Researchers from across the social sciences have found consistent deviations from the predictions of the canonical model of self-interest in hundreds of experiments from around the world. This research, however, cannot determine whether the uniformity results from universal patterns of human behavior or from the limited cultural variation available among the university students used in virtually all prior experimental work. To address this, we undertook a cross-cultural study of behavior in ultimatum, public goods, and dictator games in a range of (...) small-scale societies exhibiting a wide variety of economic and cultural conditions. We found, first, that the canonical model – based on self-interest – fails in all of the societies studied. Second, our data reveal substantially more behavioral variability across social groups than has been found in previous research. Third, group-level differences in economic organization and the structure of social interactions explain a substantial portion of the behavioral variation across societies: the higher the degree of market integration and the higher the payoffs to cooperation in everyday life, the greater the level of prosociality expressed in experimental games. Fourth, the available individual-level economic and demographic variables do not consistently explain game behavior, either within or across groups. Fifth, in many cases experimental play appears to reflect the common interactional patterns of everyday life. Key Words: altruism; cooperation; cross-cultural research; experimental economics; game theory; ultimatum game; public goods game; self-interest. (shrink)

We would like to thank the commentators for their generous comments, valuable insights and helpful suggestions. We begin this response by discussing the selfishness axiom and the importance of the preferences, beliefs, and constraints framework as a way of modeling some of the proximate influences on human behavior. Next, we broaden the discussion to ultimate-level (that is evolutionary) explanations, where we review and clarify gene-culture coevolutionary theory, and then tackle the possibility that evolutionary approaches that exclude culture might be sufficient (...) to explain the data. Finally, we consider various methodological and epistemological concerns expressed by our commentators. (shrink)

Between Deleuze and Derrida is the first book to explore and compare the work of Gilles Deleuze and Jacques Derrida, two leading philosophers of French post-structuralism. This is done via a number of key themes, including the philosophy of difference, language, memory, time, event, and love, as well as relating these themes to their respective approaches to Philosophy, Literature, Politics and Mathematics. Contributors: Eric Alliez, Branka Arsic, Gregg Lambert, Leonard Lawlor, Alphonso Lingis, Tamsin Lorraine, Jeff Nealon, Paul Patton, Arkady (...) Plotnitsky, John Protevi, Daniel W. Smith. (shrink)

The current ethical norms of genomic biobanking creating and maintaining large repositories of human DNA and/or associated data for biomedical research have generated criticism from every angle, at both the practical and theoretical levels. The traditional research model has involved investigators seeking biospecimens for specific purposes that they can describe and disclose to prospective subjects, from whom they can then seek informed consent. In the case of many biobanks, however, the institution that collects and maintains the biospecimens may not itself (...) be directly involved in research, instead banking the biospecimens and associated data for other researchers. Moreover, the future uses of biospecimens may be unknown, if not unknowable, at the time of collection. Biobanking may thus stretch the meanings of inform and consent to their breaking point: if you cannot inform subjects about what their biospecimens will be used for, what can they consent to? Given that informed consent by individual subjects is the ethical gold standard, the seeming dilution of the concept in the context of biobanking is a profound problem. (shrink)

Andres Bonifacio is a household name in the history of the Philippines.His name has been included into many discussion and controversies revolvingover his identity as the Father of the Revolution and being the founder ofKataastaasang, Kagalanggalangag Katipunan . His poems serve as legaciesthat can unlock what kind of person is Andres. Through his poems, he expressedreflections about the situation of the Indios during the time of colonization andthe rage of the revolution. This descriptive study analyzed four selected poemsof Andres Bonifacio (...) and sought to find a new insight into the poems through a Neo-Marxist perspective using a Neo-Marxist lens, specifically the theory of cultural hegemony by Antonio Gramsci. Based on the content analysis of hispoems, it was found out that Bonifacio was affected by the false consciousnesspropagated by the colonizers during the Spanish settlement in the country. Italso answered the question whether Bonifacio is a patriotic man or a nationalistichero. Keywords: Literature, revolution, neo-marxism, poems, Andres Bonifacio, descriptiveresearch, Philippines. (shrink)

