Asperó and Schindler have completely solved the Axiom [Formula: see text] vs. [Formula: see text] problem. They have proved that if [Formula: see text] holds then Axiom [Formula: see text] holds, with no additional assumptions. The key question now concerns the relationship between [Formula: see text] and Axiom [Formula: see text]. This is because the foundational issues raised by the problem of Axiom [Formula: see text] vs. [Formula: see text] arguably persist in the problem of Axiom [Formula: see text] vs. (...) [Formula: see text]. The first of our two main theorems is that Axiom [Formula: see text] is equivalent to Axiom [Formula: see text], and as a corollary we show that Axiom [Formula: see text] fails in all the known models of [Formula: see text]. This suggests that [Formula: see text] actually refutes Axiom [Formula: see text]. Our second main theorem is that the [Formula: see text] Conjecture holds assuming [Formula: see text]. This is the strongest partial result known on this conjecture which is one of the central open problems of [Formula: see text]-theory and [Formula: see text]-logic. These results identify a fundamental asymmetry between the Continuum Hypothesis and any axiom which is both [Formula: see text]-expressible and which implies [Formula: see text], on the basis of generic absoluteness for the simplest of the nontrivial sentences of Third-Order Number Theory. These are the [Formula: see text]-sentences with no parameters. Such sentences are those which simply assert the existence of a set [Formula: see text] for which some property involving only quantification over [Formula: see text] holds. (shrink)

Most philosophers have given up George Berkeley’s proof for the existence of God as a lost cause, for in it, Berkeley seems to conclude more than he actually shows. I defend the proof by showing that its conclusion is not the thesis that an infinite and perfect God exists, but rather the much weaker thesis that a very powerful God exists and that this God’s agency is pervasive in nature. This interpretation, I argue, is consistent with the texts. It is (...) also an important component of Berkeley’s philosophical project, which consists of launching many small arguments against his philosophical and theological opponents. (shrink)

It is a little understood fact that the system of formal logic presented in Wittgenstein’s Tractatusprovides the basis for an alternative general semantics for a predicate calculus that is consistent and coherent, essentially independent of the metaphysics of logical atomism, and philosophically illuminating in its own right. The purpose of this paper is threefold: to describe the general characteristics of a Tractarian-style semantics, to defend the Tractatus system against the charge of expressive incompleteness as levelled by Robert Fogelin, and to (...) give a semantics for a formal language that is the Tractarian equivalent of a first-order predicate calculus. Of note in regard to the latter is the fact that a Tractatusstyle truth-definition makes no appeal to the technical trick of defining truth in terms of the satisfaction of predicates by infinite sequences of objects, yet is materially equivalent to the usual Tarski-style truth-definitions. (shrink)

In Aristotle′s Nicomachean Ethics, at 1149b15–16, there is a quotation: Aristotle does not tell us who wrote these words, and we now find the quotation as lyric fr. adesp. 949.2.

This book comprises eleven essays in the philosophy of action, six of which were previously published. The book has a fairly extensive index. The essays are arranged in four groups. The first group contains two essays on the individuation of action. The second contains four essays that argue for the view that what makes an event an action is, not how it is caused, but that it is, or begins with, a volition, “an intrinsically actional” mental event. The third contains (...) three essays that defend the view that free and responsible action is incompatible with determinism, largely by arguing for a noncausal account of reasons explanation of action. The final group contains two essays on intention formation and rationality; the first argues that it is sometimes rational to form intentions that are inconsistent with each other or with one’s beliefs; the second argues that an important sort of practical reasoning has as its conclusion the forming of an intention for action, rather than the adopting of a belief as to what one should do. (shrink)

