Let X and Y be uncountable Polish spaces. We show in ZF that there is a coanalytic subset P of X × Y with countable sections which cannot be expressed as the union of countably many partial coanalytic, or even PCA = Σ 1 2 , graphs. If X = Y = ω ω , P may be taken to be Π 1 1 . Assuming stronger set theoretic axioms, we identify the least pointclass such that any such coanalytic P (...) can be expressed as the union of countably many graphs in this pointclass. This last result is extended (under suitable hypotheses) to all levels of the projective hierarchy. (shrink)

We show that all the projective ordinals $\delta^1_n$ are supercompact through their supremum $\aleph_{\varepsilon 0}$, and a ways beyond.

The Axiom of Projective Determinacy implies the existence of a universal $\utilde{\Pi}^{1}_{n}\setminus\utilde{\Delta}^{1}_{n}$ set for every $n \geq 1$. Assuming $\text{\upshape MA}(\aleph_{1})+\aleph_{1}=\aleph_{1}^{\mathbb{L}}$ there exists a universal $\utilde{\Pi}^{1}_{1}\setminus\utilde{\Delta}^{1}_{1}$ set. In ZFC there is a universal $\utilde{\Pi}^{0}_{\alpha}\setminus\utilde{\Delta}^{0}_{\alpha}$ set for every $\alpha$.

We prove that the least σ-algebra containing the projective sets and closed under projections is exactly the collection of hyperprojective sets which, with their complements, can be inductively defined with real parameters by an induction of countable length. This provides a construction principle for this natural class of hyperprojective sets.

Mechanistic explanation involves the attribution of functions to both mechanisms and their component parts, and function attribution plays a central role in the individuation of mechanisms. Our aim in this paper is to investigate the impact of a perspectival view of function attribution for the broader mechanist project, and specifically for realism about mechanistic hierarchies. We argue that, contrary to the claims of function perspectivalists such as Craver, one cannot endorse both function perspectivalism and mechanistic hierarchy realism: if functions (...) are perspectival, then so are the levels of a mechanistic hierarchy. We illustrate this argument with an example from recent neuroscience, where the mechanism responsible for the phenomenon of ephaptic coupling cross-cuts the more familiar mechanism for synaptic firing. Finally, we consider what kind of structure there is left to be realist about for the function perspectivalist. (shrink)

In my forthcoming book, How to Count Animals, More or Less (based on my 2016 Uehiro Lectures in Practical Ethics), I argue for a hierarchical approach to animal ethics according to which animals have moral standing but nonetheless have a lower moral status than people have. This essay is an overview of that book, drawing primarily from selections from its beginning and end, aiming both to give a feel for the overall project and to indicate the general shape of the (...) hierarchical position that I defend there. In this essay, I contrast the hierarchical approach with its most important rival (which holds that people and animals have the very same moral status), sketch the main idea behind one central argument for hierarchy, and briefly review three potentially troubling implications of the hierarchical view. I close with a discussion of a promising possible solution to the most worrisome of the three objections. (shrink)

Free/Libre Open Source Software (FLOSS) development teams provide an interesting and convenient setting for studying distributed work. We begin by answering perhaps the most basic question: what is the social structure of these teams? We conducted social network analyses of bug-fixing interactions from three repositories: Sourceforge, GNU Savannah and Apache Bugzilla. We find that some OSS teams are highly centralized, but contrary to expectation, others are not. Projects are mostly quite hierarchical on four measures of hierarchy, consistent with past (...) research but contrary to the naive image of these projects. Furthermore, we find that the level of centralization is negatively correlated with project size, suggesting that larger projects become more modular, or possibly that becoming more modular is a key to growth. The paper makes a further methodological contribution by identifying appropriate analysis approaches for interaction data. We conclude by sketching directions for future research. (shrink)

