This ambitious work reclassifies and restructures the history of ideas and the philosophy of culture through a wide-ranging and novel use of the idea of the organon. It does so by radically revising standard interpretations and theories of all branches of philosophy, and by providing an intellectual and philosophical foundation for the new organon of the cultural sciences. The seeded idea that saw its growth in the form of this book is the unshakable conviction that the only way by which (...) a new apparatus of philosophy, an organon, could be created is by harking back to the vast sources of imagination, inspiration and mimesis. This study is based on the notion that metaphysics, insofar as it is concerned with the world in its entirety and with human being's existence and thought, should provide the foundation for the organon of cultural sciences, based on symbolic forms. Given that the colossal amount of information and knowledge of philosophy, arts, humanities, logic, mathematics, social sciences and natural sciences cannot be comprised, analyzed and comprehended per se, it is the organon's objective to extract the main principles, ideas, postulates, theorems and theories of the cultural sciences, and, subsequently, to shape and restructure them as symbolic forms. Since all these principles are grounded on Becoming - which is not a stable or fixed entity such as Being, substance or thing - the symbolic forms preserve and change, elevate and further the organon of the cultural sciences, via a critical-dialectical process. (shrink)

Recovery is a commonly used concept in both professional and everyday contexts. Yet despite its extensive use, it has not drawn much philosophical attention. In this paper, I question the common understanding of recovery, show how the concept is inadequate, and introduce new and much needed terminology. I argue that recovery glosses over important distinctions and even misrepresents the process of moving away from malady as "going back" to a former state of health. It does not invite important nuances needed (...) to distinguish between biomedical, phenomenological, and social perspectives. In addition, I claim that there are many conditions where we are making use of the concept of recovery, although the person recovered from the condition in question, has not regained the same degree of soundness. I show how the concept of recovery leads to conceptual discrepancies that can result in worsening patients' conditions. To gain a fuller understanding, I propose to rethink the direction of the process in question. I define the process of moving away from malady as a move forward towards a new state of soundness. I also suggest three terms, corresponding to different perspectives, to describe this movement forward: 'curing', 'healing', and 'habilitating'. This new terminology provides a more nuanced understanding of the states of both malady and soundness and an attentiveness as to how they differ and relate. (shrink)

Montague [7] translates English into a tensed intensional logic, an extension of the typed -calculus. We prove that each translation reduces to a formula without -applications, unique to within change of bound variable. The proof has two main steps. We first prove that translations of English phrases have the special property that arguments to functions are modally closed. We then show that formulas in which arguments are modally closed have a unique fully reduced -normal form. As a corollary, translations of (...) English phrases are contained in a simply defined proper subclass of the formulas of the intensional logic. (shrink)

This paper inquires the ways in which paper folding constitutes a mathematical practice and may prompt a mathematical culture. To do this, we first present and investigate the common mathematical activities shared by this culture, i.e. we present mathematical paper folding as a material reasoning practice. We show that the patterns of mathematical activity observed in mathematical paper folding are, at least since the end of the nineteenth century, sufficiently stable to be considered as a practice. Moreover, we will argue (...) that this practice is material. The permitted inferential actions when reasoning by folding are controlled by the physical realities of paper-like material, whilst claims to generality of some reasoning operations are supported by arguments from other mathematical idioms. The controlling structure provided by this material side of the practice is tight enough to allow for non-textual shared standards of argument and wide enough to provide sufficiently many problems for a practice to form. The upshot is that mathematical paper folding is a non-propositional and non-diagrammatic reasoning practice that adds to our understanding of the multi-faceted nature of the epistemic force of mathematical proof. We then draw on what we have learned from our contemplations about paper folding to highlight some lessons about what a study of mathematical cultures entails. (shrink)

