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 $\alpha$.

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)

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...

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.

In this paper, we explore the links between emotions and creativity. Building on what we perceive as key examples, we distinguish instrumental and constitutive senses in which emotions can be creative. Emotions are instrumentally creative when they sustain novel and valuable thought processes aiming at maintaining or modifying a given emotional situation. They are constitutively creative when they function as essential parts of value understanding and when they come to carve and sometimes change the evaluative landscape. Despite their alleged passivity (...) and rigidity, we claim, emotions sometimes manifest the kind of skillfulness that creativity presupposes. (shrink)

In this essay, I will examine Henri Maldiney’s phenomenological aesthetics, focusing on his claim that “art is the truth of the sensible.” This claim is presented by Maldiney in the context of a two-fold critique of Husserl’s and Heidegger’s respective attempts to phenomenologically elucidate the experience of artworks. According to Maldiney, both Husserl and Heidegger fail to recognize what he, following Erwin Straus, terms the “pathic” moment of sense experience, which is also the key moment of the aesthetic reception of (...) art. Drawing on this concept of the pathic and its way of engaging what Maldiney calls the “transpassibility” of receptivity, I argue that his phenomenology of art can be viewed as an attempt to bring together the two senses of the aesthetic in the Kantian sense, namely as an aesthetics of sense experience and as an aesthetics of art, from within the domain of sensibility itself. I develop this idea by turning to Maldiney’s notion of rhythm and examining how he thinks that it can be applied to the visual arts. Ultimately, I suggest that Maldiney’s aesthetics imbues art with ontological significance, since he takes the rhythmic presence of artworks to be a sensuous manifestation of the rhythmic ground of the world’s constitution. The truth of art, in this sense, is a revelation of the ontological functioning of rhythm. (shrink)

The article discusses the determinants of fiscal policy in the times of COVID-19. Most economists share the opinion that fiscal packages are necessary to mitigate the health and economic costs of a pandemic. However, the scale of fiscal intervention and the types of fiscal policy instruments that should be used raise doubts. The aim of the article is to explore the factors determining the size and structure of fiscal packages which have been implemented globally in response to the crisis caused (...) by the COVID-19 pandemic. In addition, attention is drawn to the potential impact of fiscal intervention on public finance sustainability, bearing in mind that most governments have chosen to use fiscal support instruments to enhance consumption and investment following the COVID-19 hit, although the cross-country differences are evident both in the magnitude and composition of fiscal stimulus packages. A descriptive analysis was conducted along with a panel data analysis to examine the determinants of government fiscal support in response to the COVID-19 crisis. The empirical analysis is based on cross-sectional data from the International Monetary Fund, OECD and Eurostat. The sample consists of 40 countries representing advanced and emerging economies. Based on the panel analysis, it was found that the total fiscal stimulus packages depended mainly on the fiscal space. Fiscal intervention in countries with greater tax-collection capacity (such as Germany, United States, United Kingdom and Japan) was greater compared to others. A positive and statistically significant relationship between the average income level and the size of fiscal stimulus was also confirmed. Moreover, it turned out that countries with larger populations and higher fatality rates provided greater fiscal support for the COVID-19 pandemic.The empirical analysis expands the existing knowledge on the determinants of the fiscal policy implemented in response to the COVID-19 crisis under the conditions of low interest rates, when macroeconomic stabilization can only be ensured through fiscal stimulus programs. (shrink)

All the typical global quantum mechanical observables are complex relative phases obtained by interference phenomena. They are described by means of some global geometric phase factor, which is thought of as the “memory” of a quantum system undergoing a “cyclic evolution” after coming back to its original physical state. The origin of a geometric phase factor can be traced to the local phase invariance of the transition probability assignment in quantum mechanics. Beyond this invariance, transition probabilities also remain invariant under (...) the operation of complex conjugation. Most important, geometric phase factors distinguish between unitary and antiunitary transformations in terms of complex conjugation. These two types of invariance functions as an anchor point to investigate the role of loops and based loops in the state space of a quantum system as well as their links and interrelations. We show that arbitrary transition probabilities can be calculated using projective invariants of loops in the space of rays. The case of the double slit experiment serves as a model for this purpose. We also represent the action of one-parameter unitary groups in terms of oppositely oriented-based loops at a fixed ray. In this context, we explain the relation among observables, local Boolean frames of projectors, and one-parameter unitary groups. Next, we exploit the non-commutative group structure of oriented-based loops in 3-d space and demonstrate that it carries the topological semantics of a Borromean link. Finally, we prove that there exists a representation of this group structure in terms of one-parameter unitary groups that realizes the topological linking properties of the Borromean link. (shrink)

I argue that our experience of expressive properties (such as the joyfulness or sadness of a piece of music) essentially involves the sensuous imagination (through simulation) of an emotion-guided process which would result in the production of the properties which constitute the realisation of the expressive properties experienced. I compare this proposal with arousal theories, Wollheim’s Freudian account, and other more closely related theories appealing to imagination such as Kendall Walton’s. I explain why the proposal is most naturally developed in (...) terms of simulation and briefly comment upon the impact of work on cross-cultural perception of facial expression, modularity and autism for the proposal. (shrink)

Using countable support iterations of S-proper posets, we show that the existence of a definable wellorder of the reals is consistent with each of the following: , and.