In this paper we will consider two possible definitions of projective subsets of a separable metric space X. A set A subset of or equal to X is Σ11 iff there exists a complete separable metric space Y and Borel set B subset of or equal to X × Y such that A = {x ε X : there existsy ε Y ε B}. Except for the fact that X may not be completely metrizable, this is the classical definition (...) of analytic set and hence has many equivalent definitions, for example, A is Σ11 iff A is relatively analytic in X, i.e., A is the restriction to X of an analytic set in the completion of X. Another definition of projective we denote by ΣX1 or abstract projective subset of X. A set of A subset of or equal to X is ΣX1 iff there exists an n ε ω and a Borel set B subset of or equal to X × Xn such that A = {x ε X:there existsy ε Xn ε B}. These sets ca n be far more pathological. While the family of sets Σ11 is closed under countable intersections and countable unions, there is a consistent example of a separable metric space X where ΣX1 is not closed under countable intersections or countable unions. This takes place in the Cohen real model. Assuming CH, there exists a separable metric space X such that every Σ11 set is Borel in X but there exists a Σ11 set which is not Borel in X2. The space X2 has Borel subsets of arbitrarily large rank while X has bounded Borel rank. This space is a Luzin set and the technique used here is Steel forcing with tagged trees. We give examples of spaces X illustrating the relationship between Σ11 and ΣX1 and give some consistent examples partially answering an abstract projective hierarchy problem of Ulam. (shrink)

A British coffee chain’s fundraising practices constitute a background for this study to examine ideological discourses behind British charitable giving. The charity executes projects in coffee growing communities by providing education for children in disadvantaged neighbourhoods. The study takes a critical stance from a discursive paradigmatic perspective to analyse visual contents used by the charity. The applied visual critical discourse analysis was inspired by Barthes’ semiotic theory. Findings suggest that the adverts’ interpretative repertoires can serve ideologies that sustain the donors’ (...) social-cultural dominance over the recipients by justifying group-based social hierarchies. The chains of signifiers do not question the spectators’ moral position but rationalise status quo and maintain undisturbed consumption. Findings suggest the possibility that the discourses of prosocial behaviour incited under consuming conditions do not challenge but may even justify global inequality. This finding presents challenges facing charitable organisations balancing their work within wider commercial and cultural contexts. (shrink)

We investigate measure and category in the projective hierarchie in the presence of large cardinals. Assuming a measurable larger than $n$ Woodin cardinals we construct a model where every $\Delta ^1_{n+4}$ -set is measurable, but some $\Delta ^1_{n+4}$ -set does not have Baire property. Moreover, from the same assumption plus a precipitous ideal on $\omega _1$ we show how a model can be forced where every $\Sigma ^1_{n+4}-$ set is measurable and has Baire property.

Kim Sterelny's book The Pleistocene social contract provides an exceptionally well-informed and credible narrative explanation of the origins of inequality and hierarchy. In this essay review, we reflect on the role of rational choice theory in Sterelny's project, before turning to Sterelny's reasons for doubting the importance of cultural group selection. In the final section, we compare Sterelny's big picture with an alternative from David Wengrow and David Graeber.

A project conceiving of political assemblages as anything larger than just an object of intellectual history will have to face a question—what is the potential scope and entailments of the idea of political assemblages outside of the very specific late twentieth-century milieu that it was conceived in? And given the present moment, there is also is much more specific question that should well be taken up: what place any project organized as a political assemblage could have in an era of (...) global capitalist accelerated economic inequalities and anthropocentric warming? Drawing on debates in contemporary social and cultural anthropology about Dumont, hierarchy, actor-network theory, and ontology, this essay... (shrink)

