I criticize a recent paper by Thomas Tymoczko in which he attributes fundamental philosophical significance and novelty to the lately-published computer-assisted proof of the four color theorem (4CT). Using reasoning precisely analogous to that employed by Tymoczko, I argue that much of traditional mathematical proof must be seen as resting on what Tymoczko must take as being "empirical" evidence. The new proof of the 4CT, with its use of what Tymoczko calls "empirical" evidence is therefore not so novel as (...) he maintains. Finally, without attempting to give a full account of the notion of empirical mathematical evidence, I sketch a view showing how the use of calculation injects an empirical ingredient into proof. (shrink)

Sometimes we receive evidence in a form that standard conditioning (or Jeffrey conditioning) cannot accommodate. The principle of maximum entropy (MAXENT) provides a unique solution for the posterior probability distribution based on the intuition that the information gain consistent with assumptions and evidence should be minimal. Opponents of objective methods to determine these probabilities prominently cite van Fraassen’s Judy Benjamin case to undermine the generality of maxent. This article shows that an intuitive approach to Judy Benjamin’s case supports maxent. This (...) is surprising because based on independence assumptions the anticipated result is that it would support the opponents. It also demonstrates that opponents improperly apply independence assumptions to the problem. (shrink)

This paper compares and contrasts the basic income proposal with the alternative policy proposal of the state acting as employer of last resort. Two versions of the UBI proposal are distinguished: one is hard to differentiate from expanded welfare state provision. Van Parijs’s proposal is radical enough to qualify as major egalitarian revision to capitalism. However, while it removes from a capitalist class the power to determine the terms on which others labour, it leaves this class in place and able (...) to exert other powers that distort the macro-economy. These include pecuniary emulation, demand pull inflation, and political resistance to full employment so that the rentier class does not have to contend with entrepreneurs *and* the working class over the distribution of the productive surplus. The state as employer of last resort proposal addresses these deeper issues while also claiming that inflationary pressure will undermine the UBI alternative. (shrink)

Economist Robert Pollin argues that the United States needs to try to implement full employment and how it can help the economy.

This paper affirms the continuing importance of full employment, as the best prospect for most people of the goods of meaningful work and of self-respect, and welcomes the failure of new technology in Western societies to engender mass unemployment, despite predictions to the contrary. It also replies to criticismsfrom John White (in Education and the End of Work) of a previous paper of mine, 'Work and the Human Essence (1984). Employing a different sense of 'meaningful work related to (...) agents major goals in life. White claims that little work is meaningful, or capable of becoming so, and that social policy shouldrecognise this and exonerate most people from expectations of employment. His argument embodies a distinctive understanding of human flourishing, and a critique of my earlier argument from the human essence. This paper defends that argument, plus a separate argument of my earlier paper from self-respect,which White apparently ignores, for meaningful work as crucial to human flourishing. Most employment, I maintain, is capable of being modified so as to become meaningful work, and since this is most peoples best prospect ofthat good, policies of full employment should not be discarded, either in the West or in the Third World. (shrink)

Inspired by Pohlers' local predicativity approach to Pure Proof Theory and Howard's ordinal analysis of bar recursion of type zero we present a short, technically smooth and constructive strong normalization proof for Gödel's system T of primitive recursive functionals of finite types by constructing an ε 0 -recursive function [] 0 : T → ω so that a reduces to b implies [a] $_0 > [b]_0$ . The construction of [] 0 is based on a careful analysis of the Howard-Schütte (...) treatment of Gödel's T and utilizes the collapsing function ψ: ε 0 → ω which has been developed by the author for a local predicativity style proof-theoretic analysis of PA. The construction of [] 0 is also crucially based on ideas developed in the 1995 paper "A proof of strongly uniform termination for Gödel's T by the method of local predicativity" by the author. The results on complexity bounds for the fragments of T which are obtained in this paper strengthen considerably the results of the 1995 paper. Indeed, for given n let T n be the subsystem of T in which the recursors have type level less than or equal to n+2. (By definition, case distinction functionals for every type are also contained in T n .) As a corollary of the main theorem of this paper we obtain (reobtain?) optimal bounds for the T n -derivation lengths in terms of ω n+2 -descent recursive functions. The derivation lengths of type one functionals from T n (hence also their computational complexities) are classified optimally in terms of $ -descent recursive functions. In particular we obtain (reobtain?) that the derivation lengths function of a type one functional a ∈ T 0 is primitive recursive, thus any type one functional a in T 0 defines a primitive recursive function. Similarly we also obtain (reobtain?) a full classification of T 1 in terms of multiple recursion. As proof-theoretic corollaries we reobtain the classification of the IΣ n+1 -provably recursive functions. Taking advantage from our finitistic and constructive treatment of the terms of Gödel's T we reobtain additionally (without employing continuous cut elimination techniques) that PRA + PRWO ( $\varepsilon_0) \vdash \Pi^0_2$ - Refl(PA) and PRA + PRWO ( $\omega_{n+2}) \vdash \Pi^0_2$ - Refl(I Σ n+1 ), hence PRA + PRWO( $\epsilon_0) \vdash$ Con(PA) and PRA + PRWO( $\omega_{n+2}) \vdash$ Con(IΣ n+1 ). For programmatic reasons we outline in the introduction a vision of how to apply a certain type of infinitary methods to questions of finitary mathematics and recursion theory. We also indicate some connections between ordinals, term rewriting, recursion theory and computational complexity. (shrink)

This is the first volume in a new, definitive, seven-volume edition of the works of Michal Kalecki, one of the twentieth century's most distinguished economists. Kalecki was one of the three contemporary economists to arrive at the conclusions publicized by Keynes, although Kalecki arguably presented these views even earlier than Keynes. Volume I contains Kalecki's writings on the theory of the business cycle and full employment. His seminal Essay on the Business Cycle Theory is preceded by his earlier (...) theoretical studies and followed by publications which developed and defended its main concepts and ideas. This volume also contains the 1939 book Essays in the Theory of Economic Fluctuations, the work which established his reputation. Also included are papers documenting his confrontation with Keynes's General Theory, including Kalecki's review of that work, and his various studies on the theory and policies relating to full employment, both the well known `Political Aspects of Full Employment' and `Three Ways to Full Employment', and those which have unfairly received less attention. The editorial comments and annexes at the end of the volume, besides giving valuable information on the background to the main texts, include illuminating exchanges of correspondence between Kalecki and Keynes, Joan Robinson, and others. (shrink)

Reviews : John Keane, Public Life and Late Capitalism: Toward a Socialist Theory of Democracy ; John Keane and John Owens, After Full Employment.

