Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.

Anyone who has ever found herself or himself at odds with a boss, a board, a committee, a pastor, family member - or with any other institutional setting of which she or he my be a part - will find this book full of help and insight and wisdom. Conflicting Agendas is an invaluable guide to sorting out the complexities of individual moral existence in an increasingly complex and complicated world.

Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions.

We characterise explicitly the decidable predicates on integers of Infinite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down $\zeta$, the least ordinal not the length of any eventual output of an Infinite Time Turing machine ; using this the Infinite Time Turing Degrees are considered, and it is shown how the jump operator coincides with the production of mastercodes for the constructible hierarchy; further that the natural ordinals associated with the (...) jump operator satisfy a Spector criterion, and correspond to the L$_\zeta$-stables. It also implies that the machines devised are "$\Sigma_2$ Complete" amongst all such other possible machines. It is shown that least upper bounds of an "eventual jump" hierarchy exist on an initial segment. (shrink)

Filial Obligation The question of what one should do for one’s parents is often urgent; a parent needs care in the near future, and the grown child must decide what kind of care to provide, whether and to what extent to finance the provision of care, and to what extent the child ought to sacrifice … Continue reading Filial Obligation →.

A small large cardinal upper bound in $V$ for proving when certain subsets of $\omega_1$ are precisely those constructible from a real is given. In the core model we find an exact equivalence in terms of the length of the mouse order; we show that $\forall B \subseteq \omega_1 \lbrack B$ is universally Baire $\Leftrightarrow B \in L\lbrack r \rbrack$ for some real $r\rbrack$ is preserved under set-sized forcing extensions if and only if there are arbitrarily large "admissibly measurable" cardinals.

We discuss some of the relationships between the notion of "mutual stationarity" of Foreman and Magidor and measurability in inner models. The general thrust of these is that very general mutual stationarity properties on small cardinals, such as the ℵns, is a large cardinal property. A number of open problems, theorems, and conjectures are stated.

There have been periodic claims that evolutionary biology needs urgent reform, and this article tries to account for the volume and persistence of this discontent. It is argued that a few inescapable properties of the field make it prone to criticisms of predictable kinds, whether or not the criticisms have any merit. For example, the variety of living things and the complexity of evolution make it easy to generate data that seem revolutionary, and lead to disappointment with existing explanatory frameworks. (...) It is then argued that special discontent stems from misunderstandings and dislike of one well-known but atypical research programme: the study of adaptive function, in the tradition of behavioural ecology. To achieve its goals, this research needs distinct tools, often including imaginary agency, and a partial description of the evolutionary process. This invites mistaken charges of narrowness and oversimplification, and these chime with anxieties about human agency and overall purpose. The article ends by discussing several ways in which calls to reform evolutionary biology actively hinder progress in the field. (shrink)

Human decisions are conditioned by formidable uncertainty. The standard resource for dealing rationally with uncertainty is the mathematical concept of probability. The probability calculus is well-known, but since the numerical demands for applying it cannot usually be met, it is not widely applicable. By contrast, the concept of plausibility is widely applicable, but it is little known. This book relies on a generalized concept of plausibility whose strength is its adaptability. The adaptability is due to a novel form of decision (...) theory that takes plausibilities as inputs. This form of decision theory can be adapted to decisions informed by sharp probabilities and utilities as well as to decisions that must be made without them. The book illustrates its application to problems in argumentation theory, scientific theory choice, risk management, ethics, law, economics, and epistemology. (shrink)

We show in ZFC, assuming all reals have sharps, that a countable collection of $\triangle^1_3$-degrees without a minimal upper bound implies the existence of inner models with measurable cardinals.

