If you’re hungry,[there’s a (relevant/salient) assertion that] there’s pizza in the fridge. These potential literal act variables are introduced into semantic interpretations and then undergo Existential Closure. Hence, we would expect to see similar interpretations in contexts other than BCs, that is, with other if constructions, with connectives other than if, with potential literal acts other than assertion, and in root sentences. This prediction is borne out, along with the parallel prediction that we cannot quantify over purely illocutionary acts like offers, but only over potential literal acts, those conventionally associated with a particular morphosyntactic shape. (shrink)

Bare plurals (dogs) behave in ways that quantified plurals (some dogs) do not. For instance, while the sentence John owns dogs implies that John owns more than one dog, its negation John does not own dogs does not mean “John does not own more than one dog”, but rather “John does not own a dog”. A second puzzling behavior is known as the dependent plural reading; when in the scope of another plural, the ‘more than one’ meaning of the plural (...) is not distributed over, but the existential force of the plural is. For example, My friends attend good schools requires that each of my friends attend one good school, not more, while at the same time being inappropriate if all my friends attend the same school. This paper shows that both these phenomena, and others, arise from the same cause. Namely, the plural noun itself does not assert ‘more than one’, but rather the plural denotes a predicate that is number neutral (unspecified for cardinality). The ‘more than one’ meaning arises as an scalar implicature, relying on the scalar relationship between the bare plural and its singular alternative, and calculated in a sub-sentential domain; namely, before existential closure of the event variable. Finally, implications of this analysis will be discussed for the analysis of the quantified noun phrases that interact with bare plurals, such as indefinite numeral DPs (three boys), and singular universals (every boy). (shrink)

This paper argues, on the basis of data from St'át'imcets (Lillooet Salish), for a theory of wide-scope indefinites which is similar, though not identical, to that proposed by Kratzer (1998). I show that a subset of S'át'imcets indefinites takes obligatory wide scope with respect to if-clauses, negation, and modals, and is unable to be distributed over by quantificational phrases. These wide-scope effects cannot be accounted for by movement, but require an analysis involving choice functions (Reinhart 1995, 1997). However, Reinhart's particular (...) choice function analysis is unable to account for the St'át'imcets data. A Kratzer-style theory, on the other hand, accounts not only for the wide-scope effects, but also for the emergence of narrower-than-widest interpretations for indefinites which contain bound variables. I depart from Kratzer's analysis in claiming that St'át'imcets choice function indefinites are not 'specific'; the discourse context does not provide a value for the function variable. Therefore, I utilize wide- scope existential closure over choice functions rather than leaving the variables free. However, my analysis provides support for Kratzer's claim that English indefinites are ambiguous between a choice function interpretation and a quantificational interpretation, since St'át'imcets determiners overtly encode the English ambiguity. I conclude by suggesting that the proposed analysis of wide-scope indefinites may be universally valid. (shrink)

Domain extension in mathematics occurs whenever a given mathematical domain is augmented so as to include new elements. Manders argues that the advantages of important cases of domain extension are captured by the model-theoretic notions of existential closure and model completion. In the specific case of domain extension via ideal elements, I argue, Manders’s proposed explanation does not suffice. I then develop and formalize a different approach to domain extension based on Dedekind’s Habilitationsrede, to which Manders’s account is (...) compared. I conclude with an examination of three possible stances towards extensions via ideal elements. (shrink)

In Shona , bare plurals and bare singulars seem to have different scope possibilities with respect to a class of modifiers which I term “scopeless quantity words” few’, and ose ‘all’). I argue that this is due to two factors. First, the scopeless quantity words are intersective modifiers rather than quantifying determiners, so that DPs containing them denote entities rather than generalised quantifiers. Second, transitive sentences involving plural arguments are usually interpreted using the **-operator, which gives a cumulative reading; the (...) apparent wide and narrow scope readings of bare plurals are both subcases of this reading, but a narrow scope reading for bare singulars cannot be subsumed by the cumulative reading. I also discuss the scope behaviour of a quantifying determiner, oga-oga ‘every’, which shows a subject/object asymmetry: in subject position, it appears to show the expected scopal ambiguity, but in object position, it appears to have the same readings as a scopeless quantity word; I argue that this is because of the location of existential closure. This adds to the evidence suggesting that many words giving quantity are intersective modifiers rather than quantifying determiners or adverbial quantifiers. (shrink)

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.