As is well known, it was only in 1926 that a comprehensive mathematical theory of braids was published—that of Emil Artin. That said, braids had been researched mathematically before Artin’s treatment: Alexandre Theophile Vandermonde, Carl Friedrich Gauß and Peter Guthrie Tait had all attempted to introduce notations for braids. Nevertheless, it was only Artin’s approach that proved to be successful. Though the historical reasons for the success of Artin’s approach are known, a question arises as to whether other approaches to (...) deal with braids existed, approaches that were developed after Artin’s article and were essentially different from his approach. The answer, as will be shown, is positive: Modesto Dedò developed in 1950 another notation for braids, though one, which was afterward forgotten or ignored. This raises a more general question: what was the role of Artin’s notation, or, respectively, Dedò’s, that enabled either the acceptance or the neglect of their theories? More philosophically, can notation be an epistemic technique, prompting new discoveries, or rather, can it also operate an as obstacle? The paper will analyze the method introduced by Dedò to notate braids, and also its history and implications. It aims to show that Dedò, in contrast to Artin, focused on factorizations of braids and the algebraic relations between the operations done on these factorizations. Dedò’s research was done against the background of Oscar Chisini’s research of algebraic curves on the one hand and of Artin’s successful notation of braids on the other hand. Taking this into account, the paper will in addition look into the epistemic role of notation, comparing Dedò’s work with Artin’s, as both presented different notations of braids and their deformations. (shrink)

We show that, assuming the existence of the canonical inner model with one Woodin cardinal $M_1 $, there is a model of $ZFC$ in which the nonstationary ideal on $\omega _1 $ is $\aleph _2 $-saturated and whose reals admit a ${\rm{\Sigma }}_4^1 $-wellorder.

Over the course of a fifty-year scholarly career, Frank M. Oppenheim, SJ, has devotedly studied and encouraged others to study the American philosopher Josiah Royce. Early in my own study of Royce, I read and learned a great deal from Oppenheim’s book Reverence for the Relations of Life. I met Oppenheim at a 2007 conference at Harvard on Royce and William James, and he encouraged my continued study. Thus, I am honored to participate in this issue of The Pluralist celebrating (...) Oppenheim’s thought and his study of Royce.In spite of all the efforts of Oppenheim and other scholars, Royce remains too little known.1 It is tempting to ask why a contemporary scholar would devote painstaking and devoted attention... (shrink)

Provide a formal system that is a conservative extension of PA for Π02 sentences, and even a conservative extension of HA, that supports the worry free smooth development of constructive analysis in the style of Errett Bishop.

An extreme kind of logic skeptic claims that "the present formal systems used for the foundations of mathematics are artificially strong, thereby causing unnecessary headaches such as the Gödel incompleteness phenomena". The skeptic continues by claiming that "logician's systems always contain overly general assertions, and/or assertions about overly general notions, that are not used in any significant way in normal mathematics. For example, induction for all statements, or even all statements of certain restricted forms, is far too general - mathematicians (...) only use induction for natural statements that actually arise. If logicians would tailor their formal systems to conform to the naturalness of normal mathematics, then various logical difficulties would disappear, and the story of the foundations of mathematics would look radically different than it does today. In particular, it should be possible to give a convincing model of actual mathematical practice that can be proved to be free of contradiction using methods that lie within what Hilbert had in mind in connection with his program”. Here we present some specific results in the direction of refuting this point of view, and introduce the Strict Reverse Mathematics (SRM) program. (shrink)

Several decades ago, feminists differentiated between the biologically given basis of sex identity (sex) and the socially constructed cultural practices anchored by sex identity (gender). In recent years, many feminists have challenged that distinction, arguing that biological sex is as much a social construct as are the practices comprising gender. I survey two examples from biological studies of sex identity that, by contrast (I maintain), warrant saving the concept of biologically given sex identity. The result is not antithetical to feminism, (...) however, since these studies also suggest that sex identity proliferates beyond the rigid female/male dichotomy. If articulated carefully, this view can avoid metaphysically essentialist baggage while enriching feminist conceptions of sex identity. (shrink)

Jensen's remarkable Coding Theorem asserts that the universe can be included in L[R] for some real R, via class forcing. The purpose of this article is to present a simpler proof of Jensen's theorem, obtained by implementing some changes first developed for the theory of Strong Coding. In particular, our proof avoids the split into cases, according to whether or not 0# exists in the ground model.