Logic in Action/Doron Avital Nothing is more difficult, and therefore more precious, than to be able to decide (Napoleon Bonaparte) Introduction -/- This book was born on the battlefield and in nights of secretive special operations all around the Middle East, as well as in the corridors and lecture halls of Western Academia best schools. As a young boy, I was always mesmerized by stories of great men and women of action at fateful cross-roads of decision-making. Then, like as today, (...) I felt the full weight of the moment of truth as it confronts the individual, the man or woman of action, with the imminent necessity to decide. Alongside, as I was climbing up the ladder of education, I found myself just as well captivated by the great intellectual stories of our times, in particular 20th century analytic philosophy and, at its core, the machinery of modern logic. How do then the cool contemplative modes of the philosophical and analytic outlooks, that are better fitting of the philosopher's armchair at the fireplace, hang together with the heat of the battlefield or the angst of the ticking clock of time left to the completion of a daring special operation? Growing up I was pondering exactly that. Not accidently, and in fact as consequence, I have chosen a course in life that challenged me to visit the poles of both theory and practice. I set myself on a mission to unravel the tension between the contemplative inquiry, supposedly theoretical, aiming at the logical structure of things, and the uncompromising test of life and action. The puzzle of the gap between theory and practice has become ever since the guiding question of my life. -/- Not long ago, I met two friends, Avner Shor, a veteran combat soldier of the special forces unit I eventually commanded, and Aviram Halevi, a fellow officer with whom I served. Why will we not put into writing the ideas that guided us during our years of military action, we wondered. At that time, I used to deliver the keynote lectures to the senior officers' course of Israel central intelligence organization, the Mossad. For this I already had to put some of these ideas in writing. Avner was quick to introduce me with a notable publisher and even helped me write the first chapter. With Aviram I sat to many meetings, where he would challenge me with key questions, and we followed them with memories of operations and battles, aiming to draw the required lessons. This served me well when I finally sat down to write the first draft of the book. The result was more extensive than me and my friends had expected. I had to add a particularly long chapter dealing with the story of modern philosophy and logic. This was required, I felt, as no decision-making process lives in an intellectual vacuum. Knowingly or subconsciously, the intellectual climate of the time guides us for better or worse with the decisions we finally take. The initial draft was naturally cumbersome and inaccessible. But here I had the privilege of meeting a particularly talented editor, Rami Rothholtz. I found in Rami both an editor and a critical reader. As an infantry combat soldier at youth and now a senior journalist and editor, Rami insisted on simplifying and refining my ideas. Had it not been for his work, this book would have been literally unreadable. *** I opened my book with a brief description of a single night of a special operation deep at the Lebanon Bekaa valley, far away from Israel northern border. The mission was to kidnap a senior terror leader known to be holding in captivity an Israeli pilot. This was also the last special operation I commanded in my military career. A single special operation night, but what had to precede it? For sure, many months of intense and skillful preparations. What is Planning? This is the question with which I open up chapter (2) of the book. I confront in this chapter two approaches to planning. The first is the one I saw as a mission to myself to cultivate in my many years of military service. The second is the one I saw as representing a deep-rooted fallacy that holds a firm grip on today's conventional wisdom about planning. To further examine the logic of the competing models, I was required in chapter (3) to analyze the concept of "The Standard". I argue that the false model of planning has its roots in an attitude of an uncompromising adherence to the power of literal obedience to standards and rules. The standard, or what is outlined by a rule as prescribing a future course of action, is seen as an answer to the fundamental tension between theory (planning) and practice (execution). I argue in contrast that the standard does not produce an answer but rather what I call: "A Well-Defined Question". In essence, it is a meticulously-well-planned invitation to exercise a fresh judgment. A judgement that has as an anchor the default answer that the standard produces but is open to extension as it confronts the new frame of reference of the test of reality. In chapter (4), I present a new tool for planning and execution: "The Polygon of Risks" or "The Polygon of Execution". The Polygon is a geometric illustration of the underlying tension that exists between all dimensions of the operational project. The construction and conceptualization of the trade-offs that exist between the various dimensions - segments of the polygon - is the first topic on the planner's agenda. I position the concepts of "Daring" and "Taking Proactive and Well-Informed Risks" as necessary logical constituents of the polygon and show how in contrast the false model of planning is responsible for an operational culture that is risk-averse. It encourages, in fact, the piling up of false securities at the segments' level that eventually lead to the collapse of the polygon. The necessary trade-offs relationships that exist between the segments of the polygon express the fundamental tension between partnership and competition: partnership in a joint goal and competition over resources, both material and abstract. When this tension is not managed well, that is, when the players' local optimizations overshadow the global optimization required for the success of the project, the execution polygon collapses. In this scenario, we may find the setting of the bar of "High Standards" in a players' spheres of responsibility to conceal a hidden agenda of personal insurances taken against a possible failure. Once the overall risk is not mitigated by way of collaborative joint executional dialogue, the process that leads to a collapse of the polygon is literally unstoppable. *** In chapter (5), I discuss "(Fateful) Decisions". I examine the way in which we should translate the polygon into sequential critical decisions on the timeline. The execution polygon is not a rigid scaffolding but a dynamic conceptual illustration of the -/- project. It will need now to be converted into successive decision junctions. We will find the content of a decision and its timing on the timeline to be inseparable. The right decision is the one that is taken at the right time. The moment of decision is in fact the last moment of deliberation, the first moment available for action, i.e. the first possible "Can" is also the latest possible "Must". Deciding too soon is analog to the "Jumping of the Gun". The decision maker is forcing a pre-conceived answer to a state of affairs not ripe for an answer, e.g. the target in the shooting range is not yet erected. Late to decide and the decision maker may envision what he or she should have done but reality is no longer available for them to harness it right, e.g. consider a tennis player's frustration when reviewing a too-late-to-react move in the video replay. I review in this chapter many fateful decisions, both historical, from Napoleon's Waterloo, to a Bridge Too Far of WWII, to the failed rescue attempt of American hostages at the time of the Iranian Revolution, as well as fateful decisions I had to take in the course of my military life, both in combat and in special operations, and show the sense in which they all answer to our analysis. The theme of chapter (6) is "The Moment of Truth". This is the moment when everything is on the line and from which there is no turning back. I discuss the formative repetitive structure of the schooling and simulation phase and contrast it with the "One Shot, One Opportunity" nature of the moment of truth. This is extremely helpful when we analyze the logical structure of failures as unwarranted repetitions of past lessons. The schooling curriculum indeed consists of important abstractions drawn from lessons of the past. However, it is when we project them in a fashion that is literal or mechanical that we cross path with the possibility of a failure. The paradox of education is that what we must repeat in school and simulation must be extended and not repeated in real life. What is required of us so we do not fall into the fallacy of repetition in face of the moment of truth is the core subject of the discussion of this chapter. In chapter (7), I took a lengthy philosophical detour surveying the intellectual drama of modern logic, and in general, the story of 20th century analytic philosophy. Readers who choose to bypass the somehow demanding narrative of this drama can do so and still keep the argumentative thread of the book. However, even by way of skipping the more technical parts, I would still urge the readers to delve into the discussion in this chapter as I believe this would grant them a deeper understanding of the overall conceptual framework. I explore here the work of two key figures: the logician Kurt Gödel and the philosopher Ludwig Wittgenstein, both were crowned in 2000 by TIME Magazine, as the leading Logician and Philosopher, respectively, of the 20th Century. I review the fascinating logical result of Gödel's Incompleteness Theorem and examine its relevance as setting a theoretical limit to the power of formalization. This amazing logical result - a result that shakes the logical foundations of 20th century thought in as much as the discovery of irrational numbers shook the foundations of the Pythagorean program of the ancient Greeks - bears significantly on the question of action and the blind trust we place in the power of formalization in the form of protocols and rules. It is here that Wittgenstein's philosophy enters in full force. We follow Wittgenstein as he dismantles our conception of rules as if there were "Railroads to Infinite", i.e. as prescribing for us in-advance their proper employments in all possible -/- future eventualities. Instead we propose that the dilemma of action demands of us an extension of rules rather than a mechanical or blind repetition of their literal imperative. In turn, this extension can serve as a new lesson added to the curriculum of school and simulation. The theme of chapter (8), the concluding chapter, is Strategy, Logic, and Ethics. The chapter comes to place the ethical dilemma in the conceptual map we presented in the book. I discuss here the tension between strategy as a process of setting goals and deriving backward as it were the steps that are necessary for achieving these goals, to the inescapable dictation of the ethical imperative. This unavoidable tension is particularly important against the backdrop of contemporary culture that is guided by a vision of personal success and achievement that may threaten our ability to do what is right. Most of all, I am troubled in this chapter, with the role logic may play, first as a liberating force enabling a change that is tuned to the ethical imperative, and second, as a force designed to justify on logical grounds, as it were, the existing power structure. It is in this junction that brave individuals will be called to challenge the governing logic of the zeitgeist - logic that operates now as an oppressive force that serves the vested interest of beneficials of the existing order. When success is favored over doing what is right, as we must admit is the prevailing cultural mood of our times, that the words of Emanuel Kant carry their full weight: "Do the Right thing and leave the Consequences to God". For this we need heroes and heroines that challenge the time by bearing the full weight of responsibility that comes with the doing of what is Right. *** This book was written more than anything from the perspective of the heroes and heroines of action. Sometimes they may be missing the exact words or the full insight into the solid logical complexity that stands between them and the doing of what is right. They feel what is right to do on the battlefield of life, whether in real battle, in political or economic life or whether in the life of creativity and the quest of the intellect. They do need, in analogy, proper logical and intellectual artillery. I hope they will find the logical cannons they require as they travel through the pages of this book. The rest is in their hands at the Moment of Truth. -/- Doron Avital, Tel Aviv 2011 -/- . (shrink)