Free Semantics is based on normalized natural deduction for the weak relevant logic DW and its near neighbours. This is motivated by the fact that in the determination of validity in truth-functional semantics, natural deduction is normally used. Due to normalization, the logic is decidable and hence the semantics can also be used to construct counter-models for invalid formulae. The logic DW is motivated as an entailment logic just weaker than the logic MC of meaning containment. DW is the logic (...) focussed upon, but the results extend to MC. The semantics is called 'free semantics' since it is disjunctively and existentially free in that no disjunctive or existential witnesses are produced, unlike in truth-functional semantics. Such 'witnesses' are only assumed in generality and are not necessarily actual. The paper sets up the free semantics in a truth-functional style and gives a natural deduction interpetation of the meta-logical connectives. We then set out a familiar tableau-style system, but based on natural deduction proof rather than truth-functional semantics. A proof of soundness and completeness is given for a reductio system, which is a transform of the tableau system. The reductio system has positive and negative rules in place of the elimination and introduction rules of Brady's normalized natural deduction system for DW. The elimination-introduction turning points become closures of threads of proof, which are at the points of contradiction for the reductio system. (shrink)

A structure M is pregeometric if the algebraic closure is a pregeometry in all structures elementarily equivalent to M. We define a generalisation: structures with an existential matroid. The main examples are superstable groups of Lascar U-rank a power of ω and d-minimal expansion of fields. Ultraproducts of pregeometric structures expanding an integral domain, while not pregeometric in general, do have a unique existential matroid. Generalising previous results by van den Dries, we define dense elementary pairs of (...) structures expanding an integral domain and with an existential matroid, and we show that the corresponding theories have natural completions, whose models also have a unique existential matroid. We also extend the above result to dense tuples of structures. (shrink)

This paper studies the expressive power that an extra first order quantifier adds to a fragment of monadic second order logic, extending the toolkit of Janin and Marcinkowski [JM01].We introduce an operation existsn on properties S that says "there are n components having S". We use this operation to show that under natural strictness conditions, adding a first order quantifier word u to the beginning of a prefix class V increases the expressive power monotonically in u. As a corollary, if (...) the first order quantifiers are not already absorbed in V, then both the quantifier alternation hierarchy and the existential quantifier hierarchy in the positive first order closure of V are strict.We generalize and simplify methods from Marcinkowski [Mar99] to uncover limitations of the expressive power of an additional first order quantifier, and show that for a wide class of properties S, S cannot belong to the positive first order closure of a monadic prefix class W unless it already belongs to W.We introduce another operation alt on properties which has the same relationship with the Circuit Value Problem as reach has with the Directed Reachability Problem. We use alt to show that Πn⊈ FO, Σn⊈ FO, and Δn+1⊈ FOB, solving some open problems raised in [Mat98]. (shrink)

The unexpected death of a child is one of the most challenging losses as it fractures survivors’ sense of parenthood and other layers of identity. Given that not all the bereaved parents who have need for support respond well to available treatments and that many have little access to further intervention or follow-up over time, online interventions featuring therapeutic writing and peer support have strong potential. In this article we explore how a group of bereaved mothers experienced the process of (...) participating in an online course in therapeutic writing for the integration of grief. Our research questions were: How do parents who have lost a child experience being part of an online course in therapeutic writing? What are the perceived benefits and challenges of writing in processing their grief? We followed an existential phenomenological approach and analyzed fieldwork notes (n= 13), qualitative data from the application and assessment surveys (n= 35;n= 21), excerpts from the journals of some participants (n= 3), and email correspondence with some participants (n= 5). We categorized the results in three meaning units: (1) where does my story begin? The “both and” of their silent chaos; (2) standing on the middle line: a pregnancy that does not end; (3) closures and openings: “careful optimism” and the need for community support. Participants experienced writing as an opportunity for self-exploration regarding their identities and their emotional world, as well as a means to develop and strengthen a bond with their children. They also experienced a sense of belonging, validation, and acceptance in the online group in a way that helped them make sense of their suffering. Online writing courses could be of benefit for bereaved parents who are grieving the unexpected death of a child, but do not replace other interventions such as psychotherapy. In addition to trauma and attachment informed models of grief, identity informed models with a developmental focus might enhance the impact of both low-threshold community interventions and more intensive clinical ones. Further studies and theoretical development in the area are needed, addressing dialogical notions such as the multivoicedness of the self. (shrink)

