Due to the environmental and health impact of the private transport sector, social scientists have largely focused on psychosocial and contextual factors associated with people's choice over transport means. This study aims to contribute to this line of research by applying a user-centered approach, with the objective of taking into account the specific environmental and social context of the metropolitan area of Cagliari city. To accomplish this aim, four groups of people were matched according to their shared starting point: car (...) users vs. public transport users, and light-rail users vs. non-light-rail users. Groups were interviewed using a focus group method. Participants were invited to discuss their everyday travel experiences and to exchange their ideas on different sustainable and less sustainable means of transport. Both consolidated drivers/barriers in the field of environmental psychology and public transportation design features have been investigated. Other than highlighting the importance of socio-psychological factors to promote more sustainable transport choices like in previous studies, the present research offers an insight into how these aspects and factors are shaped and experienced in the narratives of residents. (shrink)

Dieses Buch bietet die erste systematische Diskussion von Husserls Cartesianischen Meditationen. Beginnend mit einem Kommentar zum Text der fünf Meditationen werden in den hier veröffentlichten Aufsätzen einige der wichtigsten Begriffe der Husserlschen Philosophie untersucht und geklärt: Intentionalität, Synthese, Evidenz, Intersubjektivität. Darüber hinaus bietet das Buch die erste Diskussion von Husserls später Version der Transzendentalphilosophie und ihrer Relevanz für zeitgenössische Debatten in der kontinentalen und analytischen Philosophie. Mit Beiträgen von Andreea Smaranda Aldea | Lilian Alweiss | Stefano Bancalari | Jakub Čapek (...) | Emanuela Carta | Daniele De Santis | Aurélien Djian | Saulius Geniusas | Sara Heinämaa | Leonard Ip | Hynek Janoušek | Federico Lijoi | Claudio Majolino | Danilo Manca | Sergio Pérez-Gatica | Witold Plotka | Alice Pugliese | Ignacio Quepons | Rosemary Rizo-Patrón de Lerner | Agustín Serrano de Haro | Wojciech Starzyński. (shrink)

Feminism is sensational -- On being directed -- Willfulness and feminist subjectivity -- Trying to transform -- Being in question -- Brick walls -- Fragile connections -- Feminist snap -- Lesbian feminism -- Conclusion 1: A killjoy survival kit -- Conclusion 2: A killjoy manifesto.

Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic (...) to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated. (shrink)

This paper gives a framework for understanding causal counterpossibles, counterfactuals imbued with causal content whose antecedents appeal to metaphysically impossible worlds. Such statements are generated by omissive causal claims that appeal to metaphysically impossible events, such as “If the mathematician had not failed to prove that 2+2=5, the math textbooks would not have remained intact.” After providing an account of impossible omissions, the paper argues for three claims: (i) impossible omissions play a causal role in the actual world, (ii) causal (...) counterpossibles have broad applications in philosophy, and (iii) the truth of causal counterpossibles provides evidence for the nonvacuity of counterpossibles more generally. (shrink)

Widespread causal overdetermination is often levied as an objection to nonreductive theories of minds and objects. In response, nonreductive metaphysicians have argued that the type of overdetermination generated by their theories is different from the sorts of coincidental cases involving multiple rock-throwers, and thus not problematic. This paper pushes back. I argue that attention to differences between types of overdetermination discharges very few explanatory burdens, and that overdetermination is a bigger problem for the nonreductive metaphysician than previously thought.

I present and develop the view that omissions are de re possibilities of actual events. Omissions do not literally fail to occur; rather, they possibly occur. An omission is a tripartite metaphysical entity composed of an actual event, a possible event, and a contextually specified counterpart relation between them. This view resolves ontological, causal, and semantic puzzles about omissions, and also accounts for important data about moral responsibility for outcomes resulting from omissions.

This paper examines both creepiness and the distinctive reaction had to creepiness, being “creeped out.” The paper defends a response-dependent account of creepiness in terms of this distinctive reaction, contrasting our preferred account to others that might be offered. The paper concludes with a discussion of the value of detecting creepiness.

