Summary The concept of unified theory is defined in logical and abstract semantic terms, and employed in the analysis of relations between empirical scientific theories. The conceptual framework of the approach applies to binary relations such as the reduction or replacement of one theory by another, and to multiple intertheory relations. Historically, unified theories tend to arise within the contexts of scientific conflicts which they may show susceptible of solution even in the most controversial cases of (...) the logical incompatibility or conceptual incommensurability of competing theories. These conclusions are exemplified by the Planck-Einstein quantum theory of thermal radiation. The analysis shows in which sense it can, and in which it cannot, be said that this theory unifies Wien's law and the Rayleigh-Jeans law of black-body radiation. (shrink)

Research in cognitive science has often assumed the existence of a privileged level that unifies theoretical explanations arising from different disciplines. Philosophical accounts differ about the locus of those intertheory relations. In this paper, four different views are analyzed: classical, connectionist, pragmatist, and reductionist, as exemplified in the works of von Eckardt, Horgan and Tienson, Hardcastle, and Bickle, respectively. Their divergences are characterized in terms of the possibility of such a privileged level. The classical view favors a privileged (...) computational level. The connectionist revision tries to draw biological intuitions into computational models to provide a link between neurons and computations. The pragmatist approach rejects the idea of a privileged level and offers a more eclectic view of cognitive theory building. The reductionist account pursues theoretical unification by means of the reduction of higher level theories to basic level ones. /// La investigatión en ciencia cognitiva suele asumir la existencia de un nivel privilegiado que unifica las explicaciones teóricas provenientes de distintas disciplinas. Las interpretaciones filósoficas difieren respecto al locus de tales relaciones interteóricas. En este artículo se analizan cuatro concepciones: clásica, conexionista, pragmática y reduccionista, ejemplificadas respectivamente en las obras de von Eckardt, Horgan y Tienson, Hardcastle y Bickle. Sus divergencias se caracterizan en términos de la posible existencia del nivel privilegiado. El enfoque clásico propugna un nivel privilegiado computacional. La revisión conexionista importa intuiciones de la biología a los modelos computacionales, con la intentión de vincular lo neuronal con lo computacional. El enfoque pragmático rechaza la idea de un nivel privilegiado y ofrece una visión más ecléctica de la teorización cognitiva. La conceptión reduccionista promueve la unificatión teórica mediante la reductión de teorías de alto nivel a teorías de nivel básico. (shrink)

In line with the semantic conception of scientific theories, I develop an account of the intertheory relation of comparative structural similarity. I argue that this relation is useful in explaining the concept of verisimilitude and I support this contention with a concrete historical example. Finally, I defend this relation against the familiar charge that the concept of similarity is insufficiently objective.

In this paper we give the gist of our reconstructed notion of (limiting case) correspondence. Our notion is very general, so that it should be applicable to all the cases in which a correspondence has been said to exist in actual science.

This paper considers the relationship between continuum hydrodynamics and discrete molecular dynamics in the context of explaining the behavior of breaking droplets. It is argued that the idealization of a fluid as a continuum is actually essential for a full explanation of the drop breaking phenomenon and that, therefore, the less "fundamental," emergent hydrodynamical theory plays an ineliminable role in our understanding.

It used to be a common view in the philosophy of science as well as among the scientists themselves that scientic change has been and will be continuos. Even in the most radical changes of theories the growth of knowledge was claimed to be cumulative. Thus, for instance, physicists may say that in radical, revolutionary changes of theories there obtains, however, some kind of correspondence between the old and new theories; the old theory can be regarded at least as a (...) limiting case of the new one. Thus, for instance, classical particle mechanics is a limiting case of both relativistic particle mechanics and quantum mechanics. Some philosophers, as, e.g., Stegmuller [17], go even further when they claim that there always obtains a reductive correlation in scientic change. The old theory can be reduced to the new one in some specic, or perhaps only intuitive, sense of reduction. However, in the light of what physicists say about correspondence and logicians about reduction, it seems obvious that correspondence should be distinguished from reduction and that one may claim the existence of the former relation, rather than the latter, in the scientic changes. We are not ready to say here what a correspondence relation would exactly consist of, but we will discuss what we think ought to be at least required in comparison with reduction and the related notion of interpre- tation. A detailed case study seems to sustain our views correspondence. (shrink)

