Grünbaum's gap conjecture

AbstractPurdy's generalization of Grünbaum's gap conjecture is proved for all arrangements with a sufficiently high maximum number of concurrent lines. We also improve Purdy's bounds for the general theorem and establish two lower bounds for ƒ2(A) for all arrangements

THE PHILOSOPHICAL SIGNIFICANCE OF QUINE'S D-THESIS

The philosophical significance of Quine's D-thesis is considered. The D-thesis - "Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system? (W.V.0. Quine, From a Logical Point of View, p. 43) - named for Pierre Duhem, marked a significant turning point in the evolution of Quine's thoughts on epistemology. A brief survey of Quine's epistemological work is presented to show the evolution of his thought. Adolf Grünbaum's criticisms are examined and it is shown that the D-thesis can be defended from Grünbaum's attacks. Writings of Harry Frankfurt and Philip Quinn are considered in this context. Using some ideas due to Israel Scheffler, we are able to show that a D-theorist can avoid the subjectivist's problems. We conclude that the D-thesis is worthy of consideration as a possible basis for a philosophy of science

Popper, Refutation and 'Avoidance' of Refutation

Popper's account of refutation is the linchpin of his famous view that the method of science is the method of conjecture and refutation. This thesis critically examines his account of refutation, and in particular the practice he deprecates as avoiding a refutation. I try to explain how he comes to hold the views that he does about these matters; how he seeks to make them plausible; how he has influenced others to accept his mistakes, and how some of the ideas or responses to Popper of such people are thus similarly mistaken. I draw some distinctions necessary to the provision of an adequate account of the so-called practice of avoiding a refutation, and try to rid the debate about this practice of at least one red herring. I analyse one case of 'avoiding' a refutation in detail to show how the rationality of scientific practice eludes both Popper and many of his commentators. Popper's skepticism about contingent knowledge prevents him from providing an acceptable account of contingent refutation, and so his method is really the method of conjecture and conjecture. He cannot do without the concepts of knowledge and refutation, however, if his account of science is to be plausible or persuasive, and so he equivocates between, amongst other things, refutation as disproof and refutation as the weaker notion of discorroboration. I criticise David Stove's account of this matter, in particular to show how he misses this point. An additional advantage Popper would secure from this equivocation is that if refutations were mere discorroborations they would be easier to achieve, and hence more common in science, than is the case. On Popper's weak notion of refutation, it would be possible to refute true theories since corroboration does not entail truth. There are two other related doctrines Popper holds about refutation which, if accepted, make some refutations seem easier to obtain than is the case. I call these doctrines 'Strong Popperian Falsificationism' (SPF) and 'Weak Popperian Falsificationism' (WPF). SPF is the false doctrine that if a prediction from some theory is refuted then that theory is refuted. Popper does not always endorse SPF. In particular, when confronted with a counterexample to it, he retreats to WPF, which is the false doctrine that if a prediction from some theory is refuted then that theory is prima facie refuted. WPF , or even SPF, can seem plausible if one has in mind predictions derived from theories in strong or conclusive tests of those theories, which I suggest Popper characteristically does. Popper is disposed to describe any such case of predictive failure which does not lead to the refutation of the theory concerned as one in which that refutation has been avoided. To reinforce his portrayal of the refutation, or the attempted refutation, of major scientific theories as the rational core of scientific practice, Popper treats the so-called practice of avoiding a refutation as untypical of science, and much so-called avoidance he dismisses as unscientific or pseudo-scientific. I argue that his notion of avoiding a refutation is incoherent. Popper is further driven to believe that such avoidance is possible, however, because he conflates sentences with propositions and propositions with propositional beliefs. Also, he wishes to avoid being saddled with the relativisim that is a consequence of his weak account of refutation as discorroboration. Popper believes that ad hoc hypotheses are the most important of the unscientific means of avoiding a refutation. I argue that his account of such hypotheses is also incoherent, and that several hypotheses thought to be ad hoc in his sense are not. Such hypotheses appear to be so largely because of Popper's use of rhetoric and partly because these hypotheses are unacceptable for other reasons. I conclude that to know that a hypothesis is ad hoc in Popper's sense does not illuminate scientific practice. Popper has also attempted to explicate ad hocness in terms of some undesirable, or allegedly