In this book, Peter Achinstein proposes and defends several objective concepts of evidence. He then explores the question of whether a scientific method, such as that represented in the four "Rules for the Study of Natural Philosophy" that Isaac Newton invoked in proving his law of gravity, can be employed in demonstrating how the proposed definitions of evidence are to be applied to real scientific cases.

In [1] Todorov has shown by means of axiomatic set theory that there exists a nonstandard function Δ: *ℝn → * ℂ such that for all continuous functions φ: ℝn → ℂ, equation image.Here *ℝ and *ℂ are the set of the nonstandard real numbers and the set of the nonstandard complex numbers, respectively, and *φ: *ℝn → *ℂ is the nonstandard extension of φ In the present note we want to prove an analogous theorem by predicative means only.

Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to (...) prove the Second Theorem, and exploring a family of related results. The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic. (shrink)

Peter Kivy is the author of many books on the history of art and, in particular, the aesthetics of music. This collection of essays spans a period of some thirty years and focuses on a richly diverse set of issues: the biological origins of music, the role of music in the liberal education, the nature of the musical work and its performance, the aesthetics of opera, the emotions of music, and the very nature of music itself. Some of these (...) subjects are viewed as part of the history of ideas, others as current problems in the philosophy of art. A particular feature of the volume is that Kivy avoids the use of musical notation so that no technical knowledge at all is required to appreciate his work. The essays will prove enjoyable and insightful not just to professionals in the philosophy of art and musicologists, or to musicians themselves, but also to any motivated general reader with a deep interest in music. (shrink)

In the history of philosophy, few topics are so relevant to today's cultural and political landscape as philosophy in the Islamic world. Yet, this remains one of the lesser-known philosophical traditions. In this Very Short Introduction, Peter Adamson explores the history of philosophy among Muslims, Jews, and Christians living in Islamic lands, from its historical background to thinkers in the twentieth century.Introducing the main philosophical themes of the Islamic world, Adamson integrates ideas from the Islamic and Abrahamic faiths to (...) consider the broad philosophical questions that continue to invite debate: What is the relationship between reason and religious belief? What is the possibility of proving God's existence? What is the nature of knowledge? Drawing on the most recent research in the field, this book challenges the assumption of the cultural decline of philosophy and science in the Islamic world by demonstrating its rich heritage and overlap with other faiths and philosophies. (shrink)

Showing that the arithmetic mean number of offspring for a trait type often fails to be a predictive measure of fitness was a welcome correction to the philosophical literature on fitness. While the higher mathematical moments of a probability-weighted offspring distribution can influence fitness measurement in distinct ways, the geometric mean number of offspring is commonly singled out as the most appropriate measure. For it is well-suited to a compounding process and is sensitive to variance in offspring number. The geometric (...) mean thus proves to be a predictively efficacious measure of fitness in examples featuring discrete generations and within- or between-generation variance in offspring output. Unfortunately, this advance has subsequently led some to conclude that the arithmetic mean is never a good measure of fitness and that the geometric mean should accordingly be the default measure of fitness. We show not only that the arithmetic mean is a perfectly reasonable measure of fitness so long as one is clear about what it refers to, but also that it functions as a more general measure when properly interpreted. It must suffice as a measure of fitness in any case where the geometric mean has been effectively deployed as a measure. We conclude with a discussion about why the mathematical equivalence we highlight cannot be dismissed as merely of mathematical interest. (shrink)

Spirtes, Glymour and Scheines [Causation, Prediction, and Search Springer] described a pointwise consistent estimator of the Markov equivalence class of any causal structure that can be represented by a directed acyclic graph for any parametric family with a uniformly consistent test of conditional independence, under the Causal Markov and Causal Faithfulness assumptions. Robins et al. [Biometrika 90 491–515], however, proved that there are no uniformly consistent estimators of Markov equivalence classes of causal structures under those assumptions. Subsequently, Kalisch and B¨uhlmann (...) [J. Mach. Learn. Res. 8 613–636] described a uniformly consistent estimator of the Markov equivalence class of a linear Gaussian causal structure under the Causal Markov and Strong Causal Faithfulness assumptions. However, the Strong Faithfulness assumption may be false with high probability in many domains. We describe a uniformly consistent estimator of both the Markov equivalence class of a linear Gaussian causal structure and the identifiable structural coefficients in the Markov equivalence class under the Causal Markov assumption and the considerably weaker k-Triangle-Faithfulness assumption. (shrink)

