The Friedman–Stanley jump, extensively studied by descriptive set theorists, is a fundamental tool for gauging the complexity of Borel isomorphism relations. This paper focuses on a natural computable analog of this jump operator for equivalence relations on $\omega $, written ${\dotplus }$, recently introduced by Clemens, Coskey, and Krakoff. We offer a thorough analysis of the computable Friedman–Stanley jump and its connections with the hierarchy of countable equivalence relations under the computable reducibility (...) $\leq _c$. In particular, we show that this jump gives benchmark equivalence relations going up the hyperarithmetic hierarchy and we unveil the complicated highness hierarchy that arises from ${\dotplus }$. (shrink)

We introduce the computable FS-jump, an analog of the classical Friedman–Stanley jump in the context of equivalence relations on the natural numbers. We prove that the computable FS-jump is proper with respect to computable reducibility. We then study the effect of the computable FS-jump on computably enumerable equivalence relations (ceers).

We introduce a reducibility preordering between classes of countable structures, each class containing only structures of a given similarity type (which is allowed to vary from class to class). Though we sometimes work in a slightly larger context, we are principally concerned with the case where each class is an invariant Borel class (i.e. the class of all models, with underlying set $= \omega$, of an $L_{\omega_1\omega}$ sentence; from this point of view, the reducibility can be thought of as a (...) (rather weak) sort of $L_{\omega_1\omega}$-interpretability notion). We prove a number of general results about this notion, but our main thrust is to situate various mathematically natural classes with respect to the preordering, most notably classes of algebraic structures such as groups and fields. (shrink)

This chapter focuses on exploring various models of spiritual development. It first addresses philosophical dilemmas underpinning the concept of spiritual development by questioning whether these can be addressed without metaphysical assumptions embedded in religious worldviews and thus understood in any consensual way across different historical and cultural contexts. Traditional models of spiritual development are then reviewed, drawing from indigenous, Eastern, and Western cultures. Integrative-philosophical and scientific models, including those from the psychology of religion, transpersonal psychology, and neurobiology, are then presented. (...) The chapter concludes by noting the complexities involved in understanding spiritual development accompanied by suggestions on future directions for these models by highlighting their commonalities and differences and by providing some evaluative perspectives for thinking critically about them. (shrink)

The study of law and information technology comes with an inherent contradiction in that while technology develops rapidly and embraces notions such as internationalization and globalization, traditional law, for the most part, can be slow to react to technological developments and is also predominantly confined to national borders. However, the notion of the rule of law defies the phenomenon of law being bound to national borders and enjoys global recognition. However, a serious threat to the rule of law is looming (...) in the form of an assault by technological developments within artificial intelligence (AI). As large strides are made in the academic discipline of AI, this technology is starting to make its way into digital decision-making systems and is in effect replacing human decision-makers. A prime example of this development is the use of AI to assist judges in making judicial decisions. However, in many circumstances this technology is a ‘black box’ due mainly to its complexity but also because it is protected by law. This lack of transparency and the diminished ability to understand the operation of these systems increasingly being used by the structures of governance is challenging traditional notions underpinning the rule of law. This is especially so in relation to concepts especially associated with the rule of law, such as transparency, fairness and explainability. This article examines the technology of AI in relation to the rule of law, highlighting the rule of law as a mechanism for human flourishing. It investigates the extent to which the rule of law is being diminished as AI is becoming entrenched within society and questions the extent to which it can survive in the technocratic society. (shrink)

We study the complexity of the isomorphism relation on classes of computable structures. We use the notion of FF-reducibility introduced in [9] to show completeness of the isomorphism relation on many familiar classes in the context of all ${\mathrm{\Sigma }}_{1}^{1}$ equivalence relations on hyperarithmetical subsets of ω.

