'..... And then there were none', is a collaborative book by four New Zealand photographers and a writer. Developed over the last two years with regular meetings indulgent in wine and homemade cheese as excuses for friendship and banter, '..... and then there were none' grew from conversations and arguments about mortality, our technologically mired existence and the degradation of the environment. Collaboration in a real sense, Harvey Benge, Jon Carapiet, Haru Sameshima, Stu Sontier, breaks out of conventional authorship (...) based story-telling, to play out their anxieties and doubts about the world they see, as one visual voice. The author Lloyd Jones adds his contribution of trenchant narrative texts of two scenes of slaughter and one execution. All addicted to travels, the project triggered its own version of flygskam [the feeling of climate guilt associated with airline travel] or the collaborators, conflicted by the international travel that made many of the photographs and the writing possible and tainted by knowing the greater price to be paid. Narratives included from such travels are drenched in sordid human histories that recall the myriad pathways that have led us to now, and to what comes next. The nod to mortality echoing through the book is rendered stark by the recent death of Benge, adding a sense of urgency to the title of the book - not just for the remaining collaborators, but for us all."--Publisher. (shrink)

An innovative theory of consciousness, drawing on the phenomenology of Edmund Husserl and supported by brain-imaging, presented in the form of a hardboiled ..

'Correlations without correlata' is an influential way of thinking of quantum entanglement as a form primitive correlation which nonetheless maintains locality of quantum theory. A number of arguments have sought to suggest that such a view leads either to internal inconsistency or to conflict with the empirical predictions of quantum mechanics. Here wew explicate and provide a partial defence of the notion, arguing that these objections import unwarranted conceptions of correlation properties as hidden variables. A more plausible account sees the (...) properties in terms of Everettian relative states. The ontological robustness of entanglement is also defended from recent objections. (shrink)

A collection of essays on the theory of history and the theory of nature. Topics include the genetic method and historical determinism, historical decision, the nature of metaphysics, empirical pluralism and unification of nature, ways of construing mind and intelligibility, and others.

The sophisticated philosophical literature on supervenience stands in need of supplementation by a treatment of more fundamental questions about what features this notion possesses solely in virtue of the form of the definition it is standardly given. We provide a discussion of these features without getting involved in the merits of particular supervenience claims advanced and contested in that literature.

This volume is a tribute by his peers, and by younger scholars of the next generation, to Harvey M. Friedman, perhaps the most profound foundationalist since Kurt Godel. Friedman's researches, beginning precociously in his mid-teens, have fundamentally shaped our contemporary understanding of set theory, recursion theory, model theory, proof theory and metamathematics. His achievements in concept formation and theory formulation have also renewed the standard set by Godel and Alfred Tarski for the general intellectual interest and importance of technical (...) work in foundations. Friedman pioneered the now well-established and flourishing field of Reverse Mathematics, whose aim is to calibrate the intrinsic logico-mathematical consistency-strength of all the important theorems of mathematics. He has relentlessly pursued the full extent of the incompleteness phenomena into which Godel provided the first revealing glimpse. The Godel--Friedman program, as it is now deservingly called, seeks to find simple, natural and elegant mathematical statements of a combinatorial nature, that can be proved to be independent of set theory even when extended by powerful large-cardinal existence axioms. (shrink)

This paper discusses the philosophical significance of 'September 11' by relating it to attempts that have been made throughout the history of philosophy to read particular events as symbols of conceptual change. It draws especially on Susan Neiman's Evil in Modern Thought and Giovanna Borradori's dialogues with Derrida and Habermas, in her Philosophy in a Time of Terror, to relate 'September 11' to Kant's versions of Progress, Providence and Cosmopolitanism.

Much discourse on school shootings tends to imply a binary separation between what is considered normal and exceptional, between an expected course of human events and sociohistorical aberrations. In this article Harvey Shapiro suggests the need for new directions in our responses: First, he shows how responses to school shootings tend to expropriate and dismiss certain kinds of violence in order to articulate a vision of the self as sovereign, exerting power over bodily life, exercising a self-removal from community (...) conversations, and thus claiming what Giorgio Agamben and others call the “sovereign exception.” Second, he suggests how Agamben's development of Walter Benjamin's concept of “divine violence” can unmask prevailing states of exception and can inform education's efforts to challenge binaries of good and evil, urban and suburban, individual and community, justice and law, normal and exceptional, that confound our deliberations and long-term responses to mass shootings. (shrink)

We consider a number of statements involving restrictions and extensions of algebras, and derive connections with large cardinal axioms.

Educational Theory and Jewish Studies in Conversation: From Volozhin to Buczacz, by Harvey Shapiro, PhD, brings together two different fields of study—modern Jewish studies and contemporary educational theory—to provide new theoretical frameworks for their interaction. Shapiro provides alternative theoretical frameworks for the relationship between Jewish studies and educational theory and discusses different ways of developing and articulating this relationship between disciplines.

Most of my intellectual efforts have focused around a single general question in the foundations of mathematics (f.o.m.). I became keenly aware of this question as a student at MIT around 40 years ago, and readily adopted it as the principal driving force behind my research.

There are two kinds of such limiting results that must be carefully distinguished. Results of the first kind state the nonexistence of any algorithm for determining whether any statement among a given set of statements is true or false.