Accuracy-based arguments for conditionalization and probabilism appear to have a significant advantage over their Dutch Book rivals. They rely only on the plausible epistemic norm that one should try to decrease the inaccuracy of one's beliefs. Furthermore, it seems that conditionalization and probabilism follow from a wide range of measures of inaccuracy. However, we argue that among the measures in the literature, there are some from which one can prove conditionalization, others from which one can prove probabilism, and (...) none from which one can prove both. Hence at present, the accuracy-based approach cannot underwrite both conditionalization and probabilism. (shrink)

While ancient civilizations worshipped strong, active emotions, modern societies have favored more peaceful attitudes, especially within the democratic process. We have largely forgotten the struggle to make use of _thymos_, the part of the soul that, following Plato, contains spirit, pride, and indignation. Rather, Christianity and psychoanalysis have promoted mutual understanding to overcome conflict. Through unique examples, Peter Sloterdijk, the preeminent posthumanist, argues exactly the opposite, showing how the history of Western civilization can be read as a suppression and (...) return of rage. By way of reinterpreting the _Iliad_, Alexandre Dumas's _Count of Monte Cristo_, and recent Islamic political riots in Paris, Sloterdijk proves the fallacy that rage is an emotion capable of control. Global terrorism and economic frustrations have rendered strong emotions visibly resurgent, and the consequences of violent outbursts will determine international relations for decades to come. To better respond to rage and its complexity, Sloterdijk daringly breaks with entrenched dogma and contructs a new theory for confronting conflict. His approach acknowledges and respects the proper place of rage and channels it into productive political struggle. (shrink)

In his book, Peter Rohs develops a dualism of process-types founded in a theory of time: a type of mental processes belonging to a time-theoretical ontology and a type of physical processes belonging to a timeless ontology (the ontology of physics). This dualism should be proved as a basis for a non-naturalistic philosophy of mind, through which a libertarian concept of freedom and of personal autonomy can be defended. This theory is, as Rohs tries to demonstrate, compatible with the (...) theory of evolution. (shrink)

Gödel argued that his incompleteness theorems imply that either “the mind cannot be mechanized” or “there are absolutely undecidable sentences.” In the precursor to this paper I examined the early arguments for the first disjunct. In the present paper I examine the most sophisticated argument for the first disjunct, namely, Penrose’s new argument. It turns out that Penrose’s argument requires a type-free notion of truth and a type-free notion of absolute provability. I show that there is a natural such system, (...) DTK. I prove a series of results which show that Gödel’s disjunction is provable in the system, Penrose’s argument is invalid in the system, there can be no proof or refutation of either disjunct in the system, the independence results are robust in that they persist when one strengthens the principles governing absolute provability, and there are reasons to believe that the situation will not improve under any plausible alteration of the underlying theory of truth. (shrink)

The basic idea of the theorem is not very new: it is a slight generalization of a theorem proved by John Harsanyi in the 1950s.[i] The power of the book comes from his interpretation of the theorem, and from his strikingly clear and insightful discussion of the various conditions.

In this paper I address the question of whether the incompleteness theorems imply that “the mind cannot be mechanized,” where this is understood in the specific sense that “the mathematical outputs of the idealized human mind do not coincide with the mathematical outputs of any idealized finite machine.” Gödel argued that his incompleteness theorems implied a weaker, disjunctive conclusion to the effect that either “the mind cannot be mechanized” or “mathematical truth outstrips the idealized human mind.” Others, most notably, Lucas (...) and Penrose, have claimed more—they have claimed that the incompleteness theorems actually imply the first disjunct. I will show that by sharpening the fundamental concepts involved and articulating the background assumptions governing them, one can prove Gödel’s disjunction, one can show that the arguments of Lucas and Penrose fail, and one can see what likely led proponents of the first disjunct astray. (shrink)