The general principles of the scientific method, which are applicable across all of the sciences, are essential for perspective, productivity, and innovation. These principles include deductive and inductive logic, probability, parsimony, and hypothesis testing, as well as science's presuppositions, limitations, ethics, and bold claims of rationality and truth. The implicit contrast is with specialized techniques confined to a given discipline, such as DNA sequencing in biology. Neither general principles nor specialized techniques can substitute for one another, but rather the winning (...) combination for scientists is mastery of both. The purposes of this book are to enhance perspective on science by drawing insights from the humanities, and to increase productivity by fostering a deep understanding of the general principles of scientific method. The examples and case studies span the physical, biological, and social sciences; include applications in agriculture, engineering, and medicine; and also explore science's interrelationships with disciplines in the humanities such as philosophy and law. This book engages a great diversity of viewpoints on science, both historical and contemporary, and responds by affirming science's rationality. Informed by position papers on science from the American Association for the Advancement of Science, National Academy of Sciences, and National Science Foundation, this book aligns with a distinctively mainstream vision of science. It is an ideal resource for anyone undertaking a systematic study of scientific method for the first time, from undergraduates to professionals in both the sciences and the humanities. (shrink)

While the debate on values in science focuses on normative questions on the level of the individual (e.g. should researchers try to make their work as value free as possible?), comparatively little attention has been paid to the institutional and professional norms that researchers are expected to follow. To address this knowledge gap, we conduct a content analysis of leading national codes of conduct for research integrity of European countries, and structure our analysis around the question: do these documents allow (...) for researchers to be influenced by “non-epistemic” (moral, cultural, commercial, political, etc.) values or do they prohibit such influence in compliance with the value-free ideal (VFI) of science? Our results return a complex picture. On the one hand, codes of conduct consider many non-epistemic values to be a legitimate influence on the decision-making of researchers. On the other, most of these documents include what we call _VFI-like positions_: passages claiming that researchers should be free and independent from any external influence. This shows that while many research integrity documents do not fully endorse the VFI, they do not reject it and continue to be implicitly influenced by it. This results in internal tensions and underdetermined guidance on non-epistemic values that may limit some of the uses of research integrity codes, especially for purposes of ethical self-regulation. While codes of conduct cannot be expected to decide how researchers should act in every instance, we do suggest that they acknowledge the challenges of how to integrate non-epistemic values in research in a more explicit fashion. (shrink)

It is a little understood fact that the system of formal logic presented in Wittgenstein?s Tractatusprovides the basis for an alternative general semantics for a predicate calculus that is consistent and coherent, essentially independent of the metaphysics of logical atomism, and philosophically illuminating in its own right. The purpose of this paper is threefold: to describe the general characteristics of a Tractarian-style semantics, to defend the Tractatus system against the charge of expressive incompleteness as levelled by Robert Fogelin, and to (...) give a semantics for a formal language that is the Tractarian equivalent of a first-order predicate calculus. Of note in regard to the latter is the fact that a Tractatusstyle truth-definition makes no appeal to the technical trick of defining truth in terms of the satisfaction of predicates by infinite sequences of objects, yet is materially equivalent to the usual Tarski-style truth-definitions. (shrink)

The results of this paper concern the effective cardinal structure of the subsets of [ω1]<ω1, the set of all countable subsets of ω1. The main results include dichotomy theorems and theorems which show that the effective cardinal structure is complicated.

Wittgenstein's scant remarks on the roots of language in instinctive behaviour have been both difficult to interpret and controversial, not least because they may seem to incline towards forms of explanation that elsewhere he eschewed. Nevertheless, they are of importance in philosophy, not least because they bear upon age-old questions of foundationalism and concept-formation. In a recent Discussion Note in this journal, H. O. Mounce is not only attracted by but also champions such explanation – though he finds Wittgenstein's own (...) “explanations” inadequate in important respects, as evidenced in his misguided criticisms of Moore in On Certainty and in his behaviouristic remarks on the roots of the “cause and effect” language-game. In this response, I try to identify the philosophical roots of this attraction and the points at which Mounce's account departs from the elucidatory and non-explanatory path established by Wittgenstein. (shrink)

Wittgenstein's scant remarks on the roots of language in instinctive behaviour have been both difficult to interpret and controversial, not least because they may seem to incline towards forms of explanation that elsewhere he eschewed. Nevertheless, they are of importance in philosophy, not least because they bear upon age-old questions of foundationalism and concept-formation. In a recent Discussion Note in this journal, H. O. Mounce is not only attracted by but also champions such explanation – though he finds Wittgenstein's own (...) “explanations” inadequate in important respects, as evidenced in his misguided criticisms of Moore in On Certainty and in his behaviouristic remarks on the roots of the “cause and effect” language-game. In this response, I try to identify the philosophical roots of this attraction and the points at which Mounce's account departs from the elucidatory and non-explanatory path established by Wittgenstein. (shrink)

This commentary on Nescolarde-Selva and Usó-Doménech (Found Sci, 2013) raises questions about the dynamic versus static nature of the model proposed, and in addition asks whether the model might be used to explain ethical flexibility and rigidity.