A beneficial effect of gesture on learning has been demonstrated in multiple domains, including mathematics, science, and foreign language vocabulary. However, because gesture is known to co‐vary with other non‐verbal behaviors, including eye gaze and prosody along with face, lip, and body movements, it is possible the beneficial effect of gesture is instead attributable to these other behaviors. We used a computer‐generated animated pedagogical agent to control both verbal and non‐verbal behavior. Children viewed lessons on mathematical equivalence in which an (...) avatar either gestured or did not gesture, while eye gaze, head position, and lip movements remained identical across gesture conditions. Children who observed the gesturing avatar learned more, and they solved problems more quickly. Moreover, those children who learned were more likely to transfer and generalize their knowledge. These findings provide converging evidence that gesture facilitates math learning, and they reveal the potential for using technology to study non‐verbal behavior in controlled experiments. (shrink)

A beneficial effect of gesture on learning has been demonstrated in multiple domains, including mathematics, science, and foreign language vocabulary. However, because gesture is known to co-vary with other non-verbal behaviors, including eye gaze and prosody along with face, lip, and body movements, it is possible the beneficial effect of gesture is instead attributable to these other behaviors. We used a computer-generated animated pedagogical agent to control both verbal and non-verbal behavior. Children viewed lessons on mathematical equivalence in which an (...) avatar either gestured or did not gesture, while eye gaze, head position, and lip movements remained identical across gesture conditions. Children who observed the gesturing avatar learned more, and they solved problems more quickly. Moreover, those children who learned were more likely to transfer and generalize their knowledge. These findings provide converging evidence that gesture facilitates math learning, and they reveal the potential for using technology to study non-verbal behavior in controlled experiments. (shrink)

In this paper, I defend the thesis that alleffects of extra-linguistic context on thetruth-conditions of an assertion are traceable toelements in the actual syntactic structure of thesentence uttered. In the first section, I develop thethesis in detail, and discuss its implications for therelation between semantics and pragmatics. The nexttwo sections are devoted to apparent counterexamples.In the second section, I argue that there are noconvincing examples of true non-sentential assertions.In the third section, I argue that there are noconvincing examples of what (...) John Perry has called`unarticulated constituents''. I conclude by drawingsome consequences of my arguments for appeals tocontext-dependence in the resolution of problems inepistemology and philosophical logic. (shrink)

SECTION I In 1972, Donald Davison and Gilbert Hannan wrote in the introduction to the volume Semantics of Natural Language: "The success of linguistics in treating natural languages as formal ~yntactic systems has aroused the interest of a number of linguists in a parallel or related development of semantics. For the most part quite independently, many philosophers and logicians have recently been applying formal semantic methods to structures increasingly like natural languages. While differences in training, method and vocabulary tend to (...) veil the fact, philosophers and linguists are converging, it seems, on a common set of interrelated problems. " Davidson and Harman called for an interdisciplinary dialogue of linguists, philosophers and logicians on the semantics of natural language, and during the last ten years such an enterprise has proved extremely fruitful. Thanks to the cooperative effort in these several fields, the last decade has brought about striking progress in our understanding of the semantics of natural language. This work on semantics has typically paid little attention to psychological aspects of meaning. Thus, psychologists or computer scientists working on artificial intelligence were not invited to join the forces in the influential introduction of Semantics of Natural Language. No doubt it was felt that while psychological aspects of language are important in their own right, they are not relevant to our immediate semantic concerns. In the last few years, several linguists and logicians have come to question the fundamental anti-psychological assumptions underlying their theorizing. (shrink)

This work represents Dr. Jaki's rebuttal of contemporary claims about the existence of, or possibility for, man-made minds. His method includes a meticulously documtned survey of computer development, a review of the relevant results of brain research, and an evaluation of the accomplishments of physicalist schools in psychology, symbolic logic, and linguistics.

This paper explores the relationship between individual work values and unethical decision-making and actual behavior at work through two complementary studies. Specifically, we use a robust and comprehensive model of individual work values to predict unethical decision-making in a sample of working professionals and accounting students enrolled in ethics courses, and IT employees working in sales and customer service. Study 1 demonstrates that young professionals who rate power as a relatively important value are more likely to violate professional conduct guidelines (...) despite receiving training regarding ethical professional principles. Study 2, which examines a group of employees from an IT firm, demonstrates that those rating power as an important value are more likely to engage in non-work-related computing even when they are aware of a monitoring software that tracks their computer usage and an explicit policy prohibiting the use of these computers for personal reasons. (shrink)

