We study the class of all strongly constructivizable models having \(\omega \) -stable theories in a fixed finite rich signature. It is proved that the Tarski–Lindenbaum algebra of this class considered together with a Gödel numbering of the sentences is a Boolean \(\Sigma ^1_1\) -algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters; moreover, this algebra is universal with respect to the class of all Boolean \(\Sigma ^1_1\) -algebras. This gives a characterization to the Tarski-Lindenbaum (...) algebra of the class of all strongly constructivizable models with \(\omega \) -stable theories. (shrink)

In this paper, we investigate the Lindenbaum algebra ℒ of the theory T fin = Th of the class M fin of all finite models of a finite rich signature. We prove that this algebra is an atomic Boolean algebra while its Gödel numeration γ is a [Formula: see text]-numeration. Moreover, the quotient algebra /ℱ, γ/ℱ) modulo the Fréchet ideal ℱ is a [Formula: see text]-algebra, which is universal over the class of all [Formula: see text] Boolean algebras. These conditions (...) characterize uniquely the algebra ℒ; moreover, these conditions characterize up to recursive isomorphism the numerated Boolean quotient algebra /ℱ, γ/ℱ). These results extend the work of Trakhtenbrot [17] and Vaught [18] on the first order theory of the class of all finite models of a finite rich signature. (shrink)

Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory is the type spectrum of some homogeneous model of. Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states (...) that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model. (shrink)

Much previous study has been done on the degree spectra of prime models of a complete atomic decidable theory. Here we study the analogous questions for homogeneous models. We say a countable model A has a d-basis if the types realized in A are all computable and the Turing degree d can list $\Delta _{0}^{0}$ -indices for all types realized in A. We say A has a d-decidable copy if there exists a model B ≅ A such that the elementary (...) diagram of B is d-computable. Goncharov, Millar, and Peretyat'kin independently showed there exists a homogeneous A with a 0-basis but no decidable copy. We prove that any homogeneous A with a 0'-basis has a low decidable copy. This implies Csima's analogous result for prime models. In the case where all types of the theory T are computable and A is a homogeneous model with a 0-basis, we show A has copies decidable in every nonzero degree. A degree d is 0-homogeneous bounding if any automorphically nontrivial homogeneous A with a 0-basis has a d-decidable copy. We show that the nonlow₂ $\Delta _{2}^{0}$ degrees are 0-homogeneous bounding. (shrink)

In the last five years there have been a number of results about the computable content of the prime, saturated, or homogeneous models of a complete decidable theory T in the spirit of Vaught's "Denumerable models of complete theories" combined with computability methods for degrees d ≤ 0′. First we recast older results by Goncharov, Peretyat'kin, and Millar in a more modern framework which we then apply. Then we survey recent results by Lange, "The degree spectra of homogeneous models," which (...) generalize the older results and which include positive results on when a certain homogeneous model of T has an isomorphic copy of a given Turing degree. We then survey Lange's "A characterization of the 0-basis homogeneous bounding degrees" for negative results about when does not have such copies, generalizing negative results by Goncharov, Peretyat'kin, and Millar. Finally, we explain recent results by Csima, Harizanov, Hirschfeldt, and Soare, "Bounding homogeneous models," about degrees d that are homogeneous bounding and explain their relation to the PA degrees. (shrink)

