• We define a notion of order of indiscernibility type of a structure by analogy with Mitchell order on measures; we use this to define a hierarchy of strong axioms of infinity defined through normal filters, the α-weakly Erdős hierarchy. The filters in this hierarchy can be seen to be generated by sets of ordinals where these indiscernibility orders on structures dominate the canonical functions.• The limit axiom of this is that of greatly Erdős and we use it to calibrate (...) some strengthenings of the Chang property, one of which, CC+, is equiconsistent with a Ramsey cardinal, and implies that where K is the core model built with non-overlapping extenders — if it is rigid, and others which are a little weaker. As one corollary we have:TheoremIf then there is an inner model with a strong cardinal. • We define an α-Jónsson hierarchy to parallel the α-Ramsey hierarchy, and show that κ being α-Jónsson implies that it is α-Ramsey in the core model. (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 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.

Axiomatic set theory is the concern of this book. More particularly, the authors prove results about the coding of models M, of Zermelo-Fraenkel set theory together with the Generalized Continuum Hypothesis by using a class 'forcing' construction. By this method they extend M to another model L[a] with the same properties. L[a] is Gödels universe of 'constructible' sets L, together with a set of integers a which code all the cardinality and cofinality structure of M. Some applications are also considered. (...) Graduate students and research workers in set theory and logic will be especially interested by this account. (shrink)

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)

Modern scientific theories of emotional behavior, almost without exception, trace their origin to Charles Darwin, and his publications On the Origin of Species (1859) and The Expression of the Emotions in Man and Animals (1872). The most famous evolutionary dilemma Darwin acknowledged as a challenge to his theory of natural selection was the incomplete sub Cambrian fossil record. However, Darwin struggled with two other rarely referenced theoretical and scientific dilemmas that confounded his theories about emotional behavior. These included (1) the (...) origin of social instincts (e.g., altruism, empathy, reciprocity and cooperation) and the reasons for their conservation in evolution and (2) the peripheral control of heart rate vis-a-vis emotional behavior outside of consciousness. Darwin acknowledged that social instincts are critical to the survival of some species, but had difficulty aligning them with his theory of natural selection in humans. Darwin eventually proposed that heart rate and emotions are controlled via one’s intellect and cortical mechanisms, and that instinctive behavior is genetically-programmed and inherited. Despite ongoing efforts, these two theoretical dilemmas are debated to this day. Simple testable hypotheses have yet to emerge for the biological mechanisms underlying instinctive behavior or the way heart rate is controlled in infants. In this paper, we review attempts to resolve ¬these issues over the past 160 years. We posit that research and theories that supported Darwin’s individualistic brain-centric and genetic model have become an “orthodox” Western view of emotional behavior, one that produced the prevailing behavioral construct of attachment as developed by John Bowlby. We trace research and theories that challenged this orthodoxy at various times, and show how these challenges were repeatedly overlooked, rejected, or misinterpreted. We review two new testable theories, emotional connection theory and calming cycle theory, which we argue resolve the two dilemmas We show emerging scientific evidence from physiology and a wide variety of other fields, as well from clinical trials among prematurely born infants, that supports the two theories. Clinical implications of the new theories and possible new ways to assess risk and intervene in emotional, behavioral and developmental disorders are discussed. (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.

Since James defined emotion as consciousness of bodily reactions and Cannon and others detailed the nature of these reactions, there has been an increasing tendency among behaviorists to equate emotions with visceral reactions and to neglect some of the genetic and adaptive aspects of emotion which had been discussed by Darwin.

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 $\Sum_{3}^{0}$.

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)

It is shown that the determinacy of $G_{\delta \sigma }$ games of length $\omega ^2$ is equivalent to the existence of a transitive model of ${\mathsf {KP}} + {\mathsf {AD}} + \Pi _1\textrm {-MI}_{\mathbb {R}}$ containing $\mathbb {R}$. Here, $\Pi _1\textrm {-MI}_{\mathbb {R}}$ is the axiom asserting that every monotone $\Pi _1$ operator on the real numbers has an inductive fixpoint.

