First year university students enrolled on courses which have remained male dominated, including engineering, physics and computer science and two courses, law and medicine, on which females now outnumber males , completed a questionnaire concerned with the reasons why they chose their particular course. Analyses were carried out using a stepwise discriminant function analysis. The results of this study indicate that the reasons women favour law and medicine, rather than more technological courses, is that the former courses are seen as (...) leading to work that contributes to playing a useful social role and that allows a higher level of social contact. It is concluded that although women tend to avoid technological courses this is not a negative choice, rather they positively choose courses which lead to careers with higher levels of social involvement. (shrink)
Retrospective rule-making has few supporters and many opponents. Defenders of retrospective laws generally do so on the basis that they are a necessary evil in specific or limited circumstances, for example to close tax loopholes, to deal with terrorists or to prosecute fallen tyrants. Yet the reality of retrospective rule making is far more widespread than this, and ranges from ’corrective’ legislation to ’interpretive regulations’ to judicial decision making. The search for a rational justification for retrospective rule-making necessitates a reconsideration (...) of the very nature of the rule of law and the kind of law that can rule, and will provide new insights into the nature of law and the parameters of societal order. This book examines the various ways in which laws may be seen as retrospective and analyses the problems in defining retrospectivity. In his analysis Dr Charles Sampford asserts that the definitive argument against retrospective rule-making is the expectation of individuals that, if their actions today are considered by a future court, the applicable law was discoverable at the time the action was performed. The book goes on to suggest that although the strength of this ’rule of law’ argument should prevail in general, exceptions are sometimes necessary, and that there may even be occasions when analysis of the rule of law may provide the foundation for the application of retrospective laws. (shrink)
William Tait is one of the most distinguished philosophers of mathematics of the last fifty years. This volume collects his most important published philosophical papers from the 1980's to the present. The articles cover a wide range of issues in the foundations and philosophy of mathematics, including some on historical figures ranging from Plato to Gdel.
This new book is a wide-ranging, contemporary and accessible analysis of familiar and recurring myths about mass education in the United Kingdom. Looking at a variety of important issues and problems, each chapter begins by dispelling myths and assumptions about the classroom, going beyond class, race and gender, to offer analysis of topics such as discipline, youth cultures, information technology and globalisation. Utilising an interdisciplinary lens, this book offers knowledge from disciplines as diverse as sociology, philosophy, jurisprudence and cultural studies. (...) Gordon Tait examines the strengths and weaknesses of different theoretical approaches to education, from critical theory to postmodernism, and Foucaultian governance to post-colonialism. Analysing the many assumptions about education taken for granted in British public discourse, important conclusions are drawn about which of these assumptions are fair and reasonable, and which we should challenge. This book is an essential resource for advanced undergraduate and postgraduate courses on the sociology of education, culture and education, and the philosophy of education. (shrink)
Does the real difference between non-consequentialist and consequentialist theories lie in their approach to value? Non-consequentialist theories are thought either to allow a different kind of value (namely, agent-relative value) or to advocate a different response to value ('honouring' rather than 'promoting'). One objection to this idea implies that all normative theories are describable as consequentialist. But then the distinction between honouring and promoting collapses into the distinction between relative and neutral value. A proper description of non-consequentialist theories can only (...) be achieved by including a distinction between temporal relativity and neutrality in addition to the distinction between agent-relativity and agent-neutrality. (shrink)
There can be no doubt about the value of Frege's contributions to the philosophy of mathematics. First, he invented quantification theory and this was the first step toward making precise the notion of a purely logical deduction. Secondly, he was the first to publish a logical analysis of the ancestral R* of a relation R, which yields a definition of R* in second-order logic.1 Only a narrow and arid conception of philosophy would exclude these two achievements. Thirdly and very importantly, (...) the discussion in §§58-60 of the G r u n d l a g e n defends a conception of mathematical existence, to be found in Cantor (1883) and later in the writings of Dedekind and Hilbert, by basing it upon considerations about meaning which have general application, outside mathematics.2.. (shrink)
The background of these remarks is that in 1967, in ‘’Constructive reasoning” , I sketched an argument that finitist arithmetic coincides with primitive recursive arithmetic, P RA; and in 1981, in “Finitism” , I expanded on the argument. But some recent discussions and some of the more recent literature on the subject lead me to think that a few further remarks would be useful.
