Artur Blaim’s Gazing in Useless Wonder. English Utopian Fictions 1516–1800, the thirteenth volume of the esteemed Ralahine Utopian Studies series, has already received praises as a must-read monograph from such renowned utopian scholars as Lyman Tower Sargent and Gregory Claeys—and indeed it challenges anyone who would dare state otherwise. And even though such flawless pieces of research are not that common, Blaim’s book definitely has the potential to set a precedent in that regard, being a thorough and cohesive analysis of (...) rather sporadically interpreted utopian texts and novels from even less often studied historical periods.Already the book’s composition reveals a direct association between the emergence of... (shrink)

In Adam Smith’s Inquiry into the Nature and Causes of the Wealth of Nations the term ‘rational’ occurs only twice. Neither of these uses assigns the property of rationality either to human beings or to economic agents. Despite that, Smith is widely recognised as the founder of modern mainstream economics, a science which is defined by the assumption of the rationality of an economic agent. This paper aims to locate and discuss the notion of rationality which is implied by Smith’s (...) work. To achieve that a double-track approach is taken. First, the current paper reconstructs Smith’s general view on human nature which was presented mainly in his earlier book The Theory of Moral Sentiments. This is followed by a discussion of Smith’s theses on selected mechanisms which drive the economy as presented in The Wealth of Nations. (shrink)

The paper examines Robert Sugden’s arguments for contractarian economics, which exclude objective valuation. From a metaethical stance we claim that it is possible and desirable to enrich the axiology of contractarian economics to make it more convincing and applicable. Analyzing Sugden’s argument against paternalism, we show that adopting a richer axiology is compatible with the contractarian framework. Examining Sugden’s claim for redistribution, we demonstrate that explaining the psychological stability of a market economy is problematic without a richer axiology. Considering sweatshop (...) problem, we argue that without a richer axiology, contractarian economists are unable to recognize mutually advantageous exploitation. The paper concludes with the postulates on contractarian economics. (shrink)

This collection of current research on logic programming languages presents results from a three-year, ESPRIT-funded effort to explore the integration of the foundational issues of functional, logic, and object-oriented programming. It offers valuable insights into the fast-developing extensions of logic programming with functions, constraints, concurrency, and objects. Chapters are grouped according to the unifying themes of functional programming, constraint, logic programming, and object-oriented programming.

Recent attempts by American theorists to produce a radical politics, characterized by the effort to translate the insights of Continental philosophy into a political register, remain trapped in that which they purport to transcend: the metaphysics of subjectivity. In their essential determinations, the works of William Connolly, Stephen White, Richard Ashley, etc. remain firmly anchored in a traditional liberal schema. The reason for this is that while these efforts have sought to de-center political identity by exposing its relational character they (...) have not re-thought 'rela tionality' itself. Our attempt to develop the more profound political impli cations of 'relationality' unfolds through a synthetic explication of Martin Heidegger's analysis of language, Jacques Derrida's logic of the gift, and Emmanuel Levinas' consideration of the Other. The emergent thematic of asymmetrical relationality reconfigures liberalism and provides for a rethinking of the structure of welfare. (shrink)

We will prove that there exists a model of ZFC+"c = ω 2 " in which every $M \subseteq \mathbb{R}$ of cardinality less than continuum c is meager, and such that for every $X \subseteq \mathbb{R}$ of cardinality c there exists a continuous function f: R → R with f[X] = [0, 1]. In particular in this model there is no magic set, i.e., a set $M \subseteq \mathbb{R}$ such that the equation f[M] = g[M] implies f = g for (...) every continuous nowhere constant functions f, g: R → R. (shrink)

Ethics of Richard M. Hare is widely considered as a classical example of the strong internalistic theory of motivation: he is thought to believe that having a moral motive is a sufficient condition to act accordingly. However, strong internalism has difficulties with explaining the phenomenon of acrasia and amoralism. For this reason some critics charge him with developing a false theory of moral motivation. In the article I present Hare's answer to these questions by dividing the discussion about motivation into (...) three levels: semantical, epistemological, and ontological. I also explain his concept of internal motivation and argue that his theory, contrary to what his critics assume, may be called a weak motivational internalism. (shrink)