The paper explores the handling of singular analogy in quantitative inductive logics. It concentrates on two analogical patterns coextensive with the traditional argument from analogy: perfect and imperfect analogy. Each is examined within Carnap’s λ-continuum, Carnap’s and Stegmüller’s λ-η continuum, Carnap’s Basic System, Hintikka’s α-λ continuum, and Hintikka’s and Niiniluoto’s K-dimensional system. Itis argued that these logics handle perfect analogies with ease, and that imperfect analogies, while unmanageable in some logics, are quite manageable in others. The paper concludes with a (...) modification of the K-dimensional system that synthesizes independent proposals by Kuipers and Niiniluoto. (shrink)

This book moves beyond traditional readings of Alexis de Tocqueville and his relevance to contemporary democracy by emphasizing the relationship of his life and work to modern feminist thought. Within the resurgence of political interest in Tocqueville during the past two decades, especially in the United States, there has been significant scholarly attention to the place of gender, race, and colonialism in his work. This is the first edited volume to gather together a range of this creative scholarship. It reveals (...) a tidal shift in the reception history of Tocqueville as a result of his serious engagement by feminist, gender, postcolonial, and critical race theorists. The volume highlights the expressly normative nature of Tocqueville’s project, thus providing an overdue counterweight to the conventional understanding of Tocquevillean America as an actual place in time and history. By reading Tocqueville alongside the writings of early women’s rights activists, ethnologists, critical race theorists, contemporary feminists, neoconservatives, and his French contemporaries, among others, this book produces a variety of Tocquevilles that unsettles the hegemonic view of his work. Seen as a philosophical source and a political authority for modern democracies since the publication of the twin volumes of _Democracy in America _, Tocqueville emerges from this collection as a vital interlocutor for democratic theorists confronting the power relations generated by intersections of gender, sexual, racial, class, ethnic, national, and colonial identities. In addition to the editors, the contributors are Jocelyn Boryczka, Richard Boyd, Christine Carey, Barbara Cruikshank, Laura Janara, Matthew Holbreich, Kathleen S. Sullivan, Alvin B. Tillery Jr., Lisa Pace Vetter, Dana Villa, Cheryl B. Welch, and Delba Winthrop. (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)

The Infinite Time Turing Machine model [8] of Hamkins and Kidder is, in an essential sense, a "Σ₂-machine" in that it uses a Σ₂ Liminf Rule to determine cell values at limit stages of time. We give a generalisation of these machines with an appropriate Σ n rule. Such machines either halt or enter an infinite loop by stage ζ(n) = df μζ(n)[∃Σ(n) > ζ(n) L ζ(n) ≺ Σn L Σ(n) ], again generalising precisely the ITTM case. The collection of (...) such machines taken together computes precisely those reals of the least model of analysis. (shrink)

We investigate and classify the notion of final derivability of two basic inconsistency-adaptive logics. Specifically, the maximal complexity of the set of final consequences of decidable sets of premises formulated in the language of propositional logic is described. Our results show that taking the consequences of a decidable propositional theory is a complicated operation. The set of final consequences according to either the Reliability Calculus or the Minimal Abnormality Calculus of a decidable propositional premise set is in general undecidable, and (...) can be -complete. These classifications are exact. For first order theories even finite sets of premises can generate such consequence sets in either calculus. (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)

This volume recreates the received notion of reflective equilibrium. It reconfigures reflective equilibrium as both a cognitive ideal and a method for approximating this ideal. The ideal of reflective equilibrium is restructured using the concept of discursive strata, which are formed by sentences and differentiated by function. Sentences that perform the same kind of linguistic function constitute a stratum. The book shows how moral discourse can be analyzed into phenomenal, instrumental, and teleological strata, and the ideal of reflective equilibrium reworked (...) in these terms. In addition, the work strengthens the method of reflective equilibrium by harnessing the resources of decision theory and inductive logic. It launches a comparative version of decision theory and employs this framework as a guide to moral theory choice. It also recruits quantitative inductive logic to inform a standard of inductive cogency. When used in tandem with comparative decision theory, this standard can aid in the effort to turn the undesirable condition of reflective disequilibrium into reflective equilibrium. (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)

Theory choice can be approached in at least four ways. One of these calls for the application of decision theory, and this article endorses this approach. But applying standard forms of decision theory imposes an overly demanding standard of numeric information, supposedly satisfied by point-valued utility and probability functions. To ameliorate this difficulty, a version of decision theory that requires merely comparative utilities and plausibilities is proposed. After a brief summary of this alternative, the article illustrates how comparative decision theory (...) affords a rational reconstruction of decisions made by exemplary scientists in two cases of theory choice: Buffon’s law and the luminiferous ether. It also offers a rational reconstruction of two cases of theory diagnosis: Mendeleev’s anomalies and the Pioneer anomaly. (shrink)