We introduce the appropriate iterated version of the system of ordinal notations from [G1] whose order type is the familiar Howard ordinal. As in [G1], our ordinal notations are partly inspired by the ideas from [P] where certain crucial properties of the traditional Munich' ordinal notations are isolated and used in the cut-elimination proofs. As compared to the corresponding “impredicative” Munich' ordinal notations (see e.g. [B1, B2, J, Sch1, Sch2, BSch]), our ordinal notations arearbitrary terms in the appropriate simple term (...) algebra based on the notion of collapsing functions (which we would rather identify as projective functions). In Sect. 1 below we define the systems of ordinal notationsPRJ( ), for any primitive recursive limit wellordering . In Sect. 2 we prove the crucial well-foundness property by using the appropriate well-quasi-ordering property of the corresponding binary labeled trees [G3]. In Sect. 3 we interprete inPRJ( ) the familiar Veblen-Bachmann hierarchy of ordinal functions, and in Sect. 4 we show that the corresponding Buchholz's system of ordinal notationsOT( ) is a proper subsystem ofPRJ( ), although it has the same order type according to [G3] together with the interpretation from Sect. 2 in the terms of labeled trees. In Sect. 5 we use Friedman's approach in order to obtain an appropriate purely combinatorial statement which is not provable in the theory of iterated inductive definitions ID< λ, for arbitrarily large limit ordinalλ. Formal theories, axioms, etc. used below are familiar in the proof theory of subsystems of analysis (see [BFPS, T, BSch]). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Renaissance Project of Knowing:Lorenzo Valla and Salvatore Camporeale’s Contributions to the Querelle Between Rhetoric and PhilosophyMelissa Meriam BullardThe Journal of the History of Ideas has published two symposia devoted to examinations of Lorenzo Valla's place in Renaissance intellectual history, both of which sought to situate Valla in his appropriate contemporary context and to assess his contributions to developing tools of rhetorical analysis and textual criticism in the fifteenth (...) century. In the first JHI debate published in 1989, Salvatore Camporeale's foundational reexamination of Valla's views on language, rhetoric, and theology was frequently cited; and his assessment served as a fulcrum in the disparate interpretations offered by John Monfasani and by Richard Waswo and Sarah Gravelle.1 In the second forum published in 1996, Camporeale was invited to contribute an essay on Valla's famous critique of the false Donation of Constantine; therein the Roman humanist had appealed for Christian renewal inspired by an early Christianity, unburdened by medieval ontological discourse, and seeking to subvert the imperial (Constantinian) model of the church that had dominated since the fourth century.2More than half a century later in the early sixteenth century, reform-minded intellectuals such as Erasmus, More, Luther, and Melanchthon picked up Valla's pleas and used his insights and textual criticism to buttress their own calls for ecclesiastical reform, challenging the claims to authority of the [End Page 477] Roman church. But despite the popularity among the reformers of Valla's two most noted and provocative texts, his rhetorical and philological refutation of the Donation of Constantine and his annotations for a new translation of the New Testament from Greek, his legacy gradually faded from prominence after the sixteenth century. By then when the Protestants' split from Rome had become an accepted reality, and their battle to achieve a place in a divided Christian world won, the reformers' use of Valla's arguments no longer seemed so controversial. For its part, Catholic discourse in the Tridentine era had reverted to reassertions of papal hierarchy along the Constantinian model. Valla's other contributions to understanding rhetorical hermeneutics and philosophy gradually receded, especially from Anglophone intellectual consciousness and in some quarters even from the metanarratives of intellectual history.3 His legacy frequently goes unacknowledged in reconstructions of antecedents to modern intellectual history and philosophy despite the late twentieth century's lingering love affair with philosophies of language and the stress on contextualization pioneered by Heidegger and Wittgenstein, which share many of the same concerns Valla had plumbed for his day.4 The present group of essays attempts to address that lacuna in various ways, by revisiting Valla's contributions to the philosophy of language, by casting his story forward to understand the nature of his legacy beyond the Renaissance and Reformation, and by exploring why his and other Renaissance humanists' contributions to the project of human knowledge have been minimized or overlooked in more recent times. It is the contention of all the contributors that Valla, and to wit Camporeale's Valla, richly deserves our attention and that his overlooked legacy endures.Beginning in the 1970s Salvatore Camporeale, the leading modern Valla specialist, wrote and lectured widely to highlight the Roman humanist's place in the history of thought and to discuss him in an idiom reflective of modern sensitivities to issues of rhetoric, philosophy, language, and historical context.5 Camporeale's massive tome, Lorenzo Valla. Umanesimo e teologia (Florence, 1972) has only slowly made its fortune beyond Italy and Europe. The book, densely written and daunting for its close philological examination of variant texts and datings, has been more often consulted than read outside [End Page 478] the select circle of Valla devotees, this despite Eugenio Garin's clearly stated appreciation in his presentation of the volume. Garin lauded the depth and precision of Camporeale's scholarship and the lucidity with which he brought into focus the rich fabric of fifteenth-century theological disputes that engaged Valla and that invested his understanding of language and philology.6 Through careful and insightful analysis, Camporeale not only established Quintilian as the major inspiration behind Valla's rhetorical theory, but, logical step by logical step, he... (shrink)