This paper is a discussion of Michael Thau's interesting critique in Chapter 2 of Consciousness and Cognition, Oxford: Oxford University Press, 2002, of the common view that beliefs are internal states.

This paper addresses an article by Felix Klein of 1886, in which he generalized his theory of polynomial equations of degree 5—comprehensively discussed in his Lectures on the Icosahedron two years earlier—to equations of degree 6 and 7. To do so, Klein used results previously established in line geometry. I review Klein’s 1886 article, its diverse mathematical background, and its place within the broader history of mathematics. I argue that the program advanced by this article, although historically overlooked due to (...) its eventual failure, offers a valuable insight into a time of crucial evolution of the subject. (shrink)

Ameliorative projects design and propagate new linguistic content for some expressions we use for political or social justice purposes. These projects are often driven by an anti-essentialist agenda: they aim to debunk the idea that social categories such as “woman,” “man,” or “race” are constituted by natural essences. But critics argue that nouns tend to trigger essentialist thinking. And because ameliorative projects typically retain nouns, it is argued that these projects cannot achieve their anti-essentialist goals. In response, I argue that (...) the psychological effects of noun use tend to support, rather than hinder, the anti-essentialist goals of ameliorators. (shrink)

The empirical phenomenon at the center of this paper is projection, which we define (uncontroversially) as follows: (1) Definition of projection An implication projects if and only if it survives as an utterance implication when the expression that triggers the implication occurs under the syntactic scope of an entailment-cancelling operator. Projection is observed, for example, with utterances containing aspectual verbs like stop, as shown in (2) and (3) with examples from English and Paraguayan Guaraní (Paraguay, Tupí-Guaraní).1 The Guaraní example in (...) (2) and its English translation have at least the following implications: (i) Carla has previously smoked, and (ii) Carla stopped smoking. The first but not the second of these implications is also conveyed by the question version of sentence (2), as in (3a), or when (2) is embedded under entailment-cancelling sentential operators, such as negation, as in (3b), the antecedent of a conditional, as in (3c), or an epistemic modal, as in (3d). Hence, by the definition in (14), the first but not the second implication of (2) projects. (shrink)

The institution of the family and its importance have recently received considerable attention from political theorists. Leading views maintain that the institution’s justification is grounded, at least in part, in the non-instrumental value of the parent-child relationship itself. Such views face the challenge of identifying a specific good in the parent-child relationship that can account for how adults acquire parental rights over a particular child—as opposed to general parental rights, which need not warrant a claim to parent one’s biological progeny. (...) I develop a view that meets this challenge. This Project View identifies the pursuit of a parental project as a distinctive non-instrumentally valuable good that provides a justification for the family and whose pursuit is necessary and sufficient for the acquisition of parental rights. This view grounds moral parenthood in a normative relation as opposed to a biological one, supports polyadic forms of parenting, and provides plausible guidance in cases of assisted reproduction. (shrink)

Let D be a strongly minimal set in the language L, and $D' \supset D$ an elementary extension with infinite dimension over D. Add to L a unary predicate symbol D and let T' be the theory of the structure (D', D), where D interprets the predicate D. It is known that T' is ω-stable. We prove Theorem A. If D is not locally modular, then T' has Morley rank ω. We say that a strongly minimal set D is pseudoprojective (...) if it is nontrivial and there is a $k < \omega$ such that, for all a, b ∈ D and closed $X \subset D, a \in \mathrm{cl}(Xb) \Rightarrow$ there is a $Y \subset X$ with a ∈ cl(Yb) and |Y| ≤ k. Using Theorem A, we prove Theorem B. If a strongly minimal set D is pseudoprojective, then D is locally projective. The following result of Hrushovski's (proved in $\S4$ ) plays a part in the proof of Theorem B. Theorem C. Suppose that D is strongly minimal, and there is some proper elementary extension D1 of D such that the theory of the pair (D1, D) is ω1-categorical. Then D is locally modular. (shrink)