The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver [20] and Harrington, Kechris and Louveau [6] show that with respect to Borel reducibility, any Borel equivalence relation strictly above equality on ω is above equality on , the power set of ω, and any Borel equivalence relation strictly above equality on the reals is above equality modulo finite on . In this article we examine the effective (...) content of these and related results by studying effectively Borel equivalence relations under effectively Borel reducibility. The resulting structure is complex, even for equivalence relations with finitely many equivalence classes. However use of Kleene’s O as a parameter is sufficient to restore the picture from the noneffective setting. A key lemma is that of the existence of two effectively Borel sets of reals, neither of which contains the range of the other under any effectively Borel function; the proof of this result applies Barwise compactness to a deep theorem of Harrington establishing for any recursive ordinal α the existence of singletons whose α-jumps are Turing incomparable. (shrink)

We study the structure of Σ11 equivalence relations on hyperarithmetical subsets of ω under reducibilities given by hyperarithmetical or computable functions, called h-reducibility and FF-reducibility, respectively. We show that the structure is rich even when one fixes the number of properly equation imagei.e., Σ11 but not equation image equivalence classes. We also show the existence of incomparable Σ11 equivalence relations that are complete as subsets of ω × ω with respect to the corresponding reducibility on sets. We study complete (...) Σ11 equivalence relations and show that existence of infinitely many properly Σ11 equivalence classes that are complete as Σ11 sets is necessary but not sufficient for a relation to be complete in the context of Σ11 equivalence relations. (shrink)

Fundamental Theory has been called an "unfinished symphony" and "a challenge to the musicians among natural philosophers of the future". This book, written in 1944 but left unfinished because Eddington died too soon, proved to be his final effort at a vision for harmonization of quantum physics and relativity. The work is less connected and internally integrated than 'Protons and Electrons' while representing a later point in the author's thought arc. The really interested student should read both books together.The physical (...) and mathematical reasoning are very deep, but it is possible to enjoy much of the flavor of the book even without following everything. The tidbits given below illustrate Eddington's beautiful and mellifluous English style. This edition contains a clickable table of contents and some interesting illustrations.WARNING: Due to the complexity of the mathematical typesetting, the only way to reproduce this book has been as a series of scanned page images. We believe this work is scientifically and culturally important, and despite a few imperfections and the inevitably small print, have brought it back into print as part of our continuing commitment to the preservation of Eddington's work. On a portable electronic reader the pages come out pretty small, but they are legible. On a desktop computer running the Amazon app, they are perfectly fine. We appreciate your understanding, and hope you enjoy this valuable book.TIDBITS:The number of protons and electrons in the universe would, in itself, be merely a matter of idle curiosity. But N has a more general significance as a fundamental constant which enters into many physical formulae. Its special interpretation as the number of particles in the universe arises in the following way. If we consider a distribution of hydrogen in equilibrium at zero temperature, the presence of the matter produces a curvature of space, and the curvature causes the space to close when the number of particles contained in it reaches a certain total; that number is N. The present investigation seeks to determine N directly from the principles of measurement. We have to show, not that there are N particles in the universe, but that anyone who accepts certain elementary principles of measurement must, if he is consistent, think there are. We have to express in mathematical symbolism what we think we are doing when we measure things; for if we had no conception of what we were doing, the results of the measurements would not persuade us to believe anything in particular. All our results are derived from the condition that the conceptual interpretation which we place on the results of measurement must be consistent with our conceptual interpretation of the process of measurement.If we play about with a pin and a meter standard, we do not become aware of any number in particular unless the standard has been graduated, or unless we use a process of displacement which we interpret as adding pin-extensions. The fact is that, although measurement is primarily a process involving four entities, the conceptual interpretation of measurement postulates in addition the existence (in the structure contemplated) as something referred to as Z. The existence of Z is the condition that makes graduation an exact concept. In the actual universe there exists a basis which is uniform to a very high approximation, and this serves for almost all purposes; but to the much higher approximation required in the calculation of N the ideal exact basis of uniformity does not exist. The finitude of N is, in fact, the cause of the failure of the approximation.It must be remembered that we are now working to what would ordinarily be considered a fantastically high approximation. For ordinary purposes a measurable has 16 eigenvalues; but under the super-magnification here employed (which is not content to overlook 1 part in 10E39) there is a fine structure which splits each of them into 16 components. (shrink)

Perhaps this is due to the belief that technology has a value-neutral nature, and that issues of value are better left to philosophers.