We’ve now proved our key version of the First Theorem, Theorem 42. If T is the right kind of ω-consistent theory including enough arithmetic, then there will be an arithmetic sentence GT such that T ￿ GT and T ￿ ¬GT. Moreover, GT is constructed so that it is true if and only if unprovable-in T (so it is true). Now recall that, for a p.r. axiomatized theory T , Prf T(m, n) is the relation which holds just if m (...) is the super g.n. of a sequence of wffs that is a T proof of a sentence with g.n. n. This relation is p.r. decidable (see §25.4). Assuming T extends Q, it can capture any p.r. decidable relation, including Prf T (§22). So we can define.. (shrink)

This article examines the relationship between compromise and fairness, and considers in particular why, if a fair outcome to a conflict is available, the conflict should still be subject to compromise. It sets out the defining features of compromise and explains how fair compromise differs from both principled and pragmatic compromise. The fairness relating to compromise can be of two types: procedural or end-state. It is the coherence of end-state fairness with compromise that proves the more puzzling case. We offer (...) reasons why people should be allowed to resolve conflicting or competing claims through compromise, even if compromise comes at the expense of end-state fairness, but we resist the suggestion that the primary rationale for compromise is to be found in non-ideal circumstances. (shrink)

Gödel initiated the program of finding and justifying axioms that effect a significant reduction in incompleteness and he drew a fundamental distinction between intrinsic and extrinsic justifications. Reflection principles are the most promising candidates for new axioms that are intrinsically justified. Taking as our starting point Tait’s work on general reflection principles, we prove a series of limitative results concerning this approach. These results collectively show that general reflection principles are either weak ) or inconsistent. The philosophical significance of (...) these results is discussed. (shrink)

The influence of the thought of the great German Idealist philosopher G.W.F Hegel on the thought of Theodor Adorno, the leading thinker of the first generation of the Frankfurt School, is unmistakeable, and has been the subject of much commentary. Much less discussed, however, is the influence of Hegel's prominent contemporary, F.W.J. Schelling. This article investigates the influence of Schelling on Adorno, and the sometimes striking parallels between fundamental motifs in the work of both thinkers. It argues that Adorno's critique (...) of Hegelian dialectics, his conception of the relation between nature and spirit, and his philosophy of history owe a considerable debt to Schelling. Furthermore, when adequately explicated, Schelling's position on a range of problems which confronted German Idealist philosophy often prove intrinsically preferable to those of Hegel. (shrink)

Why does classical equilibrium statistical mechanics work? Malament and Zabell (1980) noticed that, for ergodic dynamical systems, the unique absolutely continuous invariant probability measure is the microcanonical. Earman and Rédei (1996) replied that systems of interest are very probably not ergodic, so that absolutely continuous invariant probability measures very distant from the microcanonical exist. In response I define the generalized properties of epsilon-ergodicity and epsilon-continuity, I review computational evidence indicating that systems of interest are epsilon-ergodic, I adapt Malament and Zabell’s (...) defense of absolute continuity to support epsilon-continuity, and I prove that, for epsilon-ergodic systems, every epsilon-continuous invariant probability measure is very close to the microcanonical. (shrink)

There is a widespread belief among contemporary philosophers that skeptical hypotheses—such as that we are dreaming, or victims of an evil demon, or brains in a vat—cannot definitively be ruled out as false. This belief is ill-founded. In fact it is based on a failure to see that skeptical arguments beg the question. Such arguments assume that reality is not an immediate given of experience in order to prove that reality is not an immediate given of experience. This point (...) is explained and justified in detail. Conversely, however, the realist would beg the question in the opposite way if he tried to prove realism. The conclusion we should reach is that skepticism and realism are problems of immediacy and not of proof. They face us with a choice between alternatives that are not only radically different but also pretty much impregnable and irrelevant to each other. This choice is not arbitrary, for there are grounds to determine it. But the grounds are the immediate evidence and not the arguments. (shrink)

Here’s one version G¨ odel’s 1931 First Incompleteness Theorem: If T is a nice, sound theory of arithmetic, then it is incomplete, i.e. there are arithmetical sentences ϕ such that T proves neither ϕ nor ¬ϕ. There are three things here to explain straight away.

This episode introduces the Second Incompleteness Theorem, says something about what it takes to prove it, and why it matters. Just two very quick reminders before we start. We said..

