We first consider the entailment logic MC, based on meaning containment, which contains neither the Law of Excluded Middle (LEM) nor the Disjunctive Syllogism (DS). We then argue that the DS may be assumed at least on a similar basis as the assumption of the LEM, which is then justified over a finite domain or for a recursive property over an infinite domain. In the latter case, use is made of Mathematical Induction. We then show that an instance of the (...) LEM is intrumental in the proof of Cantor's Theorem, and we then argue that this is based on a more general form than can be reasonably justified. We briefly consider the impact of our approach on arithmetic and naive set theory, and compare it with intuitionist mathematics and briefly with recursive mathematics. Our "Four Basic Logical Issues" paper would provide useful background, the current paper being an application of the some of the ideas in it. (shrink)

In an attempt to find some new ways of tackling old problems about meaning, I explore some possible models in which meaning may be conceptually situated. I take a close look at a traditional realist conception of meaning and give some reasons as to why we may have more room to move within this than is immediately apparent. Alternative frameworks are explored along the way. The approach of thus situating meaning is an ontological one, but it is also an epistemological, (...) as well as a hermeneutical one; in that the models put forward illuminate central issues and offer potential solutions to outstanding puzzles ranging across (at least) all of these broad realms of enquiry. Such solutions give a set of initial conceptualizations of the potential role meaning can play across broader frameworks of enquiry. As such they offer fresh inroads into otherwise deadlocked debates over the nature and place of meaning across philosophical enquiry in general. (shrink)

Kants Vernunftkritik hat das Wissen zugunsten des Glaubens aufgehoben. Angeregt vor allem durch F.H. Jacobi, wird das Verhältnis von Glauben und Vernunft in der Philosophie nach Kant erneut zu einem zentralen Thema. Zur Entscheidung stehen die Fragen, ob der Glaube das Fundament von Wissen sein kann, ob der Glaube eine Grenze der Vernunft markiert oder ob eine absolut ges.

This is a book review so there is no abstract!

A half century ago electronic fetal monitoring was rushed into clinical use with the promise that the secrets of fetal heart rate decelerations had been discovered and that the newly discovered knowledge would prevent cerebral palsy with just in time cesarean sections preventing babies from experiencing asphyxia, which was thought to be the primary cause of cerebral palsy. In the years since electronic fetal monitoring’s debut, it has been discovered that asphyxia is a rare cause of cerebral palsy. At the (...) same time electronic fetal monitoring use increased to 85% of all labors, the C-section rate increased to 33% without an attributable decrease in the rate of cerebral palsy. What went wrong with electronic fetal monitoring? The answer lies in a new analysis of the physiologic theories concerning fetal heart rate decelerations, demonstrating that the earlier electronic fetal monitoring theories were wrong. This revelation is only the latest evidence that electronic fetal monitoring use today... (shrink)

In C.Q. xliii , p. 39, Mr. J. H. Quincey quotes the opening lines of Catalepton 5 as, Ite hinc,-inanes, ite, rhetorum ampullae, inflata rhoso* non Achaico verba, and adds, ‘the second line is corrupt and no satisfactory emendation has been proposed’. The MS. readings are: rhorso B, roso Mu, om. in lacuna Ar. In face of these voces nihili many have fallen back on the rore of the Aldine edition of 1517. But this does not really help, for one (...) does not inflate with dew: orators are not dew-bags, but wind-bags. It occurred to me some years ago that what is needed is some word meaning breath or wind to go with inflata, and that in view of the rh in rhorso it was probably a Greek word which a scribe had failed to recognize. I conjectured οζ, and found subsequently that this had been proposed by K. Münscher in Hermes, xlvii , pp. 153–4. οȋζος used of any rushing sound, is applied to speech by Philostratus , and by Pollux . It is easy to see how rhoezo could degenerate into rhoeso-rhoso-roso. (shrink)