Between the fourth and the recent fifth IPCC report, science as well as policy making have made great advances in dealing with uncertainties in global climate models. However, the uncertainties public decision making has to deal with go well beyond what is currently addressed by policy makers and climatologists alike. It is shown in this paper that within an anthropocentric framework, a whole hierarchy of models from various scientific disciplines is needed for political decisions as regards climate change. Via (...) what is sometimes referred to as ‘uncertainty cascade’ in the technical literature, the uncertainties of various models accumulate in the input to political decision making. This paper aims to chart the uncertainties in the multi-disciplinary enterprise of current climate modeling in broad strokes. It is shown that the uncertainty cascade makes it impossible to quantify uncertainties in the form of probability estimates. Moreover the paper highlights how global climate models fail to provide probability estimates. A better treatment of the uncertainties of climate predictions on the political level would require an overhaul of the current IPCC practice that separates the various scientific fields in various working groups. (shrink)

The dominant meta-theories in contemporary sociolinguistics include interactionism, social constructivism, poststructuralism and similarly relativist, anti-realist approaches (hereby grouped within the broader category of interpretivism). This paper argues that anti-scientific, anti-realist tendencies in contemporary sociolinguistics are ill-justified, confuse science with positivism, and weaken sociolinguists' necessary commitment to objectivity (hereby understood as commitment by scientists to explain the ontological order, or what exists regardless of whether it is known by people). The anti-realism in interpretivist sociolinguistics also considerably diminishes the ability of sociolinguists (...) to, for example, make ontological claims about language and its users, study phenomena including linguistic hierarchies and linguistic/social oppression as systems, and develop robust and effective strategies for critical engagement and social emancipation. By reaffirming sociolinguistics as part of the scientific project, and by reframing sociolinguistics within critical realism (CR), this paper offers conceptual alternatives to the dominant interpretivist tendencies in contemporary sociolinguistics. (shrink)

We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call 1/2-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the K-trivial sets. We characterize 1/2-bases as the sets computable from both halves of Chaitin’s Ω, and as the sets that obey the cost function c(x,s)=Ωs−Ωx−−−−−−−√. Generalizing these results yields a dense hierarchy (...) of subideals in the K-trivial degrees: For k<n, let Bk/n be the collection of sets that are below any k out of n columns of some random sequence. As before, this is an ideal generated by its c.e. elements and the random sequence in the definition can always be taken to be Ω. Furthermore, the corresponding cost function characterization reveals that Bk/n is independent of the particular representation of the rational k/n, and that Bp is properly contained in Bq for rational numbers p<q. These results are proved using a generalization of the Loomis–Whitney inequality, which bounds the measure of an open set in terms of the measures of its projections. The generality allows us to analyze arbitrary families of orthogonal projections. As it turns out, these do not give us new subideals of the K-trivial sets; we can calculate from the family which Bp it characterizes. We finish by studying the union of Bp for p<1; we prove that this ideal consists of the sets that are robustly computable from some random sequence. This class was previously studied by Hirschfeldt [D. R. Hirschfeldt, C. G. Jockusch, R. Kuyper and P. E. Schupp, Coarse reducibility and algorithmic randomness, J. Symbolic Logic81(3) (2016) 1028–1046], who showed that it is a proper subclass of the K-trivial sets. We prove that all such sets are robustly computable from Ω, and that they form a proper subideal of the sets computable from every (weakly) LR-hard random sequence. We also show that the ideal cannot be characterized by a cost function, giving the first such example of a Σ03 subideal of the K-trivial sets. (shrink)