The development of factor markets has opened Chinese agriculture for the penetration of capitalism. This new round of rural transformation—China’s agrarian transition— raises the agrarian question in the Chinese context. This study investigates how capitalist forms and relations of production transform agricultural production and the peasantry class in rural China. The authors identify six forms of nonpeasant agricultural production, compare the labor regimes and direct producers’ socioeconomic statuses across these forms, and evaluate the role of China’s land-rights institution in shaping (...) these forms. The empirical investigation presents three main findings: Peasant differentiation : capitalist forms of agricultural production differentiate peasants into a variety of new class positions. Market-based stratification: producers in capitalist agriculture are primarily stratified by their positions in labor and land markets; their socioeconomic statuses are linked with their varying degrees of proletarianization. Institutional mediation: rural China’s dual-track land system plays a crucial role in shaping the diverse and unique forms of capitalist production. (shrink)

Published one year after Forget Foucault, In the Shadow of the Silent Majorities may be the most important sociopolitical manifesto of the twentieth century: it calls for nothing less than the end of both sociology and politics. Disenfranchised revolutionaries hoped to reach the masses directly through spectacular actions, but their message merely played into the hands of the media and the state. In a media society meaning has no meaning anymore; communication merely communicates itself. Jean Baudrillard uses this last outburst (...) of ideological terrorism in Europe to showcase the end of the "Social." Once invoked by Marx as the motor of history, the masses no longer have sociological reality. In the electronic media society, all the masses can do--and all they will do--is enjoy the spectacle. In the Shadow of the Silent Majorities takes to its ultimate conclusion the "end of ideologies" experienced in Europe after the Soviet invasion of Hungary and the death of revolutionary illusions after May 1968. Ideological terrorism doesn't represent anything anymore, writes Baudrillard, not even itself. It is just the last hysterical reaction to discredited political illusions. (shrink)

This paper explores possible important relationships and sympathies between Amartya Sen’s Capabilities Approach framework for understanding the human condition and the educational ideas of John Dewey and Paolo Freire. All three focus on the importance of democratic values in a fair, well-functioning society, while Sen and Freire especially explore the difficulties and possibilities of oppressed populations. Sen suggests that all humans have a right to choice in determining their life trajectories and should be provided with the tools that allow (...) them to flourish. Both education and democratic values play important roles in creating the types of context that allow individuals and communities to recognize a wide array of human capabilities. We suggest here that the theories of Dewey and Freire offer avenues through educational processes for developing these contexts for expanded human capability. Dewey suggests an educational approach that stresses democratic values and the ability and willingness of individuals to reach out towards new possibilities. Freire stresses the idea of praxis playing a central role in education—a focus on the cycle of everyday action, reflection, and re-creation of action that leads to productive changes in life trajectories. We argue that Sen, Dewey, and Freire together help to offer a new way of understanding education in the twenty-first century. (shrink)

One way to characterise the difference between analytic and Continental political philosophy concerns the different roles played by normative and descriptive analysis in each case. This article argues that, even though Michel Foucault’s genealogy of liberal and neoliberal governmentality and John Rawls’s political liberalism involve different articulations of normative and descriptive concerns, they are complementary rather than antithetical to one another. The argument is developed in three stages: first, by suggesting that Foucault offers a way to conceive of public (...) reason as a historical phenomenon. Second, it is suggested that both Rawls and Foucault allow us to consider rights as historical and particular rather than a-historical and universal. Third, it is argued that Foucault’s genealogy of modern liberal government illuminates some of the tensions and some of the alternatives within the liberal tradition in relation to the concept of political legitimacy. (shrink)

Obviously medicine should be evidence-based. The issues lie in the details: what exactly counts as evidence? Do certain kinds of evidence carry more weight than others? (And if so why?) And how exactly should medicine be based on evidence? When it comes to these details, the evidence-based medicine (EBM) movement has got itself into a mess – or so it will be argued. In order to start to resolve this mess, we need to go 'back to basics'; and that means (...) turning to the philosophy of science. The theory of evidence, or rather the logic of the interrelations between theory and evidence, has always been central to the philosophy of science – sometimes under the alias of the 'theory of confirmation'. When taken together with a little philosophical commonsense, this logic can help us move towards a position on evidence in medicine that is more sophisticated and defensible than anything that EBM has been able so far to supply. (shrink)

