The contemporary operating environment for deployed United States military operations largely focuses on deployments to predominantly Islamic countries. The differences in cultural values between d...

In the Self's Place: The Approach of Saint Augustine presents Jean-Luc Marion's rethinking of the modern notion of the self by way of an original reading of Saint Augustine through the lens of a phenomenology of givenness. Here he tests the hermeneutic validity of concepts forged in his previous works. His goal is to show that the Confessiones are inscribed within the confessio, that love is an underlying epistemic condition of truth, and that God's call and our response to God (...) are both gifts. Ultimately, Marion points us toward a conception of the self that is at once postmodern and very Augustinian. (shrink)

Agriculture in Australia isacknowledged as having serious environmentalimpacts. Since the Brundtland Report in 1987, aNational Strategy for Ecologically SustainableDevelopment (ESD) has charted a course for aneconomically, environmentally, and sociallysustainable agriculture. Numerous extensioninitiatives, such as catchment management,Landcare, property management plans, and, morerecently, environmental management systems, aredriving business education programs for farmersin most states in an attempt to address theissues of ESD. Innovative accounting techniquesand models exist, particularly developmentsthat recognize and value biodiversity, monitorenvironmental impacts, and show that renewableresources are indeed ``renewable,'' which (...) couldbe the focus of integrated extensioninitiatives supportive of ecologicallysustainable development. Empirical researchconducted during 1996 that exploredenvironmental concern and actions of farmersindicated that farmwomen were better educatedand more likely to be environmentallyconcerned. In addition they were more likely tosupport that concern with actions that indicatethat the farm is being managed for sustainableoutcomes. This paper explores these issues,concluding that there is a need to reconsiderthe focus of business and natural resourcemanagement education for farmers in Australia. (shrink)

Automatic Generation Control in modern power systems is getting complex, due to intermittency in the output power of multiple sources along with considerable digressions in the loads and system parameters. To address this problem, this paper proposes an approach to calculate Power System Restoration Indices of a 2-area thermal-hydro restructured power system. This study also highlights the necessary ancillary service requirements for the system under a deregulated environment to cater to large-scale power failures and entire system outages. An abrupt change (...) in consumer load demands and disturbances in any control region of a multiarea system causes severe fluctuations in frequency and interarea power exchanges. However, simple Proportional and Integral controllers are most prevalent in the literature to effectively resolve AGC issues, while its integral gain is smaller due to the larger overshoot in transient performance. Therefore, an attempt has been made with a novel control strategy, known as the pseudoderivative feedforward with feedback controller, is developed to keep the interarea power exchanges and the frequency to the specified limits after load changes. A PDFF controller is designed and implemented using the flower pollination algorithm to obtain optimal dynamic performance for different types of potential power flows in a restructured power system under investigation. The proposed PDFF controller localizes the zero at an optimal place that reduces the rise time of the step-response to reduce the excessive overshoot and gives much better dynamic performances as compared to the PI control structure. The Integral Square Error is considered as a performance criterion to derive the optimized gain of the PDFF control structure using FPA. Different PSRI are computed based on the transient response of the 2-area deregulated multisource system and different restoration measures to be taken are also discussed. The simulation results clearly show that the proposed approach is very powerful in decreasing the frequency and tie-power digressions under different load perturbations. (shrink)

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), symbolizing English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as modal logic, soundness, and functional completeness. Exercises with solutions are available. (...) It is provided in PDF (for screen reading, printing, and a special version for dyslexics), HTML, and in LaTeX source code. (shrink)