Our scientific concepts generally are in the melting-pot. They are all infected by relativity. This is as true in psychology and philosophy as in the physical sciences. In each case we must be willing to reconstruct our concepts on the basis of new evidence. Psychology has too long been hampered by a false tradition, and incidentally it has dragged philosophy with it into the slough of subjectivism. Brilliant discoveries in the realms of physiology and pathology throw new light on many (...) of the fundamental concepts of psychology, spite of the fact that the investigators themselves have sometimes been misled by the old tradition. We are here concerned with their data, not with their theories. The evidence, as I interpret it, gives the death-blow to the old subjectivistic psychology. As regards sensations, the evidence shows, on the one hand, that their character is independent of consciousness; but, on the other hand, it equally disproves the assumption that the sense-qualities exist in the physical world just as we know them and independently of the organism. The evidence further shows that the centers of the central nervous system constitute a hierarchy of energy patterns, not storehouses or factories of content, sensational or imaginal. The content is due to lines of motion, connecting those energy patterns with the sense-organs. The processes of selection. (shrink)

This article shows that William E. Connolly’s work holds resources for projects of racial justice but must be revised to fully meet the challenge of racial inequality. There are two interrelated problems in Connolly’s theory: first, the drive to destabilize identity, for which he argues, rejects the need for collective identity, which is necessary in democratic politics. Furthermore, because domination renders identity unstable, the call to destabilize identity places too great a burden on already marginalized groups. The problem of destabilizing (...) identity is underwritten by a second problem: the white working class and its grievances occupy too important a position in Connolly’s analysis. This article uses insights provided by James Baldwin to amend Connolly’s contributions. The article argues that there is a need to destabilize the ‘we’ of American politics that allows white, male identity to occupy the ‘heart’ of liberal democracy. Baldwin’s insights help solve the problem of the ‘black hole’ at the center of liberal democracy which, Connolly argues, sustains fundamentalism and racial injustice. This article’s contribution is to amend Connolly’s work to meet the challenge of racial injustice, offer a novel reading of the place of political imagination in Baldwin’s work, and show how political imagination adds depth to conversations about democracy, racial justice, and pluralism. (shrink)

Religious leaders are being viewed as agents with influence over environmental opinion and attitude building. In public environmental project impact debate the Christian religious leaders may play an increasingly complex role due to their anthropocentric position. Roşia Montană Gold Corporation is such a project where The Romanian Orthodox Church has taken a position right from the beginning. Our study explores the local impact area religious leaders' attitudes as to the mining project in particular and the overall view of environmental concerns (...) in religious sermon in general. Orthodox, Catholic, Reformed and Baptist representatives have been interviewed. The main conclusion we drew is that environmental concerns can create leadership style dissonances between different hierarchical levels of the same religious hierarchies, but with benefits at the communitarian-religious levels. The practical implications that arise from this and the possible directions for future research are outlined in the final chapter of our study. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:What Happened to Civility: The Promise and Failure of Montaigne's Modern Project by Ann HartleVicente Raga RosalenyHARTLE, Ann. What Happened to Civility: The Promise and Failure of Montaigne's Modern Project. Notre Dame, Ind.: Notre Dame University Press, 2022. ix + 178 pp. Cloth, $100.00; paper, $30.00Why are we witnessing increasing social polarization in Western societies? What has happened to make our liberal democracies so ideologically charged? Professor Ann (...) Hartle's book tries to answer these and other questions in line with the concept of civility that, according to her thesis, Michel de Montaigne created in early modernity and that is about to disappear in our day. Not in vain is Montaigne the protagonist of this book, given that Professor Hartle is a world-renowned specialist on the author of the Essays, although in this case she is interested in the transformations that gave rise to modernity in order to understand our present day. She reads Montaigne for a better interpretation of some central problems of our time, such as the difficulty to speak freely that is experienced on university campuses and, in general, the increasing politicization of our civil societies.Thus, in the first place, Professor Hartle's work interrogates the origins of civility, the social bond created in modernity. To this end, she exposes what happened in the time of Montaigne, when societies, based on the classical and Christian tradition, were plunged into a general crisis. This is what the French essayist detected, and it led him to propose a new type of bond. For this, it is necessary to free oneself from tradition, which had legitimized the division between masters and slaves, the source of all conflicts.Montaigne's movement is philosophical in character: It consists of a split carried out in his Essays between the natural human being and the philosophical observer, which leads to a break with traditional moral standards, identified with Nature. The new human being, thus unfolded, can choose his own hierarchy of values and address the good he chooses with his own will (although this will be a will purified of particularisms, without excessive self-esteem). Such self-awareness, achieved by Montaigne as an accidental philosopher, is concretized in the predominance of the concept of judgment, in the ability to freely choose our possibilities (and not ends dictated by Nature).The new world thus created, Hartle explains, gave rise to the liberal order. It is true that Montaigne was not a theorist, but in his work it is possible to find the rupture of the traditional hierarchy between masters [End Page 351] and slaves, now considered as equals before the law, which is above all, and which is the fruit of reason. In this civil society, human beings no longer dominate each other, and each peacefully pursues his purposes. It is the state, as the embodiment of the law, that regulates everything, except the space of freedom gained with the emergence of the modern public sphere.In this context, the concept of authenticity makes sense, which, according to Professor Hartle, is the best reflection of the breakdown of the traditional order and the disappearance of its moral community. Now each individual pursues his purposes and is no longer to fulfill the ends of a universal human nature. That is why the bond of civility, in which the absolute autonomy of the subject is recognized, as well as his equality before the law, replaces the moral ties of the traditional community and its hierarchies. It is the French thinker who best exemplifies this transit, by showing himself openly in his Essays as a common subject who pursues his purposes and who relates to others as equals, no longer as someone superior, capable of disputing merit, and dominating others.However, this new society and its civil bonds are in crisis; civility fades, or that is Professor Hartle's pessimistic conclusion. Today we are witnessing an ideologization of previously depoliticized areas, such as the university, with the demand for the use of politically correct language and the fear of expressing oneself freely, especially when one's own opinions do not align with the current political trends. The failure... (shrink)