Famous for the number-theoretic first-order statement known as Goodstein's theorem, author R. L. Goodstein was also well known as a distinguished educator. With this text, he offers an elementary treatment that employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. The text begins with an informal introduction to the algebra of classes, exploring union, intersection, and complementation; the commutative, associative, and distributive laws; difference and symmetric difference; and Venn diagrams. Professor Goodstein proceeds to a (...) detailed examination of three different axiomatizations, and an outline of a fourth system of axioms appears in the examples. The final chapter, on lattices, examines Boolean algebra in the setting of the theory of partial order. Numerous examples appear at the end of each chapter, with full solutions at the end. (shrink)

We show how the notion of full Frobenius group of finite Morley rank generalizes that of bad group, and how it seems to be more appropriate when we consider the possible existence (still unknown) of nonalgebraic simple groups of finite Morley rank of a certain type, notably with no involution. We also show how these groups appear as a major obstacle in the analysis of FT-groups, if one tries to extend the Feit-Thompson theorem to groups of finite Morley (...) rank. (shrink)

Theorems of hyperarithmetic analysis (THAs) occupy an unusual neighborhood in the realms of reverse mathematics and recursion theoretic complexity. They lie above all the fixed (recursive) iterations of the Turing Jump but below ATR $_{0}$ (and so $\Pi _{1}^{1}$ -CA $_{0}$ or the hyperjump). There is a long history of proof theoretic principles which are THAs. Until Barnes, Goh, and Shore [ta] revealed an array of theorems in graph theory living in this neighborhood, there was only one mathematical denizen. In (...) this paper we introduce a new neighborhood of theorems which are almost theorems of hyperarithmetic analysis (ATHAs). When combined with ACA $_{0}$ they are THAs but on their own they are very weak. We generalize several conservativity classes ( $\Pi _{1}^{1}$, r- $\Pi _{2}^{1}$, and Tanaka) and show that all our examples (and many others) are conservative over RCA $_{0}$ in all these senses and weak in other recursion theoretic ways as well. We provide denizens, both mathematical and logical. These results answer a question raised by Hirschfeldt and reported in Montalbán [2011] by providing a long list of pairs of principles one of which is very weak over RCA $_{0}$ but over ACA $_{0}$ is equivalent to the other which may be strong (THA) or very strong going up a standard hierarchy and at the end being stronger than full second order arithmetic. (shrink)

We formulate a restriction of Hindman’s Finite Sums Theorem in which monochromaticity is required only for sums corresponding to rooted finite paths in the full binary tree. We show that the resulting principle is equivalent to \-induction over \. The proof uses the equivalence of this Hindman-type theorem with the Pigeonhole Principle for trees \ with an extra condition on the solution tree.

Employability is an important issue in the labor context. Currently, the European Union presents employability as the path to full employment and active citizenship, and a strategy to reduce unemployment and poverty. This study develops and validates an Employability Appraisal Scale. Specifically, we propose a multidimensional employability scale that analyzes both individual indicators and personal circumstances from the Bioecological Model of Employability. The Employability Appraisal Scale (EAS) assesses personal and social dimensions of employability. It was developed and tested (...) using data from 489 people from a very heterogeneous sample (precarious workers, professionals, prisoners, long-term unemployed, socially excluded, etc.). Results provide evidence for the multi-dimensional structure and validity of the EAS. This scale is a valid and reliable instrument to measure employability, and it provides criteria for interpreting scores. Finally, we present theoretical and practical implications of the EAS for social and labor integration, job transition, and career development. Our findings have positive implications for identifying effectiveness indicators in training programs, and they contribute to designing intervention policies to increase employability. (shrink)

Recent research indicates that among young women, Blacks have lower employment rates than whites. Evidence is provided about whether young Black women's lower employment rates stem from structural features of the labor market, discrimination, or changing family or individual characteristics. Data show that Black women exit full-time employment at higher rates because they are more likely to be laid off, to leave because they work in temporary/seasonal jobs, and to leave for other reasons. Structural features of (...) the labor market are key in explaining Black women's higher rates of lay-offs, exits from temporary/seasonal work, and exits for other reasons. Individual characteristics and discrimination play a role in Black women's higher rates of lay-offs and exits for other reasons while family characteristics are important in explaining Black women's higher rates of leaving temporary/seasonal work and leaving for other reasons. Evidence suggests that Black women's higher exit rates are indicative of disadvantage in the labor market. (shrink)

This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structures the results hold if and only if the underlying plausibility ordering is well-founded. We then show that neither well-foundedness nor common priors are expressible in the language commonly used to describe and reason about epistemic-plausibility models. The static agreement (...) result is, however, finitely derivable in an extended modal logic. We provide the full derivation. We finally consider dynamic agreement results. We show they have a counterpart in epistemic-plausibility models, and provide a new form of agreements via public announcements. (shrink)

Let C be a small Barr-exact category, Reg the category of all regular functors from C to the category of small sets. A form of M. Barr's full embedding theorem states that the evaluation functor e : C →[Reg, Set ] is full and faithful. We prove that the essential image of e consists of the functors that preserve all small products and filtered colimits. The concept of κ-Barr-exact category is introduced, for κ any infinite regular cardinal, (...) and the natural generalization to κ-Barr-exact categories of the above result is proved. The treatment combines methods of model theory and category theory. Some applications to module categories are given. (shrink)

A full separation theorem for the derivable rules of intuitionistic linear logic without bounds, 0 and exponentials is proved. Several structural consequences of this theorem for subreducts of (commutative) residuated lattices are obtained. The theorem is then extended to the logic LR+ and its proof is extended to obtain the finite embeddability property for the class of square increasing residuated lattices.

We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformations being equivariant under certain actions of a noncocommutative Hopf algebra called the shuffie algebra. Multiplicative sequents are assigned a vector space of such dinaturals, and we show that this space has as a basis the denotations of cut-free (...) proofs in CyLL + MIX. This can be viewed as a fully faithful representation of a free *-autonomous category, canonically enriched over vector spaces. This paper is a natural extension of the authors' previous work, "Linear Lauchli Semantics", where a similar theorem is obtained for the commutative logic MLL + MIX. In that paper, we interpret proofs as dinaturals which are invariant under certain actions of the additive group of integers. Here we also present a simplification of that work by showing that the invariance criterion is actually a consequence of dinaturality. The passage from groups to Hopf algebras in this paper corresponds to the passage from commutative to noncommutative logic. However, in our noncommutative setting, one must still keep the invariance condition on dinaturals. (shrink)

The theorem of Bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables. We show that the inequalities of Bell are special cases of theorems found 10 years earlier by Bass and stated in full generality by Vorob’ev. This fact implies precise necessary and sufficient mathematical conditions for the validity of the Bell inequalities. We show that these precise conditions differ significantly from the definition of objective local variable spaces and (...) as an application that the Bell inequalities may be violated even for objective local random variables. (shrink)

We give in this paper a short semantical proof of the strong normalization for full propositional classical natural deduction. This proof is an adaptation of reducibility candidates introduced by J.-Y. Girard and simplified to the classical case by M. Parigot.

