This paper investigates some delicate tradeoffs between the generality of an algorithmic learning device and the quality of the programs it learns successfully. There are results to the effect that, thanks to small increases in generality of a learning device, the computational complexity of some successfully learned programs is provably unalterably suboptimal. There are also results in which the complexity of successfully learned programs is asymptotically optimal and the learning device is general, but, still thanks to the generality, some of (...) those optimal, learned programs are provably unalterably information deficient—in some cases, deficient as to safe, algorithmic extractability/provability of the fact that they are even approximately optimal. For these results, the safe, algorithmic methods of information extraction will be by proofs in arbitrary, true, computably axiomatizable extensions of Peano Arithmetic. (shrink)

Background: SNOMED CT is a large terminology system designed to represent all aspects of healthcare. Its current form and content result from decades of bottom-up evolution. Due to SNOMED CT’s formal descriptions, it can be considered an ontology. The Basic Formal Ontology (BFO) is a foundational ontology that proposes a small set of disjoint, hierarchically ordered classes, supported by relations and axioms. In contrast, as a typical top-down endeavor, BFO was designed as a foundational framework for domain ontologies in the (...) natural sciences and related disciplines. Whereas it is mostly assumed that domain ontologies should be created as extensions of foundational ontologies, a post-hoc harmonization of consolidated domain ontologies in use, such as SNOMED CT, is known to be challenging. Methods: We explored the feasibility of harmonizing SNOMED CT with BFO, with a focus on the SNOMED CT Clinical Finding hierarchy. With more than 100,000 classes, it accounts for about one third of SNOMED CT’s content. In particular, we represented typical SNOMED CT finding/disorder concepts using description logics under BFO. Three representational patterns were created and the logical entailments analyzed. Results: Under a first scrutiny, the clinical intuition that diseases, disorders, signs and symptoms form a homogeneous ontological upper-level class appeared incompatible with BFO’s upper-level distinction into continuants and occurrents. The Clinical finding class seemed to be an umbrella for all kinds of entities of clinical interest, such as material entities, processes, states, dispositions, and qualities. This suggests the conclusion that Clinical finding would not be a suitable upper-level class from an BFO perspective. On closer inspection of the taxonomic links within this hierarchy and the implicit meaning derived thereof, it became clear that Clinical finding classes do not characterize the entity (e.g. a fracture, allergy, tumor, pain, hemorrhage, seizure, fever) in a literal sense but rather the condition of a patient having that fracture, allergy, pain etc. This gives sense to the current characteristic of the Clinical Finding hierarchy, in which complex classes are modeled as subclasses of their constituents. Most of these taxonomic links are inferred, as the consequence of the ‘role group’ design pattern, which is ubiquitous in SNOMED CT and has often been subject of controversy regarding its semantics. Conclusion: Our analyses resulted in the proposal of (i) equating SNOMED CT’s ‘role group’ property with the reflexive and transitive BFO relation ‘has occurrent part’; and (ii) reinterpreting Clinical Findings as Clinical Occurrents, i.e. temporally extended entities in an organism, having one or more occurrents as temporal parts that occur in continuants. This re-interpretation was corroborated by a manual analysis of classes under Clinical Finding, as well as the identification of similar modeling patterns in other ontologies. As a result, SNOMED CT does not require any content redesign to establish compatibility with BFO, apart from this re-interpretation, and a suggested re-labeling. Regarding the feasibility of harmonizing terminologies with principled foundational ontologies post-hoc, our results provide support to the assumption that this does not necessarily require major redesign efforts, but rather a careful analysis of the implicit assumptions of terminology curators and users. (shrink)

In this paper, we first briefly survey the main responses to the challenge that experimental philosophy poses to the method of cases, given the common assumption that the latter is crucially based on intuitive judgments about cases. Second, we discuss two of the most popular responses in more detail: the expertise defense and the mischaracterization objection. Our take on the expertise defense is that the available empirical data do not support the claim that professional philosophers enjoy relevant (...) expertise in their intuitive judgments about cases. In contrast, the mischaracterization objection seems considerably more promising than its largely negative reception has suggested. We argue that the burden of proof is thus on philosophers who still hold that the method of cases crucially relies on intuitive judgments about cases. Finally, we discuss whether conceptual engineering provides an alternative to the method of cases in light of the challenge from experimental philosophy. We argue that this is not clearly the case, because conceptual engineering also requires descriptive information about the concepts it aims to improve. However, its primarily normative perspective on our concepts makes it largely orthogonal to the challenge from experimental philosophy, and it can also benefit from the empirical methods of the latter. (shrink)