In this paper, I ask whether there is a defensible philosophical view according to which everybody is beautiful. I review two purely aesthetical versions of this claim. The No Standards View claims that everybody is maximally and equally beautiful. The Multiple Standards View encourages us to widen our standards of beauty. I argue that both approaches are problematic. The former fails to be aspirational and empowering, while the latter fails to be sufficiently inclusive. I conclude by presenting a hybrid ethical–aesthetical (...) view according to which everybody is beautiful in the sense that everybody can be perceived through a loving gaze. I show that this view is inclusive, aspirational and empowering, and authentically aesthetical. (shrink)

The aim of this paper is to show that Simone de Beauvoir's The Second Sex has been mistakenly interpreted as a theory of gender, because interpreters have failed adequately to understand Beauvoir's aims. Beauvoir is not trying to explain facts, events, or states of affairs, but to reveal, unveil, or uncover (découvrir) meanings. She explicates the meanings of woman, female, and feminine. Instead of a theory, Beauvoir's book presents a phenomenological description of the sexual difference.

Prevention of age-related disorders is increasingly in focus of health policies, and it is hoped that early intervention on processes of deterioration can promote healthier and longer lives. New opportunities to slow down the aging process are emerging with new fields such as personalized nutrition. Data-intensive research has the potential to improve the precision of existing risk factors, e.g., to replace coarse-grained markers such as blood cholesterol with more detailed multivariate biomarkers. In this paper, we follow an attempt to develop (...) a new aging biomarker. The vision among the project consortium, comprising both research and industrial partners, is that the new biomarker will be predictive of a range of age-related conditions, which may be preventable through personalized nutrition. We combine philosophical analysis and ethnographic fieldwork to explore the possibilities and challenges of managing aging through bodily signs that are not straightforwardly linked to symptomatic disease. We document how the improvement of measurement brings about new conceptual challenges of demarcating healthy and unhealthy states. Moreover, we highlight that the reframing of aging as risk has social and ethical implications, as it is generative of normative notions of what constitutes successful aging and good citizenship. (shrink)

This paper brings two fresh perspectives on Lewis’s theory of time travel. First: many key aspects and theoretical desiderata of Lewis’s theory can be captured in a framework that does not commit to eternalism about time. Second: implementing aspects of Lewisian time travel in a non-eternalist framework provides theoretical resources for a better treatment of time travel to the future. While time travel to the past has been extensively analyzed, time travel to the future has been comparatively underexplored. I make (...) progress on this topic. Along the way, I discuss Lewis’s lesser-known time travel oeuvre, especially his volume of correspondence and lectures on the topic collected in Beebee and Fisher (2020) and Janssen-Lauret & MacBride (forthcoming). Lewis’s body of unpublished work on time travel yields fruitful insights into his broader thinking on the subject. (shrink)

In his late reflections on values and forms of life from the 1920s and 1930s, Husserl develops the concept of personal value and argues that these values open two kinds of infinities in our lives. On the one hand personal values disclose infinite emotive depths in human individuals while on the other hand they connect human individuals in continuous and progressive chains of care. In order to get at the core of the concept, I will explicate Husserl’s discussion of personal (...) values of love by distinguishing between five related features. I demonstrate that values of love (1) are rooted in egoic depts and define who we are as persons, (2) differ from objective values in being absolute and non-comparative, (3) ground vocational lives as organizing principles, (4) are endlessly self-disclosing and self-intensifying, and (5) establish transitive relations of care between human beings. On the basis of my five-partite distinction, I argue that Husserl’s concepts of love and value of love reveal the dynamic character of human subjectivity and intersubjectivity. (shrink)

This paper suggests that time travelling scenarios commonly depicted in science fiction introduce problems and dangers for the time traveller. If time travel takes time, then time travellers risk collision with past objects, relocation to distant parts of the universe, and time travel-specific injuries. I propose several models of time travel that avoid the dangers and risks of time travel taking time, and that introduce new questions about the relationship between time travel and spatial location.

The purpose of this article is to describe the development of a model of moral distress in military nursing. The model evolved through an analysis of the moral distress and military nursing literature, and the analysis of interview data obtained from US Army Nurse Corps officers (n = 13). Stories of moral distress (n = 10) given by the interview participants identified the process of the moral distress experience among military nurses and the dimensions of the military nursing moral distress (...) phenomenon. Models of both the process of military nursing moral distress and the phenomenon itself are proposed. Recommendations are made for the use of the military nursing moral distress models in future research studies and in interventions to ameliorate the experience of moral distress in crisis military deployments. (shrink)

The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective.