The aim of this study was to compare medical and social sciences students’ outcomes in terms of self-perceived stress, quality of life, and personality traits. We put particular emphasis on external and internal differences in students of specific fields–medicine, nursing, psychology, and pedagogy. In a survey, 1,783 students from Medical University of Gdańsk and University of Gdańsk participated in our study, of whom 1,223 were included in the final statistical analysis. All of them were evaluated using valid and reliable questionnaires–TIPI-PL, (...) PSS-10, and a one-item scale of quality of life. Stress turned out to have a negative effect on quality of life, regardless of the type of field of study. Moreover, students from different fields varied in terms of personality factors: conscientiousness, agreeableness, openness to experience, and emotional stability. In conclusion, many students regardless of their field suffer from high stress and report low quality of life, which potentially further affects their academic performance and social life. (shrink)

The primary goal of this monograph is to justify the possibility of building a hybrid theory of normative ethics which can combine ethical consequentialism, deontology and virtue ethics. The aim of the book is to demonstrate the possibility of constructing a synthetic theory from ethical traditions that are generally considered to be contradictory. In addition, I propose an outline of an original theory which tries to carry out such a synthesis. I call it Institutional Function Consequentialism. The justification for a (...) hybrid theory of normative ethics requires the resolution of certain meta-ethical issues. I discuss them in part 1.1. After a brief overview of my research aims I consider the answer to the following questions: “What kind of meta-ethical beliefs must we assume for normative ethics?” and "Why should we build ethical theories?". I also discuss the various forms of ethical scepticism, which should be rejected if we develop a hybrid theory of normative ethics. I also describe possible methods of justifying any ethical theory. At the end of part 1.1 I explain that the best method for justifying any ethical theory is the method of wide reflective equilibrium. In parts 1.2, 1.3 and 1.4 I analyse three main types of normative ethics which are considered to be competitive: consequentialism, deontology, and virtue ethics. Part 1.2 is about consequentialism and its difference between utilitarianism and teleological theories. I also present the main reasons for the popularity of consequentialism. In part 1.3 I define deontology, present its variations and show important benefits that motivate its continuous growth. In part 1.4 I discuss virtue ethics, which is often referred as the viable alternative to consequentialism and deontology. If we want to build any new ethical theory, first we should describe the problems of the old ones. For this reason, in chapter 2 I describe the most important arguments against ethical consequentialism, and in chapter 3 I explain the difficulties of deontology. Critical remarks on virtue ethics are considered in part 1.4. The last two chapters directly concern the main aim of the monograph. Because in chapter 3 I show that deontology suffers from a number of problems such as the paradox of deontology, in chapters 4 and 5 I present only consequentialist versions of hybrid theories. These versions try to avoid the common pleas of utilitarianism and combine the advantages of opponents to utilitarianism. I answer the question (4.1) "What is hybrid consequentialism?" and briefly describe (4.2) the most important examples of hybrid theories by others. I discuss the prerogatives without restrictions idea by Samuel Scheffler, rule consequentialism by Brad Hooker, Kantian consequentialism by Richard M. Hare, David Cummiskey and Derek Parfit and consequentializing procedure proposed by Douglas W. Portmore. In the last chapter I present a new hybrid version of consequentialism that I call Institutional Function Consequentialism. I start from the thesis (5.1) that traditional meta-ethics of analytic philosophy incorrectly defines the main field of its research. Rather than focusing on the philosophy of language and metaphysics it should try to answer one question: “What should morality and ethics be for?”. Therefore I introduce an original methodology for meta-ethics that I call the Functional Model of Analysis (FMA). It is a meta-ethical framework in which the fundamental questions concern the practical functions of normative domains such as morality and ethics and the most rational way of achieving them. FMA is meta-ethical project that (a) explains the persistence of fundamental ethical disagreement among experts, (b) sets the background for explaining or justifying the correct structure of the ethical theory, (c) gives the possibility to create a hybrid theory of normative ethics. In part 5.2 I formulate a generalized argument against various popular theories of normative ethics which states that most of the popular theories are too narrow and one-sided, causing permanent dispute between them. There are many distinct practical functions of morality that are usually based on different types of normative theories such as Aristotelian ethics, utilitarianism, contractarianism and contractualism. In order to remove these conflicts, the correct ethical theory should try to take into account all of these relevant features of moral life. Unfortunately, most ethical theories are mono-functional. This means that their supporters consciously or unconsciously (1) recognize or accept only one genuine practical function, (2) think that this one practical function overrides all other practical functions or (3) try to reduce all practical functions to the one that is chosen. In part 5.2 I present a description and justification of a new normative account that I call Hybrid Function Consequentialism. The formal scheme of this consequentialism can be summarized in the following way: we should act according to some important focal points P1…Pn with contents C1…Cn that are selected on the basis of considerations about which kind of P with C will bring the best realization of the best mix of normative functions F1...Fn. In the next part (5.2.2) I present the new way of “consequentializing” particular theories of normative ethics by applying the scheme of Hybrid Function Consequentialism. As an example of the use of this procedure, I formulate perfectionist virtue consequentialism, contractarian institution consequentialism, contractualist rule consequentialism and consequentialism of salvation. In part 5.3 I formulate an original theoretical concept that I call Institutional Function Consequentialism (IFC). It is a hybrid theory that is based on the previously described Functional Model of Analysis and a reflection on the role of institutions in modern developed societies. IFC claims that we should always act according to some rules, virtues, motives and intentions that constitute the homeostasis of normative institutions whose internalization by the overwhelming majority of each new generation has maximum expected value in terms of the best realization of the equilibrium of the most important practical functions of normative domains. Responsibility and sanctions related to wrongful actions should be dependent on the particular institution whose standards have been violated. IFC has several unique features which are described and justified in part 5.3. It is a form of hybrid consequentialism – it mixes features of consequentialism, deontology and virtue ethics. It does this on three different levels: justification, structure and content. The main focal point of the theory is not rules or virtues, but normative institutions. Values to be optimized in the framework of consequentialism are not "happiness", "well-being" or "preferences", but the fulfilment of normative functions. IFC is not limited to the field of ethics only, but it is a meta-normative account of justification for an entire social order which is comprised of a number of different institutions. It also assumes a specific, circular relationship between practical ethics (e.g. research on such important issues as civil disobedience, fair distribution of wealth, philosophy of punishment or autonomy of conscience), and the content of the general rules that may constitute the optimal homeostasis of institutions. It rejects the simplistic belief that moral thinking is based solely on deductive implications from general ethical principles or meta-ethical beliefs. (shrink)