Classical mechanics is empirically successful because the probabilistic mean values of quantum mechanical observables follow the classical equations of motion to a good approximation (Messiah 1970, 215). We examine this claim for the one-dimensional motion of a particle in a box, and extend the idea by deriving a special case of the ideal gas law in terms of the mean value of a generalized force used to define "pressure." The examples illustrate the importance of probabilistic averaging as a method of (...) abstracting away from the messy details of microphenomena, not only in physics, but in other sciences as well. (shrink)

Classical mechanics and quantum mechanics are two of the most successful scientific theories ever discovered, and yet how they can describe the same world is far from clear: one theory is deterministic, the other indeterministic; one theory describes a world in which chaos is pervasive, the other a world in which chaos is absent. Focusing on the exciting field of 'quantum chaos', this book reveals that there is a subtle and complex relation between classical and quantum mechanics. It challenges the (...) received view that classical and quantum mechanics are incommensurable, and revives another, largely forgotten tradition due to Niels Bohr and Paul Dirac. By artfully weaving together considerations from the history of science, philosophy of science, and contemporary physics, this book offers a new way of thinking about intertheory relations and scientific explanation. It will be of particular interest to historians and philosophers of science, philosophically-inclined physicists, and interested non-specialists. (shrink)

This is the first of two papers concerned with the philosophical significance of dualities as applied in recent fundamental physics. The general idea is that, for its peculiarity, this ‘new’ ingredient in theory construction can open unexpected perspectives in the current philosophical reflection on contemporary physics. In particular, today’s physical dualities represent an unusual type of intertheory relation, the meaning of which deserves to be investigated. The aim is to show how discussing this point brings into play, at the (...) same time, what is intended by a 'theory’ and in which sense dualities are to be considered 'symmetries'. This paper is introductory and focusses on the first form of duality explicitly applied in twentieth century physics, that is electromagnetic duality as discussed in Dirac’s theory of magnetic poles. The extension of electromagnetic duality in the context of quantum field theory and string theory is explored in a forthcoming companion paper. (shrink)

The authors survey some debates about the nature and structure of physical theories and about the connections between our physical theories and naturalized metaphysics. The discussion is organized around an “ideal view” of physical theories and criticisms that can be raised against it. This view includes controversial commitments regarding the best analysis of physical modalities and intertheory relations. The authors consider the case in favor of taking laws as the primary modal notion, discussing objections related to alleged violations (...) of the laws, the apparent need to appeal to causality, and the status of probability. The “ideal view” includes a commitment that fundamental physical theories are explanatorily sufficient. The authors discuss several challenges to recovering the manifest image from fundamental physics, along with a distinct challenge to reductionism based on acknowledging the contributions of less fundamental theories in physical explanations. (shrink)

This paper discusses a conception of physics as a collection of theories that, from a logical point of view, is inconsistent. It is argued that this logical conception of the relations between physical theories is too crude. Mathematical subtleties allow for a much more nuanced and sophisticated understanding of the relations between different physical theories.

Harold Kincaid in Individualism and the Unity of Science postulates a model of unity-without-reduction in order to accurately describe the relation between individualism and macroeconomics. I present this model and apply it to the description of the relation between chemistry and quantum mechanics. I argue that, when it comes to the description of molecular structure, chemistry and quantum mechanics are unified in Kincaid’s sense. Specifically, the two disciplines contribute to the formation of a unified body of knowledge with respect to (...) molecular structure. (shrink)

How many miles to Babylon? Three-score and ten. Can I get there by candle-light? Yes, and back again. If your heels are nimble dnd light, You may get there by candle-light. Any philosopher who takes more than a fleeting interest in the sciences and their development must at some stage confront the issue of incommensurability in one or other of its many manifes tations. For the philosopher of science concerned with problems of conceptual change and the growth of knowledge, matters (...) of incommensurability are of paramount concern. After many years of skating over, skimming through and skirting round this issue in my studies of intertheory relations in science, I decided to take the plunge and make the problem of incommensurability the central and unifying theme of a book. The present volume is the result of that decision. My interest in problems of comparability and commensurability in science was awakened in the formative years of my philosophi cal studies by my teacher, Jerzy Giedymin. From him I have learnt not only to enjoy philosophical problems but also to beware of simpleminded solutions to them. The vibrant seminars of Paul Feyerabend held at Sussex University in 1974 left me in no doubt that incommensurability was, and would remain, a major topic of debate and dispute in the philosophical study of human knowledge. (shrink)

The aim of this article is to present a different perspective through which to examine reduction and emergence; namely, the perspective of chemistry’s relation to physics.