What is the relationship between saying ‘I know that Q’ and guaranteeing that Q? John Austin, Roderick Chisholm and Wilfrid Sellars all agreed that there is some important connection, but disagreed over what exactly it was. In this paper I discuss each of their accounts and present a new one of my own. Drawing on speech-act theory and recent research on the epistemic norms of speech acts, I suggest that the relationship is this: by saying ‘I know that Q’, (...) you represent yourself as having the authority to guarantee that Q. (shrink)

The aim of this paper is to show the relationship between John XXIII and Robert K. Greenleaf’s understanding of leadership. By taking into consideration Greenleaf’s theory of servant-leadership – from conceptualization to model development – and Larry Spears’ influential rubric of ten servant-leadership characteristics, we will show how servant-leadership theory goes in line with that of John XXIII when both are based on a notion of the common good and human dignity.

Closure is the epistemological thesis that if S knows that P and knows that P implies Q, then if S infers that Q, S knows that Q. Fred Dretske acknowledges that closure is plausible but contends that it should be rejected because it conflicts with the plausible thesis: Conclusive reasons (CR): S knows that P only if S believes P on the basis of conclusive reasons, i.e., reasons S wouldn‘t have if it weren‘t the case that P. Dretske develops an (...) analysis of knowing that centers on CR, and argues that the requirement undermines skepticism by implying the falsity of closure. We develop a Dretske-style analysis of knowing that incorporates CR, and we argue that this analysis not only accords with closure, but also implies it. In addition, we argue that the analysis accounts for the prima facie plausibility of closure-invoking skeptical arguments, and nonetheless implies that they are fallacious. If our arguments turn out to be sound, the acceptability of Dretske‘s analysis of knowing will be significantly enhanced by the fact that, despite implying closure, it undermines closure-based skepticism. (shrink)

What is the origin of the concept of a law of nature? How much does it owe to theology and metaphysics? To what extent do the laws of nature permit contingency? Are there exceptions to the laws of nature? Is it possible to give a reductive analysis of lawhood, or is it a primitive? -/- Twelve brand-new essays by an international team of leading philosophers take up these and other central questions on the laws of nature, whilst also examining some (...) of the most important intuitions and assumptions that have guided the debate over laws of nature since the concept's invention in the seventeenth century. -/- Laws of Nature spans the history of philosophy and of science, contemporary metaphysics, and contemporary philosophy of science. Contents: 1. Intuitions and Assumptions in the Debate over Laws of Nature, Walter Ott and Lydia Patton 2. Early Modern Roots of the Philosophical Concept of a Law of Nature, Helen Hattab 3. Laws of Nature and the Divine Order of Things: Descartes and Newton on Truth in Natural Philosophy, Mary Domski 4. Leges sive natura: Bacon, Spinoza, and a Forgotten Concept of Law, Walter Ott 5. Laws and Powers in the Frame of Nature, Stathis Psillos 6. Laws and Ideal Unity, Angela Breitenbach 7. Becoming Humean, John W. Carroll 8. A Perspectivalist Better Best System Account of Lawhood, Michela Massimi 9. Laws: An Invariance Based Account, James Woodward 10. How the Explanations of Natural Laws Make Some Reducible Physical Properties Natural and Explanatorily Powerful, Marc Lange 11. Laws and their Exceptions, Stephen Mumford 12. Are laws of nature consistent with contingency?, Nancy Cartwright and Pedro Merlussi. (shrink)

An American Ethic takes the basis for American life - freedom - and describes the reality behind that abstraction, the transcendent nature of man. The book analyzes freedom and communication along with the inalienable rights and obligations that necessarily flow from the transcendent nature of man. It explains and distinguishes the usual norms of morality: natural law, positive law, religion, and conscience; and then proceeds to discuss contemporary moral issues: sanction for crime, animal rights, business ethics, sexual morality, homosexuality, and (...) abortion. In light of that analysis, the book critiques three recent and well-known works of ethics: Robert Pirsig's Lila, James Q. Wilson's The Moral Sense, and Peter Singer's Practical Ethics. (shrink)