This paper offers a new philosophical account of vocations as deeply personal but at the same time also communal and generational forms of multimodal intending. It provides a reconstruction and a systematic development of Edmund Husserl’s scattered discussions on vocations. On these grounds, the paper argues that vocational life is a general human possibility and not determined by any set of material values, religious, epistemic or moral. Rather, vocations are distinguished from other complexes of intentional acts and attitudes by certain (...) structural features of their core valuations and volitions. (shrink)

In this chapter, I argue that a certain kind of envy is not only morally permissible, but also, sometimes, more fitting and productive than admiration. Envy and admiration are part of our emotional palette, our toolbox of evolutionary adaptations, and they play complementary roles. I start by introducing my original taxonomy of envy, which allows me to present emulative envy, a species of envy sometimes confused with admiration. After reviewing how the two emotions differ from a psychological perspective, I focus (...) in particular on the distinct and complementary roles they play in the ethical and political domains. (shrink)

In this paper I argue that philosophers of science have an obligation to recognize and engage with the social nature of the sciences they assess if those sciences are morally relevant. Morally-relevant science is science that has the potential to risk harm to humans, non-humans, or the environment. My argument and the approach I develop are informed by an analysis of the philosophy of biology literature on the criticism of evolutionary psychology, the study of the evolution of human psychology and (...) behaviour. From this literature, I tease out two different methods of scientific critique. The first I call the “truth-detectional” approach. Those who take this approach are first and foremost concerned about the truth of EP claims as that truth can be determined by evidence. The second I call the “social-dimensional” approach. Those who take this approach talk about the production and truth of EP claims but within a social framework. On this account, the legitimacy and perceived legitimacy of EP claims are not separate from the institutional and social processes and values that lend to their production. I show that the truth-detectional approach risks harms to society and to the philosophy of science, but that the social-dimensional approach avoids these harms. Philosophers of science, therefore, should take a social-dimensional approach to the assessment of morally-relevant science. (shrink)

The development of nursing ethics as a field of inquiry has largely relied on theories of medical ethics that use autonomy, beneficence, and/or justice as foundational ethical principles. Such theories espouse a masculine approach to moral decision-making and ethical analysis. This paper challenges the presumption of medical ethics and its associated system of moral justification as an appropriate model for nursing ethics. It argues that the value foundations of nursing ethics are located within the existential phenomenon of human caring within (...) the nurse/patient relationship instead of in models of patient good or rights-based notions of autonomy as articulated in prominent theories of medical ethics. Models of caring are analyzed and a moral-point-of-view (MPV) theory with caring as a fundamental value is proposed for the development of a theory of nursing ethics. This type of theory is supportive to feminist medical ethics because it focuses on the subscription to, and not merely the acceptance of, a particular view of morality. (shrink)

Many biologists appeal to the so-called Krogh principle when justifying their choice of experimental organisms. The principle states that “for a large number of problems there will be some animal of choice, or a few such animals, on which it can be most conveniently studied”. Despite its popularity, the principle is often critiqued for implying unwarranted generalizations from optimal models. We argue that the Krogh principle should be interpreted in relation to the historical and scientific contexts in which it has (...) been developed and used. We interpret the Krogh Principle as a heuristic, i.e., as a recommendation to approach biological problems through organisms where a specific trait or physiological mechanism is expected to be most distinctively displayed or most experimentally accessible. We designate these organisms “Krogh organisms.” We clarify the differences between uses of model organisms and non-standard Krogh organisms. Among these is the use of Krogh organisms as “negative models” in biomedical research, where organisms are chosen for their dissimilarity to human physiology. Importantly, the representational scope of Krogh organisms and the generalizability of their characteristics are not fixed or assumed but explored through experimental studies. Research on Krogh organisms is steeped in the comparative method characteristic of zoology and comparative physiology, in which studies of biological variation produce insights into general physiological constraints. Accordingly, we conclude that the Krogh principle exemplifies the advantages of studying biological variation as a strategy to produce generalizable insights. (shrink)

