This is the second paper of an essay in two parts. The first paper (Part I) is a critical discussion of Mark Risjord's conception of nursing knowledge where I argued against the conception of nursing knowledge as a kind of nursing science. The aim of the present paper (Part II) is to explicate and substantiate the thesis of nursing as a kind of concrete philosophy. My strategy is to elaborate upon certain themes from Wittgenstein's Tractatus in order to canvass a (...) general scheme of philosophy based on a distinction between reality and the world. This distinction will be employed in the appropriation of certain significant features of nursing and nursing knowledge. By elaborating on the contrast between the abstract and the concrete, I will suggest that nursing may be seen as a kind of concrete philosophy, being primarily concerned with reality (and secondarily with the world). This thesis, I will argue, implies that philosophy is the kind of theory that is essential to nursing (which is not so much a theory than a certain kind of activity). (shrink)

We formulate an abstract version of the finite injury method in the form of the Baire category theorem. The theorem has the following corollaries: The Friedberg-Muchnik pair of recursively enumerable degrees, the Sacks splitting theorem, the existence of a minimal degree below 0′ and the Shoenfield jump theorem.

A Hausdorff space is called effectively Hausdorff if there exists a function F—called a Hausdorff operator—such that, for every with,, where U and V are disjoint open neighborhoods of x and y, respectively. Among other results, we establish the following in, i.e., in Zermelo–Fraenkel set theory without the Axiom of Choice (): is equivalent to “For every set X, the Cantor cube is effectively Hausdorff”. This enhances the result of Howard, Keremedis, Rubin and Rubin [13] that is equivalent to “Hausdorff (...) spaces are effectively Hausdorff” in. The Boolean Prime Ideal Theorem and the statement “For every infinite set X, the Stone space of the Boolean algebra is effectively Hausdorff” are mutually independent. In particular, the latter statement is not provable in. The Axiom of Choice for non‐empty subsets of () is equivalent to each of “Separable Hausdorff spaces are effectively Hausdorff” and “The Cantor cube is effectively Hausdorff”. The Principle of Dependent Choices in conjunction with the Axiom of Choice for continuum sized families of non‐empty subsets of does not imply the axiom of choice for partitions of. The latter independence result fills the gap in information in Howard and Rubin's book “Consequences of the Axiom of Choice”. The axiom of countable choice for non‐empty subsets of is equivalent to each of “Denumerable Hausdorff spaces are effectively Hausdorff”, “Denumerable T3 spaces are completely normal” and “Denumerable Tychonoff spaces are Urysohn”. (shrink)

Previous studies have offered indications that the way pre-adolescents structure their perceptions of their teacher’s interaction in terms of Agency and Communion differs from adolescents. The purpose of this study was to delineate previous findings by thoroughly examining the structure of pre-adolescents’ perceptions of their teacher’s interpersonal behaviour, and by investigating the extent to which this structure relates to pre-adolescents’ learning outcomes. A mixed methods research design was implemented including a qualitative instrument adaptation procedure followed by a quantitative large-scale administration. (...) Participants for the latter were a random sample of 504 pre-adolescents and 36 teachers. Results showed that participants placed significantly more emphasis on their teachers’ Communion behavioural dimension and this emphasis was illustrated on the association of perceived teacher interaction and students’ learning outcomes. Implications for theory, research and practice are discussed. (shrink)

We show that some well known theorems in topology may not be true without the axiom of choice.

The ethics of artificial intelligence is a widely discussed topic. There are numerous initiatives that aim to develop the principles and guidance to ensure that the development, deployment and use of AI are ethically acceptable. What is generally unclear is how organisations that make use of AI understand and address these ethical issues in practice. While there is an abundance of conceptual work on AI ethics, empirical insights are rare and often anecdotal. This paper fills the gap in our current (...) understanding of how organisations deal with AI ethics by presenting empirical findings collected using a set of ten case studies and providing an account of the cross-case analysis. The paper reviews the discussion of ethical issues of AI as well as mitigation strategies that have been proposed in the literature. Using this background, the cross-case analysis categorises the organisational responses that were observed in practice. The discussion shows that organisations are highly aware of the AI ethics debate and keen to engage with ethical issues proactively. However, they make use of only a relatively small subsection of the mitigation strategies proposed in the literature. These insights are of importance to organisations deploying or using AI, to the academic AI ethics debate, but maybe most valuable to policymakers involved in the current debate about suitable policy developments to address the ethical issues raised by AI. (shrink)