In the very last chapter of my Introduction to Gödel Theorems, I rashly claimed that there is a sense in which we can informally prove Church’s Thesis. This sort of claim isn’t novel to me: but it certainly is still very much the minority line. So maybe it is worth rehearsing some of the arguments again. Even if I don’t substantially add to the arguments in the book, it might help to approach things in a different order, with some (...) different emphases, to make the issue as clear as possible. (shrink)

I construe Relevant Alternatives Theory (RAT) as an abstract combination of anti-skepticism and epistemic modesty, then re-evaluate the challenge posed to it by the missed clue counterexamples of Schaffer. The import of this challenge has been underestimated, as Schaffer’s specific argument invites distracting objections. I offer a novel formalization of RAT, accommodating a suitably wide class of concrete theories of knowledge. Then, I introduce ‘abstract missed clue cases’ and prove that every RA theory, as formalized, admits such a case. (...) This yields an argument—in Schaffer’s spirit—that resists easy dismissal. (shrink)

The interaction of scientific, ethical, and theological concerns raises several distinct but related problems of continuity and discontinuity. The theologian's task is to articulate a unifying vision of God and the world. He must do justice to the discontinuities which exist between the sociobiological and the ethical points of view, but he cannot accept them as ultimate. Within his own discipline he is already confronted with analogous problems of continuity and discontinuity, for example, between creation and redemption. Concepts associated with (...) love, such as freedom, risk, and patience, may prove more persuasive and coherent than concepts associated with omnipotence. (shrink)

The Fairtrade movement is a group of businesses claiming to trade ethically. The claims are evaluated, under a range of criteria derived from the Utilitarian ethic. Firstly, if aid or charity money is diverted from the very poorest people to the quite poor, or the rich, there is an increase in death and destitution. It is shown that little of the extra paid by consumers for Fairtrade reaches farmers, sometimes none. It cannot be shown that it has a positive impact (...) on Fairtrade farmers in general, but evidence suggesting it harms others is presented. Many of the weaknesses are due to an attempt to impose political views on farmers and others. Secondly, the unfair trading criteria require that sellers do not lie about their product, nor withhold information that might alter the decisions of a substantial proportion of buyers. It is argued that the system only can exist because of the failure of the Fairtrade industry to give the facts on what happens to the money and what it can be proved it achieves. This unfair trading compromises the reputation of charities in general. Much of the trading may constitute the criminal offence of Unfair Trading in the EU. (shrink)

We investigate, in a logical setting, the expressivist proposal that assertion primarily functions to express and coordinate doxastic states and that ‘might’ fundamentally expresses lack of belief. We provide a formal model of an agent’s doxastic state and novel assertability conditions for an associated formal language. We thereby prove that an arbitrary assertion always succeeds in expressing a well-defined doxastic state, and propose a fully general and intuitive update operation as a model of an agent coming to accept an (...) arbitrary assertion. Leaving a comprehensive philosophical and linguistic defense for elsewhere, we explore technical aspects of our framework, providing, for instance, a complete logic of assertability and reduction axioms for the novel update operations related to our proposal. Finally, we contrast our work with related proposals in the logic literature. (shrink)

The essays in this volume, first published in 1986, examine the philosophical foundations of social choice theory. This field, a modern and sophisticated outgrowth of welfare economics, is best known for a series of impossibility theorems, of which the first and most crucial was proved by Kenneth Arrow in 1950. That has often been taken to show the impossibility of democracy as a procedure for making collective decisions. However, this interpretation is challenged by several of the contributors here. Other central (...) issues discussed in the volume include the possibility of making interpersonal comparisons of utility, the question of whether all preferences are equally to be valued, and the normative individualism underlying the theoretical tradition. Criticisms of social choice theory are advanced and suggestions for alternative approaches are developed. (shrink)

In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, (...) showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book - extensively rewritten for its second edition - will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic. -/- (This second edition revises the first edition, with the aim of making it even more reader-friendly.). (shrink)