The philosophies of education serve as the guide of the teachers in handling the teaching-learning process. However, a belief will remain as a belief unless it is practiced. This study aimed to find the relationship between the philosophical beliefs and practices of the 30 teachers of the schools in San Roque, Mabini, Bohol - San Roque Elementary School and San Roque National High School, S.Y. 2019-2020. The study utilized a quantitative method descriptive survey research design. The research instrument used was (...) a self-constructed questionnaire in which the reliability was tested by a Cronbach’s Alpha using Statistical Package for the Social Science (SPSS) software. Simple percentage and weighted mean were some of the statistical treatments used. Kendall’s tau_b, a non-parametric test, was used to determine the correlation between philosophical beliefs and their equivalent pedagogical practices. All of the statistical treatments were also run using the SPSS software. Further, the researcher assured the proper observation of the research ethics protocol. Based on the results, the philosophies of Progressivism (3.63) and Perennialism (3.31) were the most and least prevailing philosophical beliefs, respectively. On the other hand, the most and least prevailing philosophies practiced are Progressivism (3.69) and Essentialism (3.19), respectively. Moreover, research findings revealed that there was a significant relationship between the philosophical beliefs of teachers and their pedagogical practices. In conclusion, this study claims that teachers’ pedagogical practices are dependent to their philosophical beliefs; and as the teachers believed on a particular philosophy of education, they practice it accordingly to the extent of their adherence to the belief. (shrink)

Barbarism was by no means unique to the past 100 years, Jonathan Glover tells us, but ''it is still right that much of 20th-century history has been a very unpleasant surprise.'' This was the century of Passchendaele, Dresden, Nanking, Nagasaki and Rwanda; of the Final Solution, the gulag, the Great Leap Forward, Year Zero and ethnic cleansing -- names that stand for killings in the six and seven figures and for suffering beyond comprehension. The technological progress that inspired the optimism (...) of the Victorians turned out also to multiply the effects of old-fashioned evil and criminal stupidity. (shrink)

The aim of this paper is to articulate and analyse the complexity of the concept of work in Hannah Arendt’s philosophy. Work is usually interpreted as antithetical to political action. This claim merits specification: only the instrumental, utilitarian strand of homo faber poses real danger to authentic politics. By contrast, the artistic or cultural mode of homo faber is not only compatible with Arendt’s understanding of politics, but in fact indispensable for any form of political longevity. Enduring political existence is (...) impossible without the constant support of artists, poets, historiographers and monument-builders who reify and memorialize the key meanings of political communities. This claim is substantiated by applying the phenomenological concept of sedimentation and drawing the political implications of this application. However, similarly to Edmund Husserl, Arendt identified a dual, problematic nature of sedimentation that underscores the importance of natality and thinking in artistic practice. (shrink)

In this paper I propose clearly to distinguish four fundamental types of intertheoretical relations that may be used to represent different types of theoretical change in empirical science. These four types can be represented formally through a refined version of the set-theoretical apparatus of structuralism. They may be described as: crystallization, theory-evolution, embedding, and replacement with partial incommensurability. They will be first explicated in intuitive, informal terms, and some historical examples will be suggested for each type. In the second (...) part of the paper, the four types are characterized in structuralistic terms; the notions of a partial substructure and of a diachronic theory-net will play a central role. (shrink)

There is a standard view of relations, held by philosophers and logicians alike, according to which we may meaningfully talk of a relation holding of several objects in a given order. Thus it is supposed that we may meaningfully—indeed, correctly—talk of the relation loves holding of Anthony and Cleopatra or of the relation between holding of New York, Washington, and Boston. But innocuous as this view might appear to be, it cannot be accepted as applying to all relations (...) whatever. For there is an important class of metaphysical and linguistic contexts which call for an alternative conception of relation, one for which the order of the relata plays no role and in which the application of the relation to its relata is achieved by other means. (shrink)

Charles Beitz rejects two highly influential conceptions of international theory as empirically inaccurate and theoretically misleading. In one, international relations is a Hobbesian state of nature in which moral judgments are entirely inappropriate, and in the other, states are analogous to persons in domestic society in having rights of autonomy that insulate them from external moral assessment and political interference. Beitz postulates that a theory of international politics should include a revised principle of state autonomy based on the justice (...) of a state's domestic institutions, and a principle of international distributive justice to establish a fair division of resources and wealth among persons situated in diverse national societies. (shrink)