The "space" of Lascar strong types, on some sort and relative to a given complete theory T, is in general not a compact Hausdorff topological space. We have at least three aims in this paper. The first is to show that spaces of Lascar strong types, as well as other related spaces and objects such as the Lascar group Gal L of T, have well-defined Borel cardinalities. The second is to compute the Borel cardinalities of the known examples as well (...) as of some new examples that we give. The third is to explore notions of definable map, embedding, and isomorphism, between these and related quotient objects. We also make some conjectures, the main one being roughly "smooth if and only if trivial". The possibility of a descriptive set-theoretic account of the complexity of spaces of Lascar strong types was touched on in the paper [E. Casanovas, D. Lascar, A. Pillay and M. Ziegler, Galois groups of first order theories, J. Math. Logic1 305–319], where the first example of a "non-G-compact theory" was given. The motivation for writing this paper is partly the discovery of new examples via definable groups, in [A. Conversano and A. Pillay, Connected components of definable groups and o-minimality I, Adv. Math.231 605–623; Connected components of definable groups and o-minimality II, to appear in Ann. Pure Appl. Logic] and the generalizations in [J. Gismatullin and K. Krupiński, On model-theoretic connected components in some group extensions, preprint, arXiv:1201.5221v1]. (shrink)

One position on the interpretation of purposefulness adopted by Neo-Thomists says that the principle of purposefulness has universal significance, because it concerns every entity that can be defined by the term “action”: i.e. every entity which exists and can only be known through some form of action. Entities work to preserve their existence, and their pursuit of survival seems to be the purpose of their actions. So, if entities are already working, then they must also be working purposefully. We can (...) encounter philosophers who hold that every action is purposeful in the representatives of the Lublin School, such as M.A. Krąpiec OP, A. Maryniarczyk, S. Mazierski. All three of these have based their views about purposefulness on Aristotle’s teleological considerations. The present article will examine how the views of the abovementioned scholars on teleology, based on Aristotle’s philosophy of purposefulness from 2000 years ago, explain reality. (shrink)

In the paper we introduce two conditions and ) which are strengthenings of Birkhoff’s conditions. We prove that an upper continuous and strongly atomic lattice is distributive if and only if it satisfies and ). This result extends a theorem of R.P. Dilworth characterizing distributivity in terms of local distributivity and a theorem of M. Ward characterizing distributivity by means of covering diamonds.