Theorems of hyperarithmetic analysis occupy an unusual neighborhood in the realms of reverse mathematics and recursion-theoretic complexity. They lie above all the fixed iterations of the Turing jump but below ATR $_{0}$. There is a long history of proof-theoretic principles which are THAs. Until the papers reported on in this communication, there was only one mathematical example. Barnes, Goh, and Shore [1] analyze an array of ubiquity theorems in graph theory descended from Halin’s [9] work on rays in graphs. They (...) seem to be typical applications of ACA $_{0}$ but are actually THAs. These results answer Question 30 of Montalbán’s Open Questions in Reverse Mathematics [19] and supply several other natural principles of different and unusual levels of complexity.This work led in [25] to a new neighborhood of the reverse mathematical zoo: almost theorems of hyperarithmetic analysis. When combined with ACA $_{0}$ they are THAs but on their own are very weak. Denizens both mathematical and logical are provided. Generalizations of several conservativity classes are defined and these ATHAs as well as many other principles are shown to be conservative over RCA $_{0}$ in all these senses and weak in other recursion-theoretic ways as well. These results answer a question raised by Hirschfeldt and reported in [19] by providing a long list of pairs of principles one of which is very weak over RCA $_{0}$ but over ACA $_{0}$ is equivalent to the other which may be strong or very strong going up a standard hierarchy and at the end being stronger than full second-order arithmetic. (shrink)

It is known that the full computation-tree logic CTL * is an important base logic for model checking. The bisimulation theorem for CTL* is known to be useful for abstraction in model checking. In this paper, the bisimulation theorems for two paraconsistent four-valued extensions 4CTL* and 4LCTL* of CTL* are shown, and a translation from 4CTL* into CTL* is presented. By using 4CTL* and 4LCTL*, inconsistency-tolerant and spatiotemporal reasoning can be expressed as a model checking framework.

We prove that the full completeness theorem for MLL+Mix holds by the simple interpretation via formulas as objects and proofs as Z-invariant morphisms in the *-autonomous category of topologized vector spaces. We do this by generalizing the recent work of Blute and Scott 101–142) where they used the semantical framework of dinatural transformation introduced by Girard–Scedrov–Scott , Logic from Computer Science, vol. 21, Springer, Berlin, 1992, pp. 217–241). By omitting the use of dinatural transformation, our semantics evidently allows (...) the interpretation of the cut-rule, while the original Blute–Scott's does not. Moreover, our interpretation for proofs is preserved automatically under the cut elimination procedure. In our semantics proofs themselves are characterized by the concrete algebraic notion “Z-invariance”, and our denotational semantics provides the full completeness. Our semantics is naturally extended to the full completeness semantics for CyLL+Mix owing to an elegant method of Blute–Scott 1413–1436) 101–142))). (shrink)

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with infinitely precise (...) degrees of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles. (shrink)

We show that van Lambalgen's Theorem fails with respect to recursive randomness and Schnorr randomness for some real in every high degree and provide a full characterization of the Turing degrees for which van Lambalgen's Theorem can fail with respect to Kurtz randomness. However, we also show that there is a recursively random real that is not Martin-Löf random for which van Lambalgen's Theorem holds with respect to recursive randomness.

Linear continuous logic is the fragment of continuous logic obtained by restricting connectives to addition and scalar multiplications. Most results in the full continuous logic have a counterpart in this fragment. In particular a linear form of the compactness theorem holds. We prove this variant and use it to deduce some basic preservation theorems.