Let p be a set. A function φ is uniformly σ 1 (p) in every admissible set if there is a σ 1 formula φ in the parameter p so that φ defines φ in every σ 1 -admissible set which includes p. A theorem of Van de Wiele states that if φ is a total function from sets to sets then φ is uniformly σ 1R in every admissible set if anly only if it is E-recursive. A function is (...) ES p -recursive if it can be generated from the schemes for E-recursion together with a selection scheme over the transitive closure of p. The selection scheme is exactly what is needed to insure that the ES p - recursively enumerable predicates are closed under existential quantification over the transitive closure of p. Two theorems are established: a) If the transitive closure of p is countable than a total function on sets is ES p -recursive if and only if it is uniformly σ 1 (p) in every admissible set. b) For any p, if φ is a function on the ordinal numbers then φ is ES p -recursive if and only if it is uniformly ∑ 1 (p) in every admissible set. (shrink)

While the unprecedented lockdown measures were at the heart of the debate in the first year of the pandemic, the focus since then has shifted to vaccination issues. The reason, of course, is that vaccines and vaccinations have become available by now. All experts agree: If mankind had failed to develop vaccines against SARS-CoV-2, the death toll would have been much higher. This issue seeks to explore what could be described as a “generational approach to vaccinations”. The question “What can (...) we do to avoid future pandemics?” is related to different aspects of the failures and successes of humanity’s vaccination strategy against SARS-CoV-2. Pathogens are among the existential risks to humanity that could potentially kill a large part of it in a very short time. For all the tragedy and horror it has brought upon the world, the Corona virus has not been lethal on such a large, all-encompassing scale. But it could serve as a wake-up call for more and better prevention in the future, put differently: as a call to build a “preventive society”. When people look back to the year 2022 from the year 2200, will they think of the absence of mandatory vaccination as a dangerous anachronism? And will the unequal global distribution of vaccines be seen as an unbearable vice of our epoch? And will “human infection studies” still be dismissed as unethical if a dangerous new virus boards human bodies? If intergenerational justice means improving the life chances and living conditions of future generations to the largest possible extent, then its link to (the avoidance) of infectious diseases is obvious. We should protect future generations from foreseeable damage if we have the power to do so. “We” is humankind in its entirety. Politically, humanity is divided into many single nations. But biologically, as members of the same species, we share the same vulnerability regardless of ethnicity. The regular reader of this journal might wonder why this issue of IGJR has a different structure. An unprecedented pandemic calls for an unprecedented reaction and therefore IGJR 1/2021 and 2/2021 are special issues that deal with this disruptive event. We have invited several health experts, politicians and scholars alike to share their perspectives in short opinion pieces (instead of regular peer-reviewed articles). And we are exploring something new: the publication of a FRFG policy paper. This policy paper starts off with a historical overview on how pandemics have afflicted humanity in the past. It separates moral from legal duties and formulates “epidemiological imperatives” – the way of thinking of a responsible and solidary individual facing the task of preventing an outbreak of epidemics in a community. With the discovery of vaccines, and their availability, the catalogue of duties is increased by one more: to get the jabs as an act of solidarity with others, including future generations. This would prevent states from being forced to take disease control measures that bring about drastic collateral damage. During the first two years of the Corona pandemic, states have imposed lockdowns. The closure of schools has put a special burden on the youngest members of society. This could have been prevented during the second and the further waves. The policy paper also calls for more government funding for prophylactic vaccine research and for the designation of vaccines as “global public goods”. The issue then moves on to a section dedicated to opinion papers by various different authors. The first paper, written by Agnes Binagwaho and Kedest Mathewos (both from University of Global Health Equity, Rwanda), focuses on the issue of health inequity, a concern which has gained more and more traction during the Covid-19 pandemic. The paper examines how vaccine distribution during the pandemic was mainly focused on the global north and how such actions might affect future generations’ perception of what is just, fair and morally correct. The second paper, by Samantha Vanderslott (University of Oxford), focuses on the right and wrongdoings connected to pandemic preparedness and response. The third paper, authored by Rajeev Sadanandan (Health Systems Transformation Platform, India), talks about the lessons that can and should be drawn from child immunisations. The fourth paper, by Adriano Mannino (LMU and Parmenides Foundation, Munich), delves into the question how future generations will assess our actions and our response to the current pandemic. The fifth and final paper, written by Jörg Tremmel (FRFG and University Tübingen), is centered around the question whether human infection studies could have been implemented during the early stages of the pandemic to minimise deaths and severe infections. The issue concludes with two reviews on recent books by Alberto Giubilini and Katie Wright. In his review of Giubilini’s The Ethics of Vaccination, Marius Kunte notes that it contains a “thought-provoking plea” for individual, collective and institutional obligations to reach high vaccination rates. Judith Kausch-Zongo concludes her review of Wright’s Gender, Migration and the Intergenerational Transfer of Human Wellbeing with a special emphasis on the book’s empirical findings, and praises it in its entirety as “undoubtedly important”. Both books serve as poignant reminders of how sustainable societies can only emerge once the challenges revolving around its most vulnerable members have been properly addressed. (shrink)