Background: In prior reports, we described the design and initial performance of a fully implantable, bi-directional neural interface system for use in deep brain and other neurostimulation applications. Here we provide an update on the chronic, long-term neural sensing performance of the system using traditional 4-contact leads and extend those results to include directional 8-contact leads.Methods: Seven ovine subjects were implanted with deep brain stimulation leads at different nodes within the Circuit of Papez: four with unilateral leads in the anterior (...) nucleus of the thalamus and hippocampus; two with bilateral fornix leads, and one with bilateral hippocampal leads. The leads were connected to either an Activa PC+S® or Percept PC°ledR deep brain stimulation and recording device. Spontaneous local field potentials, evoked potentials, LFP response to stimulation, and electrode impedances were monitored chronically for periods of up to five years in these subjects.Results: The morphology, amplitude, and latencies of chronic hippocampal EPs evoked by thalamic stimulation remained stable over the duration of the study. Similarly, LFPs showed consistent spectral peaks with expected variation in absolute magnitude dependent upon behavioral state and other factors, but no systematic degradation of signal quality over time. Electrode impedances remained within expected ranges with little variation following an initial stabilization period. Coupled neural activity between the two nodes within the Papez circuit could be observed in synchronized recordings up to 5 years post-implant. The magnitude of passive LFP power recorded from directional electrode segments was indicative of the contacts that produced the greatest stimulation-induced changes in LFP power within the Papez network.Conclusion: The implanted device performed as designed, providing the ability to chronically stimulate and record neural activity within this network for up to 5 years of follow-up. (shrink)

In this paper I discuss a set of problems concerning the method of cases as it is used in applied ethics and in the metaphysical debate about personal identity. These problems stem from research in social psychology concerning our access to the data with which the method operates. I argue that the issues facing ethics are more worrying than those facing metaphysics.

In this paper, I argue that the method of cases (namely, the method of using intuitive judgments elicited by intuition pumps as evidence for and/or against philosophical theories) is not a reliable method of generating evidence for and/or against philosophical theories. In other words, the method of cases is unlikely to generate accurate judgments more often than not. This is so because, if perception and intuition are analogous in epistemically relevant respects, then using intuition (...) pumps to elicit intuitive judgments is like using illusions to elicit perceptual judgments. In both cases, judgments are made under bad epistemic circumstances. (shrink)

The philosophical “method of cases” has been the subject of intense discussion. In a recent paper, Frank Jackson attempts to vindicate the method by proposing that it is underwritten by the “representational view of language.” Jackson's proposal is potentially very significant. For if it is true, then the method of cases stands, but quite possibly also falls, with the representational view of language as characterized by Jackson. The aim of this paper is to question the (...) philosophical method of cases by showing that it does in fact presuppose a particular view of language that is at the very least questionable, both philosophically and empirically. (shrink)

In recent years, there has been increasing discussion of whether philosophy actually makes progress. This discussion has been prompted, in no small part, by the depth and persistence of disagreement among philosophers on virtually every major theoretical issue in the field. In this paper, I examine the role that the Method of Cases – the widespread philosophical method of testing and revising theories by comparing their verdicts against our intuitions in particular cases – plays in creating (...) and sustaining theoretical disagreements in philosophy. Drawing on work from cognitive psychology, I argue that there is a fundamental incompatibility between the structure of the theories that philosophers seek to construct using the MoC and the structure of the concepts on which our case-specific intuitions are based. This incompatibility renders MoC-based philosophical theorizing unable ever to succeed by the very standards of adequacy that it sets for itself. And this, in turn, helps to explain the depth and persistence of theoretical disagreements – and, in certain ways, the lack of progress – in the many areas of philosophy where the MoC plays an important role. (shrink)

Volume 27, Issue 4, October 2019, Page 597-608.