Artificial intelligent (AI) systems that perform image classification tasks are being used to great success in many application contexts. However, many of these systems are opaque, even to experts. This lack of understanding can be problematic for ethical, legal, or practical reasons. The research field Explainable AI (XAI) has therefore developed several approaches to explain image classifiers. The hope is to bring about understanding, e.g., regarding why certain images are classified as belonging to a particular target class. Most of these (...) approaches use visual explanations. Drawing on Elgin’s work (True enough. MIT Press, Cambridge, 2017), I argue that analyzing what those explanations exemplify can help to assess their suitability for producing understanding. More specifically, I suggest to distinguish between two forms of examples according to their suitability for producing understanding. I call these forms samples and exemplars, respectively. Samples are prone to misinterpretation and thus carry the risk of leading to misunderstanding. Exemplars, by contrast, are intentionally designed or chosen to meet contextual requirements and to mitigate the risk of misinterpretation. They are thus preferable for bringing about understanding. By reviewing several XAI approaches directed at image classifiers, I show that most of them explain with samples. If my analysis is correct, it will be beneficial if such explainability methods use explanations that qualify as exemplars. (shrink)

Temporal binding refers to a phenomenon whereby the time interval between a cause and its effect is perceived as shorter than the same interval separating two unrelated events. We examined the developmental profile of this phenomenon by comparing the performance of groups of children (aged 6-7-, 7-8-, and 9-10- years) and adults on a novel interval estimation task. In Experiment 1, participants made judgments about the time interval between i) their button press and a rocket launch, and ii) a non-causal (...) predictive signal and rocket launch. In Experiment 2, an additional causal condition was included in which participants made judgments about the interval between an experimenter’s button press and the launch of a rocket. Temporal binding was demonstrated consistently and did not change in magnitude with age: estimates of delay were shorter in causal contexts for both adults and children. Additionally, the magnitude of the binding effect was greater when participants themselves were the cause of an outcome compared to when they were mere spectators. This suggests that although causality underlies the binding effect, intentional action may modulate its magnitude. Again, this was true of both adults and children. Taken together, these results are the first to suggest that the binding effect is present and developmentally constant from childhood into adulthood. (shrink)

By presenting a case study based on the argumentative analysis of news in the press, this article introduces and discusses strategic manoeuvring with contextual frames. Drawing on the linguistic notion of frame, I introduce the concept of contextual frame to refer to the news context, that is, the background against which a certain event is presented as a piece of news. I argue that newspapers and journalists make use of contextual frames in the apparently neutral genre of news reporting to (...) propose specific interpretations of the facts at issue, which become the basis for explicit comments and editorials. To show how this works, I investigate in detail a case of newspaper coverage of a complex episode using the pragma-dialectical notion of strategic manoeuvring and the Argumentum Model of Topics to analyse argument schemes. I show that, in the use of contextual frames, there is a prominent relation between presentational devices and topical potential; contextual frames provide the implicit material premises which are at the basis of argumentations through which newspapers interpret and comment on the news. (shrink)

Patient-derived xenografts are currently promoted as new translational models in precision oncology. PDXs are immunodeficient mice with human tumors that are used as surrogate models to represent specific types of cancer. By accounting for the genetic heterogeneity of cancer tumors, PDXs are hoped to provide more clinically relevant results in preclinical research. Further, in the function of so-called “mouse avatars”, PDXs are hoped to allow for patient-specific drug testing in real-time. This paper examines the circulation of knowledge and bodily material (...) across the species boundary of human and personalized mouse model, historically as well as in contemporary practices. PDXs raise interesting questions about the relation between animal model and human patient, and about the capacity of hybrid or interspecies models to close existing translational gaps. We highlight that the translational potential of PDXs not only depends on representational matching of model and target, but also on temporal alignment between model development and practical uses. Aside from the importance of ensuring temporal stability of human tumors in a murine body, the mouse avatar concept rests on the possibility of aligning the temporal horizons of the clinic and the lab. We examine strategies to address temporal challenges, including cryopreservation and biobanking, as well as attempts to speed up translation through modification and use of faster developing organisms. We discuss how featured model virtues change with precision oncology, and contend that temporality is a model feature that deserves more philosophical attention. (shrink)

