In The Healer's Power, Howard Brody placed the concept of power at the heart of medicine's moral discourse. Struck by the absence of “power” in the prevailing vocabulary of medical ethics, yet aware of peripheral allusions to power in the writings of some medical ethicists, he intuited the importance of power from the silence surrounding it. He formulated the problem of the healer's power and its responsible use as “the central ethical problem in medicine.” Through the prism of power he (...) refracted a wide range of ethical problems, from informed consent to truth-telling, from confidentiality to futility, from the physician's fantasies to the physician's virtues. At times this prism shed new light on old problems, enabling us to see from an unexpected angle the elements of which the problem was composed. At other times it exposed issues of ethical significance that had been neglected in the bioethics literature. (shrink)

We show that the Turing degrees are not sufficient to measure the complexity of continuous functions on [0, 1]. Computability of continuous real functions is a standard notion from computable analysis. However, no satisfactory theory of degrees of continuous functions exists. We introduce the continuous degrees and prove that they are a proper extension of the Turing degrees and a proper substructure of the enumeration degrees. Call continuous degrees which are not Turing degrees non-total. Several fundamental results are proved: a (...) continuous function with non-total degree has no least degree representation, settling a question asked by Pour-El and Lempp; every non-computable f $\epsilon \mathcal{C}[0, 1]$ computes a non-computable subset of $\mathbb{N}$ ; there is a non-total degree between Turing degrees $a _\eqslantless_{\tau}$ b iff b is a PA degree relative to a; $\mathcal{S} \subseteq 2^{\mathbb{N}}$ is a Scott set iff it is the collection of f-computable subsets of $\mathbb{N}$ for some f $\epsilon \mathcal{C}[O, 1]$ of non-total degree; and there are computably incomparable f, g $\epsilon \mathcal{C}[0, 1]$ which compute exactly the same subsets of $\mathbb{N}$ . Proofs draw from classical analysis and constructive analysis as well as from computability theory. (shrink)

We call A weakly low for K if there is a c such that $K^A(\sigma)\geq K(\sigma)-c$ for infinitely many σ; in other words, there are infinitely many strings that A does not help compress. We prove that A is weakly low for K if and only if Chaitin's Ω is A-random. This has consequences in the K-degrees and the low for K (i.e., low for random) degrees. Furthermore, we prove that the initial segment prefix-free complexity of 2-random reals is infinitely (...) often maximal. This had previously been proved for plain Kolmogorov complexity. (shrink)

We study reals with infinitely many incompressible prefixes. Call $A \in 2^{\omega}$ Kolmogorot random if $(\exists^{\infty}n) C(A \upharpoonright n) \textgreater n - \mathcal{O}(1)$ , where C denotes plain Kolmogorov complexity. This property was suggested by Loveland and studied by $Martin-L\ddot{0}f$ , Schnorr and Solovay. We prove that 2-random reals are Kolmogorov random. Together with the converse-proved by Nies. Stephan and Terwijn [11]-this provides a natural characterization of 2-randomness in terms of plain complexity. We finish with a related characterization of 2-randomness.

We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call 1/2-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the K-trivial sets. We characterize 1/2-bases as the sets computable from both halves of Chaitin’s Ω, and as the sets that obey the cost function c(x,s)=Ωs−Ωx−−−−−−−√. Generalizing these results yields a dense hierarchy of (...) subideals in the K-trivial degrees: For k<n, let Bk/n be the collection of sets that are below any k out of n columns of some random sequence. As before, this is an ideal generated by its c.e. elements and the random sequence in the definition can always be taken to be Ω. Furthermore, the corresponding cost function characterization reveals that Bk/n is independent of the particular representation of the rational k/n, and that Bp is properly contained in Bq for rational numbers p<q. These results are proved using a generalization of the Loomis–Whitney inequality, which bounds the measure of an open set in terms of the measures of its projections. The generality allows us to analyze arbitrary families of orthogonal projections. As it turns out, these do not give us new subideals of the K-trivial sets; we can calculate from the family which Bp it characterizes. We finish by studying the union of Bp for p<1; we prove that this ideal consists of the sets that are robustly computable from some random sequence. This class was previously studied by Hirschfeldt [D. R. Hirschfeldt, C. G. Jockusch, R. Kuyper and P. E. Schupp, Coarse reducibility and algorithmic randomness, J. Symbolic Logic81(3) (2016) 1028–1046], who showed that it is a proper subclass of the K-trivial sets. We prove that all such sets are robustly computable from Ω, and that they form a proper subideal of the sets computable from every (weakly) LR-hard random sequence. We also show that the ideal cannot be characterized by a cost function, giving the first such example of a Σ03 subideal of the K-trivial sets. (shrink)