We show that the set of ultimately true sentences in Hartry Field's Revenge-immune solution model to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger's revision sequence starting from the null hypothesis. We further remark that this shows that a substantial subsystem of second-order number theory is needed to establish the semantic values of sentences in Field's relative consistency proof of his theory over the ground model of the standard natural numbers: -CA0 (...) (second-order number theory with a -comprehension axiom scheme) is insufficient. We briefly consider his claim to have produced a solution to the semantic paradoxes by introducing this conditional. We remark that the notion of a operator can be introduced in other settings. (shrink)

We show that assuming modest large cardinals, there is a definable class of ordinals, closed and unbounded beneath every uncountable cardinal, so that for any closed and unbounded subclasses $P, Q, {\langle L[P],\in,P \rangle }$ and ${\langle L[Q],\in,Q \rangle }$ possess the same reals, satisfy the Generalised Continuum Hypothesis, and moreover are elementarily equivalent. Examples of such P are Card, the class of uncountable cardinals, I the uniform indiscernibles, or for any n the class $C^{n}{=_{{\operatorname {df}}}}\{ \lambda \, | \, (...) V_{\lambda } \prec _{{\Sigma }_{n}}V\}$ ; moreover the theory of such models is invariant under ZFC-preserving extensions. They also all have a rich structure satisfying many of the usual combinatorial principles and a definable wellorder of the reals. The inner model constructed using definability in the language augmented by the Härtig quantifier is thus also characterized. (shrink)

We locate winning strategies for various ${\mathrm{\Sigma }}_{3}^{0}$ -games in the L-hierarchy in order to prove the following: Theorem 1. KP+Σ₂-Comprehension $\vdash \exists \alpha L_{\alpha}\ models"\Sigma _{2}-{\bf KP}+\Sigma _{3}^{0}-\text{Determinacy}."$ Alternatively: ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}-{\mathrm{C}\mathrm{A}}_{0}\phantom{\rule{0ex}{0ex}}$ "there is a β-model of ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17 em}}{\mathrm{\Sigma }}_{3}^{0}$ -Determinacy." The implication is not reversible. (The antecedent here may be replaced with ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left({\mathrm{\Pi }}_{3}^{1}\right)-{\mathrm{C}\mathrm{A}}_{0}:\text{\hspace{0.17em}}{\mathrm{\Pi }}_{3}^{1}$ instances of Comprehension with only ${\mathrm{\Pi }}_{3}^{1}$ -lightface definable parameters—or even weaker theories.) Theorem 2. KP +Δ₂-Comprehension +Σ₂-Replacement + ${\mathrm{\Sigma }}_{3}^{0}\phantom{\rule{0ex}{0ex}}$ -Determinacy. (Here AQI (...) is the assertion that every arithmetical quasi-inductive definition converges.) Alternatively: $\Delta _{3}^{1}{\rm CA}_{0}+{\rm AQI}\nvdash \Sigma _{3}^{0}$ -Determinacy. Hence the theories: ${\mathrm{\Pi }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0},\text{\hspace{0.17em}}{\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}+\text{\hspace{0.17em}}{\mathrm{\Sigma }}_{3}^{0}-\mathrm{D}\mathrm{e}\mathrm{t}\phantom{\rule{0ex}{0ex}}$ -Det, ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}+\mathrm{A}\mathrm{Q}\mathrm{I}$ , and ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}\phantom{\rule{0ex}{0ex}}$ are in strictly descending order of strength. (shrink)

Listening for the sounds of silence: a nursing consideration of caring for the politically tortured In 1997 Amnesty International reported that 115 out of 251 countries surveyed practised torture on their citizens. Many of these victims have been forced to flee their country of origin and become refugees in the West, in countries such as Australia, Canada, the UK and the United States. However, torture itself remains an unspoken and covert problem. In addition to the obvious traumatic effects, it may (...) induce shame and dread on the part of the victim. It may be too terrifying and too painful to talk about, and yet may affect every aspect of a person’s life (Forrest 1996). All too commonly a victim of torture may pass unnoticed or unrecognised because health care providers do not know how, or may be unwilling to engage with the issue. This paper will examine the implications for nurses of caring for the tortured. It will explore the nature of torture itself, who might be the perpetrators and who might be the victims (always acknowledging that nurses and other health care staff are often both), how victims of torture may present for health care, and the possible subjective perceptions of a torture victim when faced with a Western health care process and understanding. Finally, it will argue for an increase in awareness and sensitivity on the part of all nurses in all health care settings to the needs and sensibilities of victims of torture, and suggest that caring for them is the distillation of everything good nursing practice should be. (shrink)