The ArgumentThe paper offers a reconstruction of one aspect of Bakhtin's philosophy, focusing on a deep-seated ambivalence that has been largely overlooked in studies based on his late works. Bakhtin's early work, 1920–23, is set within a distinctly metaphysical framework, an outlook that seems diametrically opposite to what has become known as the Bakhtinian conception of culture. That ideological rift is manifest in the different treatment of Dostoevsky's works in these two phases.Extrapolating Bakhtin's perspective onto Dostoevsky's work, the paper briefly (...) outlines a theory of modernism as a “crisis of authority,” with particular emphasis on the role of closure — i.e., retrospective framing, both literary and existential — in the absence of metaphysical grounding.Finally, the paper offers a comment on Bakhtin's wholesale assimilation into the postmodernist canon, in an attempt to problematize it and to reformulate some relevant and persistent questions on the significance of narrativity in human existence. (shrink)

We characterize the modal logics of elementary classes of Kripke frames as precisely those modal logics that are axiomatized by modal axioms synthesized in a certain effective way from "quasi-positive" sentences of hybrid logic. These are pure positive hybrid sentences with arbitrary existential and relativized universal quantification over nominals. The proof has three steps. The first step is to use the known result that the modal logic of any elementary class of Kripke frames is also the modal logic of (...) the closure of this class under disjoint unions, generated subframes, bounded morphic images, and ultraroots. This latter class can be defined by the first-order sentences of a special syntactic form (called pseudo-equations by Goldblatt) that are valid in the former class. The second step is to translate these pseudo-equations into equivalent quasi-positive hybrid sentences. In the third and main step, we show that any quasi-positive sentence S generates an infinite set of modal formulas called "approximants," which together axiomatize a canonical modal logic that is sound and complete for the class of frames validating S. The proof is analogous to standard proofs of Sahlqvist's theorem. It generalizes to sets of quasi-positive sentences. The main result now follows. (shrink)

We consider the problem of constructing first-order definitions in the language of rings of holomorphy rings of one-variable function fields of characteristic 0 in their integral closures in finite extensions of their fraction fields and in bigger holomorphy subrings of their fraction fields. This line of questions is motivated by similar existential definability results over global fields and related questions of Diophantine decidability.