Fundamental Theory has been called an "unfinished symphony" and "a challenge to the musicians among natural philosophers of the future". This book, written in 1944 but left unfinished because Eddington died too soon, proved to be his final effort at a vision for harmonization of quantum physics and relativity. The work is less connected and internally integrated than 'Protons and Electrons' while representing a later point in the author's thought arc. The really interested student should read both books together.The physical (...) and mathematical reasoning are very deep, but it is possible to enjoy much of the flavor of the book even without following everything. The tidbits given below illustrate Eddington's beautiful and mellifluous English style. This edition contains a clickable table of contents and some interesting illustrations.WARNING: Due to the complexity of the mathematical typesetting, the only way to reproduce this book has been as a series of scanned page images. We believe this work is scientifically and culturally important, and despite a few imperfections and the inevitably small print, have brought it back into print as part of our continuing commitment to the preservation of Eddington's work. On a portable electronic reader the pages come out pretty small, but they are legible. On a desktop computer running the Amazon app, they are perfectly fine. We appreciate your understanding, and hope you enjoy this valuable book.TIDBITS:The number of protons and electrons in the universe would, in itself, be merely a matter of idle curiosity. But N has a more general significance as a fundamental constant which enters into many physical formulae. Its special interpretation as the number of particles in the universe arises in the following way. If we consider a distribution of hydrogen in equilibrium at zero temperature, the presence of the matter produces a curvature of space, and the curvature causes the space to close when the number of particles contained in it reaches a certain total; that number is N. The present investigation seeks to determine N directly from the principles of measurement. We have to show, not that there are N particles in the universe, but that anyone who accepts certain elementary principles of measurement must, if he is consistent, think there are. We have to express in mathematical symbolism what we think we are doing when we measure things; for if we had no conception of what we were doing, the results of the measurements would not persuade us to believe anything in particular. All our results are derived from the condition that the conceptual interpretation which we place on the results of measurement must be consistent with our conceptual interpretation of the process of measurement.If we play about with a pin and a meter standard, we do not become aware of any number in particular unless the standard has been graduated, or unless we use a process of displacement which we interpret as adding pin-extensions. The fact is that, although measurement is primarily a process involving four entities, the conceptual interpretation of measurement postulates in addition the existence (in the structure contemplated) as something referred to as Z. The existence of Z is the condition that makes graduation an exact concept. In the actual universe there exists a basis which is uniform to a very high approximation, and this serves for almost all purposes; but to the much higher approximation required in the calculation of N the ideal exact basis of uniformity does not exist. The finitude of N is, in fact, the cause of the failure of the approximation.It must be remembered that we are now working to what would ordinarily be considered a fantastically high approximation. For ordinary purposes a measurable has 16 eigenvalues; but under the super-magnification here employed (which is not content to overlook 1 part in 10E39) there is a fine structure which splits each of them into 16 components. (shrink)

Quantum stochastic models are developed within the framework of a measure entity. An entity is a structure that describes the tests and states of a physical system. A measure entity endows each test with a measure and equips certain sets of states as measurable spaces. A stochastic model consists of measurable realvalued function on the set of states, called a generalized action, together with measures on the measurable state spaces. This structure is then employed to compute quantum probabilities of test (...) outcomes. We characterize those measure entities that are isomorphic to a quantum probability space. We also show that stochastic models provide a phase space description of quantum mechanics and a realistic model of spin. (shrink)

The comparison made by Ada Lovelace in 1843 between the Analytical Engine and the Jacquard loom is one of the well-known analogies between looms and computation machines. Given the fact that weaving – and textile production in general – is one of the oldest cultural techniques in human history, the question arises whether this was the first time that such a parallel was drawn. As this paper will show, centuries before Lovelace’s analogy, such a comparison was made by Gottfried Wilhelm (...) Leibniz. During the 17th century, Leibniz compared his calculating machines with another textile machine, the stocking frame, a machine which mechanized knitting and which was invented in 1589. During the following centuries, this machine was considered as a technological wonder and as a creation of God, and, during the last decades of the 17th century, Leibniz emphasized the need to consider it and other textile machines mathematically. What, then, were the reasons for the parallel drawn between this machine and Leibniz’s automatic computation machines? And what were the consequences of this analogy concerning the artisanal knowledge embedded in manual textile practices? (shrink)