I start with some of the early challenges to the widely-employed philosophical method of cases—the very challenges that originally prompted the new movement of experimental philosophy—and with some fundamental questions about the method that are yet to have been given satisfying answers. I then propose that what has allowed both ‘armchair’ and ‘experimental’ participants in the ongoing debates concerning the method to ignore or repress those early challenges—and in particular Robert Cummins’s ‘calibration objection’—and to discount fundamental (...) disagreements about those questions, is in large part ‘the claim of continuity’, which is the claim, or assumption, that there is no philosophically significant difference between whatever it is that we do when we give our answer to the theorist’s question of whether some philosophically interesting word ‘applies’ (positively or negatively) to some theoretically significant case, and our use of that same word in the course of ordinary, non-philosophical discourse. I then summarize the ordinary language philosophy (OLP) argument against the claim of continuity, and explain why answers to the theorist’s questions are vulnerable to the calibration objection in a way that our non-philosophical, everyday employment of the same words is not. This then leads me to question another widespread assumption, which is the assumption that the theorist’s questions—as raised in the theorist’s context—have clear enough sense and correct answers. I end by responding to a series of objections to my argument and to OLP more generally. (shrink)

The paper investigates to what extent the method of cases can be interpreted as either a descriptive or a normative enterprise. I demonstrate that although most instances of the method of cases in most philosophical theories could be interpreted as being intended to either discover or revise the meaning of their target concepts, within a theory of reference this method cannot be used to shift the meaning of the concept of reference. The reason for this (...) is that intuitions of extension in a theory of reference constitute a set of data that needs to be explained, while in most other philosophical theories they could either be abandoned in favor of intuitions of intension or serve as a criterion for the adequacy of the proposed definition of the target concept. This feature of a theory of reference is caused by the fact that an implicit understanding of what reference is in a theory of reference is usually assumed and is out of discussion. In effect, the claim in paradigmatic instances of the method of cases within a theory of reference does not concern whether an expression does or does not refer in particular cases, but rather what the reference of a certain expression is, and therefore it cannot be justified by intuitions of intension. (shrink)

Avner Baz argues that the philosophical method of cases presupposes a problematic view of language and linguistic competence, namely what he calls "the atomistic-compositional view". Combining key elements of social pragmatism and contextualism, Baz presents a view of language and linguistic competence, which he takes to be more sensitive to the open-endedness of human language. On this view, there are conditions for the "normal" and "felicitous" use of human words, conditions that Baz thinks are lacking in the context (...) of the philosophical method of cases, and which make the question that philosophers are prone to ask in that context and the answers they give to that question to be pointless. However, in this paper, I argue as follows. First, Baz's conditions for the "normal" and "felicitous" use of human words are in tension with the open-endedness of human language and the use of human words. Second, it is not even clear that those conditions are really missing in the context of the philosophical method of cases. And third, even if we grant that those conditions are missing in that context, this does not licence his damning conclusion on the philosophical method of cases since we are not forced to embrace the view of language and linguistic competence on which that damning conclusion is plausible. This last move is secured by advancing and defending a skill or virtue-based view of language and linguistic competence inspired by the later work of Donald Davidson. (shrink)

Most donated organs in the United States come from brain dead donors, while a small percentage come from patients who die in “controlled,” or expected, circumstances, typically after the family or surrogate makes a decision to withdraw life support. The number of organs available for transplant could be substantially if donations were permitted in “uncontrolled” circumstances–that is, from people who die unexpectedly, often outside the hospital. According to projections from the Institute of Medicine, establishing programs permitting “uncontrolled donation after circulatory (...) determination of death,” or uDCDD, throughout the United States has the potential to provide 22,000 more donation opportunities annually. In contrast, U.S. controlled donation after circulatory determination of death, or cDCDD, cases have increased progressively over the past decade from 87 to 848 donors, but currently account for only 10.6 percent of all deceased donors. Following the IOM recommendations, several projects exploring the feasibility of uDCDD were funded by the federal government, including a grant from the Health Resources and Services Administration that supported a pilot project in New York City in which the authors of this article participated.A key feature of our protocol, and indeed of many uDCDD protocols, is the initiation of preservation methods such as chest compressions and extracorporeal membrane oxygenation shortly after death in order to perfuse and preserve the donor's organs. Critics of uDCDD argue that the means of determining death deviates from generally ascribed principles. They assert that reinstituting circulation in order to preserve organs has the effect of “undoing” the prior determination of death. The result is that cDCDD is widely accepted and practiced routinely even though it only marginally increases the number of organs available for transplantation, and uDCDD is widely considered unacceptable despite being ethically embraced and proven to significantly increase organ donation opportunities in other countries. This article explores the evolution of this counterintuitive state of affairs and calls for a policy that, in line with the IOM report, allows for both cDCDD and uDCDD protocols. (shrink)