Gödel's dialectica interpretation of Heyting arithmetic HA may be seen as expressing a lack of confidence in our understanding of unbounded quantification. Instead of formally proving an implication with an existential consequent or with a universal antecedent, the dialectica interpretation asks, under suitable conditions, for explicit 'interpreting' instances that make the implication valid. For proofs in constructive set theory CZF-, it may not always be possible to find just one such instance, but it must suffice to explicitly name a (...) set consisting of such interpreting instances. The aim of eliminating unbounded quantification in favor of appropriate constructive functionals will still be obtained, as our ∧-interpretation theorem for constructive set theory in all finite types CZFω- shows. By changing to a hybrid interpretation ∧q, we show closure of CZFω- under rules that – in stronger forms – have already been studied in the context of Heyting arithmetic. In a similar spirit, we briefly survey modified realizability of CZFω- and its hybrids. Central results of this paper have been proved by Burr 2000a and Schulte 2006, however, for different translations. We use a simplified interpretation that goes back to Diller and Nahm 1974. A novel element is a lemma on absorption of bounds which is essential for the smooth operation of our translation. (shrink)

The Netherdutch Reformed Church of Africa (NRCA) did not escape this existential crisis of conflict. It manifests in various ways resulting in the bleeding of congregations, the exodus of congregants and the closure of congregations, as many congregants that declare themselves as members of the Church do not attend worship services or participate in the Holy Communion and exit the church. The study was conducted in the NRCA to determine the effect and response formation of observed conflict by (...) ministers in their respective congregations. The results of the study indicate that pastors and/or ministers do suffer emotional trauma because of the conflict in the congregation which, according to their own statements results in a loss of role performance. We provide an overview of the problem statement and methodology of the study. We discuss an abbreviated, theoretical perspective on conflict as a social phenomenon. We present the findings of our study and conclude with an abbreviated process to equip pastors with the necessary emotional maturity and self-management.Contribution: This study uncovers emotional trauma experienced by ministers, affecting their role performance. We offer a succinct problem statement, research methodology, and propose a scientifically informed process to enhance ministers’ emotional resilience within the NRCA. (shrink)

In La Métaphore Vive, spatial understandings pervade much of Ricoeur’s discussion of metaphor in terms of proximity and distance, tension, substitution, displacement, change of location, image, the ‘open’ structure of words, closure, transparency and opaqueness. Yet this is usually where space is discussed within metaphor, and as a metaphor itself, rather than as a precondition or prior system of relations to language interacting with language. Based on reinterpretation of an aspect of Lévi-Strauss’ structuralist anthropology, diametric and concentric spaces are (...) argued to be such a prior system of relations to language, actively framing metaphor. This article examines the relevance of this prelinguistic spatial discourse to Ricoeur’s framework of metaphor and interrogation of the copula, influenced centrally by Heidegger. Concentric spatial assumed connection and diametric spatial assumed separation offer a framework for understanding, in Ricoeur’s words, the “conflict between identity and difference” in metaphor and early Heidegger’s existential spatiality. (shrink)

The present article aims to provide an original interpretation of Jan Patočka’s philosophy of history starting from the consideration of the debt it holds with Heidegger’s thought, in particular with the existential analytic of Being and time. Of Heidegger’s analytics, in fact, Patočka grasps and assumes with great radicality and originality the peculiar ‘modal logic’, according to which the existential dimension of closure, inauthenticity and estrangement from oneself is not opposed ‘frontally’ to that of openness, authenticity and (...) nearness to oneself of existence, being rather co-owned by it in the form of a privative modalization. We have therefore aimed to show how such a scheme is the one by which Patočka, in his Heretical Essays, interprets the whole adventure of Western history starting from its ‘emersion’ in ancient Greece. In particular, thanks to such a reconstruction we were able to shed light on the position of the phenomenon of work in Patočka’s philosophy: the Patočkian conception of work, understood as an obstacle par excellence to authentic historical existence, represents not only the true stakes of the comparison of the phenomenological- existential line in which Patočka is inserted with a Marxist theory of alienation; starting from here, moreover, it is potentially a clearer framework of the Patočkian genealogy of Western civilization and its form of subjectivity in relation to the approach of other genealogical philosophies of the last century. (shrink)