The theory of constructive (recursive) models follows from works of Froehlich, Shepherdson, Mal'tsev, Kuznetsov, Rabin, and Vaught in the 50s. Within the framework of this theory, algorithmic properties of abstract models are investigated by constructing representations on the set of natural numbers and studying relations between algorithmic and structural properties of these models. This book is a very readable exposition of the modern theory of constructive models and describes methods and approaches developed by representatives of the Siberian school of algebra (...) and logic and some other researchers (in particular, Nerode and his colleagues). The main themes are the existence of recursive models and applications to fields, algebras, and ordered sets (Ershov), the existence of decidable prime models (Goncharov, Harrington), the existence of decidable saturated models (Morley), the existence of decidable homogeneous models (Goncharov and Peretyat'kin), properties of the Ehrenfeucht theories (Millar, Ash, and Reed), the theory of algorithmic dimension and conditions of autostability (Goncharov, Ash, Shore, Khusainov, Ventsov, and others), and the theory of computable classes of models with various properties. Future perspectives of the theory of constructive models are also discussed. Most of the results in the book are presented in monograph form for the first time. The theory of constructive models serves as a basis for recursive mathematics. It is also useful in computer science, in particular, in the study of programming languages, higher level languages of specification, abstract data types, and problems of synthesis and verification of programs. Therefore, the book will be useful for not only specialists in mathematical logic and the theory of algorithms but also for scientists interested in the mathematical fundamentals of computer science. The authors are eminent specialists in mathematical logic. They have established fundamental results on elementary theories, model theory, the theory of algorithms, field theory, group theory, applied logic, computable numberings, the theory of constructive models, and the theoretical computer science. (shrink)

We say a countable model ������ has a 0-basis if the types realized in ������ are uniformly computable. We say ������ has a (d-)decidable copy if there exists a model ������ ≅ ������ such that the elementary diagram of ������ is (d-)computable. Goncharov, Millar, and Peretyat'kin independently showed there exists a homogeneous model ������ with a 0-basis but no decidable copy. We extend this result here. Let d ≤ 0' be any low₂ degree. We show that there exists a homogeneous (...) model ������ with a 0-basis but no d-decidable copy. A degree d is 0-basis homogeneous bounding if any homogenous ������ with a 0-basis has a d-decidable copy. In previous work, we showed that the nonlow₂ $\Delta _{2}^{0}$ degrees are 0-basis homogeneous bounding. The result of this paper shows that this is an exact characterization of the 0-basis homogeneous bounding $\Delta _{2}^{0}$ degrees. (shrink)

Millar showed that for each n<ω, there is a complete decidable theory having precisely eighteen nonisomorphic countable models where some of these are decidable exactly in the hyperarithmetic set H. By combining ideas from Millar's proof with a technique of Peretyat'kin, the author reduces the number of countable models to five. By a theorem of Millar, this is the smallest number of countable models a decidable theory can have if some of the models are not 0″-decidable.

Scientists from various disciplines have begun to focus attention on the psychology and biology of human morality. One research program that has recently gained attention is universal moral grammar (UMG). UMG seeks to describe the nature and origin of moral knowledge by using concepts and models similar to those used in Chomsky's program in linguistics. This approach is thought to provide a fruitful perspective from which to investigate moral competence from computational, ontogenetic, behavioral, physiological and phylogenetic perspectives. In this article, (...) I outline a framework for UMG and describe some of the evidence that supports it. I also propose a novel computational analysis of moral intuitions and argue that future research on this topic should draw more directly on legal theory. (shrink)

Is the science of moral cognition usefully modelled on aspects of Universal Grammar? Are human beings born with an innate 'moral grammar' that causes them to analyse human action in terms of its moral structure, with just as little awareness as they analyse human speech in terms of its grammatical structure? Questions like these have been at the forefront of moral psychology ever since John Mikhail revived them in his influential work on the linguistic analogy and its implications for (...) jurisprudence and moral theory. In this seminal book, Mikhail offers a careful and sustained analysis of the moral grammar hypothesis, showing how some of John Rawls' original ideas about the linguistic analogy, together with famous thought experiments like the trolley problem, can be used to improve our understanding of moral and legal judgement. (shrink)

My primary aims in this paper are to explain what exploitation is, when it’s wrong, and what makes it wrong. I argue that exploitation is not always wrong, but that it can be, and that its wrongness cannot be fully explained with familiar moral constraints such as those against harming people, coercing them, or using them as a means, or with familiar moral obligations such as an obligation to rescue those in distress or not to take advantage of people’s vulnerabilities. (...) Its deepest wrongness, I argue, lies in our moral obligation not to extract excessive benefits from people who cannot, or cannot reasonably, refuse our offers. (shrink)