This article is targeted at analyzing the advantages of using the case study method in the course of Business English at Scientific Research University - Higher School of Economics in Saint Petersburg. Cases offer a lot of opportunities for developing academic skills in reading, writing, listening and making presentations. Students get not only linguistic skills but also non-linguistic competences. Students are taught to work in teams, to analyze the data given in the task, to make decisions. Communicative and (...) managerial skills are obtained as well. Special attention is paid to making team presentations. It is vital to mention that analysis and case solving can be compared to a play where students are actors trying to come up with a solution of a problem using the information given. This approach stimulates students to be more creative, decisive, communicative and goal-oriented. This method helps to achieve better results in developing academic skills while studying Business English. In this article, the importance of Russian companies’ problems analyses is pushed forward. (shrink)

Experimental philosophy has focused attention on the role that intuitive responses to philosophical cases play in philosophical argumentation. The method of appealing to such cases has been dubbed the “method of cases,” and, in recent work, Edouard Machery has both defended its prevalence and uniformity in philosophical practice, and criticized its epistemic value. In this paper, I argue that there is no single method of cases, but rather a set of methods of (...) class='Hi'>cases. To defend this claim, I distinguish and articulate these different methods and argue that they better explain several paradigmatic appeals to cases. This result not only challenges the homogeneity of the method of cases; it also stocks our methodological toolbox with additional interpretive tools which help us to not only better understand philosophical arguments, but to better understand the significance of experimental work. (shrink)

The Case Study Method of Instruction (CSMI) is an excellent vehicle for achieving many instructional goals, including employing critical thinking to facilitate learning. The best results occur when instructors have a clear understanding of the CSMI and critical thinking. In this article, the author describes the evolution of the CSMI, its notable characteristics, and its instructional benefits. The author also presents five detailed definitions of critical thinking, and explains how case studies can be used to lead students to think (...) critically and subsequently learn. (shrink)

The Case Study Method of Instruction (CSMI) is an excellent vehicle for achieving many instructional goals, including employing critical thinking to facilitate learning. The best results occur when instructors have a clear understanding of the CSMI and critical thinking. In this article, the author describes the evolution of the CSMI, its notable characteristics, and its instructional benefits. The author also presents five detailed definitions of critical thinking, and explains how case studies can be used to lead students to think (...) critically and subsequently learn. (shrink)

A Pragmatic Method of Reading Confused Philosophic Texts: The Case of Peirce's "Illustrations" In 1878, Charles Peirce introduced a method for making confused ideas clear. In this essay, I put Peirce's method to work as a method for making confused writing clear, in particular, for clarifying the meaning of confused philosophic arguments as they appear in philosophic essays. In Section I, I introduce the method as a Pragmatic Method of Reading Confused Philosophic Texts. In (...) Section II, I re• view Peirce's 1877-78 "Illustrations of the Logic of Science"\ as examples of confused texts. In Section III, I apply the Pragmatic Method, reading Peirce's "Illustrations' as expressions of fundamentally contradictory "leading tendencies of thought." While it does not resolve such contradictions, the Pragmatic Method renders a confused text clear by enabling us to read it as a collection of two "implicit" texts, or two sets of meanings. (shrink)

Damascius has become well-known in recent scholarship for his unique, radical use of the aporetic method, both to highlight the inherent limits of human thought and to reveal crucial tensions in Neoplatonic metaphysics. Though much attention has been paid to the subjective or skeptical aspects of Damascius’ aporiai, little has been noted of the parallels between Damascius’ aporetic strategy in the De Principiis and Aristotle’s own in Metaphysics B. This article analyzes the parallel by looking at Aristotle’s aim for (...) aporiai in Metaphysics B.1 and closely comparing, as a case study, the De Principiis’ first aporia alongside Metaphysics B’s first aporia. Despite Damascius’ aporia dealing with different principles compared to Aristotle’s, the aporetic method for both ultimately exposes the limitations of thought and, exactly in the domain of these limitations, clarifies our concepts in relating to reality and attaining determinate understanding of principles. (shrink)