The tower number ${\mathfrak t}$ and the ultrafilter number $\mathfrak {u}$ are cardinal characteristics from set theory. They are based on combinatorial properties of classes of subsets of $\omega $ and the almost inclusion relation $\subseteq ^*$ between such subsets. We consider analogs of these cardinal characteristics in computability theory.We say that a sequence $(G_n)_{n \in {\mathbb N}}$ of computable sets is a tower if $G_0 = {\mathbb N}$, $G_{n+1} \subseteq ^* G_n$, and $G_n\smallsetminus G_{n+1}$ is infinite for each n. (...) A tower is maximal if there is no infinite computable set contained in all $G_n$. A tower ${\left \langle {G_n}\right \rangle }_{n\in \omega }$ is an ultrafilter base if for each computable R, there is n such that $G_n \subseteq ^* R$ or $G_n \subseteq ^* \overline R$ ; this property implies maximality of the tower. A sequence $(G_n)_{n \in {\mathbb N}}$ of sets can be encoded as the “columns” of a set $G\subseteq \mathbb N$. Our analogs of ${\mathfrak t}$ and ${\mathfrak u}$ are the mass problems of sets encoding maximal towers, and of sets encoding towers that are ultrafilter bases, respectively. The relative position of a cardinal characteristic broadly corresponds to the relative computational complexity of the mass problem. We use Medvedev reducibility to formalize relative computational complexity, and thus to compare such mass problems to known ones.We show that the mass problem of ultrafilter bases is equivalent to the mass problem of computing a function that dominates all computable functions, and hence, by Martin’s characterization, it captures highness. On the other hand, the mass problem for maximal towers is below the mass problem of computing a non-low set. We also show that some, but not all, noncomputable low sets compute maximal towers: Every noncomputable (low) c.e. set computes a maximal tower but no 1-generic $\Delta ^0_2$ -set does so.We finally consider the mass problems of maximal almost disjoint, and of maximal independent families. We show that they are Medvedev equivalent to maximal towers, and to ultrafilter bases, respectively. (shrink)

We prove that the continuous function${\rm{\hat \Omega }}:2^\omega \to $ that is defined via$X \mapsto \mathop \sum \limits_n 2^{ - K\left} $ for all $X \in {2^\omega }$ is differentiable exactly at the Martin-Löf random reals with the derivative having value 0; that it is nowhere monotonic; and that $\mathop \smallint \nolimits _0^1{\rm{\hat{\Omega }}}\left\,{\rm{d}}X$ is a left-c.e. $wtt$-complete real having effective Hausdorff dimension ${1 / 2}$.We further investigate the algorithmic properties of ${\rm{\hat{\Omega }}}$. For example, we show that the maximal (...) value of ${\rm{\hat{\Omega }}}$ must be random, the minimal value must be Turing complete, and that ${\rm{\hat{\Omega }}}\left \oplus X{ \ge _T}\emptyset \prime$ for every X. We also obtain some machine-dependent results, including that for every $\varepsilon > 0$, there is a universal machine V such that ${{\rm{\hat{\Omega }}}_V}$ maps every real X having effective Hausdorff dimension greater than ε to a real of effective Hausdorff dimension 0 with the property that $X{ \le _{tt}}{{\rm{\hat{\Omega }}}_V}\left$; and that there is a real X and a universal machine V such that ${{\rm{\Omega }}_V}\left$ is rational. (shrink)