This chapter discusses translators’ efforts to render the grammatical gender of Plato’s Greek in passages of the Republic, and to translate his terms noting differences between men and women with terms associated with the identity-defining concepts of sex and gender. It argues that the translation of 'genos' as 'sex' reveals less about the source text than about the role of the concept of sex in the translating culture. A discussion of a similar controversy in contemporary translation shows how debates over (...) the French translation of 'gender' as genre are embroiled in issues of national identity. The chapter demonstrates how translation and its analysis may simultaneously express and contest cultural assumptions about sex and gender. (shrink)

forall x: Dortmund is an adaptation and German translation of forall x: Calgary. As such, it is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity, the syntax of truth-functional (propositional) logic and truth-table semantics, the syntax of first-order (predicate) logic with identity and first-order interpretations, formalizing German in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as the (...) syntax and (Kripke-)semantics of modal logic. The book is provided in PDF and in LaTeX source code. A booklet with solutions for the exercises in the book is available. (shrink)

English translates ‘genos’ as kind and ‘eidos’ as form, which differ in meaning as much as ‘herd’ and ‘brand’ do. But there are hard passages where ‘genos’ and ‘eidos’ have appeared to be synonyms, usually given the new meaning class. We show that, although ‘genos’ and ‘eidos’ are never synonyms and continue to mean kind and form, the word ‘eidos’ can be used figuratively, as a metonym, for a genos.

An introduction to sentential logic and first-order predicate logic with identity, logical systems that significantly influenced twentieth-century analytic philosophy. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading. -/- This books treats symbolization, formal semantics, and proof theory for each language. The discussion of formal semantics is more direct than in many introductory texts. Although forall x does not contain proofs of soundness and completeness, it (...) lays the groundwork for understanding why these are things that need to be proven. -/- The book highlights the choices involved in developing sentential and predicate logic. Students should realize that these two are not the only possible formal languages. In translating to a formal language, we simplify and profit in clarity. The simplification comes at a cost, and different formal languages are suited to translating different parts of natural language. (shrink)

This is an open-access introductory logic textbook, prepared by Jonathan Ichikawa, based on P.D. Magnus's forallx. This (v2.0, July 2020) is intended as a stable, ready-for-teaching edition.

Over twenty years since the influential revisionist studies of Roussel and Bourriot, agreement on a satisfactory theory of the Attic genos seems as elusive as ever. Although they differed on details, these two scholars were agreed in their rejection of the old monolithic account of the genos as aristocratic family whose institutionalized control over state cults and phratry admissions in the historical period was a relic of a wider political dominance. Roussel and Bourriot instead proposed a tripartite model according to (...) which the formal genos-kome—a more or less localized community similar to the later deme, with hereditary but socio-economically diverse membership, and enjoying, as a tighter community well placed to regulate its own admissions, automatic access to the wider phratry—was distinguishable both from aristocratic families, such as the Peisistratidai or Alkmeonidai, and priestly houses, such as the Kerykes and Eumolpidai of Eleusis. Subsequent discussion has moved in several directions. My analysis of the relationship between phratry and genos followed a broadly revisionist line. I found no good evidence for gene controlling the access to phratries of persons who were not genos members and presented a new interpretation of the crucial Demotionidai decrees in which, contrary to prevailing theories, neither of the two groups mentioned in them—the Demotionidai and the House of the Dekeleieis—was a privileged subgroup dominating the whole. Rather, I suggested that the Demotionidai were a phratry in process of fission, the Dekelean House a product of this process. Others, however, have taken the debate in the other direction, as it were reprivileging the genos. (shrink)

We prove the existence of a bound to the number of components of an $\forall$-definable set in the reals, using Pfaffian functions, and give some applications.

