In lieu of an abstract, here is a brief excerpt of the content:RUSSELLS ARGUMENT AGAINST FREGE'S SENSE-REFERENCE DISTINCTION PAWEL TURNAu Philosophy I Jagiellonian University Cracow, Poland I n "On Denoting"l Russell argued that Frege's theory of sense and reference was an "inextricable tangle", but, ironically, many readers found the argument even more knotry. In an effort to make sense of it, commentators were often driven to attribute to Russell quite obvious and simple fallacies. A different approach was taken by Peter (...) Geach, who suggested that Russell's argument could be given a consistent reading if it were construed as arguing, not against Frege's theory, but against Russell's own earlier theory, which he put forward in The Principles of Mathematics. It is not an implausible hypothesis, considering how prone Russell was to misrepresent' other philosophers' views and read his own powerful ideas into their writings. In order to justifY Geach's hypothesis properly, one would have to show the crucial difference between Russell's and Frege's theories that made only one of them susceptible to the attack in "On Denoting ". Russell explicitly considered the two theories to be "very nearly the same"; this self-interpretation would have to be questioned. Geach's hypothesis would be further strengthened by providing an actual exegesis of the "On Denoting" argument as directed against The Principles ofMathematics theory. In this paper 1 will try to accomplish both of these tasks. Russell is often accused of confusing use and mention. The accusation is not fair, however. It is true that he does not insist on this distinction; he does not employ it extensively. But he is certainly Russell's Argument against Frege's Distinction 53 aware of it; he simply does not think that it is an important logical distinction. Today this view may seem almost incomprehensible, but that only shows the strength of Frege's influence on our ideas. There are two striking symptoms of Russell's lack of concern for the use-mention distinction: firstly, he does not observe the convention which says that putting an expression in quotation marks produces a name of that expression; secondly, he does not feel any need to employ the pair of terms "sentence" and "proposition", but contents himself with the latter only. The claim about Russell's use of inverted commas needs to be proved; I will come to that later. Russell's assertions are often ambiguous between use and mention of expressions. For example, he asserts that "propositions do not contain words" (PaM, p. 47). However, a few pages later, he speaks of propositions that contain the phrase "any number" (p. 53). If this is not to be self-contradictory, then either the term "proposition" must sometimes signifY a linguistic expression, or the term "phrase" must sometimes be understood without implying that a phrase consists of words. This ambiguity is openly admitted in a later article, where he writes: [we shall be concerned with] the distinction between verbs and substantives, or, more correctly, between the objects denoted by verbs and the objects denoted by substantives. Since this more correct expression is long and cumbrous, I shall generally use the shorter expression to mean the same thing. Thus, when I speak of verbs, I mean the object denoted by verbs, and similarly for substantives.2. Russell's attitude towards the distinction between use and mention is not unjustified. It has its reason in his view oflanguage and the subject -matter of logic. In Russell's view, the subject-matter of logic has nothing to do with language. Words, both spoken and written, are entirely outside its realm. Logic, just as other sciences (except linguistics ), is concerned with the entities indicated by words, and not with words themselves. Even the relation of indicating, which holds between words and things in the world, is of no interest to it: "mean1 In Lf(, pp. 39-56. russ.lI: the Journal of the Bertrand Russell Archives McMaster Univecsity Library Press n.s. 11 (summer 1991): 51- 66 ISSN 0036-o16~ 2 B. Russell, "On the Relations of Universals and Particulars", Proceedings of the Aristotelian Society, n.s. 12 (r9II-12): 1-24; in Lf(, pp. 103-24 (at 107-8). 54 PAWEL TURNAU Russell's Argument... (shrink)

The article offers a rigorous truth condition for subjunctively conditional statements. The theory is framed in the system of transparent intensional logic and takes connections (especially the cause-Effect relation) as basic. Counterexamples are given to rival theories based on the notion of world similarity.