How do managers think about the relationship between the pursuit of economic success and ethical demands? This paper presents the main results of a qualitative-empirical study (Ulrich and Thielemann, 1992). The range of thinking patterns displayed by Swiss managers in this field of tension is elucidated and typologized. The results are then compared with those yielded by other studies on managerial ethics. Although the comparisons reveal essential parallels, the findings of previous investigations are interpreted in a considerably different manner. In (...) particular it is shown that, on the strength of a systematic conception of the fundamental problem of business ethics, the frequently heard assertion that the vast majority of managers are ethical opportunists must be revised. The internationally prevailing thinking pattern among managers does not prove to be ethical opportunism or even cynicism buteconomism, i.e. theethical conviction that economically appropriate actionin itself is ethically good as such. (shrink)

The primary aim is the reconstruction of the main argument of the second chapter of Anselm’s Proslogion. To be proved is the statement that God, or something than which nothing greater can be thought, exists in reality. I proceed by a piecemeal analysis of every sentence of the Latin original and its subsequent translation into a formal second-order language with choice operator. Reconstructing Anselm’s reasoning demands interpretative input and additions. For example, the formula ‘quod maius est’ has to be suitably (...) interpreted and expanded. Furthermore, I try to explicate Anselm’s maius predicate in terms of a perfection predicate and to develop a general proof for Anselm’s theorem, i.e. the statement that something/that than which something greater cannot be thought has all greater-making attributes. (shrink)

In this paper we articulate and diagnose a previously unrecognized problem for theories of entitlement, what we call the Claims Conundrum. It applies to all entitlements that are originally generated by some claim-generating action, such as laboring, promising, or contract-signing. The Conundrum is spurred by the very plausible thought that a later claim to the object to which one is entitled is a function of whether that original claim-generating action is attributable to one. This is further assumed to depend on (...) one’s being identical to the person who performed the claim-generating action. But the right theory of personal identity for grounding these later claims proves quite elusive. In demonstrating both the Claims Conundrum and diagnosing its source, we begin with its instantiation in John Locke’s theories of personal identity and initial acquisition, and then we gradually expand its net to include both Lockean and non-Lockean theories of both, moving ultimately to show that this is a problem for most entitlements generally. We then diagnose the source of the trouble, showing that a basic assumption about the link between attributability and identity that most people take to be obvious is in fact false, clearing a path for future investigation into this overlooked but serious problem’s resolution. (shrink)

This paper examines problems of order and periodicity which arise when the attempt is made to define a confirmation function for a language containing elementary number theory as applied to a universe in which the individuals are considered to be arranged in some fixed order. Certain plausible conditions of adequacy are stated for such a confirmation function. By the construction of certain types of predicates, it is proved, however, that these conditions of adequacy are violated by any confirmation function defined (...) for the type of language in question. Various possible solutions to these difficulties are explored and found to be inadequate. In particular, a proposal which stems from the suggestion to restrict a fundamental principle of confirmation to hypotheses containing only non-positional predicates is cited. This proposal, however, is shown to prevent confirmation functions from taking periodicities into account, and so is deemed unsatisfactory. A general theorem is proved to the effect that if non-positional predicates are taken to satisfy the conditions of adequacy which have been formulated, then no periodicity predicates whatsoever (i.e., predicates used in formulating hypotheses which foretell periodicities) can be subject to these conditions, on pain of contradiction. Yet it seems that periodicity predicates must be subject to these conditions of adequacy if a confirmation function is to recognize periodic occurrences. Thus, an impasse seems to be reached. In the final sections we consider the beginnings of one possible solution to these difficulties. Our proposal involves treating sets of individuals, rather than individuals themselves, as instances of an hypothesis which predicts a periodicity. On this basis we formulate new conditions of adequacy which are free from the previous difficulties and which will permit a confirmation function that satisfies them to take periodicities into account. (shrink)