Introduction -- The common hellenic meaning of "genus" -- The Pollaxos legomena or things said in many ways -- Genus in the explanation of change : the subject and substratum principles -- To what is Aristotle's theory of change a response? : the pre-socratic and platonic background -- Change : the principles of nature in physics I -- A first mention of matter and form -- Genus in the explanation of change : the definition of change -- Aristotle's definition of (...) change : physics III -- The circularity objections -- The advantages of Aristotle's theory -- The use of genus in change -- Genus in the explanation of change generation, "for man begets man" (1032-24) -- Generation -- Change and genus -- The generation of animals as organic substances -- Animal generation and the mule -- Genus in definitions : the Aristotelian and platonic division of a genus -- "What is definition?" -- Platonic division and definition -- Aristotle's use of genus and animal taxonomy -- The use of "genus" in Pa I -- Analogy vs. the more and the less -- Taxonomy : the megista gene -- Genus in definitions : why Aristotle was a realist -- Division and definition in Aristotle -- Causal definitions , substantial definitions, and definitions by matter and form -- The unity of definition and division -- The use of genus in definition -- Case study I : the definition of the psyche -- On matter as substratum -- On matter : the domain problem -- On matter : is it substance? -- On matter : potentiality -- The elements : is ontological reduction possible? -- Proper matter and generation revisited -- The indeterminacy vs. nature problem -- On genus as matter -- The analogy interpretation : Aristotle's mention of genus as matter -- The literal interpretation : Aristotle's use of genus as matter -- The principal unity of Aristotle's thought. (shrink)

In 1990, J.L. Krivine introduced the notion of storage operator to simulate 'call by value' in the 'call by name' strategy. J.L. Krivine has shown that, using Gödel translation of classical into intuitionitic logic, we can find a simple type for the storage operators in AF2 type system. This paper studies the $forall$-positive types (the universal second order quantifier appears positively in these types), and the Gödel transformations (a generalization of classical Gödel translation) of TTR type system. We generalize, by (...) using syntaxical methods, the J.L. Krivine's Theorem about these types and for these transformations. We give a proof of this result in the case of the type of recursive integers. (shrink)

Pre-existing mathematical formulations are generally used for the treatment of new scientific problems. In this note we show that the construction of mathematical structures from open physical, chemical, and biological problems leads to new intriguing mathematics of increasing complexity called iso-, geno-, and hyper-mathematics for the treatment of matter in reversible, irreversible, and multi-valued conditions, respectively, plus anti-isomorphic images called isodual mathematics for the treatment of antimatter. These novel mathematics are based on the lifting of the multiplicative unit of (...) ordinary fields (with characteristic zero) from its traditional value +1 into: (1) invertible, Hermitean, and single-valued units for isomathematics; (2) invertible, non-Hermitean, and single-valued units for genomathematics; and (3) invertible, non-Hermitean, and multi-valued units for hypermathematics; with corresponding liftings of the conventional associative product and consequential lifting of all branches of mathematics admitting a (left and right) multiplicative unit. An anti-Hermitean conjugation applied to the totality of quantities and their operation of the preceding mathematics characterizes the isodual mathematics. Intriguingly, the emerging formulations preserve the abstract axioms of conventional mathematics (that based on the unit +1). As such, the new formulations result to be new realizations of existing abstract mathematical axioms. We then show that the above mathematical advances permit corresponding liftings of conventional classical and quantum theories with a resolution of basic open problems in physics, chemistry, and biology, numerous experimental verifications, as well as new industrial applications. (shrink)

The paper is inspired by and explicitly presupposes the readers’ knowledge of the Kürbis normalization procedure for the Milne tree-like natural deduction system _C_ for classical propositional logic. The novelty of _C_ is that for each conventional connective, it has only _general_ introduction and elimination rules, whose paradigm is the rule of proof by cases. The present paper deals with the Milne–Kürbis troublemaker—adding universal quantifier—caused by extending the normalization procedure to \(\mathbf {C^{\exists }_{\forall }} \), the first-order variant of _C_. (...) For both quantifiers, \( \mathbf {C^{\exists }_{\forall }}\) has only general quantifier rules, whose paradigm is the indirect rule of existential elimination. We propose the classical first-order tree-like natural deduction system \( \mathbf {NC^{\exists }_{\forall }}\) such that it contains all the propositional and half the quantifier rules of \(\mathbf {C^{\exists }_{\forall }}\) and differs from it with respect to the other half of the quantifier rules and the notion of a deduction. We show that in the case of \(\mathbf {NC^{\exists }_{\forall }} \), whose specifics is based on the Quine treatment of _flagged_ variables in the linear-style natural deduction system as well as on the Aguilera-Baaz treatment of _characteristic_ and _side_ variables for sequent-style calculi, the troublemaker doesn’t occur. In order to handle another specifics of \(\mathbf {NC^{\exists }_{\forall }}\) —an auxiliary notion of a _finished_ deduction that makes deductions _nonhereditary_—we show soundness and completeness of \( \mathbf {NC^{\exists }_{\forall }} \). While emphasizing the former with the help of the Smirnov technique, we additionally indicate a fixable gap in the Quine soundness argument. At last, the philosophical significance of the main result of this paper is developed in more detail. (shrink)