At the beginning of Book I of the Nicomachean Ethics, Aristotle says that “the good is the same for an individual as for a city”. The good in question is εὐδαιμονία – the highest good achievable for human beings. In Book X, we learn that contemplative activity meets best the requirements set for eudaimonia. Even if we agree that contemplative activity is the good for an individual, how should we understand the claim that contemplation is also the good for a (...) city? I start by reminding readers that for Aristotle the Nicomachean Ethics is essentially a political enquiry and should be read together with his Politics. I focus on the teleological character of his political philosophy and the interlinking of the concepts of the good, nature, form, end and function. Then, I look at Aristotle’s two closely-connected statements that polis exists by nature and that men are political animals. Having taken into account Aristotle’s opinion regarding the imperfection of this world, which is exemplified by the vulnerability of human lives to fortune, luck and accidents, I conclude that Alasdair MacIntyre’s concept of the political community as a common project explains well how contemplation could be the end of polis. Only very few individuals can achieve the highest good and they can do it only if they have the support of the political community. But all the inhabitants of a polis structured towards achieving the highest good benefit from living in a well-ordered community whose constitution reflects the objective hierarchy of goods. (shrink)

Smart grids are rolling out internationally, with the United States nearing completion of a significant USD4-plus-billion federal program funded under the American Recovery and Reinvestment Act. The emergence of smart grids is widespread across developed countries. Multiple approaches to analyzing the benefits of smart grids have emerged. The goals of this white paper are to review these approaches and analyze examples of each to highlight their differences, advantages, and disadvantages. This work was conducted under the auspices of a joint U.S.-China (...) research effort, the Climate Change Working Group Implementation Plan, Smart Grid. We present comparative benefits assessments of smart grid demonstrations in the U.S. and China along with a BA of a pilot project in Europe. In the U.S., we assess projects at two sites: the University of California, Irvine campus, which consists of two distinct demonstrations: Southern California Edison’s Irvine Smart Grid Demonstration Project and the UCI campus itself; and the Navy Yard area in Philadelphia, which has been repurposed as a mixed commercial-industrial, and possibly residential, development. In China, we cover several smart-grid aspects of the Sino-Singapore Tianjin Eco-city and the Shenzhen Bay Technology and Ecology City. In Europe, we look at a BA of a pilot smart grid project in the Malagrotta area west of Rome, Italy, contributed by the Joint Research Centre of the European Commission. The Irvine sub-project BAs use the U.S. Department of Energy Smart Grid Computational Tool, which is built on methods developed by the Electric Power Research Institute. The TEC sub-project BAs apply Smart Grid Multi-Criteria Analysis developed by the State Grid Corporation of China based on the analytic hierarchy process with fuzzy logic. The B-TEC and TNY sub-project BAs are evaluated using new approaches developed by those project teams. JRC has adopted an approach similar to EPRI’s but tailored to the Malagrotta distribution grid. (shrink)

Work on the conceptual amelioration of race concepts is usually negative or critical: it uncovers social features that contribute to racial hierarchies. Much less focus has been placed on how ameliorative accounts contribute to positive change. Using an account of race developed by Steve Biko during South African apartheid, I will argue that we can extract a novel account of positive amelioration in which racial categories can have normative or aspirational force, contributing to positive change.