Context: The use of first-person micro-phenomenological interviews and their productive interaction with third-person physiological data is a challenging and pressing issue in order to offer an effective and fruitful application of Varela’s neurophenomenological hypothesis. Problem: We aim at offering a generative method of analysis of first-person micro-phenomenological interviews using third-person physiological data. Our challenge is to describe this generative first-person analysis with the third-person physiological framework rather than put Varela’s hypothesis into practice in a generative way (as we did (...) in another paper. Method: The present contribution is a first pioneering study as far as the exposition of such an interactive generative methodology is concerned. It is also a new issue insofar as it deals with a case study, surprise in depression, that has not been thoroughly dealt with so far, either in philosophy or in psychopathology. Results: We show that the analysis of first-person data is an intrinsic generative one, insofar as new refined categories and multifarious circular micro- and macro-processes were discovered in the very process of analyzing. They provide the initial structural generic third-person description of surprise inherited both from philosophical phenomenological a priori categories and from the experimental startle setting with a refined micro-segmentation of the dynamic of the experience. Implications: Our article could be of interest to neurophenomenologists looking for an effective application and to researchers in quest of a method of analysis of first-person data. The present limitations are due to the still preliminary data-results we need to complete. Constructivist content: The article is directly linked to Varela’s neurophenomenological program and aims at extending and reforming it with a cardio-phenomenological approach. Keywords: First-person micro-phenomenological interviews, surprise, generative analysis of first-person data, depression, cardio-phenomenology, generative categories. (shrink)

BackgroundMoral Case Deliberation is a specific form of bioethics education fostering professionals’ moral competence in order to deal with their moral questions. So far, few studies focus in detail on Moral Case Deliberation methodologies and their didactic principles. The dilemma method is a structured and frequently used method in Moral Case Deliberation that stimulates methodological reflection and reasoning through a systematic dialogue on an ethical issue experienced in practice.MethodsIn this paper we present a case-study of a Moral Case (...) Deliberation with the dilemma method in a health care institution for people with an intellectual disability, describing the theoretical background and the practical application of the dilemma method. The dilemma method focuses on moral experiences of participants concerning a concrete dilemma in practice. By an in-depth description of each of the steps of the deliberation process, we elucidate the educational value and didactics of this specific method.ResultsThe didactics and methodical steps of the dilemma method both supported and structured the dialogical reflection process of the participants. The process shows that the participants learned to recognize the moral dimension of the issue at stake and were able to distinguish various perspectives and reasons in a systematic manner. The facilitator played an important role in the learning process of the participants, by assisting them in focusing on and exploring moral aspects of the case.DiscussionThe reflection and learning process, experienced by the participants, shows competency-based characteristics. The role of the facilitator is that of a Socratic teacher with specific knowledge and skills, fostering reflection, inquiry and dialogue.ConclusionThe specific didactics of the dilemma method is well suited for teaching bioethics in clinical settings. The dilemma method follows an inductive learning approach through a dialogical moral inquiry in which participants develop not only knowledge but also skills, attitude and character. The role of a trained facilitator and a specific view on teaching and practicing ethics are essential when using the dilemma method in teaching health care professionals how to reflect on their own moral issues in practice. (shrink)

The method of contrast is used within philosophy of perception in order to demonstrate that a specific property could be part of our perception. The method is based on two passages. I argue that the method succeeds in its task only if the intuition of the difference, which constitutes the core of the first passage, has two specific traits. The second passage of the method consists in the evaluation of the available explanations of this difference. Among (...) the three outlined options, I will demonstrate that only in the third option – as we shall see, the case of the scenario that remains the same but is perceived in two different ways by the same perceiver – the intuition purports a difference that posses the necessary characteristics, namely being immediately evident and extremely complex and multifaceted, which determine its tensive nature. The application within auditory perception of this third option will generate two cases, a diachronic one and a synchronic one, which clearly show that we can auditorily perceive causality as a link between two sonorous episodes. The causal explanation is the only possible explanation among the many evaluated within the second passage of the method of contrast. (shrink)

Philosophers of science turned to historical case studies in part in response to Thomas Kuhn's insistence that such studies can transform the philosophy of science. In this issue Joseph Pitt argues that the power of case studies to instruct us about scientific methodology and epistemology depends on prior philosophical commitments, without which case studies are not philosophically useful. Here I reply to Pitt, demonstrating that case studies, properly deployed, illustrate styles of scientific work and modes of argumentation that are not (...) well handled by currently standard philosophical analyses. I illustrate these claims with exemplary findings from case studies dealing with exploratory experimentation and with interdisciplinary cooperation across sciences to yield multiple independent means of access to theoretical entities. The latter cases provide examples of ways that scientists support claims about theoretical entities that are not available in work performed within a single discipline. They also illustrate means of correcting systematic biases that stem from the commitments of each discipline taken separately. These findings illustrate the transformative power of case study methods, allow us to escape from the horns of Pitt's "dilemma of case studies," and vindicate some of the post-Kuhn uses to which case studies have been put. (shrink)