Despite the fact that many people face pressing questions about what they are morally required to do for their aging parents, surprisingly little has been said in the literature about filial obligations. After considering and rejecting two theories--Gratitude Theory and Special Goods Theory--this paper offers a novel, blended theory of filial obligations, called the Gratitude for Special Goods Theory. On this view, grown children often have extensive obligations to meet their parents’ needs, for doing so serves as an expression of (...) gratitude for the parents’ past provision of goods to the child. (shrink)

We characterise explicitly the decidable predicates on integers of Infinite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down ζ, the least ordinal not the length of any eventual output of an Infinite Time Turing machine (halting or otherwise); using this the Infinite Time Turing Degrees are considered, and it is shown how the jump operator coincides with the production of mastercodes for the constructible hierarchy; further that the natural ordinals associated (...) with the jump operator satisfy a Spector criterion, and correspond to the L ζ -stables. It also implies that the machines devised are "Σ 2 Complete" amongst all such other possible machines. It is shown that least upper bounds of an "eventual jump" hierarchy exist on an initial segment. (shrink)

Most ethical decisions are conditioned by formidable uncertainty. Decision makers may lack reliable information about relevant facts, the consequences of actions, and the reactions of other people. Resources for dealing with uncertainty are available from standard forms of decision theory, but successful application to decisions under risk requires a great deal of quantitative information: point-valued probabilities of states and point-valued utilities of outcomes. When this information is not available, this paper recommends the use of a form of decision theory that (...) operates on a bare minimum of information inputs: comparative plausibilities of states and comparative utilities of outcomes. In addition, it proposes a comparative strategy for dealing with second-order uncertainty. The paper illustrates its proposal with reference to a well-known ethical dilemma: Kant’s life-saving lie. (shrink)

I construct an analysis of social trust that attends distinctively to cooperation in social relations that has the capability to (begin to) counter the default social distrust obtained due to oppressive conditions via a form of collective reasoning. For social trust to overcome oppression it must be a normatively transparent form of trust. Transparent trust can counter the effects of oppression on social interaction and foster social cooperation by correcting unequal positions of social vulnerability and improving disparities in credibility resultant (...) of oppression since collective reasoning in norm legitimization permits all individuals to participate in the process of self and other defining and the development of the concomitant norms that guide these processes. (shrink)

Horace's Satires 1.8 and 1.9 have long interested commentators for the enticing glimpse they provide of the changing Roman cityscape in the 30s BCE In light of the recent problematization of the strict correspondence between the poet Horace and his elaborately constructed satiric persona, locations in the Satires should be read not so much as autobiographical accounts of the poet's movement through the city but rather as functions of other themes and motifs in the Satires. This paper examines the moral (...) and aesthetic encoding of the urban landscape in Horace's Satires Book I.Satires 1.9 and 1.8 reveal that Rome's city center and the gardens of Maecenas constitute an arena for the satirist's indirect meditation about the complex relationship between his poetry and his patron Maecenas. By mapping moral and aesthetic behavior onto these urban areas, Horace comments on the viability of satiric poetry in various social situations and settings. The emerging picture presents the city center — filled as it is with human vice and folly — as a place appropriate for satiric poetry, and Maecenas' gardens — free from competition and ambition — as a place inimical to it. Thus the gardens of Maecenas present for the satirist a moral and aesthetic problem, and their specter haunts his downtown stroll in Satires 1.9 as much as does the aspirant who dogs his steps. The decorum of patronage requires that Horace show proper subordination to his benefactors. Yet the decorum of satire requires that the poet undermine status, stability, and authority. While professing that status is not an issue in Maecenas' circle, the poems reveal instead that status is always an issue, aected no less by one's physical than one's social position. (shrink)