A sequent calculus is given in which the management of weakening and contraction is organized as in natural deduction. The latter has no explicit weakening or contraction, but vacuous and multiple discharges in rules that discharge assumptions. A comparison to natural deduction is given through translation of derivations between the two systems. It is proved that if a cut formula is never principal in a derivation leading to the right premiss of cut, it is a subformula of the conclusion. Therefore (...) it is sufficient to eliminate those cuts that correspond to detour and permutation conversions in natural deduction. (shrink)

Philosophers who have written on modesty have largely agreed that it is a virtue, and that it therefore has an important psychological component. Mere modest behavior, it is often argued, is actually false modesty if it is generated by the wrong kind of mental state. The philosophical debate about modesty has largely focused on the question of which kind of mental state—cognitive, motivational, or evaluative—best captures the virtue of modesty. We therefore conducted a series of experiments to see which philosophical (...) account matches the folk concept of modesty. Surprisingly, we found that the folk concept is primarily behavioral. This leads us to argue that modesty may not be a virtue, but that if it is none of the extant philosophical accounts have properly explained why. (shrink)

I argue that fitting envy plays a special role in safeguarding our happiness and flourishing. After presenting my theory of envy and its fittingness conditions, I contrast Kant’s view that envy is always unfitting with D’Arms and Jacobson’s defense of fitting envy as an evolutionarily-shaped response to a deep and wide human concern, that is, relative positioning. However, D’Arms and Jacobson don’t go far enough. First, I expand on their analysis of positional goodness, distinguishing between an epistemic claim, according to (...) which we use implicit or explicit comparison to know what position we occupy in a continuum of goodness, and thus to form judgments of goodness, and a metaphysical one, according to which much human goodness depends on implicit or explicit rankings and positionality. Second, I argue that fitting envy is not only intrinsically valuable qua fitting response to authentic goodness, but can be epistemically, morally and prudentially valuable. (shrink)

This article explores the usefulness of interdisciplinarity as method of enquiry by proposing an investigation of the concept of information in the light of semiotics. This is because, as Kull, Deacon, Emmeche, Hoffmeyer and Stjernfelt state, information is an implicitly semiotic term (Biological Theory 4(2):167–173, 2009: 169), but the logical relation between semiosis and information has not been sufficiently clarified yet. Across the history of cybernetics, the concept of information undergoes an uneven development; that is, information is an ‘objective’ entity (...) in first order cybernetics, and becomes a ‘subjective’ entity in second order cybernetics. This contradiction relegates the status of information to that of a ‘true’ or ‘false’ formal logic problem. The present study proposes that a solution to this contradiction can be found in Deely’s reconfiguration of Peirce’s ‘object’ (as found in his triadic model of semiosis) into ‘thing’ and ‘object’ (Deely 1981). This ontology allows one to argue that information is neither ‘true’ nor ‘false’, and to suggest that, when considered in light of its workability, information can be both true and false, and as such it constitutes an organism’s purely objective reality (Deely 2009b). It is stated that in the process of building such a reality, information is ‘motivated’ by environmental, physiological, emotional (including past feelings and expectations) constraints which are, in turn, framed by observership. Information is therefore found in the irreducible cybersemiotic process that links at once all these conditions and that is simultaneously constrained by them. The integration of cybernetics’ and semiotics’ understanding of information shows that history is the analytical principle that grants scientific rigour to interdisciplinary investigations. As such, in any attempt to clarify its epistemological stance (e.g. the semiotic aspect of information), it is argued that biosemiotics does not need only to acknowledge semiotics (as it does), but also cybernetics in its interdisciplinary heritage. (shrink)

The founding of the Carnegie Institute’s Department of Embryology in 1913, alongside its systematization of embryo staging, contributed to the mechanization of developmental stages of embryo growth in the early 20th century. For a brief period in the middle of the century, attention to the detailed interrelation between embryo development and time made pre-existing ideas about pregnancy ends less determinative of ideas about that developmental course. However, the turn to the genetic scale led to the disappearance of this attention, replaced (...) by a sense of biological life as seamlessly scripted. This study examines the history of what I refer to as temporal attention: attention to the live, unfolding potentialities within vital matter. The reintroduction of temporal attention to discussions of development allows us to more fully consider non-human vitality and the experiences of beings that house or otherwise intimately intersect with that vital tissue, regardless of outcomes. (shrink)

This comment addresses opportunities for understanding the social functions of emotion by taking a developmental perspective. I agree that understanding emotions and their development will meaningf...