The perturbative treatment of realistic quantum field theories, such as quantum electrodynamics, requires the use of mathematical idealizations in the approximation series for scattering amplitudes. Such mathematical idealizations are necessary to derive empirically relevant models from the theory. Mathematical idealizations can be either controlled or uncontrolled, depending on whether current scientific knowledge can explain whether the effects of the idealization are negligible or not. Drawing upon negative mathematical results in asymptotic analysis (failure of Borel summability) and renormalization group theory (failure (...) of asymptotic safety), we argue that the mathematical idealizations applied in perturbative quantum electrodynamics should be understood as uncontrolled. This, in turn, leads to the problematic conclusion that such theories do not have theoretical models in the natural understanding of this term. The existence of unquestionable empirically successful theories without theoretical models has significant implications both for our understanding of the theory-model relationship in physics and the concept of empirical adequacy. (shrink)

Many decades ago Patrick Suppes argued rather convincingly that theoretical hypotheses are not confronted with the direct, raw results of an experiment, rather, they are typically compared with models of data. What exactly is a data model however? And how do the interactions of particles at the subatomic scale give rise to the huge volumes of data that are then moulded into a polished data model? The aim of this paper is to answer these questions by presenting a detailed case (...) study of the construction of data models at the LHCb for testing Lepton Flavour Universality in rare decays of B-mesons. The close examination of the scientific practice at the LHCb leads to the following four main conclusions: raw data in their pure form are practically useless for the comparison of experimental results with theory, and processed data are in some cases epistemically more reliable, real and simulated data are involved in the co-production of the final data model and cannot be easily distinguished, theory-ladenness emerges at three different levels depending on the scope and the purpose for which background theory guides the overall experimental process and the overall process of acquiring and analysing data in high energy physics is too complicated to be fully captured by a generic methodological description of the experimental practice. (shrink)

Background Informed consent is a requirement for all research. It is not, however, clear how much information is sufficient to make an informed decision about participation in research. Information on an online questionnaire about childhood development was provided through an unfolding electronic participant sheet in three levels of information. Methods 552 participants, who completed the web-based survey, accessed and spent time reading the participant information sheet (PIS) between July 2008 and November 2009. The information behaviour of the participants was investigated. (...) The first level contained less information than might be found on a standard PIS, the second level corresponded to a standard PIS, and the third contained more information than on a standard PIS. The actual time spent on reading the information provided in three incremental levels and the participants' evaluation of the information were calculated. Results 77% of the participants chose to access the first level of information, whereas 12% accessed the first two levels, 6% accessed all three levels of information and 23% participated without accessing information. The most accessed levels of information were those that corresponded to the average reading times. Conclusion The brief information provided in the first level was sufficient for participants to make informed decisions, while a sizeable minority of the participants chose not to access any information at all. This study adds to the debate about how much information is required to make a decision about participation in research and the results may help inform the future development of information sheets by providing data on participants' actual needs when deciding about questionnaire surveys. (shrink)

Current cosmological observations place little constraints on the nature of dark matter, allowing the development of a large number of models and various methods for probing their properties, which seem to provide ideal grounds for the employment of robustness arguments. In this article, the extent to which such arguments can be used to overcome various methodological and theoretical challenges is examined. The conclusion is that while robustness arguments have a limited scope in the context of dark matter research, they can (...) still be used for increasing the scientists’ confidence about the properties of specific models. (shrink)

The logic of a physical system consists of the elementary observables of the system. We show that for chaotic systems the logic is not any more the classical Boolean lattice but a kind of fuzzy logic which we characterize for a class of chaotic maps. Among other interesting properties the fuzzy logic of chaos does not allow for infinite combinations of propositions. This fact reflects the instability of dynamics and it is shared also by quantum systems with diagonal singularity. We (...) also generalize the fuzzy implication to a probabilistic implication following the hint of von Neumann. In this way we can evaluate the probability of the validity of the logical inference. (shrink)