We generalize the model theory of small profinite structures developed by Newelski to the case of compact metric spaces considered together with compact groups of homeomorphisms and satisfying the existence of m-independent extensions (we call them compact e-structures). We analyze the relationships between smallness and different versions of the assumption of the existence of m-independent extensions and we obtain some topological consequences of these assumptions. Using them, we adopt Newelski's proofs of various results about small profinite structures to compact e-structures. (...) In particular, we notice that a variant of the group configuration theorem holds in this context. A general construction of compact structures is described. Using it, a class of examples of compact e-structures which are not small is constructed. It is also noticed that in an m-stable compact e-structure every orbit is equidominant with a product of m-regular orbits. (shrink)

PHILOSOPHICAL SOURCES OF ETHICAL ANTI-REALISM S u m m a r y ! In the contemporary analytic philosophy about one-third of authors tend toward moral antirealism. Sources of its popularity have to be found in many arguments justifying the abandonment of moral realism. Every realist should meet them. Unfortunately, in Polish literature about ethics it is difficult to find a presentation and a critique of these arguments. Many philosophers who represent continental philosophy like Neo-Thomism, material Value-Ethics, hermeneutic ethics, assume ethical (...) realism and do not respond to the arguments of anti-realists. The purpose of the article is to present in one place the most important arguments that are important sources of ethical antirealism in metaethics of analytic philosophy. (shrink)

Standardowy, podręcznikowy wykład etyki ujmuje kantyzm jako formę deontologii. Wpływ na to miał sam I. Kant, który krytykował konsekwencjalizm i bronił prawomocności deontycznych rygorów. Wielu jego kontynuatorów podziela jego opinie, uznając, że etyk-kantysta musi być deontologiem. Jednak kantowski konsekwencjalizm nie jest stanowiskiem wewnętrznie sprzecznym – twierdzą tak m.in. R.M. Hare, D. Cummiskey, S. Kagan czy D. Parfit. W niniejszym artykule przedstawiam sposób godzenia kantyzmu i konsekwencjalizmu, skupiając się na teoriach D. Cummiskeya i D. Parfita. Rozważam również najczęściej stawiany zarzut wobec (...) kantowskiego konsekwencjalizmu, iż nie jest on w stanie oddać kantowskiej idei autonomii i godności. Argumentuję, że nie można stwierdzić, iż konsekwencjalistyczny nakaz, aby w niektórych rzadkich sytuacjach poświęcić jedną niewinną osobę w celu ratowania kilku innych, automatycznie i z konieczności gwałcił kantowską ideę autonomii, jeśli autonomię tę rozumie się nie jako millowską autonomię osób, lecz jako kantowską autonomię zasad. (shrink)

Od początku rozwoju stuletniej historii metaetyki rozważania językowe grały kluczową rolę przy wyborze dobrej teorii metaetycznej. Celem artykułu jest ukazanie i wyjaśnienie tego faktu poprzez wskazanie na najistotniejsze motywy rozwoju dociekań metaetycznych. Postawiona została również teza, że główny problem metaetyki ująć należy szerzej, niż uczynił to w ostatnich latach we wpływowy sposób M. Smith. W tym celu zaprezentowane zostały dwa kryteria dobrej teorii metaetycznej postulowane przez M. Timmonsa i T. Horgana: kryterium koherencji i doświadczenia oraz cechy języka moralności, jak również (...) inne istotne, psychologiczne, epistemologiczne i ontologiczne fenomeny, które w kluczowy sposób determinują kształt współczesnej debaty metaetycznej. Następnie ich wpływ zobrazowany został na przykładach kilku najgłośniejszych polemik metaetycznych. (shrink)

Author: Rogucki Krzysztof Title: ANDRZEJ CHMIELECKI’S INTEGRAL ONTOLOGY (Ontologia integralna Andrzeja Chmieleckiego) Source: Filo-Sofija year: 2006, vol:.6, number: 2006/1, pages:171-206 Keywords: ANDRZEJ CHMIELECKI, INTEGRAL ONTOLOGY, MATERIALISM, TRANSFORMATIONISM Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail:The article analyses of the Andrzej Chmielecki’s system of integral ontology as a solution to the psychological problem – transformationism. From the standpoint of integral ontology Chmielecki confronts the fundamental problems of the theory of cognition, axiology, philosophy of (...) language, philosophy of mind, and anthropology. Chmielecki’s philosophical reflection is inspired by the concepts of Ch. Peirce, M. Scheler, and N. Hartmann. Chmielecki keeps a distance from some philosophical solutions popular in analytic philosophy; however, he takes full advantage of the accomplishments of modern mathematics. The presentation of Chmielecki’s most important ideas is the objective of the article. (shrink)