I. Scientific method as a mental operation [by] T. Case.--II. On some aspects of the scientific method [by] F. Gotch.--III. Physiology; its scope and method [by] C. S. Sherrington.--IV. Inheritance in animals and plants [by] W. F. R. Weldon.--V. Psycho-physical method [by] W. McDougall.--VI. The evolution of double stars [by] A. H. Fison.--VII. Anthropology: the evolution of currency and coinage [by] Sir R. C. Temple.--VIII. Archaeological evidence [by] W. M. F. Petrie.--IX. Scientific method as applied (...) to history [by] T. B. Strong. (shrink)

The idea that disputes which are heated, and apparently important, may nonetheless be 'merely verbal' or 'just semantic' is surely no stranger to any philosopher. I urge that many disputes, both in and out of philosophy, are indeed plausibly considered verbal, and that it would repay us to more frequently consider whether they are so or not. Asking this question is what I call ‘The Method of Verbal Dispute’. Neither the notion nor the method of verbal dispute is (...) new. What I do here is to urge its wider application, to suggest how widespread is the phenomenon of verbal disputes, and to clarify certain misconceptions about what is, or needs to be, involved in a verbal dispute. One central claim is that verbal disputes need not be ‘merely’ verbal disputes – that often, there is a real disagreement to be had, but it is not the one suggested by the surface form of the disagreement. I also discuss the relation between verbal disputes, relativism and cases in which ‘there is no fact of the matter’. (shrink)

Exploring the early development of an area of medical literature can inform contemporary medical debates. Different methods of inference include deduction, induction, abduction, and inference to the best explanation. I argue that early shaken baby research is best understood as using abduction to tentatively suggest that infants with unexplained intracranial and ocular bleeding have been assaulted. However, this tentative conclusion was quickly interpreted, by some at least, as a general rule that infants with these pathological signs were certainly cases (...) of abuse. Rather than focusing on inductive arguments, researchers today may be better off focusing on making a compelling inference to the best explanation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kant on the Method of MathematicsEmily Carson1. INTRODUCTIONThis paper will touch on three very general but closely related questions about Kant’s philosophy. First, on the role of mathematics as a paradigm of knowledge in the development of Kant’s Critical philosophy; second, on the nature of Kant’s opposition to his Leibnizean predecessors and its role in the development of the Critical philosophy; and finally, on the specific role of (...) intuition in Kant’s philosophy of mathematics. One of the points that I want to make is that recognizing the importance of these first two issues is essential to giving an adequate account of the third. That is, only by appreciating how Kant uses the example of mathematical knowledge, and in particular the objections he had to previous accounts of such knowledge, can we understand the philosophical role that he ascribes to intuition in his own account of mathematics.I don’t propose to explain the details of Kant’s philosophy of mathematics, but rather to compare his views on mathematics in the pre-Critical Prize Essay of 1764 to those of the Critique of Pure Reason, with the aim of showing how Kant’s doctrine of construction in pure intuition arises out of a combination of two factors: first, his attempt to ground the distinction between the respective methods of mathematics and philosophy, and second, his concern to defend the reality of mathematical knowledge against the views of those he called ‘the metaphysicians.’ The first factor demands an account of the certainty of mathematics, the second requires an account of its content. I shall argue that there is a possible conflict between Kant’s accounts of these features in the Prize Essay, a possibility which is finally ruled out only by means of the Critical doctrine of pure intuition. So I hope to show that there is a significant philosophical role for intuition in Kant’s account of mathematical knowledge (over and above the more logical role attributed to it on readings [End Page 629] such as those of Friedman, Beth, and Hintikka1) in reconciling the content of mathematics and its certainty.2. THE MATHEMATICIANS VS. THE METAPHYSICIANSThroughout his early writings, Kant appealed to the evidence and certainty of mathematics; his attitude towards metaphysics, however, underwent a dramatic shift. In the Physical Monadology of 1756, Kant asked how metaphysics and geometry can be united,[f] or the former peremptorily denies that space is infinitely divisible, while the latter, with its usual certainty, asserts that it is infinitely divisible. Geometry contends that empty space is necessary for free motion, while metaphysics hisses the idea off the stage. Geometry holds universal attraction or gravitation to be hardly explicable by mechanical causes but shows that it derives from the forces which are inherent in bodies at rest and which act at a distance, whereas metaphysics dismisses the notion as an empty delusion of the imagination [1:475–6].2He attempted in this work to reconcile the respective positions of metaphysics and geometry regarding infinite divisibility, thereby demonstrating that “it is neither the case that the geometer is mistaken nor that the opinion to be found among metaphysicians deviates from the truth” [1:480]. But in a series of works from 1762–3, Kant reveals a markedly different attitude towards metaphysics. For example, in “The only possible argument in support of a demonstration of the existence of God,” Kant says:the mania for method and the imitation of the mathematician, who advances with a sure step along a well-surfaced road, have occasioned a large number of such mishaps on the slippery ground of metaphysics. These mishaps are constantly before one’s eyes, but there is little hope that people will be warned by them, or that they will learn to be more circumspect as a result [2:71].In contrast, Kant describes the geometer as uncovering “with the greatest certainty” the most secret properties of that which is extended [2:70]. But the less conciliatory attitude to metaphysics comes out most clearly in Kant’s actual procedure in “The only possible argument.” In the Seventh Reflection, he presents an attempt to explain the origin of... (shrink)