The aim of the dissertation is to formulate a research program in moral cognition modeled on aspects of Universal Grammar and organized around three classic problems in moral epistemology: What constitutes moral knowledge? How is moral knowledge acquired? How is moral knowledge put to use? Drawing on the work of Rawls and Chomsky, a framework for investigating -- is proposed. The framework is defended against a range of philosophical objections and contrasted with the approach of developmentalists like Piaget and Kohlberg. (...) ;One chapter consists of an interpretation of the analogy Rawls draws in A Theory of Justice between moral theory and generative linguistics. A second chapter clarifies the empirical significance of Rawls' linguistic analogy by formulating a solution to the problem of descriptive adequacy with respect to a class of commonsense moral intuitions, including those discussed in the trolley problem literature originating in the work of Foot and Thomson. Three remaining chapters defend Rawls' linguistic analogy against some of its critics. In response to Hare's objection that Rawls' conception of moral theory is too empirical and insufficiently normative, it is argued that Hare fails to acknowledge both the centrality of the problem of empirical adequacy in the history of moral philosophy and the complexity of Rawls' approach to the problem of normative adequacy. In response to Nagel's claim that the analogy between moral theory and linguistics is false because whatever native speakers agree on is English, but whatever ordinary men agree in condemning is not necessarily wrong, it is argued that the criticism ignores both Rawls' use of the competence-performance distinction and the theory-dependence of the corresponding distinction in linguistics. In response to Dworkin's claim that Rawls' conception of moral theory is incompatible with naturalism and presupposes constructivism, it is argued that Dworkin's distinction between naturalism and constructivism represents a false antithesis; neither is an accurate interpretation of the model of moral theory Rawls describes in A Theory of Justice. The thesis concludes by situating Rawls' linguistic analogy within the context of broader debates in metaethics, democratic theory, natural law theory, and the theory of moral development. (shrink)

Could a computer be programmed to make moral judgments about cases of intentional harm and unreasonable risk that match those judgments people already make intuitively? If the human moral sense is an unconscious computational mechanism of some sort, as many cognitive scientists have suggested, then the answer should be yes. So too if the search for reflective equilibrium is a sound enterprise, since achieving this state of affairs requires demarcating a set of considered judgments, stating them as explanandum sentences, and (...) formulating a set of algorithms from which they can be derived. The same is true for theories that emphasize the role of emotions or heuristics in moral cognition, since they ultimately depend on intuitive appraisals of the stimulus that accomplish essentially the same tasks. Drawing on deontic logic, action theory, moral philosophy, and the common law of tort, particularly Terry's five-variable calculus of risk, I outline a formal model of moral grammar and intuitive jurisprudence along the foregoing lines, which defines the abstract properties of the relevant mapping and demonstrates their descriptive adequacy with respect to a range of common moral intuitions, which experimental studies have suggested may be universal or nearly so. Framing effects, protected values, and implications for the neuroscience of moral intuition are also discussed. (shrink)

This book is not only a major twentieth-century contribution to Dostoevsky’s studies, but also one of the most important theories of the novel produced in our century. As a modern reinterpretation of poetics, it bears comparison with Aristotle.“Bakhtin’s statement on the dialogical nature of artistic creation, and his differentiation of this from a history of monological commentary, is profoundly original and illuminating. This is a classic work on Dostoevsky and a statement of importance to critical theory.” Edward Wasiolek“Concentrating on the (...) particular features of ‘Dostoevskian discourse,’ how Dostoevsky structures a hero and a plot, and what it means to write dialogically, Bakhtin concludes with a major theoretical statement on dialogue as a category of language. One of the most important theories of the novel in this century.” The Bloomsbury Review. (shrink)

The absence of a clear influence of the responses modified by new connections created by LTP on the development of these connections casts doubt on an essential role of LTP in learning and memory formation without any association with reinforcement. The evidence for the involvement of the monoaminergic systems in synaptic potentiation in the cerebral cortex during learning is adduced, and their role in reinforcement system function is discussed.