Despite the supreme political and economic significance of boundaries--and ongoing challenges to existing national boundaries--scant attention has been paid to their ethics. This volume explores how diverse ethical traditions understand the political and property rights reflected in territorial and jurisdictional boundaries. It is the first book to bring together thinkers from a range of traditions, both religious and secular, to discuss the ethics of boundaries. Each contributor represents a tradition's views on questions surrounding the use of boundaries to delimit property (...) and political rights. What does it mean to own something? What resources should not be privately owned? What justifies the erection of political boundaries between one people and another? How ''hard'' should such boundaries be? What rights extend to minorities within a state? Should territorial boundaries coincide with social ones? Does national autonomy have an ethical basis, or is it an aspect of modern power politics? Should we aim for a more inclusive community than that afforded by modern nation-states? Cross-chapter dialogue and a substantive conclusion draw out similarities and differences among the traditions represented, traditions that include Christianity, classical liberalism, Confucianism, international law, Islam, Judaism, liberal egalitarianism, and natural law. In addition to the editors, the contributors are Nigel Biggar, Joseph Boyle, Joseph Chan, Russell Hardin, Will Kymlicka, Loren Lomasky, Robert McCorquodale, Richard B. Miller, David Novak, Sulayman Nyang, Michael Nylan, Raul C. Pangalangan, Daniel Philpott, Jeremy Rabkin, Hillel Steiner, M. Raquibuz Zaman, and Noam J. Zohar. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:American Journal of Philology 123.1 (2002) 119-122 [Access article in PDF] Mary Depew and Dirk Obbink, eds. Matrices of Genre: Authors, Canons, and Society. Center for Hellenic Studies Colloquia 4. Cambridge, Mass.: Harvard University Press, 2000. vi + 346 pp. Cloth, $50. The present collection of essays, which originated as a colloquium at the Center for Hellenic Studies, starts, in the words of editor and organizer Dirk Obbink, from (...) the premise that "genre is a conceptual orienting device that suggests to the hearer the sort of receptorial conditions in which a fictive discourse might have been delivered." Obbink goes on to note that, as the discussion at the colloquium developed, "a more text-based conception of authorial performance" began to emerge (6). This evolution in turn parallels the movement in the volume from an initial discussion of archaic and classical Greek genres to those of Hellenistic poetry and its Roman imitators. One can only applaud this attempt to provide a more sophisticated framework for the reading and reception of ancient literature. As befits the stature of the sponsoring institution and of the many distinguished participants, all the contributions are of an unquestionable competence. In the end, however, it is unclear that we have achieved a more complex, refined, or problematized concept of genre than that with which we began. Indeed, with a few exceptions, most of the modern debates about the concept of genre are either ignored or cited in passing rather than directly engaged. Nonetheless, there are a number of interesting and important individual papers in this volume and only a few that disappoint.Among the most praiseworthy is Eric Csapo's "From Aristophanes to Menander? Genre Transformation in Greek Comedy." Csapo takes dead aim at the traditional narrative of the evolution from a politically engaged Old Comedy of ribald invective to an apolitical plot-centered New Comedy typified by Menander and his Roman epigones. Csapo's argument is that this narrative was manufactured, not through the accidents of preservation, but through a deliberate selection and canonization of texts by early Peripatetic critics and scholars. When we characterize Old Comedy as being typified by Aristophanes' carnivalesque assaults on the Athenian political establishment and then point to his plays as proof, we are not only engaging in circular reasoning, we are also treading a path that has been deliberately and tendentiously drawn for us. Thus, while the traditional narrative depicts a linear evolution from iambic to Old Comedy to New Comedy, which is portrayed as a movement from the personal and the topical to the universal and the apolitical, Aristotle himself, as Csapo notes (117), admits that Crates, Aristophanes' predecessor, abandoned the iambic and began to compose generalizing plots (Po. 1449b7-8). In short, plots of the kind deemed [End Page 119] typical of New Comedy are to be found at the very beginning of the comic form. By the same token, we have evidence of political comedy surviving well past Aristophanes' supposed invention of the Middle Comic style in the Plutus. Indeed, the last example of an Athenian comedy of political invective is Demetrius' Areopagite, dating from circa 294 B.C.E.Csapo's argument, of course, is not a simpleminded refusal to acknowledge change but rather an attempt to rethink the historical evolution of the comic genre outside the bounds of a narrow, teleological narrative. Genres are always complex negotiations between competing conceptions of the same form by different producers and consumers. At various times, for various intrinsic and extrinsic reasons, different versions of the same form will be ascendant or fading into eclipse. But it is never a question of an essence that either unfolds its fullness over time or declines from a single ideal instantiation.Less revolutionary but equally persuasive is Joseph W. Day's "Epigram and Reader: Generic Force as (Re-)Activation of Ritual." Day examines the relation between dedicatory epigrams on cult statues and their ritual contexts by arguing that the dedicatory genre is essentially performative rather than constative. These epigrams do their social work by activating a performative context in the mind of the reader... (shrink)