Both sides in controversies tend to argue they have logic on their side. This book proposes that the interminable nature of these controversies suggests there is a problem with the main tool of logic, the syllogism. Drawing on contemporary developments in social theory and philosophy, Stanley Raffel argues that metaphors are not just aesthetic tools; they can also be used to judge phenomena. Featuring case studies drawn from both literary material and current controversial debates, _The Method of Metaphor_ ultimately (...) demonstrates the value of this neglected potential of metaphoric reasoning and shows its far-reaching implications in both moral behavior and moral education. (shrink)

Looks into evaluation of information provision probability from different sources, based on use of linguistic variables. Formation of functions appurtenant for its unclear variables provides for adoption of decisions by the decision maker, in conditions of nonprobabilistic equivocation. The development of market relations in Ukraine increases the independence and responsibility of enterprises in justifying and making management decisions that ensure their effective, competitive activities. As a result of the analysis, it is determined that the condition of economic facilities can be (...) described and determined by the decision-maker, in the presence of the necessary information. The confidence of the decision-maker in the information received is different and the decisions made have a correspondingly different level of information risk. It is important to substantiate the procedure for assessing the numerical extent of information risk in decision-making based on the information obtained in conditions of uncertainty. The use of a linguistic variable in the processing of expert data presented in the form of a matrix of binary relations of values of the membership function, which allowed to move to further processing of knowledge to support decision-making in the management of industrial, commercial, financial and other activities. As a mathematical model for estimating the numerical measure of information risk when making decisions based on the information obtained in conditions of non-stochastic uncertainty, a model has been developed to model natural language uncertainties, which differs from existing ones by formalizing knowledge taking into account uncertainty of input information. Making such a clear decision in a fuzzy environment has appropriate values of effectiveness and risk. The paper proposes all the functions and accessories of indicators of both quantitative nature and qualitative nature to bring their values in the field of definition to one scale. Then the indicator of the effectiveness of decision-making will be a measure of the clarity of the cross-section of fuzzy subsets, which correspond to the introduced indicators of information risk. The condition of economic facilities can be described and determined by the decision-maker, if the necessary information is available. Decision-making on thenumerical measure of information risk must be determined by a set of basic indicators, which can be both quantitative and qualitative in nature. Predictive values of indicators should be determined in conditions of nonstochastic uncertainty. In this case, the indicators of a quantitative nature can be determined by fuzzy triangular numbers, which implement a high level of confidence in the subjective judgments of experts. Indicators of qualitative nature should be presented in linguistic variables. The values of the indicators of qualitative nature that are predicted must be considered for all fuzzy variable terms-sets of linguistic variables introduced into consideration. For any fuzzy variable, the introduction to the consideration of a clear set of values as carriers of the α-level of its membership function allows to reduce to a single interpretation of the predicted values of indicators of quantitative and qualitative nature in terms of non-stochastic uncertainty. (shrink)