Drawing from a Sellarsian realist-naturalist epistemology, we trace different levels of cognitive hierarchy procedures through which a representational system learns to update its own states and improve its ‘map-making’ capabilities from pre-conscious operations which modulate base-localization functions, to patterns of epistemic revision and integration at the conceptual and theoretical levels, producing a nomological double of its world. We show how ontological theorization becomes diachronically coordinated with and constrained by empirical science, and how the formal-quantitative kernel of scientific theories corresponds (...) to qualitative-conceptual determinations at the structural level. Following Johanna Seibt’s characterization of ontology as a theory of categorial inference, we trace the preservation of inferential semantic structure across ontological theories in relation to model languages and provide provisional indications to coordinate Seibt’s account with a convergent realist assessment of systematic modeling, defining the epistemological conditions for articulating the preservation of formal structure in theories toward a limit-point of enquiry. (shrink)

Praise for Volume 1: "... a first-rate edition, which supersedes all other portable Peirces.... all the Peirce most people will ever need." —Louis Menand, The New York Review of Books Volume 2 of this convenient two-volume chronological reader’s edition provides the first comprehensive anthology of the brilliant American thinker Charles Sanders Peirce’s mature philosophy. A central focus of Volume 2 is Peirce’s evolving theory of signs and its appplication to his pragmatism.

The Bentham Project is delighted to announce a call for papers for “Bentham and Australia: Convicts, Utility, and Empire”, a conference to be held at University College London on 11-12 April 2019 to mark the forthcoming publication of Writings on Australia, a volume of The Collected Works of Jeremy Bentham. The conference will explore themes such as the influence and impact of Bentham’s ideas on the theory and practice of punishment in convict Australia, on advocates and opponents of co...

Volume 8 of this landmark edition follows Peirce from May 1890 through July 1892—a period of turmoil as his career unraveled at the U.S. Coast and Geodetic Survey. The loss of his principal source of income meant the beginning of permanent penury and a lifelong struggle to find gainful employment. His key achievement during these years is his celebrated Monist metaphysical project, which consists of five classic articles on evolutionary cosmology. Also included are reviews and essays from The Nation in (...) which Peirce critiques Paul Carus, William James, Auguste Comte, Cesare Lombroso, and Karl Pearson, and takes part in a famous dispute between Francis E. Abbot and Josiah Royce. Peirce's short philosophical essays, studies in non-Euclidean geometry and number theory, and his only known experiment in prose fiction complete his production during these years. Peirce's 1883-1909 contributions to the Century Dictionary form the content of volume 7 which is forthcoming. (shrink)

Praise for Volume 1: "... a first-rate edition, which supersedes all other portable Peirces.... all the Peirce most people will ever need." —Louis Menand, The New York Review of Books Volume 2 of this convenient two-volume chronological reader’s edition provides the first comprehensive anthology of the brilliant American thinker Charles Sanders Peirce’s mature philosophy. A central focus of Volume 2 is Peirce’s evolving theory of signs and its appplication to his pragmatism.

An open U ⊆ ℝ is produced such that (ℝ, +, ·, U) defines a Borel isomorph of (ℝ, +, ·, ℕ) but does not define ℕ. It follows that (ℝ, +, ·, U) defines sets in every level of the projective hierarchy but does not define all projective sets. This result is elaborated in various ways that involve geometric measure theory and working over o-minimal expansions of (ℝ, +, ·). In particular, there is a Cantor set (...) E ⊆ ℝ such that (ℝ, +, ·, E) defines a Borel isomorph of (ℝ, +, ·, ℕ) and, for every exponentially bounded o-minimal expansion $\germ{R}$ of (ℝ, +, ·), every subset of ℝ definable in ( $\germ{R}$ , E) either has interior or is Hausdorff null. (shrink)