El decir que todos y todas hemos nacido de mujer parece una perogrullada. Esta es, como lo expresa Rich, la única experiencia unificadora, innegable, compartida por mujeres y hombres: aquellos meses que pasamos dentro del cuerpo de una mujer, desarrollándonos. Sin embargo, es usual encontrar en el discurso cívico de las ciudades griegas, la idea de que la mujer no tiene relación alguna con el origen de la especie. Las mujeres son con frecuencia representadas como un grupo separado y cerrado (...) sobre sí mismo, el genos gynaikon, que viene a agregarse al anthropos genos una vez que este ya existe. La hipótesis del presente escrito sostiene que hay dos aspectos conceptuales que acompañan la narrativa del genos gynaikon: (i) la ambigüedad en la clasificación del grupo de las mujeres y (ii) el lugar secundario que se les asigna respecto del origen de la humanidad. Como objetivo general propongo mostrar que el tópico del genos gynaikon está presente, a través de estos aspectos conceptuales, en la concepción platónica y aristotélica de la reproducción y la diferencia sexual. (shrink)

Bioethics tends to be dominated by discourses concerned with the ethical dimension of medical practice, the organization of medical care, and the integrity of biomedical research involving human subjects and animal testing. Jacques Derrida has explored the fundamental question of the “limit” that identifies and differentiates the human animal from the nonhuman animal. However, to date his work has not received any reception in the field of biomedical ethics. In this paper, I examine what Derrida’s thought about this limit might (...) mean for the use/misuse/abuse of animals in contemporary biomedical research. For this, I review Derrida’s analysis and examine what it implies for scientific responsibility, introducing what I have coined the “Incompleteness Theorem of Bioethics.”. (shrink)

In his booklet "Contributions to a better founded presentation of mathematics" of 1810 Bernard Bolzano made his first serious attempt to explain the notion of a rigorous proof. Although the system of logic he employed at that stage is in various respects far below the level of the achievements in his later Wissenschaftslehre, there is a striking continuity between his earlier and later work as regards the methodological constraints on rigorous proofs. This paper tries to give a perspicuous and critical (...) account of the fragmentary logic of Beyträge, and it shows that there is a tension between that logic and Bolzano's methodological ban on ?kind crossing? (shrink)

In his booklet ‘Contributions to a better founded presentation of mathematics’ of 1810 Bernard Bolzano made his first serious attempt to explain the notion of a rigorous proof. Although the system of logic he employed at that stage is in various respects far below the level of the achievements in his later Wissenschaftslehre, there is a striking continuity between his earlier and later work as regards the methodological constraints on rigorous proofs. This paper tries to give a perspicuous and critical (...) account of the fragmentary logic of Beyträge, and it shows that there is a tension between that logic and Bolzano's methodological ban on ‘kind crossing’. (shrink)

A \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\forall\exists!}$$\end{document}-sentence is a sentence of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\forall x_{1}\cdots x_{n}\exists!y_{1}\cdots y_{m}O(\overline{x},\overline{y})}$$\end{document}, where O is a quantifier-free formula, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\exists!}$$\end{document} stands for “there exist unique”. We prove that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} is (up to isomorphism) a finite class of finite models then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} is axiomatizable by a set of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\forall\exists!}$$\end{document}-sentences if and only if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} is closed under isomorphic images, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} has the intersection property, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} is closed under fixed-point submodels. This result is employed to characterize the subclasses of finitely generated discriminator varieties axiomatizable by sentences of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\forall\exists!\bigwedge p=q}$$\end{document}. (shrink)