Traxler, Pickering, and Clifton found that ambiguous sentences are read faster than their unambiguous counterparts. This so-called ambiguity advantage has presented a major challenge to classical theories of human sentence comprehension because its most prominent explanation, in the form of the unrestricted race model, assumes that parsing is non-deterministic. Recently, Swets, Desmet, Clifton, and Ferreira have challenged the URM. They argue that readers strategically underspecify the representation of ambiguous sentences to save time, unless disambiguation is required by task demands. When (...) disambiguation is required, however, readers assign sentences full structure—and Swets et al. provide experimental evidence to this end. On the basis of their findings, they argue against the URM and in favor of a model of task-dependent sentence comprehension. We show through simulations that the Swets et al. data do not constitute evidence for task-dependent parsing because they can be explained by the URM. However, we provide decisive evidence from a German self-paced reading study consistent with Swets et al.'s general claim about task-dependent parsing. Specifically, we show that under certain conditions, ambiguous sentences can be read more slowly than their unambiguous counterparts, suggesting that the parser may create several parses, when required. Finally, we present the first quantitative model of task-driven disambiguation that subsumes the URM, and we show that it can explain both Swets et al.'s results and our findings. (shrink)

Chapter One: Constructions. Entities, constructions, and functions When one travels from Los Angeles to New York, going, say, by way of St. Louis, Chicago, ...

It was shown in [3] (see also [5]) that there is a duality between the category of bounded distributive lattices endowed with a join-homomorphism and the category of Priestley spaces endowed with a Priestley relation. In this paper, bounded distributive lattices endowed with a join-homomorphism, are considered as algebras and we characterize the congruences of these algebras in terms of the mentioned duality and certain closed subsets of Priestley spaces. This enable us to characterize the simple and subdirectly irreducible algebras. (...) In particular, Priestley relations enable us to characterize the congruence lattice of the Q-distributive lattices considered in [4]. Moreover, these results give us an effective method to characterize the simple and subdirectly irreducible monadic De Morgan algebras [7].The duality considered in [4], was obtained in terms of the range of the quantifiers, and such a duality was enough to obtain the simple and subdirectly irreducible algebras, but not to characterize the congruences. (shrink)

Roman Catholic and Eastern Orthodox theologians claim that the unique event of Christ’s sacrifice on Calvary is present in Eucharistic liturgies. A popular explanatory strategy for this miraculous presence suggests that due to its supernatural character the Eucharist “conquers time,” transcends its boundaries, and allows for temporal coincidence of two chronologically distant events. I discuss the four main approaches within this strategy that can be discovered in contemporary theological writings. The first approach implies a time travel of the Calvary event. (...) The second suggests the time travel of Eucharistic participants. The third eliminates the chronological distance by relocating one of the events into a timeless reality. The fourth assumes multilocation of the event across time. I argue that each of these approaches is untenable on philosophical or theological grounds. (shrink)

In the last decades, research in science mapping has delivered several powerful techniques, based on citation or textual analysis, for charting the intellectual organization of research fields. To map the social network underlying science and scholarship, by contrast, science mapping has mainly relied on one method, co-authorship analysis. This method, however, suffers from well-known limitations related to the practice of authorship. Moreover, it does not perform well on those fields where multi-authored publications are rare. In this study, a new method (...) for mapping the social structure of research fields is advanced, based on the analysis of the acknowledgments of academic publications. We first discuss the standard account of the function of acknowledgments in scholarly communication, then we introduce a new interpretative framework in which the acknowledgments are intended as positioning signals exchanged by researchers. Next, we provide the formal definition of the four acknowledgments-based networks that stand at the core of the method, and we test it on a humanities field, analytic philosophy. Results show that acknowledgement-based networks allow to reconstruct the fine-grained social structure of analytic philosophy from different perspectives. Furthermore, by comparing the citation-based maps of the field with the acknowledgments-based networks, it permits to shed light on the relationship between the intellectual and social layer of analytic philosophy. We conclude by presenting practical limitations of the method and by sketching some further research lines. (shrink)

Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond NP ≠ coNP. These conjectures formally connect computational complexity with the difficulty of proving some sentences, which means that high computational complexity of a problem associated with a sentence implies that the sentence is not provable in a weak theory, or requires a long proof. Another reason for putting forward these conjectures is that some results in proof complexity seem to be (...) special cases of such general statements and we want to formalize and fully understand these statements. Roughly speaking, we are trying to connect syntactic complexity, by which we mean the complexity of sentences and strengths of the theories in which they are provable, with the semantic concept of complexity of the computational problems represented by these sentences. -/- We have introduced the most fundamental conjectures in our earlier works. Our aim in this article is to present them in a more systematic way, along with several new conjectures, and prove new connections between them and some other statements studied before. (shrink)

