The crux of the dispute between formalism and intuitionism, it is held, is not whether certain entities exist or not, but how the term function shall be used in mathematics. The identification of effective definition with general recursion fails because an undefined function lies concealed beneath the requirement of a finite number of substitutions, and a fresh characterization of effective definition is sought in terms of a hierarchy of ordinal recursions.A correspondence exists between primitive recursive properties and direct proofs, of (...) irrationality and transcendence for instance, and between general recursive properties and indirect proofs.Mathematics is a concept creating activity and the distinction between a formal mathematics devoid of meaning, at one level, and a meaningful metamathematics at the next is considered to be untenable.RésuméLa controverse entre les formalistes et les intuitionistes ne repose pas, considére‐t‐on, sur l'existence ou la non‐existence de certaines entités, mail sur l'usage du terme fonction en mathématiques. L'identification de la définition effective avec la récursion générate n'est pas valable parce qu'une fonction indéfinié est dissimulée sous la nécessité d'un nombre fini de substitutions, et une nouvelle caractérisation de définition effective est recherchée sous forme de hiérarchie de récursions ordinates.II existe, d'une part, une correspondance entre les propriétés primitives récursives et les preuves directes, d'irrationalité et de transcendance par exemple, et, d'autre part, entre les propriétés récursives générates et les preuves par l'absurde.Les mathématiques sont une activité créatrice de concepts, et la distinction entre les mathématiques formelles dépourvues de sens et, sur le plan supérieur, une méta‐mathématique chargée de sens, ne semble pas justifiée. (shrink)

This graduate-level_text by a master in the field builds a function theory of the rational field that combines aspects of classical and intuitionist analysis. Topics include recursive convergence, recursive and relative continuity, recursive and relative differentiability, the relative integral, elementary functions, and transfinite ordinals. 1961 edition.

There are people where two or more personalities seem to have independent-and sometimes mutually forgetful-control of the same bodily individual. This chapter gives a brief account of the history of the diagnosis of "Multiple Personality Disorder" or "Dissociative Identity Disorder", and the conflicting judgment of therapists, lawyers, and philosophers as to whether this is a real syndrome. It is suggested that the diagnosis may be therapeutically helpful for some other disturbances, including anorexia, even if it does not carry the strong (...) metaphysical moral that some have supposed. The cases are of interest to philosophers as they purport to represent "real -life" difficulties for standard theories of "personal identity." The chapter argues that the diagnosis depend on prior assumptions about such identity, and so don't easily confirm or rebut any available theory, including more ancient theories about demonic possession. (shrink)

The notion that metaphorical statements are strictly false suggests that all statements, even those that seemed ‘literal’, are false, as none can ‘literally’ reflect reality. Statements about what we perceive or could perceive rely on evoking sensory images of such ‘visibles’, even though we have no direct access to what others, may perceive. In addition to what is visible, we must also deal with ‘invisibilia’ (both the fantasms that respectable moderns now reject and the realities that lie beyond or before (...) all sentient experience). Talking about such distant or long-ago realities must always be ‘metaphorical’, as they cannot have any of the merely ‘subjective’ properties of experience, nor do they explain those latter properties. Is there some way of confirming the brute conviction that there is a ‘real and intelligible world’, and that we can find it out or describe it ‘literally’? May ‘Reason’ be a route to understanding? But this too is an illusion: we seem never in practice to escape contradictions and had perhaps better turn again to consider the worlds of experience to which we are confined. What we experience is conditioned by our imagination: whether that metaphorical imagination points beyond experience remains uncertain. (shrink)

This paper attempts to explore a number of conceptual issues surrounding genetic testing. It looks at the meaning of the terms, genetic information and genetic testing in relation to the definition set out by the Advisory Committee on Genetic Testing in the UK, and by the Task Force on Genetic Testing in the USA. It argues that the special arrangements that may be required for the regulation of genetic tests should not be determined by reference to the nature or technology (...) of the test, but by considering those morally relevant features that justify regulation. Failure to do so will lead to the regulation of genetic tests that need not be regulated, and would fail to cover other tests which should be regulated. The paper also argues that there is little in the nature of the properties of gene tests, using DNA or chromosomes, that in itself justifies a special approach. (shrink)

The notion of autonomy commonly employed in medical ethics literature and practices is inadequate on three fronts: it fails to properly identify nonautonomous actions and choices, it gives a false account of which features of actions and choices makes them autonomous or nonautonomous, and it provides no grounds for the moral requirement to respect autonomy. In this paper I offer a more adequate framework for how to think about autonomy, but this framework does not lend itself to the kinds of (...) practical application assumed in medical ethics. A general problem then arises: the notion of autonomy used in medical ethics is conceptually inadequate, but conceptually adequate notions of autonomy do not have the practical applications that are the central concern of medical ethics. Thus, a revision both of the view of autonomy and the practice of “respect for autonomy” are in order. (shrink)

There is only one occurrence of the word ‘progress’ in the Philosophical Investigations. It is located in the sentence that serves as the book’s epigraph. The book, however, does not explicit prese...

Arguing for the theoretical importance of the concept of “subject” or “self” on behalf of the “psychiatric/psycho-pathological thinking” is justified in so far as, as Costa, Bezerra Jr., and Gama say, “this is still an indispensable concept for understanding the conditions for the gestation and functioning of psychological life.” In what sense are these concepts “indispensable?”All the hints suggest them as necessary complements for neurobiological investigations to become useful for clinical employment. So, if we consider that it is possible to (...) approach mental phenomena connecting in some way their two sides to favor clinical use, the neurobiological and the psychological, we might as well suppose that any... (shrink)

The percentage of accidental pregnancies, the Pearl pregnancy rate and the life-table method have all been used to study the effectiveness of contraception in Belgium, using data from the Second National Fertility Survey (1971), which covered 3397 Belgian women in the age group 30–34 years. Though all three methods yield generally similar results, it is only by using the third method that we can obtain in an optimum way changes in contraceptive effectiveness by birth order and birth interval.

A misconception regarding the ultrastructural basis of myocardial failure has been observed in laboratory studies involving medical students and practicing physicians, in medical textbooks, and in clinical instruction of students. This misconception attributes heart failure to overextension of individual cardiac muscle fibres and their sarcomeres, resulting in a mechanically based decline in contractile force production. The basis of the misconception is a set of component misconceptions which interact in reciprocally supportive ways. The interlocking nature of the component misunderstandings strengthens the (...) overall misconception, making it difficult to undermine. A contributor to many aspects of the faulty account of heart failure is a tendency toward oversimplification of complex phenomena in learning, instruction, and scientific research. Implications for medical education are considered. (shrink)