When is it immoral to take advantage of another person for one's own benefit? For some, such as Ruth Sample, John Roemer, and Will Kymlicka, the answer at least partly depends on whether what one takes advantage of is the fact that this person is, or has been, the victim of injustice. I argue, however, that whether person A wrongly exploits person B is wholly unrelated to whether A takes advantage of the fact that B is, or was, the victim (...) of injustice. I also develop a positive account regarding which personal attributes one should not exploit for personal gain. (shrink)

Adequality, or παρισóτης (parisotēs) in the original Greek of Diophantus 1 , is a crucial step in Fermat’s method of finding maxima, minima, tangents, and solving other problems that a modern mathematician would solve using infinitesimal calculus. The method is presented in a series of short articles in Fermat’s collected works (1891, pp. 133–172). The first article, Methodus ad Disquirendam Maximam et Minimam 2 , opens with a summary of an algorithm for finding the maximum or minimum value of an (...) algebraic expression in a variable A. For convenience, we will write such an expression in modern functional notation as f (a). 3 The algorithm can be broken up into six steps in the following way:Introduce an auxiliary .. (shrink)

In the paper we consider complexity of intuitionistic propositional logic and its natural fragments such as implicative fragment, finite-variable fragments, and some others. Most facts we mention here are known and obtained by logicians from different countries and in different time since 1920s; we present these results together to see the whole picture.

This guest column examines the historical fate of Russia in its catastrophic confrontation with Ukraine and the West. The piece considers the negative self-definitions of Russia that have arisen in the aftermath of the communist utopia and its virtual transformation into an anti-world — a society whose purpose is to undermine and destroy. Emerging Russian cults of war, death, and apocalypticism are stressed, as are the paradoxes and inversions by which Russia, in attempting to become stronger, becomes weaker and indeed (...) suicidal. (shrink)

I argue against the view that there is intrinsic value in making one's own decisions about the direction and shape of one's life.

kk states that knowing entails knowing that one knows, and K¬K states that not knowing entails knowing that one does not know. In light of the arguments against kk and K¬K⁠, one might consider modally qualified variants of those principles. According to weak kk, knowing entails the possibility of knowing that one knows. And according to weakK¬K⁠, not knowing entails the possibility of knowing that one does not know. This paper shows that weak kk and weakK¬K are much stronger than (...) they initially appear. Jointly, they entail kk and K¬K⁠. And they are susceptible to variants of the standard arguments against kk and K¬K⁠. This has interesting implications for the debate on positive introspection and for deeper issues concerning the structure and limits of knowability. (shrink)

_Russian Philosophy in the Twenty-First Century: An Anthology_ presents a variety of contemporary philosophic problems found in the works of prominent Russian thinkers, ranging from social and political matters and pressing cultural issues to insights into modern science and mounting global challenges.

We propose and investigate a uniform modal logic framework for reasoning about topology and relative distance in metric and more general distance spaces, thus enabling the comparison and combination of logics from distinct research traditions such as Tarski’s for topological closure and interior, conditional logics, and logics of comparative similarity. This framework is obtained by decomposing the underlying modal-like operators into first-order quantifier patterns. We then show that quite a powerful and natural fragment of the resulting first-order logic can be (...) captured by one binary operator comparing distances between sets and one unary operator distinguishing between realised and limit distances . Due to its greater expressive power, this logic turns out to behave quite differently from both and conditional logics. We provide finite axiomatisations and ExpTime-completeness proofs for the logics of various classes of distance spaces, in particular metric spaces. But we also show that the logic of the real line is not recursively enumerable. This result is proved by an encoding of Diophantine equations. (shrink)

This article argues that the key elements of the prima facie case of harmful battery may form critical building blocks of moral cognition in both humans and nonhuman animals. By contrast, at least some of the rules and representations presupposed by familiar justifications to battery appear to be uniquely human. The article also argues that many famous thought experiments in ethics and many influential experiments in moral psychology rely on harmful battery scenarios without acknowledging this fact or considering its theoretical (...) or empirical implications. The unifying factor in all these studies is goal-directed harmful contact, inflicted without consent or justification. (shrink)