The Cartesian distinction between res extensa and res cogitans initiated in the early modern age the philosophical discourse with regard to an adequate explanation of the nexus between the body and the mind. The causal closure of the body (as essentially a physical phenomenon) seems to exclude both the physical and neuronal causation of mental states and operations as well as the mental causation of bodily states and processes. The following treatise is an attempt to re-examine the causal connectivity (...) between the body and the mind and thereby to explain the mysterious interaction between these two entirely distinct modes of existence and reality. The neuronal causation of the mental existence of human beings, and conversely the mental causation of bodily volition seem to surpass the framework of ordinary causal processes which are primarily conceived as temporal sequences of causes and effects in natural phenomena. The existence of the conscious subject – as res cogitans – can hardly be reduced to momentary neuronal processes of causation; it implies a constant ontological causation in which the elementary physical and material modes of being cause constantly and ontologically the mental states and operations – which eventually form higher and unitary modes of being. This dual nature of a neuronal-ontological causation, namely the constant and existential causation of the mind and the momentary causation of mental processes (sensation, perception, cognition, thinking, etc.), seems to resolve the problem of the causal connectivity between the body and the mind. However, the ontological causation cannot be restricted to the causal interaction between the body and the mind; it can be extended to the modes of existence of the overall physical i. e. material reality. (shrink)

Starting from first person experience, I argue that early miscarriage may invoke a sense of loss that is enigmatic and ambiguous, often times complicated by the fact that the topic of miscarriage is culturally silenced. Understanding the frequency of such occurrences of early pregnancy loss (in terms of the “miscarriage iceberg”) adds to the existential need to conceptualize such losses as they bleed into life at its very emergence. The prevalent cultural discourse on loss, even when it deals with (...) ambiguity, is focused upon individuation and personhood, which may complicate the grieving process in the case of early pregnancy loss.In searching for alternative epistemologies to address early pregnancy loss and its consequent grief, I propose the following conceptual pathways to elucidate the nature of this loss. First, early pregnancy loss may be understood in terms of the dissipation of a pregnant constellation, thereby putting less emphasis on losing a “being” but rather a sense of participation. This clarifies the kind of loss involved but does not yet completely explain what kind of relationality is lost. Secondly, the grief involved in early pregnancy loss benefits from the Freudian-inspired theories of Pauline Boss and Judith Butler, who emphasize that grief entails absence and presence (Boss, The myth of closure: ambiguous loss in a time of pandemic and change. W.W. Norton & Company, New York, 2021) as well as a deep loss of identity given the loss of relational ties that inform identity (Butler, Stud Gender Sexuality 4(1):9–37, 2003). This deepens the account of grief but does not precisely address the loss of mere emergent relationality. Thirdly, following Gilbert Simondon’s theory on ontogenesis (Simondon, The genesis of the individual. In Crary J, Kwinter S (eds) Incorporations. Zone Books, New York, 297–319, 1992), pregnancy loss involves losing a bridge to a pre-individual relationality, due to which the formerly pregnant body cannot easily leap “back” into former forms of individuation nor leap forward into a socially recognized altered collectivity. This account is able to clarify the kind of relational loss involved in early pregnancy loss. (shrink)

The translation of the Guru Granth Sahib (GGS), or Sikh ‘scripture’, within the discourse of (European) colonial/modernity was enacted by the use of hermeneutics—which oversaw the shift from the openness of praxis to the closure of representation and knowledge. Such a shift demoted certain indigenous interpretive frames, wherein the GGS is assumed to enunciate an excess that far transcends the foreign demand to fix the text’s ‘call’ into singular meanings (beyond time), but rather transforms the hermeneutic desire into a (...) process of learning (Sikhi) through multiple meanings (in time). Thus the GGS is not translated according to a particular life-world, but actively transforms the life-world of those that respond to its excessive call. How should hermeneutics be reformed in this case? If the GGS as text demands interpretation, then the text as Guru demands engagement, and together they would necessarily call forth a radicalization of hermeneutics via a certain poetic reticence to all philosophical messengers. (shrink)