This paper considers the question of whether predictions of wrongdoing are relevant to our moral obligations. After giving an analysis of ‘won’t’ claims (i.e., claims that an agent won’t Φ), the question is separated into two different issues: firstly, whether predictions of wrongdoing affect our objective moral obligations, and secondly, whether self-prediction of wrongdoing can be legitimately used in moral deliberation. I argue for an affirmative answer to both questions, although there are conditions that must be met for self-prediction to (...) be appropriate in deliberation. The discussion illuminates an interesting and significant tension between agency and prediction. (shrink)
The last section of “Lecture at Zilsel’s” [9, §4] contains an interesting but quite condensed discussion of Gentzen’s ﬁrst version of his consistency proof for P A , reformulating it as what has come to be called the no-counterexample interpretation. I will describe Gentzen’s result (in game-theoretic terms), ﬁll in the details (with some corrections) of Godel's reformulation, and discuss the relation between the two proofs.
Foundations of a General Theory of Manifolds [Cantor, 1883], which I will refer to as the Grundlagen, is Cantor’s first work on the general theory of sets. It was a separate printing, with a preface and some footnotes added, of the fifth in a series of six papers under the title of “On infinite linear point manifolds”. I want to briefly describe some of the achievements of this great work. But at the same time, I want to discuss its connection (...) with the so-called paradoxes in set theory. There seems to be some agreement now that Cantor’s own understanding of the theory of transfinite numbers in that monograph did not contain an implicit contradiction; but there is less agreement about exactly why this is so and about the content of the theory itself. For various reasons, both historical and internal, the Grundlagen seems not to have been widely read compared to later works of Cantor, and to have been even less well understood. But even some of the more recent discussions of the work, while recognizing to some degree its unique character, misunderstand it on crucial points and fail to convey its true worth. (shrink)
Gödel regarded the Dialectica interpretation as giving constructive content to intuitionism, which otherwise failed to meet reasonable conditions of constructivity. He founded his theory of primitive recursive functions, in which the interpretation is given, on the concept of computable function of finite type. I will (1) criticize this foundation, (2) propose a quite different one, and (3) note that essentially the latter foundation also underlies the Curry-Howard type theory, and hence Heyting's intuitionistic conception of logic. Thus the Dialectica interpretation (in (...) so far as its aim was to give constructive content to intuitionism) is superfluous. (shrink)
There are some puzzles about G¨ odel’s published and unpublished remarks concerning finitism that have led some commentators to believe that his conception of it was unstable, that he oscillated back and forth between different accounts of it. I want to discuss these puzzles and argue that, on the contrary, G¨ odel’s writings represent a smooth evolution, with just one rather small double-reversal, of his view of finitism. He used the term “finit” (in German) or “finitary” or “finitistic” primarily to (...) refer to Hilbert’s conception of finitary mathematics. On two occasions (only, as far as I know), the lecture notes for his lecture at Zilsel’s [G¨ odel, 1938a] and the lecture notes for a lecture at Yale [G¨ odel, *1941], he used it in a way that he knew—in the second case, explicitly—went beyond what Hilbert meant. Early in his career, he believed that finitism (in Hilbert’s sense) is openended, in the sense that no correct formal system can be known to formalize all finitist proofs and, in particular, all possible finitist proofs of consistency of first-order number theory, P A; but starting in the Dialectica paper.. (shrink)
This paper contains a defense against anti-realism in mathematics in the light both of incompleteness and of the fact that mathematics is a ‘cultural artifact.’. Anti-realism (here) is the view that theorems, say, of aritltmetic cannot be taken at face value to express true propositions about the system of numbers but must be reconstrued to be about somctliiiig else or about nothing at all. A ‘bite-the-bullet’ aspect of the defease is that, adopting new axioms, liitherto independent, is not. a matter (...) of recognizing trutlis wliich had previoasly been unrecognized, but of extending the domain of what is true. (shrink)
Some have characterized patients living with intractable pain as a vulnerable population in both clinical and research settings. Labeling the population as vulnerable, however, does not provide clarity regarding the potential risks that they face when they participate in research. Instead, research vulnerability for patients in pain is a function of an interaction between their pain conditions and elements of the research enterprise. Therefore, the identification of potential risks requires consideration not only of characteristics of patients with chronic pain, but (...) also consideration of features of researchers, the quality of institutional oversight, and the medical/social environment within which the research is conducted. This paper provides an analysis of those risks and provides some suggestions as to how the risks might be better managed. (shrink)
Restricted to ﬁrst-order formulas, the rules of inference in the Curry-Howard type theory are equivalent to those of ﬁrst-order predicate logic as formalized by Heyting, with one exception: ∃-elimination in the Curry-Howard theory, where ∃x : A.F (x) is understood as disjoint union, are the projections, and these do not preserve ﬁrstorderedness. This note shows, however, that the Curry-Howard theory is conservative over Heyting’s system.