The work of the Brussels-Austin groups on irreversibility over the last years has shown that Quantum Large Poincaré systems with diagonal singularity lead to an extension of the conventional formulation of dynamics at the level of mixtures which is manifestly time asymmetric. States with diagonal singularity acquire meaning as linear fractionals over the involutive Banach algebra of operators with diagonal singularity. We show in this paper that the logic of quantum systems with diagonal singularity is not the conventional logic of (...) Hilbert space, because only finite combinations of prepositions are allowed. (shrink)

I undertake a metaphysical investigation of Saul Kripke's modern classic, Naming and Necessity . The general problem of my study may be expressed as follows: What is the metaphysical justification of the validity and existence of the pertinent classes of truths, the necessary a posteriori and the contingent a priori, according to the Kripke Paradigm? My approach is meant to disclose the logical and ontological principles underlying Kripke's arguments for the necessary a posteriori and the contingent a priori respectively. The (...) results of my study are to a certain extent negative: They attempt to show that the classes of the necessary a posteriori and the contingent a priori statements cannot possibly be valid. If the general argument of this thesis is sound, then, on this ground, the realist conception of metaphysical essentialism is rejected. The positive thesis of this study is the articulation of certain ways to frame the necessary a posteriori and the contingent a priori which avoid the problems of realistic essentialism and which suggest a certain transcendental reading of modality. According to the Kripke Paradigm, any de dicto modal status derives ultimately from the de re modality inherent in the object designated, as the object is characterised by contingent and necessary properties on the ontological level. Thus, the Kripke Paradigm is primarily a thesis in de re realist essentialism. The final verdict in this study is that the Kripke Paradigm cannot sustain the realistic conception of de re metaphysical essentialism. If we should adopt a transcendental reading of modality, then certain portions of the Kripke Paradigm are valid. I do not delineate or possess the details of a comprehensive doctrine of transcendental metaphysic. Nevertheless, the observations I make should suffice to bring about the rough orientation of how I conceive the notion of transcendental modality. (shrink)

It is shown that AC, the axiom of choice for families of non-empty subsets of the real line ℝ, does not imply the statement PW, the powerset of ℝ can be well ordered. It is also shown that the statement “the set of all denumerable subsets of ℝ has size 2math image” is strictly weaker than AC and each of the statements “if every member of an infinite set of cardinality 2math image has power 2math image, then the union has (...) power 2math image” and “ℵ ≠ ℵω” is Hartogs' aleph, the least ℵ not ≤ 2math image), is strictly weaker than the full axiom of choice AC. (shrink)

From the early 1930s to the early 1960s many scholars, whether liberalminded or socialist ideologues, Marxist or scientific positivists, classical scholars or political theorists and historians, have shown a widespread consensus in discrediting and assailing the man and political philosopher Plato. Such an extensive assault led the ‘Platonic Legend’ to an unprecedented crisis. Philosophically, it was a reaction to the undisguised Platonolatry coming from Oxford and the school of the British Idealists. Ideologically, the appropriation of Plato by Nazi apologists fostered (...) further this vehement indictment. But a lot of other causes worked to the same effect. The general anguish and humanistic anxiety on the eve ofWorldWar II and the postwar traumas led scholars to reconsider the meaning of history and historicism, the psychology of the masses and the ethical responsibility of the citizen, the role of propaganda and state education. Such complementary elements converged in sustained anti-Platonic polemics, which in turn provoked a vigorous defence. Here an attempt is made to offer a preliminary survey of this complex debate and to provide a general intellectual framework in terms of which that controversy can be further explored. (shrink)

The purpose of the present study was to test the hypothesis that goal orientation is associated with divergent forms of emotional reactivity under frustration. Goal orientations were assessed using bifurcations of performance goals described earlier. Physiological stress levels were measured via a blood volume pulse analysis after individuals were subjected to a computerized Stroop task using a malfunctioning mouse to induce enhanced frustration. The results indicated that performance-avoidance goals were associated with the highest levels of emotional reactivity, with normative outcome (...) goals being significantly more detrimental than ability goals. We concluded that the motivation to avoid failure or to outperform others is the most detrimental determinant of stress and needs to be avoided by all means. Instead, it is suggested that educators emphasize performance using personal best outcomes or by valuing engagement, deep processing and task completion. (shrink)