The principle of clinical equipoise has been variously characterized by ethicists and clinicians as fundamentally flawed, a myth, and even a moral balm. Yet, the principle continues to be treated as the de facto gold standard for conducting randomized control trials in an ethical manner. Why do we hold on to clinical equipoise, despite its shortcomings being widely known and well-advertised? This paper reviews the most important arguments criticizing clinical equipoise as well as what the most prominent proposed alternatives are. (...) In the process, it evaluates the justification for continuing to use clinical equipoise as the gold standard for randomized control trials. (shrink)

We prove that if $V = L [s]$ where $s$ is an $\omega$ -sequence of ordinals then the GCH holds.

In the first part of this article an attempt was made to clear the ground for a functional theory of knowledge, and the discussion of structure and function with which it concluded enables us to approach the problem of cognition. If the view already set forth is sound, it seems clear that the relation of the mind to its object is a function and not a structure of the mental processes involved. The mere existence of a mental content, however complex (...) it may be, however decorated with fringes or set off by a background, does not constitute an act of knowledge or give the content a meaning. In order to see a mental act as cognitive we must consider its function, its origin, its results, and in general the circumstances in which it stands. (shrink)

ABSTRACT This paper takes issue with the idea that there is a variety of moral theories available which can in some way usefully be applied to problems in ethics. The idea is reflected in the common view that those favouring a systematic approach would do well to abandon consequentialist thinking and turn to some alternative theory. It is argued here that this is not an option, since each of the usual supposed alternatives lacks the independent resources to meet the minimal (...) requirements of being a moral theory at all. The aim is to demonstrate that virtue ethics, rights theory and deontology lack the different forms of explanation that would make them genuinely alternative theories. The conclusion is that this part of ethics is much more of a unity than is standardly assumed and that, far from our being able to move on from consequentialism, certain problems that arise from its very nature are bound to remain central to any attempt at moral theory. (shrink)

The most important, or at least the most central, part of Ferdinand de Saussure's Course in General Linguistics is found in the first six chaptersof Part Two. Here, Saussure formulates one of the basic principles of Structuralism. Yet the text is in some ways oddly impenetrable. It is dear enough on a quick reading, but closer attention discovers doubtful meanings, ambiguity, the beginnings even of contradictions. These defects may, of course, be inevitable in a reconstructed text. Or they may testify (...) to some profound erroneousness in the thought, to a theory whose natal difficulties are symptoms, not of the elusiveness of truth, but of a miscarriage. It is mypurpose here to argue the latter. (shrink)

Almost everyone believes in modality de dicto. Necessarily, puppies are young dogs. The necessity here derives from the meaning of “puppy.” The term means young dog. Essentialism is belief in a more exotic sort of modality, one that does not derive from meaning in this direct and simple way. In the first two sections of this paper, I consider indexical and nonindexical kind terms and the sort of modality applicable to each. In the last section, I consider individuals and proper (...) names. (shrink)

Utilitarianism faces a difficulty in that what are typically regarded as natural goods seem to have possible occurrences that strike most people as morally reprehensible, yet which according to the theory must be taken to add to the good in the world. Thus, totake a recent treatment of the problem by Geoffrey Scarre, it would seem that even sadistic pleasures must contribute to human happiness and thus morally offset the concomitant suffering of the victim. Scarre has offered a defence of (...) utilitarianism, arguing that in fact such pleasures will undermine the self-respect that is required for happiness. In this paper I argue that a partial undermining is plausible but leaves the problem untouched, while a complete undermining can be established only by a stipulation that is unmotivated from a utilitarian point of view. (shrink)