People use commonsense science knowledge to flexibly explain, predict, and manipulate the world around them, yet we lack computational models of how this commonsense science knowledge is represented, acquired, utilized, and revised. This is an important challenge for cognitive science: Building higher order computational models in this area will help characterize one of the hallmarks of human reasoning, and it will allow us to build more robust reasoning systems. This paper presents a novel assembled coherence theory of human conceptual change, (...) whereby people revise beliefs and mental models by constructing and evaluating explanations using fragmentary, globally inconsistent knowledge. We implement AC theory with Timber, a computational model of conceptual change that revises its beliefs and generates human-like explanations in commonsense science. Timber represents domain knowledge using predicate calculus and qualitative model fragments, and uses an abductive model formulation algorithm to construct competing explanations for phenomena. Timber then scores competing explanations with respect to previously accepted beliefs, using a cost function based on simplicity and credibility, identifies a low-cost, preferred explanation and accepts its constituent beliefs, and then greedily alters previous explanation preferences to reduce global cost and thereby revise beliefs. Consistency is a soft constraint in Timber; it is biased to select explanations that share consistent beliefs, assumptions, and causal structure with its other, preferred explanations. In this paper, we use Timber to simulate the belief changes of students during clinical interviews about how the seasons change. We show that Timber produces and revises a sequence of explanations similar to those of the students, which supports the psychological plausibility of AC theory. (shrink)

_Pathologies of Rational Choice Theory_, a book written by Donald Green and Ian Shapiro and published in 1994, excited much controversy among political scientists and promoted a dialogue among them that was printed in a double issue of the journal Critical Review in 1995. This new book reproduces thirteen essays from the journal written by senior scholars in the field, along with an introduction by the editor of the journal, Jeffrey Friedman, and a rejoinder to the essays by Green and (...) Shapiro. The scholars—who include John Ferejohn, Morris P. Fiorina, Stanley Kelley, Jr., Robert E. Lane, Peter C. Ordeshook, Norman Schofield, and Kenneth A. Shepsle—criticize, agree with, or build on the issues raised by Green and Shapiros critique. Together the essays provide an interesting and accessible way of focusing on competing approaches to the study of politics and the social sciences. (shrink)

Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two entanglement measures for all quantum states, however, allows for meaningful conceptualization of sensitivity to entanglement, which will be greater for the entanglement measure that produces the larger numerical values. Here, we have investigated the partial order between the normalized versions of four entanglement measures based on Schmidt (...) decomposition of bipartite pure quantum states, namely, concurrence, tangle, entanglement robustness and Schmidt number. We have shown that among those four measures, the concurrence and the Schmidt number have the highest and the lowest sensitivity to quantum entanglement, respectively. Further, we have demonstrated how these measures could be used to track the dynamics of quantum entanglement in a simple quantum toy model composed of two qutrits. Lastly, we have employed state-dependent entanglement statistics to compute measurable correlations between the outcomes of quantum observables in agreement with the uncertainty principle. The presented results could be helpful in quantum applications that require monitoring of the available quantum resources for sharp identification of temporal points of maximal entanglement or system separability. (shrink)

Certainty (and the lack thereof) is a major issue in mathematics and computer science. Mathematicians strongly believe in a special kind of certainty for their theorems.

This work-in-progress paper consists of four points which relate to the foundations and physical realization of quantum computing. The first point is that the qubit cannot be taken as the basic unit for quantum computing, because not every superposition of bit-strings of length n can be factored into a string of n-qubits. The second point is that the “No-cloning” theorem does not apply to the copying of one quantum register into another register, because the mathematical representation of this copying is (...) the identity operator, which is manifestly linear. The third point is that quantum parallelism is not destroyed only by environmental decoherence. There are two other forms of decoherence, which we call measurement decoherence and internal decoherence, that can also destroy quantum parallelism. The fourth point is that processing the contents of a quantum register “one qubit at a time” destroys entanglement. (shrink)