Background Families whose child has unexplained intellectual or developmental differences often hope that a genetic diagnosis will lower barriers to community-based therapeutic and support services. However, there is little known about efforts to mobilize genetic information outside the clinic or how socioeconomic disadvantage shapes and constrains outcomes.Methods We conducted an ethnographic study with predominantly socioeconomically disadvantaged families enrolled in a multi-year genomics research study, including clinic observations and in-depth interviews in English and Spanish at multiple time points. Coding and thematic (...) development were used to collaboratively interpret fieldnotes and transcripts.Results Thirty-two families participated. Themes included familial expectations that a genetic diagnosis could be translated into information, understanding, and assistance to improve the quality of a child’s day-to-day life. After sequencing, however, genetic information was not readily converted into improved access to services beyond the clinic, with families often struggling to use a genetic diagnosis to advocate for their child.Conclusion Families’ ability to use a genetic diagnosis as an effective advocacy tool beyond the clinic was limited by the knowledge and resources available to them, and by the eligibility criteria used by therapeutic service providers’ – which focused on clinical diagnosis and functional criteria more than etiologic information. All families undertaking genomic testing, particularly those who are disadvantaged, need additional support to understand the limits and potential benefits of genetic information beyond the clinic. (shrink)

Novel neurotechnologies, like deep brain stimulation and brain‐computer interface, offer great hope for treating, curing, and preventing disease, but raise important questions about effects these devices may have on human identity, authenticity, and autonomy. After briefly assessing recent narrative work in these areas, we show that agency is a phenomenon key to all three goods and highlight the ways in which neural devices can help to draw attention to the relational nature of our agency. Drawing on insights from disability theory, (...) we argue that neural devices provide a kind of agential assistance, similar to that provided by caregivers, family, and others. As such, users and devices participate in a kind of co‐agency. We conclude by suggesting the need for developing relational agency‐competencies—skills for reflecting on the influence of devices on agency, for adapting to novel circumstances ushered in by devices, and for incorporating the feedback of loved ones and others about device effects on agency. (shrink)

The chapter studies the ethical dimensions of Beauvoir’s existentialism and Irigaray’s ontology of difference. It argues that Irigaray builds on one central but largely neglected result of Beauvoir’s moral philosophical argumentation: the claim that fundamentally sexual subordination constitutes an ethical problem that cannot be adequately solved merely through social reforms, political interventions, or theoretical reflections. By comparing Beauvoir’s concept of erotic generosity to Irigaray’s discussion of wonder and love, the chapter demonstrates that both philosophers conceive of male privilege as an (...) ethical issue that must be worked out between individual women and men in their concrete encounters. The task is to reform and cultivate not just human behaviors, actions, beliefs and cognitions, but also one’s own emotions and desires. (shrink)

Explores the complex nature of truth in Wittgenstein’s philosophy.

Bioethics has already had a rich interaction with the relatively new field of neurotechnology. Scholars have wondered whether neurotechnological interventions, such as deep brain stimulation, are threats to personal identity, lead to alienation or create dilemmas between authenticity and autonomy, impact autonomy, detract from agency, or lead to self-estrangement. Many of these ethical investigations are concerned not with the targeted health benefits of neurotechnology but with whether and how they fit into users' lives in more personal and profound ways.In some (...) ways, this focus on general bioethical issues... (shrink)

A constructive definition of the continuum based on formal topology is given and its basic properties studied. A natural notion of Cauchy sequence is introduced and Cauchy completeness is proved. Other results include elementary proofs of the Baire and Cantor theorems. From a classical standpoint, formal reals are seen to be equivalent to the usual reals. Lastly, the relation of real numbers as a formal space to other approaches to constructive real numbers is determined.