The most cursory examination of the history of artificial intelligence highlights numerous egregious claims of its researchers, especially in relation to a populist form of ‘strong’ computationalism which holds that any suitably programmed computer instantiates genuine conscious mental states purely in virtue of carrying out a specific series of computations. The argument presented herein is a simple development of that originally presented in Putnam’s (Representation & Reality, Bradford Books, Cambridge in 1988 ) monograph, “Representation & Reality”, which if correct, has (...) important implications for turing machine functionalism and the prospect of ‘conscious’ machines. In the paper, instead of seeking to develop Putnam’s claim that, “everything implements every finite state automata”, I will try to establish the weaker result that, “everything implements the specific machine Q on a particular input set ( x )”. Then, equating Q ( x ) to any putative AI program, I will show that conceding the ‘strong AI’ thesis for Q (crediting it with mental states and consciousness) opens the door to a vicious form of panpsychism whereby all open systems, (e.g. grass, rocks etc.), must instantiate conscious experience and hence that disembodied minds lurk everywhere. (shrink)

The argument presented in this paper is not a direct attack or defence of the Chinese Room Argument (CRA), but relates to the premise at its heart, that syntax is not sufficient for semantics, via the closely associated propositions that semantics is not intrinsic to syntax and that syntax is not intrinsic to physics. However, in contrast to the CRA’s critique of the link between syntax and semantics, this paper will explore the associated link between syntax and physics. The main (...) argument presented here is not significantly original – it is a simple reflection upon that originally given by Hilary Putnam (Putnam 1988) and criticised by David Chalmers and others: instead of seeking to justify Putnam’s claim that, “every open system implements every Finite State Automaton (FSA)”, and hence that psychological states of the brain cannot be functional states of a computer, I will seek to establish the weaker result that, over a finite time window every open system implements the trace of a particular FSA Q, as it executes program (p) on input (x). That this result leads to panpsychism is clear as, equating Q (p, x) to a specific Strong AI program that is claimed to instantiate phenomenal states as it executes, and following Putnam’s procedure, identical computational (and ex hypothesi phenomenal) states (ubiquitous little ‘pixies’) can be found in every open physical system. (shrink)

The most cursory examination of the history of artificial intelligence highlights numerous egregious claims of its researchers, especially in relation to a populist form of ‘strong’ computationalism which holds that any suitably programmed computer instantiates genuine conscious mental states purely in virtue of carrying out a specific series of computations. The argument presented herein is a simple development of that originally presented in Putnam’s (Representation & Reality, Bradford Books, Cambridge in 1988) monograph, “Representation & Reality”, which if correct, has important (...) implications for turing machine functionalism and the prospect of ‘conscious’ machines. In the paper, instead of seeking to develop Putnam’s claim that, “everything implements every finite state automata”, I will try to establish the weaker result that, “everything implements the specific machine Q on a particular input set (x)”. Then, equating Q (x) to any putative AI program, I will show that conceding the ‘strong AI’ thesis for Q (crediting it with mental states and consciousness) opens the door to a vicious form of panpsychism whereby all open systems, (e.g. grass, rocks etc.), must instantiate conscious experience and hence that disembodied minds lurk everywhere. (shrink)

Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate (...) Q is one whose existentialization, ∃ x Q, is logically true; otherwise, Q is existential-import-free or simply import-free.How abundant or widespread is existential import? How abundant or widespread are existential-import predicates in themselves or in comparison to import-free predicates? We show that existential-import predicates are quite abundant, and no less so than import-free predicates. Existential.. (shrink)

The initial argument presented herein is not significantly original—it is a simple reflection upon a notion of computation originally developed by Putnam and criticised by Chalmers et al. . In what follows, instead of seeking to justify Putnam’s conclusion that every open system implements every Finite State Automaton and hence that psychological states of the brain cannot be functional states of a computer, I will establish the weaker result that, over a finite time window every open system implements the trace (...) of FSA Q, as it executes program on input . If correct the resulting bold philosophical claim is that phenomenal states—such as feelings and visual experiences—can never be understood or explained functionally. (shrink)