The purpose of the present paper is to prove the interpolation theorem for many-sorted languages which are, in terminology of Feferman neither restricted nor unrestricted. Such languages are often used in mathematical practice and have been investigated by several authors . The result is a generalization of the well-known Stern interpolation theorem for restricted m.s.l. and its proof depends heavily on that of Stern’s theorem. In place of the functions Rel + and Rel − our theorem treats the functions T (...) yp + and T yp − giving much more information about any formula. (shrink)

We investigate profinite structures in the sense of Newelski interpretable in fields. We show that profinite structures interpretable in separably closed fields are the same as profinite structures weakly interpretable in . We also find a strong connection with the inverse Galois problem. We give field theoretic constructions of profinite structures weakly interpretable in and satisfying some model theoretic properties, like smallness, m-normality, non-triviality, being -rank 1. For example we interpret in this way the profinite structure consisting of the profinite (...) group together with a distinguished Sylow p-subgroup of its standard structural group. (shrink)

Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin–Löf. We extend this result and demonstrate that QM is algorithmic $$\omega$$ -random and generic, precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo–Fraenkel Solovay random on (...) infinite-dimensional Hilbert spaces. Moreover, it is more likely that there exists a standard transitive ZFC model M, where QM is expressed in reality, than in the universe V of sets. Then every generic quantum measurement adds to M the infinite sequence, i.e. random real $$r\in 2^{\omega }$$, and the model undergoes random forcing extensions M[r]. The entire process of forcing becomes the structural ingredient of QM and parallels similar constructions applied to spacetime in the quantum limit, therefore showing the structural resemblance of both in this limit. We discuss several questions regarding measurability and possible practical applications of the extended Solovay randomness of QM. The method applied is the formalization based on models of ZFC; however, this is particularly well-suited technique to recognising randomness questions of QM. When one works in a constant model of ZFC or in axiomatic ZFC itself, the issues considered here remain hidden to a great extent. (shrink)

The paper discusses the origin of two Germanic terms for ‘Atlantic herring, _Clupea harengus _L.’. The Proto-Germanic noun _*siled- _m. ‘herring’, attested in most North Germanic languages (e.g. ON. _sild_, Far. _síld_, OSv. _sild_, Sv. _sill_, Norw. _sil_), cannot be treated as inherited. It seems to represent a Saami (or Laponian) borrowing, cf. Saa. (Northern) _sâlled_, (Lule) _sallēt _‘herring’.

Recently, two apparently quite different duality-based approaches to automata minimisation have appeared. One is based on ideas that originated from the controllability-observability duality from systems theory, and the other is based on ideas derived from Stone-type dualities specifically linking coalgebras with algebraic structures derived from modal logics. In the present paper, we develop a more abstract view and unify the two approaches. We show that dualities, or more generally dual adjunctions, between categories can be lifted to dual adjunctions between categories (...) of coalgebras and algebras, and from there to automata with initial as well as final states. As in the Stone-duality approach, algebras are essentially logics for reasoning about the automata. By exploiting the ability to pass between these categories, we show that one can minimize the corresponding automata. We give an abstract minimisation algorithm that has several instances, including the celebrated Brzozowski minimisation algorithm. We further develop three examples that have been treated in previous works: deterministic Kripke frames based on a Stone-type duality, weighted automata based on the self-duality of semimodules, and topological automata based on Gelfand duality. As a new example, we develop alternating automata based on the discrete duality between sets and complete atomic Boolean algebras. (shrink)

We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cut-free proof net. A key role is played by the notion of history-free strategy; strong connections are made between history-free strategies and the Geometry of Interaction. Our semantics incorporates a (...) natural notion of polarity, leading to a refined treatment of the additives. We make comparisons with related work by Joyal, Blass, et al. (shrink)