We prove two of the inequalities needed to obtain the following result on the ordinal values of ptykes of type 2, which are definable in Gödel'sT. LetG be a dilator satisfyingG(0)=ω, ∀x:G(x)≧x, and ∀η<Ω:G(η)<Ω, and letg be the ordinal function induced byG. Then sup{A(G)∣A ptyx of type 2 definable in Gödel'sT} = sup{x∣x is∑ 1 g -definable without parameters provably in KP(G)} =J (2 +Id) g (ω) (0) = the “Bachmann-Howard ordinal relative tog”. KP(G) is obtained from Kripke-Platek set (...) theory without urelements KP by adjoining a two-place relation symbolG and axioms expressing thatG is the graph of a total function from ordinals to ordinals.J D g is an iteration hierarchy defined relative tog by primitive recursion on dilators. (2 +Id)(ω) is the dilator $$\mathop {\sup }\limits_{n< \omega } (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{2} + Id)_{(n)} $$ with (2 +Id)(0)≔1 and $$(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{2} + Id)_{(n + 1)} : = (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{2} + Id)^{(2 + Id)_{(n)} } $$ . The “Bachmann-Howard ordinal relative tog” is the closure ordinal of a Bachmann hierarchy of lengthε Ω + 1, which is built on an iteration ofg as initial function.For the caseG=(1+Id)·ω, KP(G) is equivalent to Jäger's theory KPu, and the “Bachmann-Howard ordinal relative tog” is the usual “Bachmann-Howard ordinal”. For the caseG=Ξ1 KP(G) can be replaced by Jäger's theory KPi, andg can be replaced by the functionλx. x +.x + is the successor admissible ofx, andΞ 1 is the sum of all recursive dilators in an arbitrary enumeration. (shrink)

A formal result is proved which is used in Juhani Yli-Vakkuri’s ‘Epistemicism and Modality’ to argue that certain two-dimensional possible world models are inadequate for a language with operators for ‘necessarily’, ‘actually’, and ‘definitely’.

Ordinary semantic compositionality (meaning of whole determined from meanings of parts plus composition) can serve to explain how a hearer manages to assign an appropriate meaning to a new sentence. But it does not serve to explain how the speaker manages to find an appropriate sentence for expressing a new thought. For this we would need a principle of inverse compositionality, by which the expression of a complex content is determined by the expressions of it parts and the mode of (...) composition. But this presupposes that contents have constituent structure, and this cannot be taken for granted. However, it can be proved that if a certain principle of substitutivity is valid for a particular language, then the meanings expressed by its sentences can justifiably be treated as structured. In its simplest form, this principle says that if in a complex expression a constituent is replaced by another constituent with a different meaning, the new complex has a meaning different from the original. This principle is again inversely related to the normal compositional principle of substitutivity. The combination of ordinary and inverse compositionality is here called 'strong compositionality'. The proof is carried out in the algebraic framework developed by Wilfrid Hodges and Dag Westerståhl. (shrink)

The Trek Separation Theorem states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various sub-matrices of the covariance matrix is less than or equal to n, for any given n. In this paper, I extend the Trek Separation Theorem in two ways: I prove that the same necessary and sufficient conditions apply even when the generating model is partially non-linear and contains some (...) cycles. This justifies application of constraint-based causal search algorithms to data generated by a wider class of causal models that may contain non-linear and cyclic relations among the latent variables. (shrink)

A groundbreaking new look at the story of America At the heart of the nation's spiritual history are audacious and often violent scenes. But the Puritans and the shining city on the hill give us just one way to understand the United States. Rather than recite American history from a Christian vantage point, Peter Manseau proves that what really happened is worth a close, fresh look. Thomas Jefferson himself collected books on all religions and required that the brand new (...) Library of Congress take his books, since Americans needed to consider the "twenty gods or no god" he famously noted were revered by his neighbors. Looking at the Americans who believed in these gods, Manseau fills in America's story of itself, from the persecuted "witches" at Salem and who they really were, to the persecuted Buddhists in WWII California, from spirituality and cults in the '60s to the recent presidential election where both candidates were for the first time non-traditional Christians. One Nation, Under Gods shows how much more there is to the history we tell ourselves, right back to the country's earliest days. Dazzling in its scope and sweep, it is an American history unlike any you've read. (shrink)

Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary refinement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary refinement implies that the class of detachable subsets of a set form a set. Binary refinement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was sufficient to prove that (...) the Dedekind reals form a set. Here we show that the Cauchy reals also form a set. More generally, binary refinement ensures that one remains in the realm of sets when one starts from discrete sets and one applies the operations of exponentiation and binary product a finite number of times. (shrink)