This guide accompanies the following article(s): ‘Full Disclosure of the “Raw Data” of Research on Humans: Citizens’ Rights, Product Manufacturer’s Obligations and the Quality of the Scientific Database.’Philosophy Compass 6/2 (2011): 90–99. doi: 10.1111/j.1747‐9991.2010.00376.x Author’s Introduction Securing consent (and informed consent) from patients and research study participants is a key concern in patient care and research on humans. Yet, the legal doctrines of consent and informed consent differ in their applications. In patient care, the judicial doctrines of consent and (...) informed consent are disclosure doctrines based on the obligation of physicians to inform their patients of the following types of information: the nature of the procedure the physician is recommending in the patent’s care (P), the alternatives to the physician‐recommendation (A), and the risks of procedure and its alternatives (R). In addition, the physician must provide truthful answers to the patient’s questions (Q) to the best of the physician’s abilities. In research on humans, the onus of disclosure by study sponsors and principal investigators is much greater than in patient care precisely because the purpose of research is not patient care. The purpose of research is the identification and development of new generalizable knowledge. Thus, participation in a research study or trial may not benefit the study volunteer at all. In addition, the participant may carry a heavy risk burden in relationship to any testing of a newly designed drug or device as part of their experiences in the research study. Presently, despite the risks borne by the research study participant, the raw data collected from volunteers in research trials are treated by courts as if they were the private property of the study sponsor rather than generally owed to the public as would be expected by an effort like research participation aimed at contributing to the development of generalizable knowledge. This paper reviews the obligations that study sponsors owe to their study participants based on the very definition of research as a systematic activity whose purpose is to develop generalizable knowledge to help all humans. Author Recommends Court cases Canterbury v. Spence, United States Court of Appeals, District of Columbia Circuit 464 F.2d 772 (1972). (Federal appellate decision heard in the District of Columbia, USA) Reibl v. Hughes, 2 S.C.R. 880 (1980). (Supreme Court of Canada) Rogers v. Whitaker, 175 C.L. R. 479 (1992). (High Court of Australia) Sidaway v. Board of Governors of the Bethlem Royal Hospital and the Maudsley Hospital and Others. 1 A.C. 871 (1985) (House of Lords) Canterbury v. Spence is the landmark Federal informed consent case in the United States heard in the District of Columbia. In this case, Judge Spottswood Robinson articulated the reasonable person standard of informed consent. This standard was subsequently adopted by the Supreme Court of Canada (Reibl v. Hughes, 2 S.C.R. 880 (1980)) and the High Court of Australia (Rogers v. Whitaker, 175 C.L. R. 479 (1992)). The House of Lords rejected the reasonable person standard in England in Sidaway v. Board of Governors of the Bethlem Royal Hospital and the Maudsley Hospital and Others. 1 A.C. 871 (1985). Book Mazur, Dennis J. The Science and Ethics of Research on Humans. Baltimore, MD: Johns Hopkins University Press, 2007. This book is a detailed guide for the review of scientific and ethical aspects of research on humans contained in the research study protocols and research informed consent forms which need to be submitted by study sponsors and principal investigators to institutional review boards (IRBs) for IRB review before a research study can receive approval to be conducted within a human study population in those institutions over which the IRB has authority. It also presents basic definitions in the area of research on humans and basic approaches to help conduct a deep review of the underlying scientific and ethical issues that are present within a research study protocol and its accompanying research informed consent form. Report National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research. The Belmont Report: Ethical Guidelines for the Protection of Human Subjects of Research. Washington, DC: DHEW Publications, 1978 (78‐0012). This U.S. National Commission in the Belmont Report argued for the necessity of a reasonable volunteer standard in research on humans in the United States. Arguing that the professional standard and the reasonable person standard of consent and informed consent were insufficient to base a disclosure standard in research on humans, this National Commission developed the reasonable volunteer standard where a study participant is to be approached in research informed consent with that information that a reasonable volunteer would want to know. Online Materials Belmont Report: Syllabus Topics for Lecture and Discussion Week I: Introduction and Overview Readings: Rogers v. Whitaker, 175 C.L.R. 479 (1992). (High Court of Australia) Sidaway v. Board of Governors of the Bethlem Royal Hospital and the Maudsley Hospital and Others. 1 A.C. 871 (1985) (House of Lords) Week II: The Different Standards of Consent and Informed Consent Readings: Canterbury v. Spence, 464 F.2d 772 (1972). (Federal appellate opinion heard in the District of Columbia) Sidaway v. Board of Governors of the Bethlem Royal Hospital and the Maudsley Hospital and Others. 1 A.C. 871 (1985) (House of Lords) Week III: Definition of Research Reading: Mazur, Dennis J. The Science and Ethics of Research on Humans. Baltimore, MD: Johns Hopkins University Press, 2007. (Especially Chapters 2 and 3) Week IV: How to Review a Research Study Protocol and Research Informed Consent Form Reading: Mazur, Dennis J. The Science and Ethics of Research on Humans. Baltimore, MD: Johns Hopkins University Press, 2007. (Especially Chapters 4–6, 10, and 12–14) Week V: Obligations in Research of Humans Versus Patient Care Reading: National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research. The Belmont Report: Ethical Guidelines for the Protection of Human Subjects of Research. Washington, DC: DHEW Publications, 1978 (78‐0012). Focus Questions • How do the judicial doctrines of consent in England and Australia compare to the judicial doctrines of informed consent in the United States and Canada? • How does a professional standard of disclosure differ from a reasonable person standard of disclosure? • What is the definition of research? • How is a research study (study proposal and research informed consent form) reviewed from scientific and ethical bases for considerations of approval by an IRB? • How do the obligations of a study sponsor, a principal investigator, and a research team conducting a research trial on human study participants differ from the obligations of a physician caring for a patient? • Should all raw data of research derived from humans be made available to the public for use in developing generalizable knowledge to help others, or should raw data be considered the private property of the study sponsors (for example, prescription drug manufacturers), who fund the research trials? Seminar/project Idea Draw a timeline of the development of the basic concepts of consent and informed consent in patient care and in patient research. On this timeline, first place the dates of the key court cases in England, the United States, Canada, and