In his preface, Hunter explains that this volume is intended to provide for non-mathematicians an introduction to the most important results of modern mathematical logic. The reader will find here the work of Post, Skolem, Gödel, Church, Henkin, and others, presented in a terse and closely-knit style. Though acknowledging the trend toward natural deduction systems, Hunter sticks to more classical axiomatic systems on the grounds that the proofs of metatheorems are simplified by that choice. He begins with a formal system (...) of propositional logic, for which he develops proofs of completeness, consistency, and decidability. Systems of first order predicate logic are then dealt with, and Church's and Gödel's results on undecidability and incompleteness are presented. There is a brief, useful discussion indicating what parts of first order predicate logic are decidable. It is assumed that the reader has some familiarity with elementary formal logic: Hunter develops the set-theoretical results he requires. The compactness of the presentation is facilitated by the use of earlier results for propositional logic to obtain certain results for predicate logic. Especially helpful is Hunter's technique of prefacing each of the longer and more difficult proofs with a section explaining the key ideas and the general method of proof; summaries are also often provided in conclusion. Because of the orientation of the book, a more extensive discussion of the significance of the results obtained and the philosophical issues which have been raised concerning some of them, would have been welcome. Nonetheless, this is a good, concise introduction for those who are not yet prepared to tackle the more technical literature. A bibliography is provided for those interested in pursuing the subject in greater detail.--E. M. F. (shrink)

There is general acknowledgement that both the anterior cingulate and orbitofrontal cortex are implicated in reinforcement-guided decision making, and emotion and social behaviour. Despite the interest that these areas generate in both the cognitive neuroscience laboratory and the psychiatric clinic, ideas about the distinctive contributions made by each have only recently begun to emerge. This reflects an increasing understanding of the component processes that underlie reinforcement- guided decision making, such as the representation of reinforcement expectations, the exploration, updating and representation (...) of action values, and the appreciation that choices are guided not just by the prospect of reward but also by the costs that action entails. Evidence is emerging to suggest that the anterior cingulate and orbitofrontal cortex make distinct contributions to each of these aspects of decision making. (shrink)

Background: Informed consent is regarded as a contract between autonomous and equal parties and requires the elements of information disclosure, understanding, voluntariness and consent. The validity of informed consent for critically ill patients has been questioned. Little is known about how these patients experience the process of consent.Objective: The aim of this study was to explore critically ill patients’ experience with the principle of informed consent in a clinical trial and their ability to give valid informed consent.Design: 11 stroke patients (...) who had been informed about thrombolytic treatment and had been through the process of deciding whether or not to participate in a thrombolysis trial went through repeated qualitative semistructured interviews.Results: None of the patients had any clear understanding of the purpose of the trial. Neither did they understand the principles of randomisation and voluntariness. Reasons for giving or not giving consent were trust, conceptions of benefits and risks and altruism. Several patients found it immoral to involve patients in the consent procedure and argued that this was the doctors’ responsibility. Others argued that it is a duty to question patients and perceived it as a sign of being treated with respect and dignity. A majority of the patients found the consent process vague and ambiguous.Conclusions: The results indicate that the principle of informed consent from critically ill patients cannot be seen as a contract between equal and autonomous parties. Further studies are needed to explore critically ill patients’ experiences with the process of informed consent. (shrink)

We give a review of recent progress on the application of the relativistic chiral SU(3) Lagrangian to meson–baryon scattering. It is shown that a combined chiral and 1/Nc expansion of the Bethe–Salpeter interaction kernel leads to a good description of the kaon–nucleon, antikaon–nucleon and pion–nucleon scattering data typically up to laboratory momenta of p lab ≃500 MeV. We solve the covariant coupled channel Bethe–Salpeter equation with the interaction kernel truncated to chiral order Q 3 where we include only those terms (...) which are leading in the large Nc limit of QCD. (shrink)

New class of therapies, including bipolar therapies (BPT) and paradoxical unipolar therapies (PUT) were firstly proposed in relation to a clinical insight and to some results of biological investigations, then they gave rise to mathematical modeling which brought a justification of these therapies, at least from a theoretical point of view. After recalling the mathematical model for the regulation of agonistic antagonistic couples, and reporting the fundamental types of control simulation by means of it, we point out the validity of (...) therapeutical applications inferred from this model. These therapy modalities, including BPT and PUT, now concern the following diseases: astrocytomas, epilepsia and trials on multiple sclerosis. Even if such attempts are in their early stage, noticeably for the last case where biological changes have mainly been studied, it seems that a large span of treatments is open to BPT and PUT. Improvement of these techniques in the future depends, in our opinion, on a parallel working on the dynamics of the mathematical model and the dynamics, perceived by clinical insight and confirmed by biological investigations, of the body reactions to such strategies. Justification of BPT and PUT was given, by resorting to the notion of pathological homeostasis which, too often, intervenes in order to nullify the effects of unilateral (not paradoxical) therapies. This research has elicited some therapies which use two agents with antagonistic effects or only an agent with effects similar to the agent already in excess in the body - in both cases at nearly physiological doses. (shrink)