This paper refutes two important and influential views in one fell stroke. The first is G.E. Moore’s view that assertions of the form ‘Q but I don’t believe that Q’ are inherently “absurd.” The second is Gareth Evans’s view that justification to assert Q entails justification to assert that you believe Q. Both views run aground the possibility of being justified in accepting eliminativism about belief. A corollary is that a principle recently defended by John Williams is also false, (...) namely, that justification to believe Q entails justification to believe that you believe Q. (shrink)

In 1949 the great logician Kurt Gödel constructed the first mathematical models of the universe in which travel into the past is, in theory at least, possible. Within the framework of Einstein’s general theory of relativity Gödel produced cosmological solutions to Einstein’s field equations which contain closed time-like curves, that is, curves in spacetime which, despite being closed, still represent possible paths of bodies. An object moving along such a path would travel back into its own past, to the very (...) moment at which it “began” the journey. More generally, Gödel showed that, in his “universe”, for any two points P and Q on a body’s track through spacetime, such that P temporally precedes Q, there is a timelike curve linking P and Q on which Q temporally precedes P. This means that, in principle at least, one could board a “time machine” and travel to any point of the past. Gödel inferred, in consonance with the views of Parmenides, Kant and the modern idealists, that under these circumstances there could be no such thing as an objective lapse of time, that time or, more generally, change, is an illusion arising from our special mode of perception. For consider an observer initially at point P. At point Q he boards a time machine and travels back to point P, taking time t′′ to do so. In that case, according to his own clock, t′ – t + t′′ > 0 seconds have elapsed, and yet an identical clock left at P would show that 0 seconds have elapsed. In short, there has been no “objective” lapse of time at all. Gödel remarks that in his universe this situation is typical: for every possible definition of an “objective” time one could travel into regions which are past according to that definition. He continues. (shrink)

In spacetime physics any set C of events—a causal set—is taken to be partially ordered by the relation ≤ of possible causation: for p, q ∈ C, p ≤ q means that q is in p’s future light cone. In her groundbreaking paper The internal description of a causal set: What the universe looks like from the inside, Fotini Markopoulou proposes that the causal structure of spacetime itself be represented by “sets evolving over C” —that is, in essence, by the (...) topos SetC of presheaves on Cop. To enable what she has done to be the more easily expressed within the framework presented here, I will reverse the causal ordering, that is, C will be replaced by Cop, and the latter written as P—which will, moreover, be required to be no more than a preordered set. Specifically, then: P is a set of events preordered by the relation ≤, where p ≤ q is intended to mean that p is in q’s future light cone—that q could be the cause of p, or, equally, that p could be an effect of q. In that case, for each event p, the set p↓ = {q: q ≤ p} may be identified as the causal future of p, or the set of potential effects of p. In requiring that ≤ be no more than a preordering—in dropping, that is, the antisymmetry of ≤—I am, in physical terms, allowing for the possibility that the universe is of Gödelian type, containing closed timelike lines. (shrink)