Australia on consent and informed consent. Then place the date of the development of the Belmont Report. Why do differences exist between these four countries in terms of the legal requirements of informedness of a patient (in medical care) and a study participant (in medical research)? What roles if any do the concepts of self‐determination and self‐decision have in consent and informed consent in patient care and in informed consent in research on humans among the four countries of interest? What are the realities of research on human participants that require a new standard of informed consent, the reasonable volunteer standard, to be developed beyond the two standards in patient care, the professional standard, and the reasonable person standard? Counterpoint Arguments The following are counterpoint arguments that need to be appreciated to more fully understand the concepts that impact the thesis that ‘raw data’ should be open to the public to allow the opportunity of checking of the results of its associated scientific paper and for further analysis. De‐Identified (Anonymized) Raw Data A current approach to identifying (anonymizinig) raw data is based on the Health Insurance Portability and Accountability Act (HIPAA) of 1996 (P.L.104‐191). HIPAA was enacted by the U.S. Congress in 1996 to keep a person’s medical information private. In a research study, a person’s private medical information can become research data. HIPAA’s Privacy Rule allows a covered entity to de‐identify data by removing all 18 elements that could be used to identify the individual or the individual’s relatives, employers, or household members; these elements are enumerated in the Privacy Rule. The covered entity must also have no actual knowledge that the remaining information could be used alone or in combination with other information to identify the individual who is the subject of the information. Under this method, the identifiers that must be removed are the following: 1 Names. 2 All geographic subdivisions smaller than a state, including street address, city, county, precinct, ZIP Code, and their equivalent geographical codes, except for the initial three digits of a ZIP Code if, according to the current publicly available data from the Bureau of the Census: 2a. The geographic unit formed by combining all ZIP Codes with the same three initial digits contains more than 20,000 people. 2b. The initial three digits of a ZIP Code for all such geographic units containing 20,000 or fewer people are changed to 000. 3 All elements of dates (except year) for dates directly related to an individual, including birth date, admission date, discharge date, and date of death, and all ages over 89 and all elements of dates (including year) indicative of such age, except that such ages and elements may be aggregated into a single category of age 90 or older. 4 Telephone numbers. 5 Facsimile numbers. 6 Electronic mail addresses. 7 Social security numbers. 8 Medical record numbers. 9 Health plan beneficiary numbers. 10 Account numbers. 11 Certificate/license numbers. 12 Vehicle identifiers and serial numbers, including license plate numbers. 13 Device identifiers and serial numbers. 14 Web universal resource locators (URLs). 15 Internet protocol (IP) address numbers. 16 Biometric identifiers, including fingerprints and voiceprints. 17 Full‐face photographic images and any comparable images. 18 Any other unique identifying number, characteristic, or code, unless otherwise permitted by the Privacy Rule for re‐identification. Even though ‘raw data’ can be de‐identified (anonymized) so that there is no way to trace back the data to the study participant from which it was drawn, there are still questions whether the ‘de‐identified raw data’ can be given to other researchers or made public without the original study participant’s approval. It may be the case that this approval could be done at the start of any research study where the individual considering study participation would be counseled on what the process of de‐identification consists of and would be asked whether the participant would allow use of the data by other researchers or made available to the public in a de‐identified state. However, there may be questions of the study participants as to whether the data are truly de‐identified and untraceable back to the study participant since the participant would not be able to see the process actually being carried out in detail in all relevant circumstances. Using Raw Data in Context Simply being in possession of raw data is never enough to build on that data from a research perspective. Researchers need to understand the context of the scientific research study in which the data were collected. This research context includes (but is not limited to): (i) the scientific hypothesis of the research study, (ii) the inclusion and exclusion criteria selected by the research designers of the study to determine which study participants were included and which were excluded from the study, (iii) the methods used to collect the data and possibilities of errors in the data collection processes, and (iv) answers to questions regarding whether any data were excluded from the study data and why these data were excluded. Ownership Rights Over Data There are ownership rights over data. Ownership rights include court decision making related to the question which parties are to be considered as the owners of the data. Possible owners here include (but are not limited to) (i) the study sponsor whose only role was to fund that study, (ii) the principal investigator(s) who developed the scientific hypothesis, and (iii) individual study participants through special contracts made by individual participants who negotiate such contracts with study sponsors and principal investigators to share in the ownership of data. Examples of such data are participant sources of unique gene lines or unique cell lines to be used in future research. Objections to Data Sharing Finally, individual researchers may simply object to sharing data. A researcher’s arguments here may be simply stating that he or she has a right to fully analyze the data since the collection of the data was the researchers’ idea in the first place. These researchers may argue that they have the right to mine the data as fully as they can before deciding to make the data open to the public for others to analyze. Works Cited 1 Kaiser, J. ‘Making Clinical Data Widely Available.’Science 322.5899 (10 Oct. 2008): 217–8. 2 de Lusignan, S., J.F. Metsemakers, P. Houwink, V. Gunnarsdottir, and J. van der Lei. ‘Routinely Collected General Practice Data: Goldmines for Research? A Report of the European Federation for Medical Informatics Primary Care Informatics Working Group (EFMI PCIWG) from MIE2006, Maastricht, The Netherlands.’Informatics in Primary Care 14.3 (2006): 203–9. 3 Sim, I. ‘Human Studies Database Project’, CTSA Data Repositories Symposium (17 Oct. 2008). 23 Nov. 2010. 4 Sim, I., C.G. Chute, H. Lehmann, R. Nagarajan, M. Nahm, and R.H. Scheuermann. ‘Keeping Raw Data in Context.’Science 323.5915 (6 Feb. 2009): 713. 5 U.S. Department of Health and Human Services, National Institutes of Health, HIPAA Privacy Rule, Information for Researchers. 13 Nov. 2010. 6 Wilczynski, N.L., R.B. Haynes, and Hedges Team. ‘EMBASE Search Strategies for Identifying Methodologically Sound Diagnostic Studies for Use by Clinicians and Researchers.’BMC Medicine 29.3 (March 2005): 7. (shrink)