If the bounded proper forcing axiom BPFA holds and ω 1 = ${\mathrm{\omega }}_{1}^{\mathrm{L}}$ , then there is a lightface ${\mathrm{\Sigma }}_{3}^{1}$ well-ordering of the reals. The argument combines a well-ordering due to Caicedo-Veličković with an absoluteness result for models of MA in the spirit of "David's trick." We also present a general coding scheme that allows us to show that BPFA is equiconsistent with R being lightface ${\mathrm{\Sigma }}_{4}^{1}$ , for many "consistently locally certified" relations R on $\mathrm{\mathbb{R}}$ . (...) This is accomplished through a use of David's trick and a coding through the ∑ 2 stable ordinals of L. (shrink)

In recent years, several scholars have been investigating Frege’s mathematical background, especially in geometry, in order to put his general views on mathematics and logic into proper perspective. In this article I want to continue this line of research and study Frege’s views on geometry in their own right by focussing on his views on a field which occupied center stage in nineteenth century geometry, namely, projective geometry.

We show that Σ1 4-Amoeba-absoluteness implies that $\forall a \in \mathbb{R}(\omega^{L\lbrack a \rbrack}_1 < \omega^V_1)$ and, hence, Σ1 3-measurability. This answers a question of Haim Judah (private communication).

This report recounts three developments during the last two years of the SIEPM Project to revise and complete the repertory of commentaries on Peter Lombard’s Sentences published by Friedrich Stegmüller in 1947. The chronological sections of the project have been established, and scholars have been assigned to lead them. A centralized administration for the Project is now located in Freiburg im Breisgau, which will co-ordinate the various sections and preserve their findings, as well as facilitate and oversee the various editorial (...) projects on commentaries on the Sentences currently underway. (shrink)

The axioms of projective and affine plane geometry are turned into rules of proof by which formal derivations are constructed. The rules act only on atomic formulas. It is shown that proof search for the derivability of atomic cases from atomic assumptions by these rules terminates . This decision method is based on the central result of the combinatorial analysis of derivations by the geometric rules: The geometric objects that occur in derivations by the rules can be restricted to (...) those known from the assumptions and cases. This “subterm property” is proved by permuting suitably the order of application of the geometric rules. As an example of the decision method, it is shown that there cannot exist a derivation of Euclid’s fifth postulate if the rule that corresponds to the uniqueness of the parallel line construction is taken away from the system of plane affine geometry. (shrink)

We determine the consistency strength of determinacy for projective games of length ω^2. Our main theorem is that $\Pi _{n + 1}^1$-determinacy for games of length ω^2 implies the existence of a model of set theory with ω + n Woodin cardinals. In a first step, we show that this hypothesis implies that there is a countable set of reals A such that M_n(A), the canonical inner model for n Woodin cardinals constructed over A, satisfies $A = R$ and (...) the Axiom of Determinacy. Then we argue how to obtain a model with ω + n Woodin cardinal from this. We also show how the proof can be adapted to investigate the consistency strength of determinacy for games of length ω^2 with payoff in $R^R\Pi _1^1$ or with σ-projective payoff. (shrink)

In the middle part of his Brouillon Project on conics, Girard Desargues develops the theory of the traversale, a notion that generalizes the Apollonian diameter and allows to give a unified treatment of the three kinds of conics. We showed elsewhere that it leads Desargues to a complete theory of projective polarity for conics. The present article, which shall close our study of the Brouillon Project, is devoted to the last part of the text, in which Desargues puts his (...) theory of the traversal into practice by giving a very elegant tratment of the classical theory of parameters and foci. This will lead us to show that Desargues’ proofs can only be understood if one accepts that he reasons in a resolutely projective framework, completely assimilating elements at infinity to those at finite distance in his proofs. (shrink)

Using interviews and group discussions, researchers and students from the Free University of Berlin and psychological practitioners work together in a project called 'The Analysis of Psychological Practice', theoretically based on 'Critical Psychology'. The aim is to find out whether and how practitioners deal with the contradictions between experimental-statistical orientation of traditional academic psychology and the single-case-orientation of psychological practice. Can practitioners relate to 'scientific' psychology at all? How do they deal with the contradiction that psychological practitioners are expected to (...) cure psychological problems without having the possibility to change objective conditions with reference to which alone psychological problems are understandable? How are 'official' academic or clinical theories and individual or team-related experiences combined? What can we learn from the explication and development of a 'social-subjective knowledge of the context and contradictions' of professional practitioners of psychology? We discuss theoretical foundations and problems in the empirical development of the project, and resent - from our workshop - three examples or dimensions of our work: life problems, problems of and alternatives to traditional diagnostics, and common sense normative ideas in the guise of psychological theories. (shrink)

The Desarguesian nature of angular-momentum theory is illustrated by drawing correspondences between relations satisfied by then-j symbols and various collinearity properties of the appropriate diagrams. No examples of Pappus' theorem have been found. A relation is suggested between the operations of angular-momentum theory and Hilbert's constructions for the addition and multiplication of points on a line.