The reduction of the lambda calculus to the theory of combinators in [Sch¨ onfinkel, 1924] applies to positive implicational logic, i.e. to the typed lambda calculus, where the types are built up from atomic types by means of the operation A −→ B, to show that the lambda operator can be eliminated in favor of combinators K and S of each type A −→ (B −→ A) and (A −→ (B −→ C)) −→ ((A −→ B) −→ (A −→ C)), (...) respectively.1 I will extend that result to the case in which the types are built up by means of the general function type ∀x : A.B(x) as well as the disjoint union type ∃x : A.B(x)– essentially to the theory of [Howard, 1980]. To extend the treatment of −→ to ∀ we shall need a generalized form of the combinators K and S, and to deal with ∃ we will need to introduce a new form of the combinator S.. (shrink)
AT PHAEDO 96A-C Plato portrays Socrates as describing his past study of "the kind of wisdom known as περὶ φυσέως ἱστορία." At 96c-97b, Socrates says that this study led him to realize that he had an inadequate understanding of certain basic concepts which it involved. In consequence, he says at 97b, he abandoned this method and turned to a method of his own. But at this point in the dialogue, instead of proceeding immediately to describe his method, Plato has him (...) interjecting a complaint concerning Anaxagoras and his view that everything should be explained in terms of Mind. His complaint is that Mind would order things in the best possible way and that, therefore, an account of things in terms of Mind would amount to showing that they are ordered in the best possible way. But Anaxagoras did not show this and, instead, offered other kinds of explanations of the various phenomena. Socrates is not just criticizing Anaxagoras here for not doing what he set out to do; he makes it clear, for example at 99b-c, that he believes that the best kind of explanation of the phenomena would be to show that they are ordered in the best possible way. But he was unable to discover an explanation of this kind, either for himself or from others, and so turned to a method which he calls "second best". The actual description of this method is contained in two passages, 99e5-100a7 and 101d5-e1. Between these passages, Socrates invokes the doctrine of Forms and, in particular, the formula. (shrink)
One of the oldest problems in philosophy concerns the relationship between free will and moral responsibility. If we adopt the position that we lack free will, in the absolute sense—as have most philosophers who have addressed this issue—how can we truly be held accountable for what we do? This paper will contend that the most significant and interesting challenge to the long-standing status-quo on the matter comes not from philosophy, jurisprudence, or even physics, but rather from psychology. By examining this (...) debate through the lens of contemporary behaviour disorders, such as ADHD, it will be argued that notions of free will, along with its correlate, moral responsibility, are being eroded through the logic of psychology which is steadily reconfiguring large swathes of familiar human conduct as pathology. The intention of the paper is not only to raise some concerns over the exponential growth of behaviour disorders, but also, and more significantly, to flag the ongoing relevance of philosophy for prying open contemporary educational problems in new and interesting ways. (shrink)
This paper discusses strategic decision making in firms pursuing biotechnology innovation and the influence of risk regulation on firm strategy. Data from three research projects, involving interviews with over 60 managers from agricultural and food related biotechnology companies and also over 60 key participants in the regulatory process in the UK and EC, shows a diversity of strategy and opinion. While some industry representatives identified new risk regulations governing the release of genetically manipulated organisms (GMOs) as the primary constraint on (...) biotechnology innovation, the findings of the study painted a more complex picture. The controversies surrounding the issue of risk regulation and its impact on innovation are best understood if viewed in the context of other political and economic factors. We conclude that the actual impact of risk regulation on industry strategies is probably less than the rhetoric of industry lobbyists would suggest. At the same time, the very act of lobbying so forcefully could lead to a public backlash against industry that would be much more damaging than the regulation itself. (shrink)