undesirable, properties of hypotheses or the explanations they would provide. The first such property is circularity, which is undesirable; the second such property is reduction in empirical content, which is not. In the former case I argue that non-circularity is clearly preferable to non-ad hocness as a criterion for a satisfactory explanation or explanans, as the case may be, and in the latter case that Popper is barking up the wrong tree. Some cases of so-called avoidance are obviously not unscientific. The discovery of Neptune from a prediction based on the reasonable belief that there were residual perturbations in the motion of Uranus is an important case in point, and one that is much discussed in the literature. The manifest failure of astronomers to account for Uranus's motion did not lead to the refutation of Newton's law of gravitiation, yet significant scientific progress obviously did result. Retreating to WPF, Popper claims that Newton's law was prima facie refuted. In general, astronomers have never shared this view, and they are correct in not doing so. I argue that the law of gravitation would have been prima facie refuted only if there had been good reason at the time to believe as false what is true, namely, that an unknown trans-Uranian planet was the cause of those Uranian residuals. Knowledge of the trans-Uranian region was then so slight that it was merely a convenient assumption, one which there was little reason to believe was false, that the known influences on Uranus's motion were the only such influences. I conclude that in believing or supposing that it was this assumption that was false, rather than the law of gravitation, Leverrier and Adams, the co-predictors of Neptune, were acting rationally and intelligently. Popper's commentators offer a variety of accounts of the alleged practice of avoiding a refutation, and of this case in particular. I analyse a sample of their accounts to show how common is the acceptance of some of Popper's basic mistakes, even amongst those who claim to reject his falsificationism, and to display the effects on their accounts of this acceptance of his mistakes. Many commentators recognize that anomalies are typically dealt with by changes in the boundary conditions or in other of the auxiliary propositions employed. Where many still go wrong, however, is in retaining the presupposition of WPF which encouraged Popper to hold the contradictory view about anomalies in the first place. Thus Imre Lakatos and others, for example, have developed a 'siege mentality' about major scientific theories; they see them as under continual threat of refutation from anomalies, and so come to believe that dogmatism is essential in science if such theories are to survive as they do. I examine various such doomed attempts to reconcile Popper with the history of science. It is a common failure in this literature to conflate or to fail to see the need to distinguish a belief from a supposition, and an epistemic reason from a pragmatic reason. I argue that only if one does draw these distinctions can one give an adequate account of how anomalies are rationally dealt with in science. The other important strand in Popper's thinking about 'avoidance' of refutation which has seriously misled some of his commentators is his unfounded belief in the dangers of ad hoc hypotheses. I examine the accounts that a sample of such commentators provide of the trans-Uranian planet hypotheses of Leverrier and Adams. These commentators imply or assert what Popper only hints at, namely, that there is something fishy about this hypothesis. I provide a further defence of the rationality of entertaining this hypothesis at the time. I conclude with a few remarks about Popper's dilemma in respect of scientific practice and his long standing emphasis on refutations

"Consciousness". Selected Bibliography 1970 - 2001

This is a bibliography of books and articles on consciousness in philosophy, cognitive science, and neuroscience over the last 30 years. There are three main sections, devoted to monographs, edited collections of papers, and articles. The first two of these sections are each divided into three subsections containing books in each of the main areas of research. The third section is divided into 12 subsections, with 10 subject headings for philosophical articles along with two additional subsections for articles in cognitive science and neuroscience. Of course the division is somewhat arbitrary, but I hope that it makes the bibliography easier to use. This bibliography has first been compiled by Thomas Metzinger and David Chalmers to appear in print in two philosophical anthologies on conscious experience (Metzinger 1995a, b). From 1995 onwards it has been continuously updated by Thomas Metzinger, and now is freely available as a PDF-, RTF-, or HTML-file. This bibliography mainly attempts to cover the Anglo-Saxon and German debates, in a non-annotated, fully formatted way that makes it easy to "cut and paste" from the original file. To a certain degree this bibliography also contains items in other languages than English and German - all submissions in other languages are welcome. Last update of current version: July 13th, 2001