In this paper we argue that Aristotle operates with a particular theoretical model in his explanation of animal locomotion, what we call the ‘centralized incoming and outgoing motions’ model. We show how the model accommodates more complex cases of animal motion and how it allows Aristotle to preserve the intuition that animals are self-movers, without jeopardizing his arguments for the eternity of motion and the necessary existence of one eternal unmoved mover in Physics VIII. The CIOM model helps to elucidate (...) Aristotle’s two central yet problematic claims, namely that the soul is the efficient cause of animal motion and that it is the internal supporting-point necessary for animal motion. Moreover, the CIOM model helps us to explain the difference between voluntary, involuntary and non-voluntary motions, and to square Aristotle’s cardiocentrism with his hylomorphism, but also, more generally, it provides an interesting way of thinking about the place of intentionality in the causal structure of the world. (shrink)

2 Popper's Logical Definition of Verisimilitude. 3 Popper's Probabilistic Definition of Verisimilitude. 4 Conclusion.

Introduction. The article is focused on analyzing the aesthetic aspect of A. Kojève’s philosophy, the ability of his philosophy, from an aesthetic point of view, to clarify a number of key problems of the modern political and cultural environment. The purpose of the study is to determine the epistemological attitude of A. Kojève’s philosophy able to clarify the way in which his philosophy problematizes the current cultural and political reality. Methods. Hermeneutics, comparative analysis and deconstruction are used as research methods. (...) Comparative analysis allows us to demarcate A. Kojève’s own line of reasoning, in the context of aesthetic and epistemological theories, as well as Hegelian themes themselves. Hermeneutics is the central method in the work, since the philosophy of A. Kojeve requires interpretation as an aesthetic theory. Deconstruction, formalized to the status of a method according to P. de Man, allows us to detect inconsistencies, the principle of mutual problematization of Kojeve’s philosophy and the current political and epistemological agenda. Scientific novelty of the research. The standard way of interpreting the work of A. Kojève is to evaluate him as an interpreter of G. Hegel. The author analyzes some meaning of A. Kojève’s philosophy, separate from G. Hegel’s explanation of the text. The novelty lies not only in the fact that A. Kojève’s philosophy is defined as theorizing that goes beyond technical hermeneutics (clear presentation), but also as a specific representation of such theorizing as epistemological aesthetic theory. The latter is a rather rare interpretation of the philosophy of A. Kojeve. This allows us to expand the traditional assumption that post-Hegelian epistemesthetics is the property of an extremely limited number of authors (for example, B. Croce). Moreover, such an interpretation of A. Kojève’s theories is a new element in the emerging trend of considering political issues within the framework of epistemological aesthetics. Results. The specific mode of interpreting G. Hegel, which is carried out by A. Kojève, turns the philosophy of the former into a unique aesthetic project. In this project, the category of aesthetic experience comes to the foreground, indicating the empty, formal nature of any discourse. In this regard, any claim to knowledge of reality, to a correct idea of the subject is replaced by the idea of creating the subject of discourse. Consistent treatment of this idea is symptomatic of the philosophy of A. Kojève. This philosophy is a reflection of those historical changes that gave rise to the culture of “aesthetic rationality”: empty and formal. In A. Kojève’s philosophy, one can see how such a culture of the End of History is, contrary to Hegelian ideas, not the era of the struggle decline, but the era of its strange transformation, a symptom of increasing political violence. Conclusions. A. Kojève’s philosophy is considered not as a utopian political project, but as a problematization of the modern cultural and political sphere. The latter is understood as an indication of the inconsistency of ontological discourses of Truth, the discovery in the very essence of discursive practices of an empty, formal principle, and therefore primarily of interest to aesthetics. The modern era of the End of History and the end of the era of persuasive speech gives an idea of the main political paradox (at least for the philosophy of A. Kojève, and at most for the modern political environment). The era of disappointment in discourse should become an era of refusal to fight for discourses, but it becomes an era of maximizing violence, since it is in a situation of disappointment that discourses can only be supported by force. We move from unconvincing speech to convincing violence, but it is possible to understand the origins and specifics of this transition only by considering A. Kojève’s philosophy in the light of such a discipline as aesthetics. (shrink)

In this article I explore Maimon’s role in the evolution of Kant’s understanding of the function of the history of philosophy in philosophical enquiry. Kant is often viewed as holding an ambivalent...