The iterative concept of set is standardly taken to justify ZFC and some of its extensions. In this paper, we show that the maximal iterative concept also lies behind a class of further maximality principles expressing the maximality of the universe of sets V in height and width. These principles have been heavily investigated by the first author and his collaborators within the Hyperuniverse Programme. The programme is based on two essential tools: the hyperuniverse, consisting of all countable transitive models (...) of ZFC, and V -logic, both of which are also fully discussed in the paper. (shrink)

Aristotle's doctrine of the four causes--formal, final, efficient and material--is famous. But Posterior Analytics B 11 lists "if certain things hold, it is necessary that this does" in place of a standard expression for the material cause. This cause has been dubbed the grounding cause. It has interested scholars since the Greek commentators, who simply assumed that Aristotle meant the material cause. This traditional thesis has been challenged by two views: first, that the grounding cause is a special type of (...) material cause ; second, that it is no material cause at all . ;I set out two arguments for the traditional thesis and consider nine objections to it. Since most of these objections, which constitute the support for the revisionist thesis, can be answered, I reject the revisionist thesis. But in my treatment of one objection it also becomes clear that the traditional thesis is mistaken. The grounding cause is a necessitating cause, yet in Physics B 9 Aristotle makes it clear that many material causes are not necessitating causes. Thus, some form of the modified traditional thesis is true. ;But which form? D. M. Balme suggests that Aristotle means to include only mathematical causes because hypothetical necessity covers all of the relation between matter and product in things which come to be. But Aristotle seems to accept necessitating material causes in several passages in the biological works. In other passages he seems to adopt the position Balme attributes to him. I argue that he does not actually adopt this position, and that he does accept simple necessity in some things which come to be. Thus, the grounding cause is a necessitating material cause, and such causes are found not only in mathematics, but also among things which come to be. (shrink)

What makes the question of grandparental investment so very interesting is trying to tease out the underlying motivations. Grandparental investment is variable and grandparental altruism, if it exists at all, is also variable. Neither evolutionary theory nor rational choice theory has an easy time explaining this variation, and insight is further impeded by the absence of any compelling empirical studies designed for the purpose of testing alternative explanations of variations in grandparental investment.

The American Journal of Bioethics, Volume 11, Issue 7, Page 28-29, July 2011.

My argument owes much to two contemporary philosophical scholars of the development of modern physics beginning with Newton and extending through the late nineteenth and early twentieth centuries: George Smith and Howard Stein. From the former I take a conception of theory-mediated measurement, from the latter a conception of abstract structures in the phenomena. The relevant notion of phenomena, as we shall see, is closely related to Newtonian scientific methodology, a methodology that is clearly embraced by both philosophers. The conception (...) of abstract structures, however, is not so clear, and it is especially to be distinguished from the more recent conception of “structural realism.”. (shrink)

This book is a passionate report on the state of feminist thinking and practice after the linguistic turn. A critical assessment of masculinist notions of the sublime in modern and postmodern accounts grounds the author's positive and constructive recuperation of sublime experience in a feminist voice.

Recently, some contradictory statements have been made concerning whether or not the Buddha taught free will. Here, a comparative method is used to examine what exactly is meant by free will, and to determine to what extent this meaning is applicable to early Buddhist thought as recorded in the Pāli Nikāyas. The comparative method reveals parallels between contemporary criticisms of Cartesian philosophy and Buddhist criticisms of Brahmanical and Jain doctrines. Although in Cartesian terms Buddhism promotes no recognizable theory of free (...) will, it does promote a primitive theory of compatibilism which shares some keyfeatures with Daniel Dennett's position on this issue. It is argued that the implicit Buddhist stance on freedom of the will allows the existence of choice and responsibility without calling upon an ultimate controlling agency that transcends the causal nexus of mind and body. (shrink)

ABSTRACT W. E. B. Du Bois’s groundbreaking scholarship on race and racial prejudice was inseparable from his lifelong struggle for racial justice, Black liberation, and against social and political oppression. Both in his theoretical and in his historical-political work, Du Bois substantially and critically engaged with the “Jewish question”: with Jewish life, history, and politics, with the experiential perspective of an oppressed minority, and with the fight against prejudice and racial hatred. Throughout in life, and in particular in later years, (...) Du Bois was influenced by Karl Marx’s critical analysis of social and economic life; Marx’s own discussion of the “Jewish question,” concerning the difference between political equality and human emancipation, proved substantial to his argument on civil rights and racial justice. In this article, I argue that Du Bois did not only draw from the Jewish experience and from Marx’s work on the “Jewish question” in his work on African American history and politics, but also that he, in fact, reconsidered the “Jewish question” from an African American perspective, offering his own reading and understanding of the “Jewish question,” thus applying his concept of double consciousness for rethinking it as a question of racial identity and racial consciousness, and as relevant and applicable to Black liberation and the fight against racism. (shrink)