In his recent The Parmenidean Ascent, Michael Della Rocca develops a regress-theoretic case, reminiscent of F.H. Bradley’s famous argument in Appearance and Reality, against the intelligibility of relations and in favor of a monistic conception of reality. I argue that Della Rocca illicitly supposes that “internal” relations – in one sense of that word – lead to a “chain” regress, a regress of relations relating relations and relata. In contrast, I contend that if “internal” or grounded (...) relations lead to a regress at all, it is a kind of “fission” regress within the relata themselves, and that a chain regress for relations only arises, if at all, for so-called “external” relations, relations not grounded in their relata. In this way, I contend that Della Rocca pursues a regress for so-called “internal” or grounded relations that only arises, if at all, for so-called “external” relations, relations not grounded in their relata. I compare Della Rocca’s case against relations with Bradley’s reasoning in Appearance and Reality, and suggest in this context that Bradley may, perhaps, have the upper hand. (shrink)

This paper revisits the conception of intelligence and understanding as embodied in the Turing Test. It argues that a simple system of meaning relations drawn from words/lexical items in a natural language and framed in terms of syntax-free relations in linguistic texts can help ground linguistic inferences in a manner that can be taken to be 'understanding' in a mechanized system. Understanding in this case is a matter of running through the relevant inferences meaning relations allow for, (...) and some of these inferences are plain deductions and some can serve to act as abductions. Understanding in terms of meaning relations also supervenes on linguistic syntax because such understanding cannot be simply reduced to syntactic relations. The current approach to meaning and understanding thus shows that this is one way, if not the only way, of framing Alan Turing's original insight into the nature of thinking in computing systems. (shrink)

“Realization” is a technical term that is used by metaphysicians, philosophers of mind, and philosophers of science to denote some dependence relation that is thought to obtain between higher-level properties and lower-level properties. It is said that mental properties are realized by physical properties; functional and computational properties are realized by first-order properties that occupy certain causal/functional roles; dispositional properties are realized by categorical properties; so on and so forth. Given this wide usage of the term “realization”, it would be (...) right to think that there might be different dependence relations that this term denotes in different cases. Any relation that is aptly picked out by this term can be taken to be a realization relation. The aim of this state-of-the-field article is to introduce the central questions about the concept of realization, and provide formulations of a number of realization relations. In doing so, I identify some theoretical roles realization relations should play, and discuss some theories of realization in relation to these theoretical roles. (shrink)

In this article, we present a new conception of internal relations between quantity tropes falling under determinates and determinables. We begin by providing a novel characterization of the necessary relations between these tropes as basic internal relations. The core ideas here are that the existence of the relata is sufficient for their being internally related, and that their being related does not require the existence of any specific entities distinct from the relata. We argue that quantity tropes (...) are, as determinate particular natures, internally related by certain relations of proportion and order. By being determined by the nature of tropes, the relations of proportion and order remain invariant in conventional choice of unit for any quantity and give rise to natural divisions among tropes. As a consequence, tropes fall under distinct determinables and determinates. Our conception provides an accurate account of quantitative distances between tropes but avoids commitment to determinable universals. In this important respect, it compares favorably with the standard conception taking exact similarity and quantitative distances as primitive internal relations. Moreover, we argue for the superiority of our approach in comparison with two additional recent accounts of the similarity of quantity tropes. (shrink)

Presupposing that most predicates do not correspond directly to genuine relations, I argue that all genuine relations are symmetric. My main argument depends on the premise that there are no brute necessities, interpreted so as to require logical and metaphysical necessity to coincide for sentences composed entirely of logical vocabulary and primitive predicates. Given this premise, any set of purportedly primitive predicates by which one might hope to express the facts about non-symmetric relations order their relata will (...) generate an objectionable multiplication of possibilities. In the final section I give a different argument, based on the weaker premise that brute necessities should not be multiplied without necessity. (shrink)

The full-text of this article is not currently available in ORA, but you may be able to access the article via the publisher copy link on this record page. N.B. Prof Williamson is now based at the Faculty of Philosophy, University of Oxford.