If ethics consultation services influence medical decisions it is important to evaluate how ethical dilemmas are dealt with by clinical ethics committees (CECs). Such evaluation is rare. This study presents a feasible and practical method of evaluating case discussions in CECs and the results emerging from the use of this method. A written presentation of an end-of-life dilemma was sent to all Norwegian ethics committees. The committees were asked to deal with the case as they would do if (...) it was a real case, and to prepare a written report of the discussion. A majority of the committees approached the case systematically. All emphasized the importance of good communication with the next of kin. However, their conclusions varied, medical facts were interpreted differently, possible patient suffering was dealt with differently, and some committees revealed insufficient legal knowledge. Such findings are useful in the future education of committee members. (shrink)

The history of Physical Science appears to exhibit, periodically, a race between the acmulation of data and the ability of its codification to find a natural place for much of the empirical findings. If the codifying scheme is a mathematical theory, capable of interpolation and extrapolation, according to the rules of the particular branch of mathematics employed, the ablest handlers of the theory are frequently confronted with a situation in which mathematical computation alone does not suffice. In such a situation (...) the introduction of symbols, whose interpretation is not direct and simple is resorted to. This symbol is usually involved in a mathematical relation by a species of reasoning, which may be somewhat unfamiliar and remote from customary habits of thought. It is generally accepted as physically valid, if the mathematical formulation which involves it can produce results which account for the mass of data uncovered by experimenters. As an example of such a procedure we may mention the case of the Schrödinger Ψ-symbol, a symbol which was involved in Schrödinger's famous matter wave equation. The successes which such a theory enjoyed, particularly, in its initial stages, in formally relating the relative positions and intensities of spectral lines, with the atomistic concepts of gross matter which were inferred from the data of macroscopic measurement, such as the atomic mass, the electronic charge, Planck quantum of action, etc.,—these successes, gave a certain physical dignity to the Ψ-function itself. This dignity was further enhanced by the disclosure, by Schrödinger, of four functions of the Ψ-symbol which held the same place in the “continuity equation” as the classical charge density and the three components of current density. The successes accompanying this discovery for spectroscopic problems, in particular, are well known to Physicists. (shrink)

Jaśkowski’s discussive logic D2 was formulated with the help of the modal logic S5 as follows (see [7, 8]): \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \in {D_{2}}}$$\end{document} iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\rm S}5}$$\end{document}, where (–)• is a translation of discussive formulae from Ford into the modal language. We say that a modal logic L defines D2 iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm D}_{2} = (...) \{A \in {\rm For^{\rm d}} : \ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\it L}\}}$$\end{document}. In [14] and [10] were respectively presented the weakest normal and the weakest regular logic which (†): have the same theses beginning with ‘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamond}$$\end{document}’ as S5. Of course, all logics fulfilling the above condition, define D2. In [10] it was prowed that in the cases of logics closed under congruence the following holds: defining D2 is equivalent to having the property (†). In this paper we show that this equivalence holds also for all modal logics which are closed under replacement of tautological equivalents (rte-logics).We give a general method which, for any class of modal logics determined by a set of joint axioms and rules, generates in the given class the weakest logic having the property (†). Thus, for the class of all modal logics we obtain the weakest modal logic which owns this property. On the other hand, applying the method to various classes of modal logics: rte-logics, congruential, monotonic, regular and normal, we obtain the weakest in a given class logic defining D2. (shrink)

In this article, I argue that Habermas’s method of rational reconstruction faces limitations when it comes to analysing newly emerging and contested political practices. As rational reconstruction aims to criticize existing practices by determining their normative meaning as reflected in the participants’ idealizing presuppositions, it reaches its limits where emerging and contested practices make it impossible to identify a shared self-understanding and a single participants’ perspective. Using the example of membership politics, I argue that this is often the case (...) where nationally constituted forms of politics become controversial or are fundamentally questioned. Building on the work of Benhabib and Fraser, I develop an alternative reconstructive method of plural reconstruction, which modifies the basic premises of rational reconstruction, adjusting it to emerging and contested political contexts. (shrink)

The article is dedicated to the application questions of a case study method known as casuistry. In its long tradition, it focuses on an influential variant of the early modern period and reconstructs its functionality. In the course of reading recent receptions, it is noted that some studies speak of a “casuistic revival” in moral case deliberation in health care. As a result of this revival, casuistry has been modified in such a way that it guides case discussions in (...) practice with the help of a tripartite methodology. However, as it turns out, casuistry, a case comparison method of ethical judgement based on reasoning logic, is less suitable for moral case deliberations in direct patient care. This stems from the fact that casuistry is a detailed procedure of ethical learning beneficial to institutionalized ethics committees or similar forms of ethics consultation in health care. (shrink)