Measured inequality has increased tremendously between the 1960s and 1990s, not only in the United States but throughout the majority of industrial nations. Wages among people of the same race and gender have become less equal. The hours worked by men have fallen, and the drop has been more pronounced among those who earn lower wages—as a result, inequality in labor income, which is the product of the wage rate and hours worked, has increased relative to inequality in wage rates. (...) Moreover, among married couples, employment of the wives of high-income men has increased until these wives are approximately as likely to be employed outside the home as are the wives of low-income men, who have always worked for wages. In addition, due to assortative mating, wage rates of husbands and wives are positively correlated, and it is clear that the growth in inequality of labor incomes among families has outstripped the growth in inequality in individual labor income. Finally, only the highest-income families have savings in excess of home equity and company-sponsored pensions, which implies that inequality in wealth among families has been exacerbated by the growth in stock prices. (shrink)

In this article, we consider music and noise in terms of vibrational and transferable energy as well as from the evolutionary significance of the hearing system of Homo sapiens. Music and sound impinge upon our body and our mind and we can react to both either positively or negatively. Much depends, in this regard, on the frequency spectrum and the level of the sound stimuli, which may sometimes make it possible to set music apart from noise. There are, however, two (...) levels of description: the physical-acoustic description of the sound and the subjective-psychological reactions by the listeners. Starting from a vibrational approach to sound and music, we first investigate how sound may activate the sense of touch and the vestibular system of the inner ear besides the sense of hearing. We then touch upon distinct issues such as the relation between low-frequency sounds and annoyance, the harmful effect of loud sound and noise, the direct effects of overstimulation with sound, the indirect effects of unwanted sounds as related to auditory neurology, and the widespread phenomenon of liking loud sound and music, both from the point of view of behavioral and psychological aspects. (shrink)

This book traces the historical lineages of Alvin Plantinga’s religious epistemology from Plato through Augustine and Calvin. It focuses upon this epistemology as a philosophical interpretation of what is generally taken to be a narrow theological doctrine. The author provides a textually based and closely reasoned introduction to the epistemological ideas of Plato, Augustine, Calvin, Plantinga, and several other writers and shows the continuity of a certain approach to the knowledge of God; it may be called the Platonic—Augustinian—Reformed approach.

After an introduction to the major issues confronting intellectuals, this book explores the various aspects of the intellectual's role including: * philosophers and academics who have tried to define the function of the intellectual * how intellectuals have assumed the status of the conscience of the nation and the voice of the oppressed * the interaction of intellectuals with Marxism * the place of the intellectual in American society Covering regions as diverse as Israel, Algeria, Britain, Ireland, central Europe and (...) America, this collection considers the question of whether the intellectual can still lay claim to the language of truth. In answering, this study tells us much about the modern world in which we live. _Coverage includes the following thinkers:_ Gramsci, Weber, Yeats, Auden, Levy, Mailer, Walzer, Marx and many more. (shrink)

Religious considerations in medical decision-making have enjoyed newfound attention in recent years, challenging the assumption that the domains of biological and spiritual flourishing can be cleanly separated in clinical practice. A surprising majority of patients desire their physicians to engage their religious and spiritual concerns, yet most never receive such attention, particularly in cases near the end of life where such attention seems most warranted.1–3 As physicians Aparna Sajja and Christina Puchalski recently wrote in the AMA Journal of Ethics theme (...) issue on ‘Religion and Spirituality in Healthcare Practice’, modern medical training is ‘falling short of preparing physicians to help patients with the metaphysical needs of their illness’.4 It would seem then that both patients and physicians might challenge the conclusions proffered by philosophers Jake Greenblum and Ryan Hubbard in ‘Responding to Religious Patients: Why Physicians Have No Business Doing Theology’, in which they claim that physicians ought not to engage religious reasoning for medical decisions. Their conclusion relies on two core arguments: a ‘public reason’ argument and a ‘fiduciary argument’, both of which contend that theology and religious considerations have no place in medical reasoning. We find that two central errors undergird these arguments. First is the fraught notion of an epistemically and ethically normative public reason, and second is a fundamental mischaracterisation of the fiduciary nature of the patient–physician relationship and the nature of medicine itself. In response, we argue that all physicians essentially ‘do theology’ and that, rather than divorcing theology from medical practice, clinicians should make it their business to do theology well. To support the exclusion of religious reasoning from medical decision-making, the authors open with a ‘public reason argument’, suggesting that physicians serve in roles closely resembling those of public officials. As such, the physician as public official ought to limit himself …. (shrink)