Computer technology has become an integral part of daily life. From online banking and shopping to email and instant messaging, cyberspace is increasingly woven into the fabric of our everyday lives. The mouse, the monitor and keyboard are all a part of the interfacing devices that over time become extensions of our bodies as we “surf” through graphical user interfaces. Icons patterned together in a mosaic on our screens link to infinite possibilities. We can visit museums, chat with family and (...) friends around the world, not to mention shop to have virtually anything we want shipped to our door. What happens to notions of infinity and transcendence when they are conflated with cyberspatial matrices? Does cyberspatial disembodiment allow us to transcend ourselves or does it blind us from the notion that transcendence in a box is not transcendence at all? (shrink)

The main powerful method for establishing termination of term rewriting systems was discovered by Nachum Dershowitz through the introduction of certain natural well founded orderings (lexicographic path orderings). This leads to natural decision problems which may be of the highest computational complexity of any decidable problems appearing in a natural established computer science context.

In lieu of an abstract, here is a brief excerpt of the content:Reply to Flage Lesley Friedman "The chiefexercise of the memory," Hume tells us, "is not to preserve the simple ideas, but their order and position."1 On Daniel Flage's interpretation ofHume, however, it is the only exercise ofthe memory (1985a, 1985b, 1990). Flage's account can accommodate onlymemories of complex ideas; he disallows the possibility of 'preserving* a simple idea in its simplicity. Yet there is an example of a purely (...) simple impression in the Treatise; and since for every impression there is in principle a corresponding idea which we can later recall, this example establishes the existence of a purely simple memory-idea. In what follows I will provide support for this claim, Flage's counterarguments (this volume) notwithstanding. Flage argues that given any perceived object, say a coloured dot, there is a visual field in which we perceive it. This field and the impression we receive from it, "must be a complex impression, that is, an impression that is composed of indefinitely many colour points. In this respect it is analogous to a pointillist painting or, to use a more contemporary example, a computer array composed of pixels" (1993, 190). Flage is probably right about this; from our point of view, it is implausible to suggest that there is any purely simple background, or worse, that there is no impression ofa background at all. Nonetheless, my concern is with what Hume thought and not with what is plausible orimplausible; and Hume does give an example ofa "background" that is notcomplex, namely, the scenarioinwhichwe perceive points oflight in darkness. We may observe, that when two bodies present themselves, where there wasformerly an entire darkness, the onlychange, that is discoverable, is in the appearance ofthese two objects, and that all the rest continues to be as before, a perfect negation oflight, and of every colour'd or visible object. This is not only true of what may be said to be remote from these bodies, but also of the very distance; which is interpos'd betwixt them; that being nothing but darkness, or the negation of light; without parts, without composition, invariable and indivisible. (T 57, bold italics added) I originally considered the ink spot experiment and theidea ofred in the dark as examples ofpurely simple impressions. Let me try this Volume XLX Number 1 199 LESLEYFRIEDMAN again, elaborating a bit more on the latter (what I take to be Hume's example of a version of the ink spot experiment). Early on in the Treatise Hume speaks of"that idea ofred which we form in the dark" (T 3). Let us then consider a red spot in complete darkness. Flage and I agree that this spot is qualitatively simple. Our disagreement is rooted in the nature ofthe "background," in this case the darkness. Flage claims that "the sighted-person sitting in the dark has an impression or impressions, namely, an impression of darkness" (1993, 190); and therefore the impression we have of the spot of red in darkness is not purely simple. In support of this claim he cites the followingevidence: Hume's remarks that (1) "the sighted-person sitting in the dark "receives no other perception... than what is common to him with one born blind' " (ibid., 189; T 55-56), and (2) "the idea of utter darkness can never be the same with that of vacuum" (T 56). Let me take each ofthese in turn. Presumably, the first quote is cited in order to estabUsh that the blind person does indeed have a perception (impression) of darkness. This cannot be right; ifsuch a person had an impression ofdarkness, he would also have an idea of darkness, and if we look to the part of the sentence which Flage leaves out of his quotation, we find the following: "and 'tis certain such-a-one [that is, a blind person] has no idea either of light or darkness" (T 56). Hume's point is simple: the reason that the blind person has no idea ofdarkness is because he has no impression of darkness; and we are in the same position as him when we are sitting in the dark. Nor does the second quote provide evidence for the... (shrink)