The present note was prompted by Weber’s approach to proving Cantor’s theorem, i.e., the claim that the cardinality of the power set of a set is always greater than that of the set itself. While I do not contest that his proof succeeds, my point is that he neglects the possibility that by similar methods it can be shown also that no non-empty set satisfies Cantor’s theorem. In this paper unrestricted abstraction based on a cut free Gentzen type (...) sequential calculus will be employed to prove both results. In view of the connection between Priest’s three-valued logic of paradox and cut free Gentzen calculi this, a fortiori, has an impact on any paraconsistent set theory built on Priest’s logic of paradox. (shrink)

This article presents an investigation of the dynamics of women’s gender attitudes from the perspective of women’s conflicting employment and child-rearing responsibilities. It examines the independent and joint effects of motherhood and employment on gender attitudes using combined data from the British Household Panel Survey and the Understanding Society panel study. The results of fixed effects models show no evidence supporting a direct influence of either motherhood or employment on women’s attitudes toward a traditional division of labor. (...) However, changes in attitudes are observed when motherhood and employment statuses are considered jointly. Specifically, women are less traditional after the transition to motherhood than before only if motherhood is combined with full-time employment. By contrast, women are more traditional after the transition to motherhood than before only if motherhood coincides with their withdrawal from the labor force. These associations remain robust after considering feedback from earlier attitudes. All the findings suggest that the emergence and realization of incompatibility between women’s employment and child-rearing responsibilities reshape women’s gender attitudes during the transition to motherhood. (shrink)