The subject of the study is the socio-cultural threats to the information security of Russian citizens associated with ChatGPT technologies (Chat Generative Pre-trained Transformer, a machine-generated text response generator simulating a dialogue). The object of research − evaluation of the ratio of advantages and threats of generative language models based on "machine learning" in modern (2021-2023) scientific literature (journals HAC K1, K2 and Scopus Q1, Q2). The scientific novelty of the research lies in the culturological approach to the analysis of (...) threats to the security of Russian citizens associated with the use of ChatGPT as one of the technologies of "artificial intelligence". The formulation of the problem of the classical Turing test "to distinguish a person from a machine" is characterized as a scholastic abstraction, instead a more correct and productive approach is proposed: a socio-cultural assessment of the value (based on cultural axiology) of new computer technologies. The starting point of the analysis is the determination of socio-cultural value (or, conversely, damage) as a result of the use of generative language models based on machine learning. Further, the contribution and responsibility of various socio-cultural subjects of its creation and application are revealed − user, creator and developer. The result of the application of the proposed approach is the deconstruction of the discourse of the "philosophy of artificial intelligence" in terms of uncritical translation of developer declarations intended for marketing and attracting financing. Hypertrophied perception, precariously balancing on the edge of utopia and dystopia, is assessed as a risk of incorrect identification and ranking of threats to information security. Assumptions about the hypothetical "superweapon of psychological warfare" mask modern incidents of cross-border leakage of confidential data, the risks of being held accountable for publishing deliberately false information and illegal content as a result of using ChatGPT. National security measures are recommended, including restrictive measures and increasing the general civil culture of information security of users, as well as the orientation of domestic developments of solutions of this type on traditional values, socio-cultural identity and interests of Russian citizens. (shrink)

I. The framework. 1, Aristotle's project and methods. 2, The perceptual capacity of the soul. 3, The sensory apparatus. 4, The common sense and the related capacities -- II. The terminology. 1, Overlooked occurrences of the phrase 'common sense'. 2, De anima III.1 425a27. 3, De partibus animalium IV.10 686a31. 4, De memoria et reminiscentia 1 450a10. 5, De anima III.7 431b5. 6, Conclusions on the terminology -- III. Functions of the common sense. 1, Simultaneous perception and cross-modal binding. 2, (...) Perceptual discrimination. 3, Waking, sleep, and control of the senses. 4, Perceiving that what we see and hear, and monitoring of the senses. 5, Other roles of the common sense -- Conclusion. (shrink)

We prove an exponential lower bound on the length of cutting plane proofs. The proof uses an extension of a lower bound for monotone circuits to circuits which compute with real numbers and use nondecreasing functions as gates. The latter result is of independent interest, since, in particular, it implies an exponential lower bound for some arithmetic circuits.

Purpose. To turn to the diaries and journalistic works by Leo Tolstoy, to study the content and method of his religious and ethical search. To doubt the faithfulness of his interpretation of the evangelical message of Christ. Theoretical basis. The author proceeded from the necessity of a dialectical understanding of the concepts of nonviolence, mercy, justice and a cultural-historical focus on the possibilities of society in realizing the spirituality principles. Originality. The author focuses on the unilateral nature of the methodology (...) that Leo Tolstoy uses to deny violence, as well as on the ambiguous role of Tolstoy's ideology in the morality of society. Conclusions. The spiritual activities an individual person is able to do and that are instructive for society from the point of view of its moral influence may not be sufficient means for educating moral responsibility in a society as a whole. Tolstoy's methodological approach to justifying the absoluteness of nonviolence principle is one-sided and not productive for a true interpretation of the spiritual nature of the Christ’s message about love and mercy. (shrink)

“Eco-labels” are an increasingly important form of private regulation for sustainability in areas such as carbon emissions, water consumption, ethical sourcing, or organic produce. The growing interest and popularity of eco-labels has also been coupled with growing concerns about their credibility, in part because the standard-setting and conformity assessment practices that eco-labels adopt exhibit striking differences. In this paper, we assess which assurance practices contribute to eco-labels being perceived as better governed, in the eyes of experts as well as the (...) media. Unlike previous studies, which are mostly conceptual, qualitative, or focused on one or few eco-labels, we study a large set of eco-labels, combining data from three different sources. Our findings suggest that experts and media are primarily concerned about “re-assurance” practices, looking for one or preferably multiple layers of “re-assurance” that independent parties are overseeing the eco-label and the firms certified under it. (shrink)