Saul Kripke has made fundamental contributions to a variety of areas of logic, and his name is attached to a corresponding variety of objects and results. 1 For philosophers, by far the most important examples are ‘Kripke models’, which have been adopted as the standard type of models for modal and related non-classical logics. What follows is an elementary introduction to Kripke’s contributions in this area, intended to prepare the reader to tackle more formal treatments elsewhere.2 2. WHAT IS A (...) MODEL THEORY? Traditionally, a statement is regarded as logically valid if it is an instance of a logically valid form, where a form is regarded as logically valid if every instance is true. In modern logic, forms are represented by formulas involving letters and special symbols, and logicians seek therefore to define a notion of model and a notion of a formula’s truth in a model in such a way that every instance of a form will be true if and only if a formula representing that form is true in every model. Thus the unsurveyably vast range of instances can be replaced for purposes of logical evaluation by the range of models, which may be more tractable theoretically and perhaps practically. Consideration of the familiar case of classical sentential logic should make these ideas clear. Here a formula, say (p & q) ∨ ¬p ∨ ¬q, will be valid if for all statements P.. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Aquinas's Ethics beyond Thomistic Virtue Ethics:The Gifts of the Holy Spirit, Spiritual Instinct, and Complete Human PerfectionJohn BerkmanThis paper offers a new reading and interpretation of Aquinas's doctrine of the gifts of the Holy Spirit. In the contemporary Thomist literature on ethics, there is far more discussion—and a far more developed discussion—of the nature and role of a virtue-habitus than a gift-habitus. Why might there be so little discussion (...) of the gifts and their distinctive habitus? Is it because Aquinas devotes many more questions to the virtues than to the gifts? Is it because the majority of self-professed Thomist ethicists have not been taught the gifts, and are either unaware or have merely a notional awareness that the gifts have a principle of action distinct from and superior to that of the virtues?1 Regardless of the reason, this paper seeks to mitigate the current paucity of analysis of the gifts and the gift-habitus.This paper will discuss Aquinas's doctrine of the gifts of the Holy Spirit from a resolutely gift-centered perspective. I do so because discussions of the gifts often presume a virtue-centered perspective. That is, treatments of the gifts typically interpret what Aquinas says about the gifts through the lens of a pre-existing virtue framework, the gifts then being made to fit into that pre-existing framework. I will argue that we see this not only in interpretations of Aquinas on the gifts, but also in English translations of the Summa theologiae [ST] on the question of the gifts. [End Page 47]As a result, in contemporary scholarship on Aquinas's ethics, the virtues typically receive extended treatment, whereas the gifts of the Holy Spirit receive no treatment at all. And when the gifts are addressed, their treatment is brief, with the main point being that the gifts provide assistance to the virtues, like a spiritual butler. In the best-case scenario, the gifts are like Jeeves to the virtues' Bertie—undoubtedly wiser, but rarely listened to.The paper is divided into four sections. The first section compares and contrasts a gift-habitus and a vinue-habitus. The second section focuses on Aquinas's notion of instinctus. The instinct of the Holy Spirit (divine instinct) is the principle of motion Aquinas associates with the gifts of the Holy Spirit (ST I-II, q. 68, aa. 1–2). I argue that—contrary to the judgment of most commentators—instinctus is a highly appropriate term to describe the character of the work of the Holy Spirit. In this section I also show how Aquinas's doctrine of instinctus has been made "invisible" in part by various translations of the ST, including the translation of Fr. Shapcote.2In the third section, I analyze Aquinas' argument that the gifts are more perfective of human beings than the virtues (ST I-II, q. 68, a. 8). This analysis also constitutes a "case study" of the ways in which Shapcote's translation (the dominant English translation for the last hundred years) contributes to misunderstandings of Aquinas's views on the relationship between the gifts and the virtues. In comparing and contrasting the virtues and gifts, an original part of my argument is my claim that, while charity sometimes operates from a virtue-habitus, at other times it operates according to a gift-habitus. Commentators have failed to adequately account for the fact that truly perfect (simpliciter) charity cannot be attained solely by the operations of virtue. The ultimate expression of charity requires a habitus superior to a virtue-habitus.3 While the wayfarer's expression of charity is always in one [End Page 48] sense a gift from God, in that it relies on God's grace, as the wayfarer grows in charity, charity increasingly functions as a gift of the Holy Spirit, or perhaps the form of all the gifts.4The fourth and final section focuses on how the gifts and infused virtues operate in the wayfarer who is growing in spiritual maturity. I argue that, although infused virtue-habitus and gift-habitus are given at baptism, facility in either typically grows slowly. Increasing facility in... (shrink)

This paper ties together much of the model theory of the last 50 years. Shelah's attempts to generalize the Morley theorem beyond first order logic led to the notion of excellence, which is a key to the structure theory of uncountable models. The notion of Abstract Elementary Class arose naturally in attempting to prove the categoricity theorem for L ω 1 ,ω (Q). More recently, Zilber has attempted to identify canonical mathematical structures as those whose theory (in an appropriate logic) (...) is categorical in all powers. Zilber's trichotomy conjecture for first order categorical structures was refuted by Hrushovski, by the introducion of a special kind of Abstract Elementary Class. Zilber uses a powerful and essentailly infinitary variant on these techniques to investigate complex exponentiation. This not only demonstrates the relevance of Shelah's model theoretic investigations to mainstream mathematics but produces new results and conjectures in algebraic geometry. (shrink)