The question of the nature of Hegel’s metaphysics is a continuing one. In the last few decades the idea that Hegel even has a metaphysics has been challenged. Recently Stephen Houlgate has responded to this latter idea and tried to show not only that Hegel has a metaphysics, but of what sort it is. In my view Houlgate is right about Hegel having a metaphysics and also right generally about what sort of metaphysics it is. However, it seems to me (...) that he has made too weak a case for the metaphysics in his presentation of what he takes to be Hegel’s arguments, and as a consequence cannot escape a charge that Hegel might still be either a Kantian or some sort of subjective idealist. What I mean by this is that, to the extent that we are simply limited in our metaphysics to what we can think being to be, there may still be an absolute other which we simply cannot know. Houlgate has made things very clear concerning the conclusion to which we should come about the nature of Hegel’s metaphysics, but has not, in my view, made his argument leading to his conclusions quite strong enough. (shrink)

This book aims to spell out the consequences of taking the technologies behind the doing of science seriously.

We argue that there is a conflict among classical theism's commitments to divine simplicity, divine creative freedom, and omniscience. We start by defining key terms for the debate related to classical theism. Then we articulate a new argument, the Aloneness Argument, aiming to establish a conflict among these attributes. In broad outline, the argument proceeds as follows. Under classical theism, it's possible that God exists without anything apart from Him. Any knowledge God has in such a world would be wholly (...) intrinsic. But there are contingent truths in every world, including the world in which God exists alone. So, it's possible that God contingently has wholly intrinsic knowledge. But whatever is contingent and wholly intrinsic is an accident. So, God possibly has an accident. This is incompatible with classical theism. Finally, we consider and rebut several objections. (shrink)

Universities are generally understood as organizations that extend knowledge based on codified bodies of work developed from systematic research and scholarship. This article examines the emergence of an organizational form that increasingly competes in contemporary higher education: the therapeutic university. A recent phenomenon, the therapeutic university is predicated on emotion in which the goal is to make the experience as a student as comfortable as possible. The article discusses organizational morphology of the therapeutic university by identifying practices within it. The (...) practices establish a contest between a rational-universalistic orientation of the university on the one hand and an emotion-particularistic orientation on the other. The article provides an explanation for why this organizational form arose and what it purports to accomplish. Its operations are ensnared by major paradox: as its identity implies, the therapeutic university postures to do good, but its practices, it is argued, debilitate students and higher learning. The mandate that the broader society gives to higher education is thereby susceptible to lost confidence. The article concludes by discussing a way in which universities may be inoculated from the conditions that support their present-day therapeutic proclivities. (shrink)