Science maps are visual representations of the structure and dynamics of scholarly knowl­edge. They aim to show how fields, disciplines, journals, scientists, publications, and scientific terms relate to each other. Science mapping is the body of methods and techniques that have been developed for generating science maps. This entry is an introduction to science maps and science mapping. It focuses on the conceptual, theoretical, and methodological issues of science mapping, rather than on the mathematical formulation of science mapping techniques. After (...) a brief history of science mapping, we describe the general procedure for building a science map, presenting the data sources and the methods to select, clean, and pre-process the data. Next, we examine in detail how the most common types of science maps, namely the citation-based and the term-based, are generated. Both are based on networks: the former on the network of publications connected by citations, the latter on the network of terms co-occurring in publications. We review the rationale behind these mapping approaches, as well as the techniques and methods to build the maps. We also present less-common types of science maps, including co-authorship networks, interlocking editorship networks, maps based on patents’ data, and geographic maps of science. Moreover, we consider how time can be represented in science maps to investigate the dynamics of science. We also discuss some epistemological and sociological topics that can help in the interpretation, contextualization, and assessment of science maps. Then, we present some possible applications of science maps in science policy. In the conclusion, we point out why science mapping may be interesting for all the branches of meta-science, from knowl­edge organization to epistemology. (shrink)

This article is concerned with an analysis of semantics and the normativity of evaluative judgments, in which “aesthetic concepts” and “predicates of personal taste” are used in the context of the evaluation of selected cultural forms. Qualitative data obtained through semi-structured interviews with representatives in four categories of actors in the cultural field are analyzed. In the light of the findings, theories of aesthetic judgment are critically assessed, which on the one hand, postulate the categorical semantic and normative difference between (...) aesthetic concepts and predicates of personal taste and, on the other hand, conceive aesthetic disputes from an epistemological point of view and do not sufficiently take into account their pragmatic context. In conclusion, a functional analysis of the semantics and normativity of evaluative judgments is presented, in which the speakers use terms from the field of aesthetics. (shrink)

This article provides an ethical analysis of the moral conflict over access to premium audio-visual online content, which is currently regulated by geo-blocking in the domain of digital film distri...

_Abstract_: Fueled by the rapid development of neuroscientific tools and techniques, some scholars consider the shift from traditional cognitive psychology toward cognitive neuroscience to be a _revolution_ (most notably Boone and Piccinini). However, the term “revolution” in philosophy of science can easily be construed as involving a paradigm shift in the sense of Kuhn’s _The Structure of Scientific Revolutions_. Is a Kuhnian account sound in the case at hand? To answer this question, we consider heuristic indicators of two features of (...) paradigm shifts: the incommensurability of ontologies; and a gap between scientific communities. Based on our evidence, we argue that no revolution has occurred (at least, not yet). _Keywords_: Cognitive Neuroscience; Cognitive Psychology; Philosophy of Science; Thomas Kuhn; Scientometrics _La “rivoluzione delle neuroscienze cognitive” non è una rivoluzione (in senso kuhniano). Evidenze scientometriche _ _Riassunto_:_ _Complice il rapido sviluppo di strumenti e tecniche in neuroscienze, alcuni studiosi (in particolare Boone e Piccinini) intendono il passaggio dalla psicologia cognitiva classica alla neuroscienza cognitiva nei termini di una _rivoluzione_. Tuttavia, il termine ‘rivoluzione’ in filosofia della scienza è strettamente associato alla nozione di successione di paradigmi esposta da Kuhn ne _La struttura delle rivoluzioni scientifiche_. Obiettivo di questo lavoro è capire se effettivamente la concezione kuhniana offra una corretta descrizione di questa dinamica storica. In particolare, prenderemo in esame due indicatori euristici delle rivoluzioni kuhniane: l’incommensurabilità ontologica trai due paradigmi e la diversa composizione demografica delle comunità scientifiche. Sulla base delle evidenze scientometriche che prenderemo in esame, affermeremo che non è avvenuta nessuna rivoluzione (almeno per ora). _Parole chiave_: Neuroscienze cognitive; Psicologia cognitiva; Filosofia della scienza; Thomas Kuhn; Scientometria. (shrink)