Organisms engage in various activities that are directed at objects, whether real or imagined. Such activities may be termed “intentional relations.” We present a four-level framework of social understanding that organizes the ways in which social organisms represent the intentional relations of themselves and other agents. We presuppose that the information available to an organism about its own intentional relations (or first person information) is qualitatively different from the information available to that organism about other agents’ intentional (...) relations (or third person information). However, through the integration of these two sources of information, it is possible to generate representations of intentional relations that are uniformly applicable to the activities of both self and other. The four levels of the framework differ in the extent to which such integration occurs and in the degree to which imagination is involved in generating these representations. Most animals exist at the lowest level, at which integration of first and third person sources of information does not occur. Of nonhuman species, only great apes exhibit social understanding at intermediate levels, at which integration of these sources of information provides uniform representations of intentional relations. Only humans attain the highest level, at which it is possible to represent intentional relations with mental objects. We propose that with the development of the imagination, children progress through three stages, equivalent to the later three levels of the framework. The abnormalities in social understanding of autistic individuals are hypothesized to result from a failure to develop integrated representations of intentional relations. (shrink)

Philosophers have proposed various kinds of relations between Mendelian genetics and molecular biology: reduction, replacement, explanatory extension. This paper argues that the two fields are best characterized as investigating different, serially integrated, hereditary mechanisms. The mechanisms operate at different times and contain different working entities. The working entities of the mechanisms of Mendelian heredity are chromosomes, whose movements serve to segregate alleles and independently assort genes in different linkage groups. The working entities of numerous mechanisms of molecular biology are (...) larger and smaller segments of DNA plus related molecules. Discovery of molecular DNA mechanisms filled black boxes that were noted, but unilluminated, by Mendelian genetics. (shrink)

The present paper investigates the first step of rational belief acquisition. It, thus, focuses on justificatory relations between perceptual experiences and perceptual beliefs, and between their contents, respectively. In particular, the paper aims at outlining how it is possible to reason from the content of perceptual experiences to the content of perceptual beliefs. The paper thereby approaches this aim by combining a formal epistemology perspective with an eye towards recent advances in philosophy of cognition. Furthermore the paper restricts its (...) focus, it concentrates on the case of color perception and perceptual beliefs about color. (shrink)

In this revised edition of his 1979 classic Political Theory and International Relations, Charles Beitz rejects two highly influential conceptions of international theory as empirically inaccurate and theoretically misleading. In one, international relations is a Hobbesian state of nature in which moral judgments are entirely inappropriate, and in the other, states are analogous to persons in domestic society in having rights of autonomy that insulate them from external moral assessment and political interference. Beitz postulates that a theory of (...) international politics should include a revised principle of state autonomy based on the justice of a state’s domestic institutions, and a principle of international distributive justice to establish a fair division of resources and wealth among persons situated in diverse national societies. (shrink)

This article articulates and defends F. H. Bradley's regress argument against external relations using contemporary analytic techniques and conceptuality. Bradley's argument is usually quickly dismissed as if it were beneath serious consideration. But I shall maintain that Bradley's argument, suitably reconstructed, is a powerful argument, plausibly premised, and free of such obvious fallacies as petitio principii. Thus it does not rest on the question‐begging assumption that all relations are internal, as Russell, and more recently van Inwagen, maintain. Bradley (...) does not attack external relations in order to affirm a doctrine of internal relations, and his monism is not derived from the internality of all relations, but from the self‐contradictory nature of all relations. For Bradley, it is the “relational situation”as such that is ontologically defective. (shrink)

Why does equality matter, as a social and political value, and what does it require? Relational egalitarians argue that it does not require that people receive equal distributive shares of some good, but that they relate as equals. Christian Schemmel here provides the first comprehensive development of a liberal conception of relational equality, one which understands relations of non-domination and egalitarian norms of social status as stringent demands of social justice. He first argues that expressing respect for the freedom (...) and equality of individuals in social cooperation requires stringent protections against domination. Taking this as a starting point, he then develops a substantive, liberal conception of non-domination and argues that non-domination is a particularly important, but not the only, concern of social justice. From there, Schemmel develops an account of the wrongness of inegalitarian norms of social status which shows how status-induced foreclosure of important social opportunities is a social injustice in its own right, over and above the role of status inequality in enabling domination, and the threats it poses to individuals' self-respect. Finally, Schemmel articulates the core requirements of liberal relational egalitarianism for political, economic, and health justice: these amount to demands for far-reaching forms of equality in all three domains, which can rarely, if ever, be overridden by competing concerns. With expert rigor and creativity, Justice and Egalitarian Relations brings together scholarship in a variety of related topics, from social justice and liberalism to distributive and relational equality, social equality, neo-republicanism, and non-denomination. (shrink)