Artificial intelligence ethics requires a united approach from policymakers, AI companies, and individuals, in the development, deployment, and use of these technologies. However, sometimes discussions can become fragmented because of the different levels of governance or because of different values, stakeholders, and actors involved. Recently, these conflicts became very visible, with such examples as the dismissal of AI ethics researcher Dr. Timnit Gebru from Google and the resignation of whistle-blower Frances Haugen from Facebook. Underpinning each debacle was a conflict between (...) the organisation’s economic and business interests and the morals of their employees. This paper will examine tensions between the ethics of AI organisations and the values of their employees, by providing an exploration of the AI ethics literature in this area, and a qualitative analysis of three workshops with AI developers and practitioners. Common ethical and social tensions will be discussed, along with proposals on how to avoid or reduce these conflicts in practice. Altogether, we suggest the following steps to help reduce ethical issues within AI organisations: improved and diverse ethics education and training within businesses; internal and external ethics auditing; the establishment of AI ethics ombudsmen, AI ethics review committees and an AI ethics watchdog; as well as access to trustworthy AI ethics whistle-blower organisations. (shrink)

Aim The aim is to understand current research into the impact of undergraduate nursing education on the development of professional values. Background Values are evident in the professional standards for nurses and the guidelines and healthcare policies of many countries. These professional values guide decisions and behaviour and are recognised as an essential component in the professions ability to provide safe and professional care. This literature review presents the current research on the impact of education on professional values in undergraduate (...) nurse education. Design An integrative review of the findings was conducted to provide insight into the current research on the professional value development in undergraduate nurses. Data sources CINAHL, PubMed and Scopus. Review methods A literature search was undertaken within defined date parameters 2010–2021 using a systematic approach. The Preferred Reporting Items for Systematic Reviews and Meta-analysis guide PRISMA was used to guide and illustrate the process. Papers were assessed for quality using the Mixed Methods Appraisal Tool. Results Two distinct areas of inquiry were identified. (a) Changes in professional values as an outcome of undergraduate nursing education or (b) changes in professional values as an outcome of specifically designed educational content. These areas were further explored to better understand the influences of undergraduate education on students’ professional values. Conclusion There is a lack of evidence in the literature to support the premise that professional values develop in line with academic year progression; however, there is strong evidence to support the inclusion of explicit learning in undergraduate education that engages students in education specifically designed to explore and develop professional values. (shrink)

We establish the following results: 1. In ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC), for every set I and for every ordinal number α ≥ ω, the following statements are equivalent: (a) The Tychonoff product of| α| many non-empty finite discrete subsets of I is compact. (b) The union of| α| many non-empty finite subsets of I is well orderable. 2. The statement: For every infinite set I, every closed subset of the Tychonoff product [0, 1] (...) I which consists of functions with finite support is compact, is not provable in ZF set theory. 3. The statement: For every set I, the principle of dependent choices relativised to I implies the Tychonoff product of countably many non-empty finite discrete subsets of I is compact, is not provable in ZF⁰ (i.e., ZF minus the Axiom of Regularity). 4. The statement: For every set I, every ℵ₀-sized family of non-empty finite subsets of I has a choice function implies the Tychonoff product of ℵ₀ many non-empty finite discrete subsets of I is compact, is not provable in ZF⁰. (shrink)

We show that the both assertions “in every vector space B over a finite element field every subspace V ⊆ B has a complementary subspace S” and “for every family [MATHEMATICAL SCRIPT CAPITAL A] of disjoint odd sized sets there exists a subfamily ℱ={Fj:j ϵω} with a choice function” together imply the axiom of choice AC. We also show that AC is equivalent to the statement “in every vector space over ℚ every generating set includes a basis”.

We show that the countable axiom of choice CAC strictly implies the statements “Lindelöf metric spaces are second countable” “Lindelöf metric spaces are separable”. We also show that CAC is equivalent to the statement: “If is a Lindelöf topological space with respect to the base ℬ, then is Lindelöf”.

We show that the statement “separable, countably compact, regular spaces are Baire” is deducible from a strictly weaker form than AC, namely, CAC . We also find some characterizations of the axiom of dependent choices.