The focus of this study is cognitive choice: the selection of one cognitive option (a hypothesis, a theory, or an axiom, for instance) rather than another. The study proposes that cognitive choice should be based on the plausibilities of states posited by rival cognitive options and the utilities of these options' information outcomes. The proposal introduces a form of decision theory that is novel because comparative; it permits many choices among cognitive options to be based on merely comparative plausibilities and (...) utilities. This form of decision theory intersects with recommendations by advocates of decision theory for cognitive choice, on the one hand, and defenders of comparative evaluation of scientific hypotheses and theories, on the other. But it differs from prior decision-theoretic proposals because it requires no more than minimal precision in specifying plausibilities and utilities. And it differs from comparative proposals because none has shown how comparative evaluations can be carried out within a decision-theoretic framework. (shrink)

This book investigates the phenomenological ways that dance choreographing and dance performance exemplify both Truth and meaning-making within Native American epistemology, from an analytic philosophical perspective. Given that within Native American communities dance is regarded both as an integral cultural conduit and “a doorway to a powerful wisdom,” Shay Welch argues that dance and dancing can both create and communicate knowledge. She explains that dance—as a form of oral, narrative storytelling—has the power to communicate knowledge of beliefs and histories, (...) and that dance is a form of embodied narrative storytelling. Welch provides analytic clarity on how this happens, what conditions are required for it to succeed, and how dance can satisfy the relational and ethical facets of Native epistemology. (shrink)

Tocqueville's contradictory writings on imperialism have produced interpretations that range from unrepentant realism to lapsed universalism. This essay considers the moral psychology that underlies his position. It argues that Tocqueville's writings on colonialism exemplify his resort to apologia when his deepest apprehensions are aroused and offers a typology of Tocquevillean rhetorical evasions: the mechanisms by which he attempts to quell perceptions of moral dissonance. It also argues that Tocqueville's evasion of the challenge of Algeria illustrates a particular kind of liberal (...) failure and a peculiar liberal temptation. By avoiding rather than confronting the conflicting intuitions underlying his moral judgments, Tocqueville betrays the promise of his liberalism by failing to explore the tensions implicit in the practice of liberal democracy. These strategies to deaden awareness of complicity in colonial violence appear disturbingly familiar in a world in which national interests and universally acknowledged "human maxims" increasingly collide in the liberal conscience. (shrink)

In this paper, I explore a number of issues related to a life lived with borderline personality disorder (BPD). Primarily, I am interested in discussing how one unwillingly changes their personal identity by forced medicating—demanded by others implicitly and explicitly. My motivation is something deep and invasive in me. I want to know, I have always wanted to know, why others want me to not be Me so badly. I have thought about this question for years, and though others may (...) simply chalk it up to just one of the standard paranoid or narcissistic traits of borderline personality disorder, there is something more to this question that many of us agonize over most of our lives. There is a deeply normative component to this question that extends beyond the mere fear of abandonment; it is tied to a desire by others to erase—literally—who we are for their own comfort. In this sense, then, I invite you to travel along a path of what it can mean to be a BPDer, from a narrative, phenomenological, and cognitive lived, embodied perspective. My purpose is to show that the treatments for us that others desire cannot avoid (and usually do not want to avoid) the unraveling of who we really are. Whether we want to or not, we give up our self to keep other people with us. And for many, this is too much to ask, and can be one, though not the only, reason suicide and self‐harm seem to be necessary recourses. One in 10 people with BPD commit suicide. So this is a serious matter, indeed. (shrink)

This article is concerned with reflection principles in the context of Cantor’s conception of the set-theoretic universe. We argue that within such a conception reflection principles can be formulated that confer intrinsic plausibility to strong axioms of infinity.

We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set.

Academic productivity is realized through resources obtained from professional networks in which scientists are embedded. Using a national survey of academic faculty in Science, Technology, Engineering, and Mathematics fields across multiple institution types, we examine how the structure of professional networks affects scholarly productivity and how those effects may differ by race, ethnicity, and gender. We find that network size masks important differences in composition. Using negative binomial regression, we find that both the size and composition of professional networks affect (...) scientific productivity, but bigger is not always better. We find that instrumental networks increase scholarly productivity, while advice networks reduce it. There are important interactive effects that are masked by modeling only direct effects. We find that white men are especially advantaged by instrumental networks, and women are especially advantaged by advice networks. (shrink)

The logician Kurt Godel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the (...) mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Godel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field. (shrink)

We follow [8] in asking when a set of ordinals $X \subseteq \alpha$ is a countable union of sets in K, the core model. We show that, analogously to L, and X closed under the canonical Σ 1 Skolem function for K α can be so decomposed provided K is such that no ω-closed filters are put on its measure sequence, but not otherwise. This proviso holds if there is no inner model of a weak Erdős-type property.