We examine two competing solutions to Benardete paradoxes: causal finitism, according to which nothing can have infinitely many causes, and the unsatisfiable pair diagnosis (UPD), according to which such paradoxes are logically impossible and no metaphysical thesis need be adopted to avoid them. We argue that the UPD enjoys notable theoretical advantages over causal finitism. Causal finitists, however, have levelled two main objections to the UPD. First, they urge that the UPD requires positing a ‘mysterious force’ that prevents paradoxes from (...) arising. Since such a force is implausible, the UPD is in trouble. Second, they employ recombination or patchwork principles to argue that paradoxical situations would be possible if causal finitism were false. Since such situations are not possible, causal finitism is true, and so a substantive metaphysical thesis is needed to avoid the paradoxes. We argue that the UPD proponent can successfully respond to these objections. (shrink)

Benardete paradoxes involve a beginningless set each member of which satisfies some predicate just in case no earlier member satisfies it. Such paradoxes have been wielded on behalf of arguments for the impossibility of an infinite past. These arguments often deploy patchwork principles in support of their key linking premise. Here I argue that patchwork principles fail to justify this key premise.

Modal collapse arguments are all the rage in certain philosophical circles as of late. The arguments purport to show that classical theism entails the absurdly fatalistic conclusion that everything exists necessarily. My first aim in this paper is bold: to put an end to action-based modal collapse arguments against classical theism. To accomplish this, I first articulate the ‘Simple Modal Collapse Argument’ and then characterize and defend Tomaszewski’s criticism thereof. Second, I critically examine Mullins’ new modal collapse argument formulated in (...) response to the aforementioned criticism. I argue that Mullins’ new argument does not succeed. Third, I critically examine a powers-based modal collapse argument against classical theism that has received much less attention in the literature. Fourth, I show why God’s being purely actual, as well God’s being identical to each of God’s acts, simply cannot entail modal collapse given indeterministic causation. This, I take it, signals the death of modal collapse arguments. But not all hope is lost for proponents of modal collapse arguments—for the death is a fruitful one insofar as it paves the way for new inquiry into at least two new potential problems for classical theism. Showing this is my paper’s second aim. (shrink)

The question is how do Scanning Electron Microscopes (SEMs) give us access to the nano world? The images these instruments produce, I argue, do not allow us to see atoms in the same way that we see trees. To the extent that SEMs and STMs allow us to see the occupants of the nano world it is by way of metaphorical extension of the concept of “seeing”. The more general claim is that changes in scientific instrumentation effect changes in the (...) concepts central to our understanding of scientific results. (shrink)

Study of the foreign magistri and protomagistri of the medieval cathedral of Ragusa (Dubrovnik) (ca 1130-1350, rebuilt after 1693) reveals the social dynamics of artists’ travel in Mediterranean ports. Building on previous research of the builders’ artistic contexts and references, this analysis combines close reading and comparison of contract documents, discussion of Ragusa’s foreign citizenship law, and questions informed by the sociology of mobility. The study concludes that the governor patrons of Ragusa Cathedral exploited the increased physical and occupational mobility (...) of Adriatic builders, then arrested that mobility by offering the builders social advantages in the form of professional security and a path to citizenship. This balance of mobility at multiple levels manifested in the cathedral’s cosmopolitan and open-ended design. (shrink)

