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...

In this paper we examine the contributions of the Italian geometrical school to the Foundations of Projective Geometry. Starting from De Paolis' work we discuss some papers by Segre, Peano, Veronese, Fano and Pieri. In particular we try to show how a totally abstract and general point of view was clearly adopted by the Italian scholars many years before the publication of Hilbert's Grundlagen.We are particularly interested in the interrelations between the Italian and the German schools (mainly the influence (...) of Staudt's and Klein's works). We try also to understand the reason of the steady decline of the Italian school during the twentieth century. (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.

We show that every dominating analytic set in the Baire space has a dominating closed subset. This improves a theorem of Spinas [15] saying that every dominating analytic set contains the branches of a uniform tree, i.e. a superperfect tree with the property that for every splitnode all the successor splitnodes have the same length. In [15], a subset of the Baire space is called u-regular if either it is not dominating or it contains the branches of a uniform tree, (...) and it was proved that Σ21-Kσ-regularity implies Σ21-u-regularity. Here we show that these properties are in fact equivalent. Since the proof of analytic u-regularity uses a game argument it was clear that determinacy implies u-regularity of all sets. Here we show that an inaccessible cardinal is enough to construct a model for projective u-regularity, namely it holds in Solovay's model. Finally we show that forcing with uniform trees is equivalent to Laver forcing. (shrink)

We extend the work of Fischer et al. [6] by presenting a method for controlling cardinal characteristics in the presence of a projective wellorder and 2ℵ0>ℵ2. This also answers a question of Harrington [9] by showing that the existence of a Δ31 wellorder of the reals is consistent with Martinʼs axiom and 2ℵ0=ℵ3.

Explications of the reconstruction of Leibniz’s metaphysics that Deleuze undertakes in 'The Fold: Leibniz and the Baroque' focus predominantly on the role of the infinitesimal calculus developed by Leibniz.1 While not underestimat- ing the importance of the infinitesimal calculus and the law of continuity as reflected in the calculus of infinite series to any understanding of Leibniz’s metaphysics and to Deleuze’s reconstruction of it in The Fold, what I propose to examine in this paper is the role played by other (...) developments in mathematics that Deleuze draws upon, including those made by a number of Leibniz’s near contemporaries – the projective geometry that has its roots in the work of Desargues (1591–1661) and the ‘proto-topology’ that appears in the work of Du ̈rer (1471–1528) – and a number of the subsequent developments in these fields of mathematics. Deleuze brings this elaborate conjunction of material together in order to set up a mathematical idealization of the system that he considers to be implicit in Leibniz’s work. The result is a thoroughly mathematical explication of the structure of Leibniz’s metaphysics. What is provided in this paper is an exposition of the very mathematical underpinnings of this Deleuzian account of the structure of Leibniz’s metaphysics, which, I maintain, subtends the entire text of The Fold. (shrink)

Ken Pledger devised a one-sorted approach to the incidence relation of plane geometries, using structures that also support models of propositional modal logic. He introduced a modal system 12g that is valid in one-sorted projective planes, proved that it has finitely many non-equivalent modalities, and identified all possible modality patterns of its extensions. One of these extensions 8f is valid in elliptic planes. These results were presented in his 1980 doctoral dissertation, which is reprinted in this issue of the (...) Australasian Journal of Logic. Here we show that 12g and 8f are strongly complete for validity in their intended one-sorted geometrical interpretations, and have the finite model property. The proofs apply standard technology of modal logic together with a step-by-step procedure introduced by Yde Venema for constructing two-sorted projective planes. (shrink)

After presenting the foundation and the basic equations of a new 5-dimensional projective unified field theory, the problem of incorporating spinor fields into this framework is investigated. Apart from Pauli's method, we propose a new approach which leads to a consistent 5-dimensional spinor theory with a series of physical consequences (variability of the 4-dimensional “rest mass,” instability of 4-dimensional “stationary states,” etc.).

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

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)

Todorčević (Fund Math 150(1):55–66, 1996) shows that there is no Hausdorff gap (A, B) if A is analytic. In this note we extend the result by showing that the assertion “there is no Hausdorff gap (A, B) if A is coanalytic” is equivalent to “there is no Hausdorff gap (A, B) if A is ${{\bf \it{\Sigma}}^{1}_{2}}$ ”, and equivalent to ${\forall r \; (\aleph_1^{L[r]}\,< \aleph_1)}$ . We also consider real-valued games corresponding to Hausdorff gaps, and show that ${\mathsf{AD}_\mathbb{R}}$ for pointclasses (...) Γ implies that there are no Hausdorff gaps (A, B) if ${{\it{A}} \in {\bf \it{\Gamma}}}$. (shrink)

L’épreuve projective intitulée « spatiographie projective familiale » a pour objectif de comprendre l’image inconsciente du corps familial à travers l’analyse du dessin groupal de la « maison de rêve ». Par cette méthodologie, les auteurs peuvent établir un diagnostic de la structure des liens inconscients de la famille et en faire un objet médiateur pour la prise en charge psychothérapique et une épreuve projective groupale familiale pour le diagnostic. Le dessin de la « maison de rêve (...) » est un outil original qui investigue les dimensions diachronique et synchronique permettant une approche complète de la structuration de l’image du corps familial. (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.