We explore the finite model theory of the characterisation theorems for modal and guarded fragments of first-order logic over transition systems and relational structures of width two. A new construction of locally acyclic bisimilar covers provides a useful analogue of the well known tree-like unravellings that can be used for the purposes of finite model theory. Together with various other finitary bisimulation respecting model transformations, and Ehrenfeucht–Fraïssé game arguments, these covers allow us to upgrade finite approximations for full bisimulation (...) equivalence towards approximations for elementary equivalence. These techniques are used to prove several ramifications of the van Benthem–Rosen characterisation theorem of basic modal logic for refinements of ordinary bisimulation equivalence, both in the sense of classical and of finite model theory. (shrink)

This books presents the refereed proceedings of the Fifth International Workshop on Analytic Tableaux and Related Methods, TABLEAUX '96, held in Terrasini near Palermo, Italy, in May 1996. The 18 full revised papers included together with two invited papers present state-of-the-art results in this dynamic area of research. Besides more traditional aspects of tableaux reasoning, the collection also contains several papers dealing with other approaches to automated reasoning. The spectrum of logics dealt with covers several nonclassical logics, including modal, (...) intuitionistic, many-valued, temporal and linear logic. (shrink)

The two theories that revolutionized physics in the twentieth century, relativity and quantum mechanics, are full of predictions that defy common sense. Recently, we used three such paradoxical ideas to prove “The Free Will Theorem” (strengthened here), which is the culmination of a series of theorems about quantum mechanics that began in the 1960s. It asserts, roughly, that if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity. More (...) precisely, if the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle’s response (to be pedantic—the universe’s response near the particle) is not determined by the entire previous history of the universe. Our argument combines the well-known consequence of relativity theory, that the time order of space-like separated events is not absolute, with the EPR paradox discovered by Einstein, Podolsky, and Rosen in 1935, and the Kochen-Specker Paradox of 1967 (See [2].) We follow Bohm in using a spin version of EPR and Peres in using his set of 33 directions, rather than the original configuration used by Kochen and Specker. More contentiously, the argument also involves the notion of free will, but we postpone further discussion of this to the last section of the article. Note that our proof does not mention “probabilities” or the “states” that determine them, which is.. (shrink)

Barbara Fried described John Rawls’s response to libertarianism as “the unwritten theory of justice.” This paper argues that while there is no need for a new theory of justice to address the libertarian challenge, there is a need for an additional chapter. Taking up Fried’s suggestion that the Rawlsian response would benefit from a revised list of primary goods, I propose to add employment to the list, thus leading to adoption of a full employment principle in the (...) original position that ensures that anyone who wants to work will be able to do so. I argue that although Rawls famously proposed government as employer of last resort, he never integrated that comment into his theory, which lacks a full employment principle and says nothing about the injustice of involuntary unemployment in its ideal theory. I first refute the received view of Rawls’s treatment of employment as required by its importance for citizens’ self-respect, then show that in fact, the full employment assumption is the result of the role of general equilibrium theory in Rawls’s model of a well-ordered society, and indicate why developments in economic theory and economic policy support the proposed revision. (shrink)

Although the use of stakeholder analysis to investigate corporate responsibilities has burgeoned over the past two decades, there has been relatively little workon howcorporate responsibilities may change for firms with operations in developing countries. This article argues, from a critical theory perspective, that two sets of factors tend to come together to increase the responsibilities of corporations active in developing countries to a full range of stakeholder groups: (a) the different (economic, political, and sociocultural) circumstances under which corporations have (...) to operate in developing countries and (b) several key normative principles, which typically do not come into play in the context of developed countries. (shrink)

The aim of this paper is to evaluate the prevalence in the 27 member states of the European Union of a little discussed illicit wage arrangement in which formal employees are paid two wages by their formal employers – an official declared salary and an additional undeclared wage, thus allowing employers to evade their full social insurance and tax liabilities. Reporting the results of a 2007 Eurobarometer survey involving 26,659 face-to-face interviews, the finding is that one in 18 formal (...) employees received such an envelope wage from their formal employer and that envelope wage payments are more prevalent in member states with lower (rather than higher) levels of state intervention. The tentative conclusion is that illicit envelope wage payments are a product of under-regulation, rather than over-regulation, and that further research is now required to test the validity analysis of this thesis in other global regions. (shrink)

We prove a full completeness theorem for multiplicative–additive linear logic using a double gluing construction applied to Ehrhard’s *-autonomous category of hypercoherences. This is the first non-game-theoretic full completeness theorem for this fragment. Our main result is that every dinatural transformation between definable functors arises from the denotation of a cut-free proof. Our proof consists of three steps. We show:• Dinatural transformations on this category satisfy Joyal’s softness property for products and coproducts.• Softness, together with multiplicative (...) full completeness, guarantees that every dinatural transformation corresponds to a Girard proof-structure.• The proof-structure associated with any dinatural transformation is a proof-net, hence a denotation of a proof. This last step involves a detailed study of cycles in additive proof-structures.The second step is a completely general result, while the third step relies on the concrete structure of a double gluing construction over hypercoherences. (shrink)

One of the problems in economics that economists have devoted a considerable amount of attention in prevalent years has been to ensure consistency in the models they employ. Assuming markets to be generally in some state of equilibrium, it is asked under what circumstances such equilibrium is possible. The fundamental mathematical tools used to address this concern are fixed point theorems: the conditions under which sets of assumptions have a solution. This book gives the reader access to the mathematical techniques (...) involved and goes on to apply fixed point theorems to proving the existence of equilibria for economics and for co-operative and noncooperative games. Special emphasis is given to economics and games in cases where the preferences of agents may not be transitive. The author presents topical proofs of old results in order to further clarify the results. He also proposes fresh results, notably in the last chapter, that refer to the core of a game without transitivity. This book will be useful as a text or reference work for mathematical economists and graduate and advanced undergraduate students. (shrink)