This article argues that descriptions of the Black Sea found in the Archaic poets, Herodotus, and later geographers were influenced by commercial itineraries circulated amongst Greek slave traders in the north. Drawing on an epigraphic corpus of twenty-three merchant letters from the region dating between c. 550 and 450 BCE, I contrast the travels of enslaved persons recorded in the documents with stylized descriptions found in literary accounts. This article finds that slaves took a variety of routes into—and out of—slavery, (...) and that fear of enslavement was widely felt even among Greeks. Law courts might have been as important as “barbarian” warfare in ensnaring captives for export, and even slave traders themselves risked enslavement alongside their victims. Reconstructing the travels of individual slaves allows us to pursue a study in the spirit of what Joseph C. Miller has called the “biographical turn” in the study of slavery, privileging the experiences of the enslaved over the accounts of their masters. Although the lands around the distant Black Sea were never the leading source of slaves for Aegean cities, the wealth of primary testimony from the region puts it at the forefront in the history of slavery in ancient Greece. (shrink)

Essays on the Philosophy of Wilfrid Sellars.

We draw out significant consequences of a relatively popular theory of metaphysical modality—branching actualism—for cosmological arguments for God’s existence. According to branching actualism, every possible world shares an initial history with the actual world and diverges only because causal powers (or dispositions, or some such) are differentially exercised. We argue that branching actualism undergirds successful responses to two recent cosmological arguments: the Grim Reaper Kalam argument and a modal argument from contingency. We also argue that branching actualism affords a response (...) to one popular defense of the classic contingency argument. What results are new difficulties for several cosmological arguments arising from the metaphysics of modality. (shrink)

Although sports and athletics provide a nearly universal social context for the learning of such cherished values as courage, honesty, discipline, communal efforts, and the pursuit of excellence, little attention has been devoted to the philosophy of this important element in human life. In a fascinating survey of the philosophic dimensions of sports and athletics, the author delves into a variety of topics, including game and play theory, play-forms and game principles in history, existentialism and sports, the popularity of sports, (...) its educational values, the function of ethics and moral values, and the role of competition, violence and aggression, self discovery, spirituality, and joy. He also considers recurrent problems such as corruption, the excessive emphasis on winning, and the exploitation of student athletes and suggests specific ways of preserving perspective and integrity. -- From publisher's description. (shrink)

James Henry Collin recently developed a new symmetry breaker favouring the ontological argument’s possibility premiss over that of the reverse ontological argument. The symmetry breaker amounts to an undercutting defeater for the reverse possibility premiss based on Kripkean cases of a posteriori necessity. I argue, however, that symmetry re-arises in two forms. First, I challenge the purported asymmetry in epistemic entitlements to the original and reverse possibility premisses. Second, relevantly similar Kripkean cases equally undercut the original possibility premiss.

Edward Feser defends the ‘Aristotelian proof’ for the existence of God, which reasons that the only adequate explanation of the existence of change is in terms of an unchangeable, purely actual being. His argument, however, relies on the falsity of the Existential Inertia Thesis, according to which concrete objects tend to persist in existence without requiring an existential sustaining cause. In this article, I first characterize the dialectical context of Feser’s Aristotelian proof, paying special attention to EIT and its rival (...) thesis—the Existential Expiration Thesis. Next, I provide a more precise characterization of EIT, after which I outline two metaphysical accounts of existential inertia. I then develop new lines of reasoning in favor of EIT that appeal to the theoretical virtues of explanatory power and simplicity. Finally, I address the predominant criticisms of EIT in the literature. (shrink)

BOOK REVIEWS 151 excellent companion). It is an insightful account of Schelling's writing and makes a successful run at actualizing Schelling's potential contribution to contemporary debate. BRAD PRAGER CorneU University Terry Pinkard. Hegel's Phenomenology: The Sociality of Reason. New York: Cambridge University Press, 1994. Pp. vii + 45 I. Cloth, $59-95. This book is a significant addition to contemporary literature on Hegel. The writing is clear and is free of confusing Hegelian language. At the same time, Pinkard penetrates to the (...) heart of important interpretative and general philosophical questions. His style makes the work accessible not only to Hegel scholars and other philosophers interested in Hegel, but also to graduate students and advanced undergraduates. The scholarship is sound, although a bit limited, referring to recent work in English and some recent, as well as classical, work in German. The volume concentrates on.. (shrink)