After a chapter which is an introduction to and summary of the rest of the book, chapter 2 begins by criticizing various attempts to do away with theories, such as the Reichenbach-Salmon conception of theoretical truth in terms of observational consequences, and the Ramsey strategy of replacing first-order theoretical sentences by second-order nontheoretical ones; it then argues against hypothetico-deductivist theories of confirmation on the grounds that they are unable to handle the relevance of evidence to theory, whether or not other (...) formal constraints or even nonformal ones such as simplicity and explanatory power are added to those theories; it ends with an exposition of the Reichenbach-Carnap conventionalist thesis that the confirmation of hypotheses with evidence presupposes analytic principles connecting hypothetical and empirical concepts. Chapter 3 criticizes Bayesian theories of confirmation on such grounds as that the a priori arguments for Bayesian restrictions on beliefs are insufficient; that the Bayesian explanations of notions like variety of evidence, ad hocness, and simplicity are inadequate; and that they cannot account, without drastic revisions, for the relevance of evidence to theory, especially old evidence to new theory. Chapter 4 is an unsympathetic account of historically oriented philosophies of science; Lakatos’s notion of progressive research programs and Laudan’s theory of problem-solving effectiveness are found to be insufficiently precise and dubbed examples of "new fuzziness", while the Sneed-Stegmüller dynamics of theories is regarded as "a paradigm of misplaced rigor" ; and all three are criticized as unable to explicate the concept of evidential relevance. Chapter 5 is a formal and informal elaboration of the basic idea in Glymour’s account of theory and evidence, namely that confirmation or support is a three-term relation among evidence, hypothesis, and theory, so that evidence confirms an hypothesis only relative to a theory, and such that evidence e confirms hypothesis h relative to T if T with e implies, but T without e does not imply, an instance of h, and T with e does not imply a comparable hypothesis h’ different from h; the most interesting part of this chapter is a series of discussions showing how such an idea makes sense of the "methodological truisms" that it is possible selectively to test certain parts of a theory but not others, that a theory is supported better by a greater variety of evidence, that redundant or physically meaningless quantities are an undesirable feature of theories, that there are no inviolable rules, that a "white shoe" does not confirm "all ravens are black," that a theory is more useful and better supported than the set of its observational consequences, and that the hypothetico-deductive method often works. Since Glymour claims no originality for the conception of this general account, but only for its description, he plausibly thinks it necessary to apply it to some important historical cases of actual science; he does so in the next chapter by discussing at some length the structure and merits of Ptolemaic and Copernican astronomy, of Newton’s universal gravitation, of nineteenth century atomism, of Freud’s Rat Man, and of general relativity. For example, he argues convincingly that Copernicanism was better supported by the evidence available even before the telescope because it alone, and not the Ptolemaic theory, can determine some planetary properties which are presupposed by both theories, can test and confirm some common hypotheses, and can be confirmed in an essential rather than incidental manner; and though Glymour admits that the Copernicans tended to argue in terms of explanatory rather than confirmatory superiority, he sketches an interesting account of the relation between explanation and confirmation which strengthens his case. He also analyzes the text at the beginning of book 3 of Newton’s Principia and compiles a reconstruction of the intricate details of the inferential structure of the argument to universal gravitation; his impressive reconstruction clearly shows that Newton’s method is neither the inductivist one he himself thought he was following, nor the one attributed to him by Pierre Duhem, but rather one in accordance with Glymour’s so-called "bootstrap strategy" of repeatedly using the evidence from Kepler’s second and third laws, from lunar data, and from falling bodies, together with the theory consisting of the second and third laws of motion, to arrive at increasingly general instances of the principle of universal gravitation. Glymour’s account of arguments for and against the atomic theory from Thomson to Cannizzaro is his longest historical example, but he himself admits that this illustration of the bootstrap strategy is "certainly not the neatest", and rather "diffuse, and perhaps disconnected". Chapter 7 is a detailed application of the same principles to the technique known among social scientists as "causal modeling"; since such "causal models" are essentially systems of algebraic equations, Glymour’s account shows indirectly that the bootstrap strategy is applicable to any scientific theory presented as a set of algebraic equations; this, of course is not surprising, since the formal considerations with which Glymour begins the exposition of his theory in chapter 5 involve systems of algebraic equations. Chapter 8 is an attempt to apply Glymour’s theory of evidence to the very common scientific practice of curve-fitting, where one measures values of two or more quantities and then infers a functional relationship; Glymour argues that simpler polynomials are preferred because they are tested more frequently and more severely by the data and because they are more informative; but then he criticizes his own explanation and concludes that "the bootstrap procedures of chapter 5 do not seem to help the problem much more than a whit" ; this is admirably honest, but if one wants an additional logical or methodological rationale, then one would perhaps have to go to the meta-level and say that Glymour is here testing his own theory, and he is more interested in a further illustration of the bootstrap methodology even with a failed test, than he is to claim universal or exclusive validity for it. In chapter 9 Glymour uses his bootstrap theory of confirmation to criticize geometrical conventionalism; he considers the alternative theories of space or space-time proposed by conventionalists to show the radical undetermination of geometries by evidence, for example, a non-Euclidean geometry with no universal force instead of Newtonian gravitation with Euclidean geometry; he argues that such alternatives are simply not as well tested as the originals and that their equivalence to the originals is questionable. The last chapter is a brief discussion of further problems worthy of future investigation. (shrink)

Theaetetus, asked what knowledge is, replies that geometry and the other mathematical disciplines are knowledge, and so are crafts like cobbling. Socrates points out that it does not help him to be told how many kinds of knowledge there are when his problem is to know what knowledge itself is, what it means to call geometry or a craft knowledge in the first place—he insists on the generality of his question in the way he often does when his interlocutor, asked (...) for a definition, cites instead cases of the concept to be defined. (shrink)