A small large cardinal upper bound in V for proving when certain subsets of ω 1 (including the universally Baire subsets) are precisely those constructible from a real is given. In the core model we find an exact equivalence in terms of the length of the mouse order; we show that $\forall B \subseteq \omega_1 \lbrack B$ is universally Baire $\Leftrightarrow B \in L\lbrack r \rbrack$ for some real r] is preserved under set-sized forcing extensions if and only if there (...) are arbitrarily large "admissibly measurable" cardinals. (shrink)

Vagueness is epistemic, according to some. Vagueness is ontological, according to others. This article deploys what I take to be a compromise position. Predicates are coined in specific contexts for specific purposes, but these limited practices do not automatically fix the extensions of predicates over the domain of all objects. The linguistic community using the predicate has rarely considered, much less decided, all questions that might arise about the predicate’s extension. To this extent, the ontological view is correct. But a (...) predicate that applies in some contexts can be reasonably extended to other contexts where it is initially vague. This process of development approximates the cognitive remedy for vagueness that the epistemic view prescribes. The process is piecemeal and inductive, akin to what von Wright described as the molding of concepts. Vagueness cannot be understood apart from the backdrop of classification, for vagueness is classification gone awry. Hence these pages explore the classification of particulars, both its clear successes and vague failures. How we classify unique particulars is the theme of Sections 2 and 3, which are primarily descriptive. Section 2 identifies a way of classifying particulars that pervades discourse of all sorts, and Section 3 illustrates its use in a field notorious for vagueness: ethics. Why a certain particular should (or should not) be classified in a certain way is a normative question, however, and it occupies Sections 4 and 5. Section 4 proposes a norm for strong arguments by analogy, and Section 5 illustrates how the norm might resolve vagueness in one kind of ethical dispute. This norm, which has a strong probabilistic component, is one way of affirming that probability is a guide to life. (shrink)

We show how in the hierarchies${F_\alpha }$of Fieldian truth sets, and Herzberger’s${H_\alpha }$revision sequence starting from any hypothesis for${F_0}$ that essentially each${H_\alpha }$ carries within it a history of the whole prior revision process.As applications we provide a precise representation for, and a calculation of the length of, possiblepath independent determinateness hierarchiesof Field’s construction with a binary conditional operator. We demonstrate the existence of generalized liar sentences, that can be considered as diagonalizing past the determinateness hierarchies definable in Field’s recent (...) models. The ‘defectiveness’ of such diagonal sentences necessarily cannot be classified by any of the determinateness predicates of the model. They are ‘ineffable liars’. We may consider them a response to the claim of Field that ‘the conditional can be used to show that the theory is not subject to “revenge problems”.’. (shrink)

In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to reject (...) many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate 'is necessary' can then be replaced by 'is necessarily true'. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators. (shrink)

We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of all sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games considered here are simple, those over the natural model of arithmetic being all within the arithmetical class of $\Sum_{3}^{0}$.

Welch's essay addresses the complicated issue of whether to hold leaders accountable for their ethical decisions and conduct. Are there minimal standards for ethical behavior?

Advancing Medical Posthumanism Through Twenty-First Century American Poetry places contemporary poetics in dialogue with posthumanism and biomedicine in order to create a framework for advancing a posthuman-affirmative ethics within the culture of medical practice. This book makes a case for a posthumanist understanding of the body—one that sees health and illness not as properties possessed by individual bodies, but as processes that connect bodies to their social and natural environment, shaping their capacity to act, think, and feel. Tana Jean (...) class='Hi'>Welch demonstrates how contemporary American poetry is specifically poised to develop a pathway toward a posthuman intervention in biomedicine, the field of medical humanities, medical discourse, and the value systems that guide U.S. healthcare in general. (shrink)