Subcreative sets, introduced by Blum, are known to coincide with the effectively speedable sets. Subcreative sets are shown to be the complete sets with respect to S-reducibility, a special case of Turing reducibility. Thus a set is effectively speedable exactly when it contains the solution to the halting problem in an easily decodable form. Several characterizations of subcreative sets are given, including the solution of an open problem of Blum, and are used to locate the subcreative sets with respect to (...) the complete sets of other reducibilities. It is shown that q-cylindrification is an order-preserving map from the r.e. T-degrees to the r.e. S-degrees. Consequently, T-complete sets are precisely the r.e. sets whose q-cylindrifications are S-complete. (shrink)

1 Choice conjecture In axiomatizing nonclassical extensions of classical sentential logic one tries to make do, if one can, with adding to classical sentential logic a finite number of axiom schemes of the simplest kind and a finite number of inference rules of the simplest kind. The simplest kind of axiom scheme in effect states of a particular formula P that for any substitution of formulas for atoms the result of its application to P is to count as an axiom. (...) The simplest kind of onepremise inference rule in effect states of a particular pair of formulas P and Q that for any substitution of formulas for atoms, if the result of its application to P is a theorem, then the result of its application to Q is to count as a theorem; similarly for many-premise rules. Such are the schemes and rules of all the best-known modal and tense logics, for instance. Sometimes it is difficult to find such simple schemes and rules. In that case one may resort to less simple schemes or less simple rules. There is no generally recognized rigorous definition of "next simplest kind" of scheme. Neither is there any generally recognized definition of "next simplest kind" of rule, and hence there is no fully rigorous enunciation of the choice conjecture, the conjecture that schemes of the next simplest kind can always be avoided in favor of rules of the next simplest kind and vice versa. Nonetheless, there are cases where intuitively one does recognize that the schemes or rules in a given axiomatization are only slightly more complex than the simplest kind, including cases where one does have a choice between adopting slightly-more-complex-than-simplest schemes and adopting slightly-more-complex-than-simplest rules. In tense logic early examples of slightly more complex rules are found in [2] and [3] : there is one example of the embarrassed use of such rules in the former, and many examples of the enthusiastic use of such rules in the latter and its sequels. Accordingly the rules in question have come to be called "Gabbay-style" rules. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

The concept of being in a position to know is an increasingly popular member of the epistemologist’s toolkit. Some have used it as a basis for an account of propositional justification. Others, following Timothy Williamson, have used it as a vehicle for articulating interesting luminosity and anti-luminosity theses. It is tempting to think that while knowledge itself does not obey any closure principles, being in a position to know does. For example, if one knows both p and ‘If p then (...) q’, but one dies or gets distracted before being able to perform a modus ponens on these items of knowledge and for that reason one does not know q, one is still plausibly in a position to know q. It is also tempting to suppose that, while one does not know all logical truths, one is nevertheless in a position to know every logical truth. Putting these temptations together, we get the view that being in a position to know has a normal modal logic. A recent literature has begun to investigate whether it is a good idea to give in to these twin temptations—in particular the first one. That literature assumes very naturally that one is in a position to know everything one knows and that one is not in a position to know things that one cannot know. It has succeeded in showing that, given the modest closure condition that knowledge is closed under conjunction elimination, being a position to know cannot satisfy the so-called K axiom of normal modal logics. In this paper, we explore the question of the normality of the logic of being in a position to know in a more far-reaching and systematic way. Assuming that being in a position to know entails the possibility of knowing and that knowing entails being in a position to know, we can demonstrate radical failures of normality without assuming any closure principles at all for knowledge. Moreover, the failure of normality cannot be laid at the door of the K axiom for knowledge, since the standard principle NEC of necessitation also fails for being in a position to know. After laying out and explaining our results, we briefly survey the coherent options that remain. (shrink)