Parmi les activités indispensables à la survie et à l’équilibre de Callipolis, la cité décrite dans la _République_, les fonctions politiques et militaires occupent une place prépondérante. Dans cette mesure, leur exercice est conditionné à la possession d’un certain nombre de qualités physiques, morales et intellectuelles parmi lesquelles un mélange proportionné de deux traits de caractère opposées : la douceur et l’agressivité. Pour confirmer la coexistence de ce curieux mélange chez un individu, Socrate évoque l'image d'un chien de race, chez (...) qui la coexistence de ces deux qualités s’exprime dans sa docilité envers ses maîtres et son hostilité envers les étrangers. L’image du chien joue un roll décisif dans la _République _en ce qu’elle permet à Socrate de démontrer le caractère naturel de son projet et de justifier la radicalité des méthodes destinées au perfectionnement du _génos_ affecté aux fonctions politiques et militaires. L’objectif de cet article est d’analyser les incidences théoriques de l’emploi de cette image comme modèle de l’ordre politique et du genre de vie des gardiens de la _République_ et la manière dont cette image intervient dans la construction d’une conception de la _phusis _qui, loin d’être univoque, varie selon les besoins de l’argumentation socratique. (shrink)

The properties of the ${\forall^{1}}$ quantifier defined by Kontinen and Väänänen in [13] are studied, and its definition is generalized to that of a family of quantifiers ${\forall^{n}}$ . Furthermore, some epistemic operators δ n for Dependence Logic are also introduced, and the relationship between these ${\forall^{n}}$ quantifiers and the δ n operators are investigated.The Game Theoretic Semantics for Dependence Logic and the corresponding Ehrenfeucht- Fraissé game are then adapted to these new connectives.Finally, it is proved that the ${\forall^{1}}$ quantifier (...) is not uniformly definable in Dependence Logic, thus answering a question posed by Kontinen and Väänänen in the above mentioned paper. (shrink)

An ‘Information Centre’ has recently been established by law which has the power to collect, collate and provide access to the medical information forall patients treated by the National Health Service in England, whether in hospitals or by General Practitioners. This so-called ‘care.data’ scheme has given rise to major and ongoing controversies. We will sketch the background of the scheme and look at the responses it has elicited from citizens and medical professionals. In Autumn 2013, NHS England set up a (...) care.data website where citizens could record their concerns regarding the collection of health-related data by the Information Centre. We have reviewed all the comments on this website up until June 2015. We have also analysed the readers’ comments on the coverage of the care.data scheme in one of the main national UK newspapers. When discussing the responses of citizens, we will make a distinction between the problems that citizens detect and the solutions they propose. The solutions that are being perceived as the most relevant ones can be summarized as follows: citizens wish to further the common good without being manipulated into doing it, while at the same time being safeguarded against various abuses. The issue of trust turns out to figure prominently. Our analysis of reactions to the scheme in no way pretends to be exhaustive, yet it provides various relevant insights into the concerns identified by citizens as well as medical professionals. These concerns, moreover, have a more general relevance in relation to other contexts of medical data-mining as well as biobank research. Our analysis also offers important pointers as to how those concerns might be addressed. (shrink)

Scheinerman (2023) proposes that at the Human Genome Editing Initiative international summit (held in March 2023) there should have been a parallel, separate Citizens’ Jury, and that the Human Geno...

I discuss the issue whether Aristotle's philosophy of science allows the use of mathematical premises or mathematical tools in general for explanaing phenomena in the natural sciences. I thereby discuss the concept of "metabasis eis allo genos" as it appears in Posterior Analytics I.7.