Let {: i ∈I } be a family of compact spaces and let X be their Tychonoff product. [MATHEMATICAL SCRIPT CAPITAL C] denotes the family of all basic non-trivial closed subsets of X and [MATHEMATICAL SCRIPT CAPITAL C]R denotes the family of all closed subsets H = V × Πmath imageXi of X, where V is a non-trivial closed subset of Πmath imageXi and QH is a finite non-empty subset of I. We show: Every filterbase ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL (...) C]R extends to a [MATHEMATICAL SCRIPT CAPITAL C]R-ultrafilter ℱ if and only if every family H ⊂ [MATHEMATICAL SCRIPT CAPITAL C] with the finite intersection property extends to a maximal [MATHEMATICAL SCRIPT CAPITAL C] family F with the fip. The proposition “if every filterbase ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL C]R extends to a [MATHEMATICAL SCRIPT CAPITAL C]R-ultrafilter ℱ, then X is compact” is not provable in ZF. The statement “for every family {: i ∈ I } of compact spaces, every filterbase ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL C]R, Y = Πi ∈IYi, extends to a [MATHEMATICAL SCRIPT CAPITAL C]R-ultrafilter ℱ” is equivalent to Tychonoff's compactness theorem. The statement “for every family {: i ∈ ω } of compact spaces, every countable filterbase ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL C]R, X = Πi ∈ωXi, extends to a [MATHEMATICAL SCRIPT CAPITAL C]R-ultrafilter ℱ” is equivalent to Tychonoff's compactness theorem restricted to countable families. The countable Axiom of Choice is equivalent to the proposition “for every family {: i ∈ ω } of compact topological spaces, every countable family ℋ ⊂ [MATHEMATICAL SCRIPT CAPITAL C] with the fip extends to a maximal [MATHEMATICAL SCRIPT CAPITAL C] family ℱ with the fip”. (shrink)

We show that none of the following statements is provable in Zermelo-Fraenkel set theory (ZF) answering the corresponding open questions from Brunner in ``The axiom of choice in topology'':(i) For every T2 topological space (X, T) if X is well-ordered, then X has a well-ordered base,(ii) For every T2 topological space (X, T), if X is well-ordered, then there exists a function f : X × W T such that W is a well-ordered set and f ({x} × W) is (...) a neighborhood base at x for each x X,(iii) For every T2 topological space (X, T), if X has a well-ordered dense subset, then there exists a function f : X × W T such that W is a well-ordered set and {x} = f ({x} × W) for each x X. (shrink)

What are scientific models? Philosophers of science have been trying to answer this question during the last three decades by putting forward a number of different proposals. Some say that models are best understood as abstract Platonic objects or fictional entities akin to Sherlock Holmes, while others focus on their mathematical nature and see them as set theoretical structures. Although each account has its own strengths in offering various insights on the nature of models, several objections have been raised against (...) these views which still remain unanswered, making the debate on the ontology of models seem unresolvable. The primary aim of this paper is to show that a large part of these difficulties stems from an inappropriate reading of the main question on the ontology of models as a purely metaphysical question. Building on Carnap, it is argued that the question of the ontology of scientific models is either an internal theoretical question within an already accepted linguistic framework or an external practical question regarding the choice of the most appropriate form of language in order to describe and explain the practice of scientific modelling. The main implication of this view is that the question of the ontology of models becomes a means of probing other related questions regarding the overall practice of scientific modelling, such as questions on the capacity of models to provide knowledge and the relation of models with background theories. (shrink)

It is shown that in ZF Martin's -axiom together with the axiom of countable choice for finite sets imply that arbitrary powers 2X of a 2-point discrete space are Baire; and that the latter property implies the following: (a) the axiom of countable choice for finite sets, (b) power sets of infinite sets are Dedekind-infinite, (c) there are no amorphous sets, and (d) weak forms of the Kinna-Wagner principle.

Constantin Caratheodory offered the first systematic and contradiction free formulation of thermodynamics on the basis of his mathematical work on Pfaff forms. Moreover, his work on measure theory provided the basis for later improved formulations of thermodynamics and physics of continua where extensive variables are measures and intensive variables are densities. Caratheodory was the first to see that measure theory and not topology is the natural tool to understand the difficulties (ergodicity, approach to equilibrium, irreversibility) in the Foundations of Statistical (...) Physics. He gave a measure-theoretic proof of Poincaré's recurrence theorem in 1919. This work paved the way for Birkhoff to identify later ergodicity as metric transitivity and for Koopman and von Neumann to introduce spectral analysis of dynamical systems in Hilbert spaces. Mixing provided an explanation of the approach to equilibrium but not of irreversibility. The recent extension of spectral theory of dynamical systems to locally convex spaces, achieved by the Brussels–Austin groups, gives new nontrivial time asymmetric spectral decompositions for unstable and/or non-integrable systems. In this way irreversibility is resolved in a natural way. (shrink)