Aristotle's notion of experience plays an important role in his epistemology as the link between perception and memory on the one side, and higher cognitive capacities on the other side. However, Aristotle does not say much about it, and what he does say seems inconsistent. Notably, some passages suggest that it is a non-rational capacity, others that it is a rational capacity and that it provides the principles of science. This paper presents a unitary account of experience. It explains how (...) experience grows from perception and memory into a rational capacity, and in what way it provides the principles. (shrink)

This essay sheds additional light on the biographies and fates of Ayn Rand’s closest relatives in the Soviet Union and abroad after young Alissa Rosenbaum left the “country of workers and peasants” in 1926 for the pursuit of a new life in the United States. Previously unknown facets of her relatives’ lives were intertwined with the complex and often tragic historical events of the first half of the twentieth century. Among these relatives are victims of the German blockade of Leningrad, (...) a music teacher, a European bacteriologist, a doctor who was twice a refugee, and a Soviet Medical Service Corps officer. (shrink)

This book offers an unprecedented quantitative portrait of analytic philosophy focusing on two seemingly marginal features of philosophical texts: citations and acknowledgements in academic publications. Originating from a little network of philosophers based in Oxford, Cambridge, and Vienna, analytic philosophy has become during the Twentieth century a thriving philosophical community with thousands of members worldwide. Leveraging the most advanced techniques from bibliometrics, citations and acknowledgments are used in this book to shed light on both the epistemology and the sociology of (...) this philosophical field, illuminating the intellectual trajectory of analytic philosophy as well as the social characteristics of the analytic community. Special attention is dedicated to the last forty years, providing insights into a phase of analytic philosophy which is still understudied by historians of philosophy. In the eight chapters of the book, readers will find not only numerous quantitative investigations and technical explanations, but also a robust theoretical framework and epistemological reflections on the strengths and limitations of quantitative methods for the study of philosophy. With its strong interdisciplinary appeal, this book will engage a wide range of scholars, including historians of philosophy seeking new methodologies, analytic philosophers interested in a new look at their discipline, and scholars in digital humanities, bibliometrics, and quantitative studies of science, who will find many innovative techniques for investigating disciplinary fields. (shrink)

Evangelical Protestant spirituality, under the influence of the Enlightenment, has assumed a somewhat modernist flavor. As a result, traditional forms of religious symbol and piety were demoted in favor of religious affections, true spirituality was now discerned by means of “heart knowledge,” and the assurance of salvation assumed a place of prominence in the emerging market of spiritual autobiography. This essay explores several ways that a non-monastic, non-modern Protestant tradition, which lives according to a community rule, can contribute to the (...) spiritual formation conversation. I begin by introducing the reader to the Amish narrative and discuss how two theological themes shape their approach to spirituality–-the cross of Christ and the relationship between faith and works, justification and sanctification. Next, I question a common view of Jesus’ ministry as being diametrically opposed to that of the Pharisees and suggest that the Sermon on the Mount deserves to be central to the enterprise of spiritual formation. I conclude this essay by revealing how the Amish put spiritual theology into practice, via a locally constructed Ordnung and while seated around the supper table. (shrink)

The paper gives a survey of results related to a problem of automatic recognizing important properties of non-classical logics.

Khoussainov and Nerode [14] posed various open questions on model-theoretic properties of automatic structures. In this work we answer some of these questions by showing the following results: There is an uncountably categorical but not countably categorical theory for which only the prime model is automatic; There are complete theories with exactly 3,4,5,…3,4,5,… countable models, respectively, and every countable model is automatic; There is a complete theory for which exactly 2 models have an automatic presentation; If LOGSPACE=PLOGSPACE=P then there is (...) an uncountably categorical but not countably categorical theory for which the prime model does not have an automatic presentation but all the other countable models are automatic; There is a complete theory with countably many countable models for which the saturated model has an automatic presentation but the prime model does not have one. (shrink)

We study the following open question in computable model theory: does there exist a structure of computable dimension two which is the prime model of its first-order theory? We construct an example of such a structure by coding a certain family of c.e. sets with exactly two one-to-one computable enumerations into a directed graph. We also show that there are examples of such structures in the classes of undirected graphs, partial orders, lattices, and integral domains.