Freud after Wittgenstein: a re-evaluation of Freudian psychoanalytic concepts

The remarks reported in Lectures and Conversations, make it clear that Wittgenstein thought both there to be "a way of thinking" in Freud's work that needed combatting, and also there to be something valuable that needed preserving. This thesis explores what underlies these remarks. The negative part of the thesis examines exactly what are the "ways of thinking" that need combatting. I argue that these include the confusion of reasons with causes and the related confusion of the "grammar" of physiology with the "grammar" of psychology. The positive part of the thesis argues that Freudian psychoanalysis can be better understood by a proper understanding of the way patients are persuaded to see their behaviour as falling under new descriptions, descriptions which are secondary or metaphorical applications of the ordinary language.In the course of my argument I examine and criticise the claims made by such writers and would -be defenders of Freud as Donald Davidson and Marcia Cavell. I further explore the work of David Pears and Jean -Paul Sartre on self -deception, and the bearing that their views have on an understanding of Freudian psychoanalysis. I also invoke contributions by Sabina Lovibond and Peter Winch to illuminate my thesis that psychoanalytic explanations can be true, even though parasitic on acceptance by the patient.Others who have written on these matters have tended to focus on the direct, though elliptical, comments reported in Wittgenstein's Lectures and Conversations. I contend, however, that some of the fundamental ideas of Wittgenstein's later thinking, notably in the Philosophical Investigations and The Remarks on the Philosophy of Psychology are also crucial to a proper understanding of Freudian psychoanalysis

Physics and scientific realism

In this thesis I argue for a realist interpretation of physics. I respond to claims to the contrary by submitting rebuttals of some of the more serious objections, and by formulating and defending counter-claims. It would be too ambitious to try to argue here for realism throughout physics, so I restrict my constructive efforts to the classical domain. Attempted rebuttals of the anti-realist case, however, involve intrusions into the quantum arena. I take issue in Part 1 with Nancy Cartwright. She argues in How the Laws o f Physics Lie that: (i) the fundamental laws of physics are false; (ii) causal explanation can ensure truth, in which case the theoretical entities invoked are real; and (iii) current theories of explanation are misconceived. To support (i) she analyses cases drawn from both classical and modern physics, and my response is to show in detail how, in these examples, I believe she is mistaken. Whilst I agree with (ii), I argue that there is incoherence in simultaneously holding (ii) with (i). As for (iii), I defend the D-N model of explanation and point to the inadequacies of Cartwright s simulacrum model. In Representing and Intervening Ian Hacking argues for the reality of (theoretical) entities that can be manipulated in interactions with other things. However, he is agnostic on realism about theories, because he believes that incompatible theories can equally well cover a given range of phenomena. The case to which he points to instantiate the view is Hertz s treatment of mechanics in which Hacking claims to find three equally good theories, with the overt threat of inconsistency among them. In Part 2 I argue that there is but one theory of mechanics and that Hertz s project was to investigate three different ways of axiomatising it. Only one of the three ways (as conceived by Hertz) survives. To support their position, anti-realists commonly seize on the doctrine, supposedly due to Pierre Duhem, that a given range of phenomena can be accommodated by different, mutually incompatible, theories. Part 3 examines the basis for Duhem's view and establishes that he had a quasi-realist attitude to theories. The originator of the doctrine, it transpires, was not Duhem, but Henri Poincare. I explain how the subsequent course of physics invalidated the grounds which misled these two philosophers into adopting it. Part 4 examines Bas van Fraassen's claim to reduce to absurdity the demand for explanation that he thinks is exemplified in J.J.C. Smart's classic cosmic coincidence' argument for realism. I show that Smart s argument comprehends two different sorts of cosmic coincidence, and that van Fraassen addresses only the less formidable of these. In so doing, van Fraassen's strategy is to assert that Smart's argument relies on Reichenbach s principle of the common cause, and to offer an abstract schema (deriving from the EPR correlation experiments) which, he claims, refutes Reichenbach's principle. I set all of this in context and argue that the schema fails to bear the load that van Fraassen places on it, and that Smart s argument stands