The riddle of the Cleitophon is a creature of nineteenth-century German scholarship which premised that Plato had developed a profound philosophical system. Thus, having no intrinsic purpose to serve in the context of the development of Plato's philosophy, Cleitophon was disallowed as spurious. Documenting the reception of this minor dialogue provides insights into the pluralism and the perplexities of modern Platonic exegesis. The more recent idea of a genre of literary fiction helps to restore cleitophon to its place in the (...) Platonic corpus. S.R. Slings's edition of this dialogue, with introduction, translation and commentary reconsiders both Plato's dialogical engagements and intellectual commitments, utilizes a two-dimensional approach to the text that avoids exaggerated conjectures, and effectively defends the authenticity of Cleitophon. (shrink)

We study within the framework of Zermelo-Fraenkel set theory ZF the role that the axiom of choice plays in the theory of Lindelöf metric spaces. We show that in ZF the weak choice principles: Every Lindelöf metric space is separable and Every Lindelöf metric space is second countable are equivalent. We also prove that a Lindelöf metric space is hereditarily separable iff it is hereditarily Lindelöf iff it hold as well the axiom of choice restricted to countable sets and to (...) topologies of Lindelöf metric spaces as the countable union theorem restricted to Lindelöf metric spaces. (shrink)

We study the role that the axiom of choice plays in Tychonoff's product theorem restricted to countable families of compact, as well as, Lindelöf metric spaces, and in disjoint topological unions of countably many such spaces.

PREFACE Strange or inappropriate as it may appear, we propose to start this little book by stating as flatly and unrhetorically as possible a fundamental ...

Nearly 20 years after the Shonubi case and an extended discussion in the Anglophone world on the admissibility and probative force of statistical evidence, the labour courts of Germany seem not to have learned a simple lesson: aleatory probabilities are not informative for the individual in question. In this paper I argue that innumeracy (that is the lack of ability to understand and apply simple numerical concepts) is underestimated – if not ignored – both within the German jurisprudence and legal (...) theory. In this paper the pseudo-scientific methods of analyzing the evidence in the recent GEMA case by the labor courts of Berlin-Brandenburg and the Federal Labor Court are examined and it is shown that the persistence on applying reference class evidence to an individual-case ends up being not only theoretically unacceptable but also socially harmful. (shrink)

The purpose of the present study was to test the measurement invariance of the baby pediatric symptom checklist across gender and age as a means to provide for valid comparisons in point estimates across groups. A secondary goal involved confirming the earlier identified factor structure and re-examining the presence of differentially item functioning in the BPSC across grouping variables. Participants were 601 children aged below 1 year and 1 year to 12 months. Data were collected as part of the National (...) Health Interview Survey in 2020. Results related to gender indicated satisfying all five levels of measurement and structural invariance. When testing measurement invariance across age groups, a few modifications were necessary. Specifically, partial metric invariance was satisfied after freeing slope estimates of items 1 and 2, partial scalar after freeing intercept terms of items 6 and 10, and partial residual invariance through freeing error terms of items 2 and 12. These non-invariant estimates, however, provide support for partial invariance and do not invalidate the comparison of latent means. The BPSC can be used for the valid assessment of social–emotional skills in infants up to the age of 18 months. (shrink)

An overview is provided of how the concept of the thought experiment has developed and changed for the natural sciences in the course of the 20th century. First, we discuss the existing definitions of the term 'thought experiment' and the origin of the thought experimentation method, identifying it in Greek Presocratics epoch. Second, only in the end of the 19th century showed up the first systematic enquiry on thought experiments by Ernst Mach's work. After the Mach's work, a negative attitude (...) towards thought experiments came in the beginning of the 20th century, which went on until the Thomas Kuhn's and Karl Popper's work on thought experiments. Only from the mid-1980s did thought experiments begin to be considered relevant to scientific enterprise. Finally, we show the existing empirical and 'functional' theories which have developed about the nature and purpose of thought experiments. (shrink)

In the realm of metric spaces the role of choice principles is investigated.