Over the last 25 years, evolutionary game theory has grown with theoretical contributions from the disciplines of mathematics, economics, computer science and biology. It is now ripe for applications. In this book, Daniel Friedman---an economist trained in mathematics---and Barry Sinervo---a biologist trained in mathematics---offer the first unified account of evolutionary game theory aimed at applied researchers. They show how to use a single set of tools to build useful models for three different worlds: the natural world studied by biologists; the (...) social world studied by anthropologists, economists, political scientists and others; and the virtual world built by computer scientists and engineers. The first six chapters offer an accessible introduction to core concepts of evolutionary game theory. These include fitness, replicator dynamics, sexual dynamics, memes and genes, single and multiple population games, Nash equilibrium and evolutionarily stable states, noisy best response and other adaptive processes, the Price equation, and cellular automata. The material connects evolutionary game theory with classic population genetic models, and also with classical game theory. Notably, these chapters also show how to estimate payoff and choice parameters from the data. The last eight chapters present exemplary game theory applications. These include a new coevolutionary predator-prey learning model extending rock-paper-scissors; models that use human subject laboratory data to estimate learning dynamics; new approaches to plastic strategies and life cycle strategies, including estimates for male elephant seals; a comparison of machine learning techniques for preserving diversity to those seen in the natural world; analyses of congestion in traffic networks and the. (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)

There is a very simple way in which the safe/normal variable discipline of Bellantoni–Cook recursion [S. Bellantoni, S. Cook, A new recursion theoretic characterization of the polytime functions, Computational Complexity 2 97–110] can be imposed on arithmetical theories like PA: quantify over safes and induct on normals. This weakens the theory severely, so that the provably recursive functions become more realistically computable . Earlier results of D. Leivant [Intrinsic theories and computational complexity, in: D. Leivant , Logic and Computational (...) Complexity, Lecture Notes in Computer Science, vol. 960, Springer-Verlag, 1995, pp. 177–194] are re-worked and extended in this new context, giving proof-theoretic characterizations of complexity classes between Grzegorczyk’s E2 and E3. (shrink)

The main result in this paper is a method for obtaining derivation trees from sentences of certain formal grammars. No parsing algorithm was previously known to exist for these grammars.Applied to Montague's PTQ the method produces all parses that could correspond to different meanings. The technique directly addresses scope and reference and provides a framework for examining these phenomena. The solution for PTQ is implemented in an efficient and useful computer program.

Beginning with Emerson's turn from his pulpit, many argue that American philosophy has rigorously held forth against supernaturalism and metaphysics. While most read self-reliance as a call for individualism, I argue that self-reliance is the application of the moral sentiment to the source of existence Emerson calls the Over-soul. Figures like George Kateb, Stanley Cavell, and Jeffrey Stout have presented a very different picture of American pragmatism. Stout, in particular, is responsible for building up what I call "the myth of (...) the Emersonian democrat." We find that a few philosophical positions generally constitute this myth. The Emersonian democrat is secular, sceptical, relativist, anti-realist, and anti-metaphysical. In fact, on my reading of the strand of pragmatism running from Emerson through James to Dewey, the pluralism of the Emersonian democrat depends on certain metaphysical commitments. The traditional reading of Emerson as anti-religion, and by extension, anti-religious, impedes a better understanding of self-reliance and obfuscates some of the Emersonian inheritances in James and Dewey. (shrink)

A classic result of Baumgartner-Harrington-Kleinberg [1] implies that assuming CH a stationary subset of ω1 has a CUB subset in a cardinal-perserving generic extension of V, via a forcing of cardinality ω1. Therefore, assuming that $\omega_2^L$ is countable: { $X \in L \mid X \subseteq \omega_1^L$ and X has a CUB subset in a cardinal -preserving extension of L} is constructible, as it equals the set of constructible subsets of $\omega_1^L$ which in L are stationary. Is there a similar such (...) result for subsets of $\ omega_2^L$ ? Building on work of M. Stanley [9], we show that there is not. We shall also consider a number of related problems, examining the extent to which they are "solvable" in the above sense, as well as defining a notion of reduction between them. (shrink)