The Projectability Challenge states that a metaethical view must explain how ordinary agents can, on the basis of moral experience and reflection, accurately and justifiably apply moral concepts to novel situations. In this paper, we argue for two primary claims. First, paradigm nonnaturalism can satisfactorily answer the projectability challenge. Second, it is unclear whether there is a version of moral naturalism that can satisfactorily answer the challenge. The conclusion we draw is that there is an important respect in which nonnaturalism (...) holds an advantage over its most prominent naturalist rivals. The conclusion is interesting if only because it is widely assumed that naturalism has an easier time handling thorny problems in moral epistemology. We argue that there is at least one such problem of which this assumption is not true. (shrink)

This article provides a semantic analysis of Protagonist Projection, the phenomenon by which things are described from a point of view different from that of the speaker. Against what has been argued by some, the account vindicates the intuitive idea that Protagonist Projection does not give rise to counterexamples to factivity, and similar plausible principles. A pragmatics is sketched that explains the attitude attributions generated by Protagonist Projection. Further, the phenomenon is compared to Free Indirect Discourse, and the proposed account (...) is seen to preserve the relation between them. (shrink)

Two sets are said to be almost disjoint if their intersection is finite. Almost disjoint subsets of [ω]ω and ωω have been studied for quite some time. In particular, the cardinal invariants \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{a}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{a}_e}$$\end{document}, defined to be the minimum cardinality of a maximal infinite almost disjoint family of [ω]ω and ωω respectively, are known to be consistently less than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{c}}$$\end{document}. Here we examine analogs for functions in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^\omega}$$\end{document} and projections on l2, showing that they too can be consistently less than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{c}}$$\end{document}. (shrink)

: This commentary focuses on the scientific status of perceptual projection-a central feature of Pereira’s projective theory of consciousness. In his target article, he draws on my own earlier work to develop an explanatory framework for integrating first-person viewable conscious experience with the third-person viewable neural correlates and antecedent causes that form conscious experience into a bipolar structure that contains both a sense of self and a sense of the world. I stress that perceptual projection is a psychological effect (...) and list many of the ways it has been studied within experimental psychology, for example in studies of depth perception in vision and audition and experiences of depth arising from cues arranged on two-dimensional surfaces in stereoscopic pictures, 3D cinemas, holograms, and virtual realities. I then juxtapose Pereira’s explanatory model with two other models that have similar aims and background assumptions but different orientations, Trehub’s Retinoid model, which focuses largely on the neural functioning of the visual system, and Rudrauf et al’s Projective Consciousness Model, which draws largely on projective geometries to specify the requirements of organisms that need to navigate a three-dimensional world, and how these might be implemented in human information processing. Together, these models illustrate both converging and diverging approaches to understanding the role of projective processes in human consciousness. Resumo: Este comentário enfoca o status científico da projeção perceptiva - uma característica central da teoria da consciência de Pereira. Em seu artigo alvo, ele recorre ao meu trabalho anterior para desenvolver uma estrutura explicativa para integrar a experiência consciente visível em primeira pessoa com os correlatos neurais visíveis de terceira pessoa e as causas antecedentes que formam a experiência consciente em uma estrutura bipolar que contém tanto um sentido de eu e um sentido do mundo. Enfatizo que a projeção perceptiva é um efeito psicológico e relaciono modalidades de seu estudo na psicologia experimental, por exemplo em estudos de percepção de profundidade em visão e audição, experiências de profundidade em superfícies bidimensionais em imagens estereoscópicas, cinemas 3D, hologramas e realidades virtuais. Eu então justaponho o modelo explicativo de Pereira com dois outros modelos que têm objetivos e suposições similares, mas orientações diferentes, o modelo do sistema retinóide de Trehub, que se concentra principalmente no funcionamento neural do sistema visual, e o modelo de consciência projetiva de Rudrauf et al., que estabelece raciocínios geométricos para especificar os requisitos de organismos que precisam navegar em um mundo tridimensional, e como eles podem ser implementados no processamento de informação no contexto humano. Juntos, esses modelos ilustram abordagens convergentes e divergentes para compreender o papel dos processos projetivos na consciência humana. (shrink)

A brochure stating the objectives of a project initiated by the author in 1973.