When does a woman give valid consent to sexual relations? When does her consent render it morally or legally permissible for a man to have sexual relations with her? Why is sexual consent generally regarded as an issue about female consent? And what is the moral significance of consent? These are some of the questions discussed in this important book, which will appeal to a wide readership in philosophy, law, and the social sciences. Alan Wertheimer develops a theory (...) of consent to sexual relations that applies to both law and morality in the light of the psychology of sexual relations, the psychology of perpetrators, and the psychology of the victims. He considers a wide variety of difficult cases such as coercion, fraud, retardation, and intoxication. We can all agree that 'no' means 'no'. This book suggests that the difficult question is whether 'yes' means 'yes'. (shrink)

According to Vallicella's 'Relations, Monism, and the Vindication of Bradley's Regress' (2002), if relations are to relate their relata, some special operator must do the relating. No other options will do. In this paper we reject Vallicella's conclusion by considering an important option that becomes visible only if we hold onto a precise distinction between the following three feature-pairs of relations: internality/externality, universality/particularity, relata-specificity/relata-unspecificity. The conclusion we reach is that if external relations are to relate their (...) relata, they must be relata-specific (and no special operator is needed). As it eschews unmereological complexes, this outcome is of relevance to defenders of the extensionality of composition. (shrink)

When does a woman give valid consent to sexual relations? When does her consent render it morally or legally permissible for a man to have sexual relations with her? Why is sexual consent generally regarded as an issue about female consent? And what is the moral significance of consent? These are some of the questions discussed in this important book, which will appeal to a wide readership in philosophy, law, and the social sciences. Alan Wertheimer develops a theory (...) of consent to sexual relations that applies to both law and morality in the light of the psychology of sexual relations, the psychology of perpetrators, and the psychology of the victims. He considers a wide variety of difficult cases such as coercion, fraud, retardation, and intoxication. We can all agree that 'no' means 'no'. This book suggests that the difficult question is whether 'yes' means 'yes'. (shrink)

Machine generated contents note: -- Acknowledgements -- Introduction - The Problem of Moral Status -- PART I: MORAL ONTOLOGIES: FROM INDIVIDUAL TO RELATIONAL DOGMAS -- Individual Properties -- Appearance and Virtue -- Relations: Communitarian and Metaphysical -- Relations: Natural and Social -- Relations: Hybrid and Environmental -- Conclusion Part I: Diogenes's Challenge -- PART II: MORAL STATUS ASCRIPTION AND ITS CONDITIONS OF POSSIBILITY: A TRANSCENDENTAL ARGUMENT -- Words and Sentences: Forms of Language Use -- Societies and Cultures (...) (1): Forms of Living Together -- Societies and Cultures (2): Forms of Life -- Bodies and Things: Forms of Feeling and Making -- Spirits and Gods: Forms of Religion -- Fences, Walls, and Maps: Forms of Historical Space -- Moral Metamorphosis: Concluding the Transcendental Argument -- General Conclusion -- References -- Index. (shrink)

I examine and discuss in this paper Orilia’s theory of external, non-symmetrical relations, that is based on ontological roles (O-Roles). I explore several attempts to interpret O-Roles from an ontological viewpoint and I reject them because of two problems concerning the status of asymmetrical relations (to be distinguished from non-symmetrical relations simpliciter) and of exemplification as an external, non-symmetrical relation. Finally, following Heil’s and Lowe’s characterization of modes as particular properties that ontologically depend on their “bearers”, I (...) introduce relational modes in order to define a new solution to the problems of the ontological status of both external, non-symmetrical relations and O-Roles. I also deal with five objections raised by Fraser MacBride against relational modes and O-Roles and I elaborate an analysis of the relations of being to the left of and being to the right of. (shrink)

We study the complexity of the isomorphism relation on classes of computable structures. We use the notion of FF-reducibility introduced in [9] to show completeness of the isomorphism relation on many familiar classes in the context of all ${\mathrm{\Sigma }}_{1}^{1}$ equivalence relations on hyperarithmetical subsets of ω.