For much of its history, philosophy was not merely a theoretical discipline but a way of life, an "art of living." This practical aspect of philosophy has been much less dominant in modernity than it was in ancient Greece and Rome, when philosophers of all stripes kept returning to Socrates as a model for living. The idea of philosophy as an art of living has survived in the works of such major modern authors as Montaigne, Nietzsche, and Foucault. Each of (...) these writers has used philosophical discussion as a means of establishing what a person is and how a worthwhile life is to be lived. In this wide-ranging, brilliantly written account, Alexander Nehamas provides an incisive reevaluation of Socrates' place in the Western philosophical tradition and shows the importance of Socrates for Montaigne, Nietzsche, and Foucault. Why does each of these philosophers—each fundamentally concerned with his own originality—return to Socrates as a model? The answer lies in the irony that characterizes the Socrates we know from the Platonic dialogues. Socratic irony creates a mask that prevents a view of what lies behind. How Socrates led the life he did, what enabled or inspired him, is never made evident. No tenets are proposed. Socrates remains a silent and ambiguous character, forcing readers to come to their own conclusions about the art of life. This, Nehamas shows, is what allowed Montaigne, Nietzsche, and Foucault to return to Socrates as a model without thereby compelling them to imitate him. This highly readable, erudite study argues for the importance of the tradition within Western philosophy that is best described as "the art of living" and casts Montaigne, Nietzsche, and Foucault as the three major modern representatives of this tradition. Full of original ideas and challenging associations, this work will offer new ways of thinking about the philosophers Nehamas discusses and about the discipline of philosophy itself. (shrink)

Adorno and Horkheimer critically develop the concept of the “culture industry” in the third chapter of Dialectic of Enlightenment. The treatment there has some right to be considered one of the core texts in Critical Theory's philosophy of art. This essay discusses the main claims and arguments of that work, as well as earlier essays in Adorno's music theory and later essays that turn to film aesthetics. Attention focuses on illuminating the basis for Adorno and Horkheimer's views on the culture (...) industry in light of their social ontology and epistemology, their account of aesthetic form, and their conception of commodity as style. (shrink)

Rush Rhees (1905-1989) was a philosopher, and a pupil and close friend of Ludwig Wittgenstein. While some of Rhees's own published papers became classics, most of his work remained unpublished during his lifetime. After his death, his papers were found to comprise sixteen thousand pages of manuscript on every aspect of philosophy, from philosophical logic to Simone Weil. This collection of unpublished papers, edited by D. Z. Phillips, includes Rhees's outstanding work on philosophy and religion. Written over an academic (...) lifetime, some of the papers are sympathetic to religion while others are not. It is Rhees's ability to interweave the personal and philosophical, and his integrity and intellectual honesty, which make this one of the most impressive books in twentieth-century philosophy of religion. (shrink)

The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...) Winkler Risk Analysis, 19, 187–203, [7]; Dietrich and List [14]; Herzberg Theory and Decision, 1–19, [28]). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi, 3–11, [39]), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus. (shrink)

In many assessment problems—aptitude testing, hiring decisions, appraisals of the risk of recidivism, evaluation of the credibility of testimonial sources, and so on—the fair treatment of different groups of individuals is an important goal. But individuals can be legitimately grouped in many different ways. Using a framework and fairness constraints explored in research on algorithmic fairness, I show that eliminating certain forms of bias across groups for one way of classifying individuals can make it impossible to eliminate such bias across (...) groups for another way of dividing people up. And this point generalizes if we require merely that assessments be approximately bias-free. Moreover, even if the fairness constraints are satisfied for some given partitions of the population, the constraints can fail for the coarsest common refinement, that is, the partition generated by taking intersections of the elements of these coarser partitions. This shows that these prominent fairness constraints admit the possibility of forms of intersectional bias. (shrink)

I provide a characterization of weakly pseudo-rationalizable choice functions---that is, choice functions rationalizable by a set of acyclic relations---in terms of hyper-relations satisfying certain properties. For those hyper-relations Nehring calls extended preference relations, the central characterizing condition is weaker than (hyper-relation) transitivity but stronger than (hyper-relation) acyclicity. Furthermore, the relevant type of hyper-relation can be represented as the intersection of a certain class of its extensions. These results generalize known, analogous results for path independent choice functions.

Our aim here is to present a result that connects some approaches to justifying countable additivity. This result allows us to better understand the force of a recent argument for countable additivity due to Easwaran. We have two main points. First, Easwaran’s argument in favour of countable additivity should have little persuasive force on those permissive probabilists who have already made their peace with violations of conglomerability. As our result shows, Easwaran’s main premiss – the comparative principle – is strictly (...) stronger than conglomerability. Second, with the connections between the comparative principle and other probabilistic concepts clearly in view, we point out that opponents of countable additivity can still make a case that countable additivity is an arbitrary stopping point between finite and full additivity. (shrink)

Recent impossibility theorems for fair risk assessment extend to the domain of epistemic justice. We translate the relevant model, demonstrating that the problems of fair risk assessment and just credibility assessment are structurally the same. We motivate the fairness criteria involved in the theorems as also being appropriate in the setting of testimonial justice. Any account of testimonial justice that implies the fairness/justice criteria must be abandoned, on pain of triviality.