The cross-cultural differences in epistemic intuitions reported by Weinberg, Nichols and Stich (2001; hereafter: WNS) laid the ground for the negative program of experimental philosophy. However, most of WNS’s findings were not corroborated in further studies. The exception here is the study concerning purported differences between Westerners and Indians in knowledge ascriptions concerning the Zebra Case, which was never properly replicated. Our study replicates the above-mentioned experiment on a considerably larger sample of Westerners (n = 211) and Indians (n = (...) 204). The analysis found a significant difference between the ethnic groups in question in the predicted direction: Indians were more likely to attribute knowledge in the Zebra Case than Westerners. In this paper, we offer an explanation of our result that takes into account the fact that replications of WNS’s other experiments did not find any cross-cultural differences. We argue that the Zebra Case is unique among the vignettes tested by WNS since it should not be regarded as a Gettier case but rather as a scenario exhibiting skeptical pressure concerning the reliability of sense-perception. We argue that skepticism towards perception as a means of gaining knowledge is a trope that is deeply rooted in Western epistemology but is very much absent from Classical Indian philosophical inquiry. This line of reasoning is based on a thorough examination of the skeptical scenarios discussed by philosophers of the Indian Nyaya tradition and their adversaries. (shrink)

This book offers an original approach to avant-garde art and its transformative force. Presenting an alternative to the approaches to art developed in postmodern theory or cultural studies, Ziarek sees art's significance in its critique of power and the increasing technologization of social relations. Re-examining avant-garde art and literature, from Italian and Russian Futurism and Dadaism, to Language poetry, video and projection art, as well as transgenic and Internet art, this book argues that art's importance today cannot be explained simply (...) in aesthetic or cultural terms but has to take into consideration how artworks question the technological character of modern power. To emphasize the transformative character of art, the book redefines art as a force field, in which forces drawn from historical and social reality come be to formed into an alternative relationality. Through discussions of such key avant-garde figures as Marinetti, Duchamp, Khlebnikov, and Vertov, and innovative contemporary artists like Viola, Wodiczko and Kac, The Force of Art counters the pessimism about art's social function by recovering and redefining art's transformative role in modernity. (shrink)

In the contemporary philosophy of mathematics there is an ongoing discussion concerning the issue of the justification of mathematical axioms and independent sentences. The works of P. Maddy in which the author focuses on the set theory are extensive studies devoted to that problem. In one of the monographs she deals with the problem of the justification of set theory's sentences in a new way, assuming a different metaphilosophical standpoint. In the paper (which is the first part of the two-part (...) whole) Maddy's conception is faithfully presented. The author makes no comments of his own, except for the first - introductory - chapter and footnotes, in which some additional explanations and comments can be found. (shrink)

We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges’ semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics (...) is the logic of Bunched Implications due to Pym and O’Hearn, which combines intuitionistic and multiplicative connectives. This introduces several new connectives not previously considered in logics of informational dependence, but which we show play a very natural rôle, most notably intuitionistic implication. As regards the quantifiers, we show that their interpretation in the Hodges semantics is forced, in that they are the image under the general construction of the usual Tarski semantics; this implies that they are adjoints to substitution, and hence uniquely determined. As for the dependence predicate, we show that this is definable from a simpler predicate, of constancy or dependence on nothing. This makes essential use of the intuitionistic implication. The Armstrong axioms for functional dependence are then recovered as a standard set of axioms for intuitionistic implication. We also prove a full abstraction result in the style of Hodges, in which the intuitionistic implication plays a very natural rôle. (shrink)

Abramsky, S., Domain theory in logical form, Annals of Pure and Applied Logic 51 1–77. The mathematical framework of Stone duality is used to synthesise a number of hitherto separate developments in theoretical computer science.• Domain theory, the mathematical theory of computation introduced by Scott as a foundation for detonational semantics• The theory of concurrency and systems behaviour developed by Milner, Hennesy based on operational semantics.• Logics of programsStone duality provides a junction between semantics and logics . Moreover, the underlying (...) logic is geometric, which can be computationally interpreted as the logic of observable properties—i.e., properties which can be determined to hold of a process on the basis of a finite amount of information about its execution.These ideas lead to the following programme. A metalanguage is introduced, comprising• types = universes of discourse for various computational situations;• terms = PROGRAMS = syntactic intensions for models or points. A standard denotational interpretation of the metalanguage is given, assigning domains to types and domain elements to terms. The metalanguage is also given a logical interpretation, in which types are interpreted as propositional theories and terms are interpreted via a program logic, which axiomatises the properties they satisfy. The two interpretations are related by showing that they are Stone duals of each other. Hence, semantics and logic are guaranteed to be in harmony with each other, and in fact each determines the other up to isomorphism. This opens the way to a whole range of applications. Given a denotational description of a computational situation in our metalanguage, we can turn the handle to obtain a logic for that situation. (shrink)