We axiomatize EFA in strictly mathematical terms, involving only the ring operations, without extending the language by either exponentiation, finite sets of integers, or polynomials.

Most of the research in foundations of mathematics that I do in some way or another involves the use of nonstandard models. I will give a few examples, and indicate what is involved.

We present several selection theorems for Borel relations, involving only Borel sets and functions, all of which can be obtained as consequences of closely related theorems proved in [DSR 96,99,01,01X] involving coanalytic sets. The relevant proofs given there use substantial set theoretic methods, which were also shown to be necessary. We show that none of our Borel consequences can be proved without substantial set theoretic methods. The results are established for Baire space. We give equivalents of some of the main (...) results for the reals. (shrink)

We present two forms of “sentential reflection”, which are shown to be mutually interpretable with Z2 and ZFC, respectively.

A lot of the well known impact of the Gödel phenomena is in the form of painful messages telling us that certain major mathematical programs cannot be completed as intended. This aspect of Gödel – the delivery of bad news –is not welcomed, and defensive measures are now in place.

By a consequence relation on a set L of formulas we understand a relation I — c p(L) x L satisfying the conditions called 'Overlap', 'Dilution', and 'Cut for Sets' at p.15 of [25]; we do not repeat the conditions here since we are simply fixing notation and the concept of a consequence relation is well known in any case. (The characterization in [25] amounts to that familiar from Tarski's work, except that there is no 'finitariness' restriction to the effect (...) that when I I — A, for I c L, A c L, we must have I o I — A for some finite I o c I . The presence or absence of this condition makes no difference to anything that follows.) Each language L to be considered will be a sentential language whose formulas are built in the usual way by application of it-ary (primitive) connectives to it simpler formulas, starting with the simplest formulas — the propositional variables (or 'sentence letters') — not constructed with the aid of connectives. We assume, as usual, that there are countably many such variables, and they will be denoted by p, q, r, ... possibly with numerical subscripts. A consequence relation I- on such an L has the Unrestricted Interpolation Property when for any A, C c L with A I — C, there exists B c L with A I — B and B I — C, such that C is constructed only out of such propositional variables as occur both in A and in C. (Such a B is called an interpolant for A and C.) Note that we take the usual notational liberties here, writing "A I — C" (and the like) for "iAi I — C", "I, A I — C" to mean "I u iAi I — C", and "I — C" to mean "8 I — C". Further, we sometimes abbreviate the claim that A I — B and B I — C to "A I — B I — C", and when C is A itself, we always write this simply as "A — II— B".. (shrink)

Mathematical Logic had a glorious period in the 1930s, which was briefly rekindled in the 1960s. Any Shock Value, such as it is, has surrounded unprovability from ZFC.

In 1922 Charles Hartshorne, then an aspiring young philosopher, wrote to Edgar Sheffield Brightman, a preeminent philosopher of religion for twenty-three subsequent years and, remarkably, almost every letter was preserved. In their introductory essays, editors Randall Auxier and Mark Davies place the unusually rich and intensive correspondence in its intellectual context and address the relationship between personalism and process philosophy/theology in metaphysics, epistemology, ethics, and social philosophy.

The space CS(R) has a unique “Borel structure” in the following sense. Note that there is a natural mapping from R¥ onto CS(R}; namely, taking ranges. We can combine this with any Borel bijection from R onto R¥ in order to get a “preferred” surjection F:R ® CS(R).

Cian Dorr considered the case of a fair coin that is tossed every day throughout an infinite past and an infinite future (an ``Eternal Coin''). Against intuition, he argued that, conditional on the Coin having landed {\it heads} throughout the past, one should believe, with full probability, that it will also land {\it heads} today. In this paper, we critique Dorr's arguments, as well as part of a reply by Myrvold.

All axiomatizations in sections 1,2,4-8 are in the language L(Î,W) with just Î and the constant symbol W standing for a Subworld. Think of W as yesterday's world, and think of the quantifiers in the theory as ranging over today's world. The philosophy is that since the universe cannot be completed, every time we reflect on the universe and what we have reflected on previously, we obtain a larger universe.

This submission explores the concept of aesthetic justice pedagogy, and advocates on behalf of it. In contrast to aesthetic injustice, which denotes any harm done to a person’s aesthetic capacities, aesthetic justice pedagogy aims at facilitating the development of students’ imagination, perception, and feelings, wherein narrative and story-making are prime locations to contest coloniality and oppression. We emphasize the practice of this philosophy, refusing to see it as only as metaphor or theory. In our attempt to build a praxis of (...) philosophy, education, and art, we lean upon diverse thinkers such as Augusto Boal, John Dewey, Paulo Freire, and Ursula K. Le Guin. We maintain that aesthetic justice pedagogy requires spaces of liberation whereby initiates can practice, rehearse, and perform new realities and create counter-narratives through various modalities of story-writing. Boal’s Aesthetics of the Oppressed, Dewey’s understanding of dramatic rehearsal, Freire’s work in Culture Circles, and Le Guin’s critique of the father tongue combine art, re-storying, and imagination in ways that are unique to the traditional practices of arts education. We conclude by reemphasizing the liberatory ways in which practice (aesthetic work that is done alone), rehearsal (art work with others), and performance (imagination’s accomplishment) come to identify unique qualities and practices of an aesthetic justice pedagogy. (shrink)