There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalised Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here, we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalised Odds in non-trivial scenarios. We show that it is not, thereby establishing (...) an even more general impossibility theorem. (shrink)

In these discussions, Rush Rhees, who was a student and close friend of Wittgenstein, works out what he has learned from Wittgenstein's personal teaching and from study of his published and (at the time) unpublished writings. Some are review articles of books on Wittgenstein, and these are devoted to exposition of Wittgenstein's views. Others are independent discussions of special points in Wittgenstein's philosophy. The longest article, here published for the first time, is an account or record of what Wittgenstein (...) said about continuity in private discussion in 1938. (shrink)

This paper generalizes rationalizability of a choice function by a single acyclic binary relation to rationalizability by a set of such relations. Rather than selecting those options in a menu that are maximal with respect to a single binary relation, a weakly pseudo-rationalizable choice function selects those options that are maximal with respect to at least one binary relation in a given set. I characterize the class of weakly pseudo-rationalizable choice functions in terms of simple functional properties. This result also (...) generalizes Aizerman and Malishevski's characterization of pseudo-rationalizable choice functions, that is, choice functions rationalizable by a set of total orders. (shrink)

Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. (...) We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling. (shrink)

Essays offer a glimpse of the Vienna-born philosopher's personality, character, and life's work.

Four years after the publication of Wittgenstein's Investigations, Rush Rhees began writing critical reflections on the masterpiece he had helped to edit. In this edited collection of his previously unpublished writings, Rhees argues, contra Wittgenstein, that although language lacks the unity of a calculus it is not simply a family of language games. The unity of language is found in its dialogical character. It is in this context that we say something, and grow in understanding: notions not captured in (...) Wittgenstein's emphasis on language games, following rules, and using language. Rhees develops Wittgenstein's notion that to imagine a language is to image a form of life, without suggesting that we are all engaged in an all-inclusive conversation. The result is not only a major contribution to Wittgenstein scholarship, but an original discussion of central philosophical questions concerning the possibility of discourse. (shrink)

In this book, Rhees brings out the continuity in Wittgenstein's thought, and the radical character of his conclusions.

Rhees draws on wittgenstein's writings and on several conversations with him to discuss wittgenstein's views on, Among other things, The separation of judgments of value from statements of fact, The nature of an ethical rule, The ways in which people work out their ethical problems, And the multifariousness of the phenomena we consider under the heading of ethics. (staff).

Supra-Bayesianism is the Bayesian response to learning the opinions of others. Probability pooling constitutes an alternative response. One natural question is whether there are cases where probability pooling gives the supra-Bayesian result. This has been called the problem of Bayes-compatibility for pooling functions. It is known that in a common prior setting, under standard assumptions, linear pooling cannot be nontrivially Bayes-compatible. We show by contrast that geometric pooling can be nontrivially Bayes-compatible. Indeed, we show that, under certain assumptions, geometric and (...) Bayes-compatible pooling are equivalent. Granting supra-Bayesianism its usual normative status, one upshot of our study is thus that, in a certain class of epistemic contexts, geometric pooling enjoys a normative advantage over linear pooling as a social learning mechanism. We discuss the philosophical ramifications of this advantage, which we show to be robust to variations in our statement of the Bayes-compatibility problem. (shrink)

The incredible achievements of modern scientific theories lead most of us to embrace scientific realism: the view that our best theories offer us at least roughly accurate descriptions of otherwise inaccessible parts of the world like genes, atoms, and the big bang. In Exceeding Our Grasp, Stanford argues that careful attention to the history of scientific investigation invites a challenge to this view that is not well represented in contemporary debates about the nature of the scientific enterprise. The historical record (...) of scientific inquiry, Stanford suggests, is characterized by what he calls the problem of unconceived alternatives. Past scientists have routinely failed even to conceive of alternatives to their own theories and lines of theoretical investigation, alternatives that were both well-confirmed by the evidence available at the time and sufficiently serious as to be ultimately accepted by later scientific communities. Stanford supports this claim with a detailed investigation of the mid-to-late 19th century theories of inheritance and generation proposed in turn by Charles Darwin, Francis Galton, and August Weismann. He goes on to argue that this historical pattern strongly suggests that there are equally well-confirmed and scientifically serious alternatives to our own best theories that remain currently unconceived. Moreover, this challenge is more serious than those rooted in either the so-called pessimistic induction or the underdetermination of theories by evidence, in part because existing realist responses to these latter challenges offer no relief from the problem of unconceived alternatives itself. Stanford concludes by investigating what positive account of the spectacularly successful edifice of modern theoretical science remains open to us if we accept that our best scientific theories are powerful conceptual tools for accomplishing our practical goals, but abandon the view that the descriptions of the world around us that they offer are therefore even probably or approximately true. (shrink)

We explore which types of probabilistic updating commute with convex IP pooling. Positive results are stated for Bayesian conditionalization, imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of externally Bayesian pooling operators due to Wagner :336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.