The function of rationality in A Theory of Justice (1971), which is of paramount importance for John Rawls’ (1921–2002) project, is often criticised as ambiguous.David Gauthier, for example, claims that Rawls develops principles for recipients who essentially share his intuitions of morality, without managing to prove theirvalidity. In Political Liberalism (1993), Justice as Fairness (2001) and other writings Rawls himself embarks upon the task to throw more light on this issue, making the Kantian distinction between ‘rational’ and ‘reasonable’. I (...) intend to demonstrate that in A Theory of Justice the formulation and the compliance with the principles of justice are based on the interaction between the rationality, represented in the idea of the good, and the sense of justice of individuals. (shrink)

We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are d-separated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the procedure is point-wise consistent assuming (a) the causal relations can be represented by a directed acyclic graph (DAG) satisfying the Markov Assumption and the Faithfulness Assumption; (b) unrecorded variables are not caused by (...) recorded variables; and (c) dependencies are linear. We compare the procedure with standard approaches over a variety of simulated structures and sample sizes, and illustrate its practical value with brief studies of social science data sets. Finally, we consider generalizations for non-linear systems. Keywords: latent variable models, causality, graphical models.. (shrink)

performances. But comparatively little work has been by way of elucidating such speech acts,[1] and without an adequate account of them, such comparisons will ultimately prove to be empty. In this paper, I will defend an illocutionary pretense view, according to which actors pretend to perform various kinds of illocutionary acts rather than genuinely performing them. This is, of course, a fairly intuitive position to take. What I want to argue, however, is that this is the route one must (...) take: there are simply no tenable alternatives. (shrink)

There is a pedagogical method of bringing undergraduate students to conceive the body–soul question. Similarly, there is a simple philosophical argument in defense of the existence of the soul via contemporary autobiographical stories, recent neuroscientific literature, and Socrates’s distinction between condition and cause in Plato’s Phaedo. This method has proved helpful in enabling students to gain access to the mystery and grandeur of the body–soul question and its foundational importance with respect to ethics and, indeed, to the meaning of life. (...) There must be a revival of collaboration between neuroscientists and philosophers to coauthor papers that explicitly challenge the materialist assumptions in the fields of neuroscience and psychology. (shrink)

The most prevalent modes of philosophy, educational theory, and philosophy of education currently extant in the United States represent a pronounced departure from the fundamental patterns of the Greek-Jewish- Christian tradition. Among the noteworthy characteristics of the more popular trends is a tendency toward the denial of, or an indifference regarding, the existence of a Transcendent Being. This feature alone has effected a radical departure from the scholarly traditions which are characterized by investigations into the relationships between theology and philosophy. (...) This factor, in turn, bears potentially strong influence upon the theory and practice of education. Partially in order to promote the revivification of a heritage not unrelated to that of many early American intellectual leaders, the main purpose of this paper is to exemplify the structure and an aspect of the substance of a theology-philosophy of Catholic education in accord with a selected passage from A New Catechism: Catholic Faith for Adults. The theological-philosophical dimension of this structure is represented by a developmental process entailing three stages of progression: from human love through an awareness of the “God of the philosophers” to belief in Christ. It is shown how theological and philosophical elements of this process bear upon the importance of early childhood religious education as well as of Catholic education somewhat more broadly conceived. It is noted that, although the theological-philosophical foundations allow for numerous options in education, there are bounds within which the direction of this education must be retained. The current importance of this kind of investigation lies in 1) the fundamentally empiricist approaches in philosophy of education so prominent today, 2) the inability of empiricist philosophies to confront prescriptive values in an authentically rational fashion, and 3) the necessity of a theological-philosophical approach for the Christian who wishes to think rationally about prescriptive values, and to formulate the kinds of educational plans which will prove to be effective in promoting authentic human happiness. Brief references to the practical efficacy of theoretical conceptions, and to teacher education, conclude the paper. (shrink)

Aristotle claims that narrative can depict virtue and vice in particular cases, and that literature's moral meanings are not subject to philosophical paraphrase. He distrusts generalization in ethics, asserting that valid judgments rest on the perception of particulars. But this position is itself an unprovable generalization. If philosophy cannot prove the superiority of narrative over moral theory, perhaps literature can show it. In "Lolita", Nabokov reveals the moral hazards of theory while depicting one man's profound evil. Thus "Lolita" is (...) an illuminating example of pure Aristotelian fiction that serves a moral function without recourse to theory. (shrink)