Mikhail L. Gasparov. Intertextual analysis today. The paper provides a discussion about recent results and perspectives of intertextual analysis — the method that has been a contemporary with Tartu-Moscow school. The connections between the classical philological methods and intertextual analysis are described, together with specifying the concept of intertext and emphasizing the need for the correctness of a researcher, because such an analysis always carries a danger of overinterpretation. Several examples are used to illustrate how the imagination of a (...) researcher can create arbitrary allusions that are not based on the original text and are usually misleading. As a result, the text under study will not become more clear, vice versa, it turns to be less understandable. (shrink)

Mikhail L. Gasparov. Intertextual analysis today. The paper provides a discussion about recent results and perspectives of intertextual analysis — the method that has been a contemporary with Tartu-Moscow school. The connections between the classical philological methods and intertextual analysis are described, together with specifying the concept of intertext and emphasizing the need for the correctness of a researcher, because such an analysis always carries a danger of overinterpretation. Several examples are used to illustrate how the imagination of a (...) researcher can create arbitrary allusions that are not based on the original text and are usually misleading. As a result, the text under study will not become more clear, vice versa, it turns to be less understandable. (shrink)

Mikhail L. Gasparov. Intertextual analysis today. The paper provides a discussion about recent results and perspectives of intertextual analysis — the method that has been a contemporary with Tartu-Moscow school. The connections between the classical philological methods and intertextual analysis are described, together with specifying the concept of intertext and emphasizing the need for the correctness of a researcher, because such an analysis always carries a danger of overinterpretation. Several examples are used to illustrate how the imagination of a (...) researcher can create arbitrary allusions that are not based on the original text and are usually misleading. As a result, the text under study will not become more clear, vice versa, it turns to be less understandable. (shrink)

Most of the time our utterances are automatically interpreted as speech acts: as assertions, conjectures and testimonies; as orders, requests and pleas; as threats, offers and promises. Surprisingly, the cognitive correlates of this essential component of human communication have received little attention. This book fills the gap by providing a model of the psychological processes involved in interpreting and understanding speech acts. The theory is framed in naturalistic terms and is supported by data on language development and on autism spectrum (...) disorders. Mikhail Kissine does not presuppose any specific background and addresses a crucial pragmatic phenomenon from an interdisciplinary perspective. This is a valuable resource for academic researchers and graduate and undergraduate students in pragmatics, semantics, cognitive linguistics, psycholinguistics and philosophy of language. (shrink)

The opposition between transcendentalism and naturalism plays a key role in discussions about consciousness at the confluence of phenomenology and analytical philosophy. Associated with it is a whole range of research programs. However, the opposition between transcendentalism and naturalism in these programs is, as a rule, operational and not thematic in nature and presupposes that 1) Transcendentalism and naturalism as traditions are initially alien to each other; 2) The domain of their opposition is ontology. The article attempts to problematize these (...) premises based on one historical circumstance. Turning to the texts of Kant, the founder of transcendental philosophy, I intend to show that transcendentalism, which was first substantiated in them, is a version of naturalistic ontology, that is, a peculiarly interpreted naturalism that identifies nature with its natural scientific model and excludes constituting subjectivity from ontology. It is built not on the naturalization of phenomenology, but on the transcendentalization of natural science. Reinterpreting the experimental method in the spirit of the Copernican turn, Kant substantiates the apodictic nature and lack of alternative to the ontology of nature by turning nature into a correlate of consciousness and strictly limiting the principles of mathematical natural science to the boundaries of the phenomenal world. As a result, the true theme of philosophy—the thing in itself and transcendental subjectivity itself—is taken beyond the boundaries of ontology. The thematization of the naturalistic origins of transcendentalism and the removal of transcendental consciousness beyond the boundaries of ontology, carried out within its framework, thus reveals the problematic nature of these premises. The article also demonstrates that, despite significant differences in the understanding of transcendental philosophy and ontology between Kant and Husserl, the identified motives—the naturalistic nature of the ontological foundation and the meta-ontological character of transcendental subjectivity—remain of fundamental importance for the founder of phenomenology. This allows us to conclude that ontology is not the original domain of confrontation between transcendentalism and naturalism and to substantiate the compatibilist thesis according to which transcendentalism is compatible with ontological naturalism. (shrink)