We give a uniform proof of the theorems of Yao and Beigel–Tarui representing ACC predicates as constant depth circuits with MODm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {MOD}_{m}$$\end{document} gates and a symmetric gate. The proof is based on a relativized, generalized form of Toda’s theorem expressed in terms of closure properties of formulas under bounded universal, existential and modular counting quantifiers. This allows the main proofs to be expressed in terms of formula classes instead of (...) Boolean circuits. The uniform version of the Beigel–Tarui theorem is then obtained automatically via the Furst–Saxe–Sipser and Paris–Wilkie translations. As a special case, we obtain a uniform version of Razborov and Smolensky’s representation of AC0[p]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {AC}^{0}[p]$$\end{document} circuits. The paper is partly expository, but is also motivated by the desire to recast Toda’s theorem, the Beigel–Tarui theorem, and their proofs into the language of bounded arithmetic. However, no knowledge of bounded arithmetic is needed. (shrink)

This article draws in particular on existential-phenomenological notions of “witnessing.” Witnessing, often conceived in the context of testimony, obviously involves epistemological concerns, such as how we come to know through the experiences and reports of others. I shall argue, however, that witnessing as a mode of intersubjectivity offers understandings that involve questions about how people come to be. More specifically, I want to consider the positive potential of “witnessing” to disrupt intersubjective completeness or closure, particularly as this relates (...) to work on organizing subjectivities, as well as, in the field of organization studies. (shrink)

n + 1 nested k-ary fixed point operators are more expressive than n. This holds on finite structures for all sublogics of partial fixed point logic PFP that can express conjunction, existential quantification and deterministic transitive closure of binary relations using at most k-ary fixed point operators and that are closed against subformulas. Among those are a lot of popular fixed point logics.

Endocrinologists apply the idea of feedback loops to explain how hormones regulate certain bodily functions such as glucose metabolism. In particular, feedback loops focus on the maintenance of the plasma concentrations of glucose within a narrow range. Here, we put forward a different, organicist perspective on the endocrine regulation of glycaemia, by relying on the pivotal concept of closure of constraints. From this perspective, biological systems are understood as organized ones, which means that they are constituted of a set (...) of mutually dependent functional structures acting as constraints, whose maintenance depends on their reciprocal interactions. Closure refers specifically to the mutual dependence among functional constraints in an organism. We show that, when compared to feedback loops, organizational closure can generate much richer descriptions of the processes and constraints at play in the metabolism and regulation of glycaemia, by making explicit the different hierarchical orders involved. We expect that the proposed theoretical framework will open the way to the construction of original mathematical models, which would provide a better understanding of endocrine regulation from an organicist perspective. (shrink)

Charles S. Peirce’s pragmatist theory of logic teaches us to take the context of utterances as an indispensable logical notion without which there is no meaning. This is not a spat against compositionality per se , since it is possible to posit extra arguments to the meaning function that composes complex meaning. However, that method would be inappropriate for a realistic notion of the meaning of assertions. To accomplish a realistic notion of meaning (as opposed e.g. to algebraic meaning), Sperber (...) and Wilson’s Relevance Theory (RT) may be applied in the spirit of Peirce’s Pragmatic Maxim (PM): the weighing of information depends on (i) the practical consequences of accommodating the chosen piece of information introduced in communication, and (ii) what will ensue in actually using that piece in further cycles of discourse. Peirce’s unpublished papers suggest a relevance-like approach to meaning. Contextual features influenced his logic of Existential Graphs (EG). Arguments are presented pro and con the view in which EGs endorse non-compositionality of meaning. (shrink)