Models and modelling are central not only to management but to all human affairs. Models provide grounds for decision making and action-taking. This paper investigates the concept of ‘model’, showing that the conventional notion of a model as understood in management science, a notion founded on positivism and realism, is insufficient for the complex practical needs of management models. To remedy this situation, an alternative notion founded on Projective Constructivist Epistemology (PCE) is proposed. Some of the implications of the (...) new notion for modelling practice and model validation are also discussed. The new notion results from theoretical investigations and empirical experience gleaned over the last five years in public-sector, military and business contexts. The paper concludes with a brief discussion of areas that might merit investigation in the future. (shrink)

Journal of Mathematical Logic, Ahead of Print. We identify a particular mouse, [math], the minimal ladder mouse, that sits in the mouse order just past [math] for all [math], and we show that [math], the set of reals that are [math] in a countable ordinal. Thus [math] is a mouse set. This is analogous to the fact that [math] where [math] is the sharp for the minimal inner model with a Woodin cardinal, and [math] is the set of reals that (...) are [math] in a countable ordinal. More generally [math]. The mouse [math] and the set [math] compose the next natural pair to consider in this series of results. Thus we are proving the mouse set theorem just past projective. Some of this is not new. [math] was known in the 1990s. But [math] was open until Woodin found a proof in 2018. The main goal of this paper is to give Woodin’s proof. (shrink)

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 $\alpha$.

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.

The fact that the space of states of a quantum mechanical system is a projective space (as opposed to a linear manifold) has many consequences. We develop some of these here. First, the space is nearly contractible, namely all the finite homotopy groups (except the second) vanish (i.e., it is the Eilenberg-MacLane space K(ℤ, 2)). Moreover, there is strictly speaking no “superposition principle” in quantum mechanics as one cannot “add” rays; instead, there is adecomposition principle by which a given (...) ray has well-defined projections in other rays. When the evolution of a system is cyclic, any representativevector traces out an open curve, defining an element of the holonomy group, which is essentially the (geometrical) Berry phase. Finally, for the massless case of the representations of the Poincaré group (the so-called “Wigner program”), there could be in principle arbitrarily multivalued representations coming from the Lie algebra of the Euclidean plane group. In fact they are at most bivalued (as commonly admitted). (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.

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)

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.

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).

While there is an extensive subfield in sociology studying the sources, content, and consequences of collective memory, the study of future projections has been much more fragmentary. In part, this has to do with the challenge of measurement; how do you measure something that has not happened yet? In this article, I argue that future projections can be studied via their externalizations in attitudes, narratives, performance, and material forms. They are particularly evident in what I call “sites of hyperprojectivity,” that (...) is, sites of heightened, future-oriented public debate about possible futures. As a pilot project, I examine contending narratives about possible futures in the online documents of the United Nations Conference on Sustainable Development and the accompanying “People’s Summit,” held in Rio de Janeiro in June 2012. I propose a framework for studying how public interventions into debates about “sustainable futures” and the “green economy” differ on various dimensions of projectivity, including their temporal reach, attention to contingency and causality, and network mapping of future actors. I present a preliminary analysis at the level of narrative and grammar, by analyzing the use of predictive, imperative, and subjunctive verb forms in both programmatic and oppositional texts. I close with a discussion of how different genres of future projection might be put to analytical use in studying processes of interest to social scientists, such as coalition formation, institution building, political mobilization, and policy change. (shrink)

In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they correspond (...) to pure orthogeometries, irreducible pure orthogeometries, Hilbertian geometries and irreducible Hilbertian geometries, respectively. The discovery of these correspondences raises interesting research topics and will enrich the study of logic. (shrink)

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)

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)

We identify a particular mouse, [Formula: see text], the minimal ladder mouse, that sits in the mouse order just past [Formula: see text] for all [Formula: see text], and we show that [Formula: see text], the set of reals that are [Formula: see text] in a countable ordinal. Thus [Formula: see text] is a mouse set. This is analogous to the fact that [Formula: see text] where [Formula: see text] is the sharp for the minimal inner model with a Woodin (...) cardinal, and [Formula: see text] is the set of reals that are [Formula: see text] in a countable ordinal. More generally [Formula: see text]. The mouse [Formula: see text] and the set [Formula: see text] compose the next natural pair to consider in this series of results. Thus we are proving the mouse set theorem just past projective. Some of this is not new. [Formula: see text] was known in the 1990s. But [Formula: see text] was open until Woodin found a proof in 2018. The main goal of this paper is to give Woodin’s proof. (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)

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)