The place of the emotions among the passions -- The analytic of the emotions I -- The analytic of the emotions II -- The dialectic of the emotions -- Pride, arrogance, and humility -- Shame, embarrassment, and guilt -- Envy -- Jealousy -- Anger -- Love -- Friendship -- Sympathy and empathy.

This text has as a purpose the realization of a comparative analysis between two points view about the history of science. Ilya Prigogine (Nobel Prize 1977) and Eduardo Nicol (Mexican-Spanish philosopher) discuss about time and history of science, allowing us to find a coincidence between physics an..

When in May 1930, the Council of Trinity College, Cambridge, had to decide whether to renew Wittgenstein's research grant, it turned to Bertrand Russell for an assessment of the work Wittgenstein had been doing over the past year. His verdict: The theories contained in this new work... are novel, very original and indubitably important. Whether they are true, I do not know. As a logician who like simplicity, I should like to think that they are not, but from what I (...) have read of them I am quite sure that he ought to have the opportunity to work them out, since, when completed, they may easily prove to constitute a whole new philosophy. (shrink)

Rush Rhees questions the viability of moral theories and the general claims they make in ethics. He shows how one can both be concerned with knowing what one ought to do while recognizing that one's answer is a personal one. These insights, arrived at in a distinctive style, characteristic of Rhees, are then applied to issues of life and death, human sexuality, and our relations to animals. To recognize why philosophy cannot answer such questions for us is an affirmation, (...) not a denial, of their importance. (shrink)

An aspect of Peirce’s thought that may still be underappreciated is his resistance to what Levi calls _pedigree epistemology_, to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce’s criticisms of subjectivism, to the extent they grant such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection of pedigree in the (...) context of probabilistic epistemology, however, _does_ challenge prominent subjectivist responses to the problem of the priors. (shrink)

Our challenge begins with America's aversion to science. The problem is, of course, that nonscientists could understand scientific thinking, and would understand it, if they were encouraged and expected to do so. Though Members of Congress and their staff may avoid science, the institution itself cannot. Until the day comes when science is fully integrated into education for all, and even Members of Congress and congressional staff Members can deal with technical subjects, we will need special help for our legislation. (...) Likewise, ensuring that good science informs and infuses good public policy requires scientists engage in the process of self-governance. Science should not only be a tool of public policy, it should be its foundation. With a scientifically literate society and public policy grounded in sound science, America can maintain its leadership in the emerging global knowledge economy. Without these, America will lose the very things that have fueled its greatness. (shrink)

For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No.

In the face of an impossibility result, some assumption must be relaxed. The Mere Addition Paradox is an impossibility result in population ethics. Here, I explore substantially weakening the decision-theoretic assumptions involved. The central finding is that the Mere Addition Paradox persists even in the general framework of choice functions when we assume Path Independence as a minimal decision-theoretic constraint. Choice functions can be thought of either as generalizing the standard axiological assumption of a binary “betterness” relation, or as providing (...) a general framework for a normative (rather than axiological) theory of population ethics. Path Independence, a weaker assumption than typically (implicitly) made in population ethics, expresses the idea that, in making a choice from a set of alternatives, the order in which options are assessed or considered is ethically arbitrary and should not affect the final choice. Since the result establishes a conflict between the relevant ethical principles and even very weak decision-theoretic principles, we have more reason to doubt the ethical principles. (shrink)

Epistemic states of uncertainty play important roles in ethical and political theorizing. Theories that appeal to a “veil of ignorance,” for example, analyze fairness or impartiality in terms of certain states of ignorance. It is important, then, to scrutinize proposed conceptions of ignorance and explore promising alternatives in such contexts. Here, I study Lerner’s probabilistic egalitarian theorem in the setting of imprecise probabilities. Lerner’s theorem assumes that a social planner tasked with distributing income to individuals in a population is “completely (...) ignorant” about which utility functions belong to which individuals. Lerner models this ignorance with a certain uniform probability distribution, and shows that, under certain further assumptions, income should be equally distributed. Much of the criticism of the relevance of Lerner’s result centers on the representation of ignorance involved. Imprecise probabilities provide a general framework for reasoning about various forms of uncertainty including, in particular, ignorance. To what extent can Lerner’s conclusion be maintained in this setting? (shrink)