In this paper I shall present a method for proving determinacy from large cardinals which, in many cases, seems to yield optimal results. One of the main applications extends theorems of Martin, Steel and Woodin about determinacy within the projective hierarchy. The method can also be used to give a new proof of Woodin's theorem about determinacy in L.The reason we look for optimal determinacy proofs is not only vanity. Such proofs serve to tighten the connection between large (...) cardinals and descriptive set theory, letting us bring our knowledge of one subject to bear on the other, and thus increasing our understanding of both. A classic example of this is the Harrington-Martin proof that -determinacy implies -determinacy. This is an example of a transfer theorem, which assumes a certain determinacy hypothesis and proves a stronger one. While the statement of the theorem makes no mention of large cardinals, its proof goes through 0#, first proving that-determinacy ⇒ 0# exists,and then that0# exists ⇒ -determinacyMore recent examples of the connection between large cardinals and descriptive set theory include Steel's proof thatADL ⇒ HODL ⊨ GCH,see [9], and several results of Woodin about models of AD+, a strengthening of the axiom of determinacy AD which Woodin has introduced. These proofs not only use large cardinals, but also reveal a deep, structural connection between descriptive set theoretic notions and notions related to large cardinals. (shrink)

§1. I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually called Polish spaces. Typical examples are ℝn, ℂn, Hilbert space and more generally all separable Banach spaces, the Cantor space 2ℕ, the Baire space ℕℕ, the infinite symmetric group S∞, the unitary group, the group of measure preserving transformations of the unit interval, etc.In this theory sets are (...) classified in hierarchies according to the complexity of their definitions and the structure of sets in each level of these hierarchies is systematically analyzed. In the beginning we have the Borel sets in Polish spaces, obtained by starting with the open sets and closing under the operations of complementation and countable unions, and the corresponding Borel hierarchy. After this come the projective sets, obtained by starting with the Borel sets and closing under the operations of complementation and projection, and the corresponding projective hierarchy.There are also transfinite extensions of the projective hierarchy and even much more complex definable sets studied in descriptive set theory, but I will restrict myself here to Borel and projective sets, in fact just those at the first level of the projective hierarchy, i.e., the Borel (), analytic () and coanalytic () sets. (shrink)

The separation, uniformization, and other properties of the Borel and projective hierarchies over hyperfinite sets are investigated and compared to the corresponding properties in classical descriptive set theory. The techniques used in this investigation also provide some results about countably determined sets and functions, as well as an improvement of an earlier theorem of Kunen and Miller.

We extend work of H. Friedman, L. Harrington and P. Welch to the third level of the projective hierarchy. Our main theorems say that (under appropriate background assumptions) the possibility to select definable elements of non-empty sets of reals at the third level of the projective hierarchy is equivalent to the disjunction of determinacy of games at the second level of the projective hierarchy and the existence of a core model (corresponding to this fragment (...) of determinacy) which must then contain all real numbers. The proofs use Sacks forcing with perfect trees and core model techniques. (shrink)

A materialist construction of semiosis requires system embodiment at particular locales, in order to function as systems of interpretance. I propose that we can use a systemic model of scientific measurement to construct a systems view of semiosis. I further suggest that the categories required to understand that process can be used as templates when generalizing to biosemiosis and beyond. The viewpoint I advance here is that of natural philosophy—which, once granted, incurs no principled block to further generalization all the (...) way to pansemiotics—nearer to Peirce’s own very general perspective. This project requires a hylozooic framework, which I present in the form of a specification hierarchy, whereby physical dynamics subsume all other transactions at more highly developed integrative levels. The upshot of the paper is a proposal that meanings can be assimilated most generally to final causes. (shrink)

A basis for a set C of functions on natural numbers is a set F of functions such that C is the closure with respect to substitution of the projection functions and the functions in F. This paper introduces three new bases, comprehending only common functions, for the Grzegorczyk classes ℰ_n with n ≥ 3. Such results are then applied in order to show that ℰ_{n+1} = K_n for n ≥ 2, where {K_n}n∈ℕ is the Axt hierarchy.