This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (J Philos Logic 34(2):155–192, 2005), and the dependence digraph by Beringer and Schindler (Reference graphs and semantic paradox, 2015. https://www.academia.edu/19234872/reference_graphs_and_semantic_paradox). Unlike the usual discussion about self-reference of paradoxes centering around Yablo’s paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb’s dependence relation. They are called ‘locally finite paradoxes’, satisfying that any sentence in (...) these paradoxes can depend on finitely many sentences. I prove that all locally finite paradoxes are self-referential in the sense that there is a directed cycle in their dependence digraphs. This paper also studies the ‘circularity dependence’ of paradoxes, which was introduced by Hsiung (Logic J IGPL 22(1):24–38, 2014). I prove that the locally finite paradoxes have circularity dependence in the sense that they are paradoxical only in the digraph containing a proper cycle. The proofs of the two results are based directly on König’s infinity lemma. In contrast, this paper also shows that Yablo’s paradox and its ∀∃\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\forall \exists $$\end{document}-unwinding variant are non-self-referential, and neither McGee’s paradox nor the ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-cycle liar has circularity dependence. (shrink)

We use a $\kappa^{+}-Mahlo$ cardinal to give a forcing construction of a model in which there is no sequence $\langle A_{\beta} : \beta \textless \omega_{2} \rangle$ of sets of cardinality $\omega_{1}$ such that $\{\lambda \textless \omega_{2} : \existsc \subset \lambda & (\bigcupc = \lambda otp(c) = \omega_{1} & \forall \beta \textless \lambda (c \cap \beta \in A_{\beta}))\}$ is stationary.

A new method of "minimal" realizability is proposed and applied to show that the definable functions of Heyting arithmetic (HA)--functions f such that HA $\vdash \forall x\exists!yA(x, y)\Rightarrow$ for all m, A(m, f(m)) is true, where A(x, y) may be an arbitrary formula of L(HA) with only x, y free--are precisely the provably recursive functions of the classical Peano arithmetic (PA), i.e., the $ -recursive functions. It is proved that, for prenex sentences provable in HA, Skolem functions may always be (...) chosen to be $ -recursive. The method is extended to intuitionistic finite-type arithmetic, HA ω 0 , and elementary analysis. Generalized forms of Kreisel's characterization of the provably recursive functions of PA and of the no-counterexample-interpretation for PA are consequently derived. (shrink)

Стаття являє собою дослідження у сфері природної мови (та мови поетичної) і репрезентує певні спільні аспекти, які містяться у працях Франсуа Реканаті та Юлії Крістєвої, не зважаючи на наявні методологічні розбіжності. Зазвичай, дослідження з поетики відокремлюють власний предмет від предмета аналізу лінгвістичного, зокрема, та – природної мови загалом, оскільки поетичній мові притаманні особливі властивості. Проте автор виходить із переконання, що між дослідженнями текстів художніх творів, попри їхню складну семантику, та виразів природної мови є можливим плідний консенсус. Подібне переконання, що випливає (...) зі співставлення певних фрагментів вчень та понять Крістєвої і Реканаті, дає можливість вгледіти парадоксальну подібність предметів їхніх досліджень або специфіки їхнього опису. Так, розгляд Реканаті, приміром, індексальних виразів не лише не суперечить концепту наративної темпоральності Крістєвої, а й відсилає до єдиного осередку (чи то зазнаваного впливу) підходів, що зумовлює цікавість не так до тексту або виразу, як до фігури мовця. У даному випадку за спільне впливове джерело покладається вчення Ж. Лакана, хоча автор і не вдається до розгорнутого розгляду такої думки, що потребує окремого ґрунтовного дослідження. Проте згадувані у статті теоретичні положення (принаймні, щодо статусу мовця) названих авторів можуть мати сенс у випадку спільного використання як у річищі поетики, так і відносно аналізу виразів природної мови. У цьому сенсі наголос ставиться на використанні теоретичних розробок Крістєвої та Реканаті з погляду зв’язку між ними, що дає можливість обопільно розширити горизонти дослідження мови як такої поза конкретних форм її репрезентації. (shrink)