The Buddhist concept of skillful means , as introduced inMahāyāna sūtras, exposes a new awareness of the gap between text and meaning. Although the term is sometimes taken to point to the Buddha's pedagogical skills, this interpretation ignores the provocative use of the term in Mahāyāna texts. Treating skillful means as a universal Buddhist concept also fails to explain why and for what purpose it first became predominant in the Mahāyāna. Looking at the use of skillful means in the Lotus (...) Sūtra and in the Skill in Means Sūtra reveals a hermeneutic device aimed at criticizing an existing corpus of Buddhist literature. As such, skillful means is used to demonstrate that the old doctrine and the life of the Buddha contained fictitious features and were nothing but skillful means. This indicates a growing awareness of a gap between literal expressions and their hidden meaning that can only arise after some kind of religious corpus has been established. (shrink)

We construct a model [Formula: see text] of [Formula: see text] which lies between [Formula: see text] and [Formula: see text] for a Cohen real [Formula: see text] and does not have the form [Formula: see text] for any set [Formula: see text]. This is loosely based on the unwritten work done in a Bristol workshop about Woodin’s HOD Conjecture in 2011. The construction given here allows for a finer analysis of the needed assumptions on the ground models, thus taking (...) us one step closer to understanding models of [Formula: see text], and the HOD Conjecture and its relatives. This model also provides a positive answer to a question of Grigorieff about intermediate models of [Formula: see text], and we use it to show the failure of Kinna–Wagner Principles in [Formula: see text]. (shrink)

With less than 0# two generic extensions ofL are identified: one in which ${\aleph_1}$ , and the other ${\aleph_2}$ , is almost precipitous. This improves the consistency strength upper bound of almost precipitousness obtained in Gitik M, Magidor M (On partialy wellfounded generic ultrapowers, in Pillars of Computer Science, 2010), and answers some questions raised there. Also, main results of Gitik (On normal precipitous ideals, 2010), are generalized—assumptions on precipitousness are replaced by those on ∞-semi precipitousness. As an application it (...) is shown that if δ is a Woodin cardinal and there is an ${f:\omega_1 \to \omega_1}$ with ${\|f\|=\omega_2}$ , then after ${Col(\aleph_2,\delta)}$ there is a normal precipitous ideal over ${\aleph_1}$ . The existence of a pseudo-precipitous ideal over a successor cardinal is shown to give an inner model with a strong cardinal. (shrink)

This chapter explores the interrelations between Theodor W. Adorno and Gershom Scholem's thought. It argues that despite the overt differences between Adorno's materialist social philosophy and Scholem's scholarship of Jewish mysticism, both intellectuals were motivated by similar concerns and interests. Following a brief historical contextualization of the intellectual exchange between Adorno and Scholem, the chapter focuses on three main thematic intersections between their thought and writings: The concept of myth and the dialectical entanglement of myth and reason; the heretical element (...) in its relation to natural and social life, and to the critique of normativity; and the theological dimension in their work, and the role of negativity, metaphysics, and materialism within it. (shrink)

J. L. Krivine developed a new method based on realizability to construct models of set theory where the axiom of choice fails. We attempt to recreate his results in classical settings, i.e., symmetric extensions. We also provide a new condition for preserving well ordered, and other particular type of choice, in the general settings of symmetric extensions.

This paper analyzes the treatment of nature and technology in the writings of two prominent early Zionist thinkers, A. D. Gordon and Theodor Herzl. At the heart of Herzl’s vision, we find technocrats applying industrial systems to dominate the naked nature that Gordon is committed to preserve. Gordon, in contrast, describes Jewish national revival as triggered by farmers utilizing Eretz Israel’s natural world to extract Jews from industrial society, underwriting Herzl’s Zionist vision. Expanding the analysis to the domains of nature (...) and technology reveals the two thinkers’ creeds to be rival Zionist ideologies in which nature and technology serve as catalysts for competing visions of national revival. (shrink)

Herman Levin Goldschmidt delineates and critiques four types of “dialogism,” four ways of derailing dialogical discourse and praxis. In the following, I examine two of them: “Pan-dialogism” is the glossing over the effect of power differentials such as gender, class, and race as relevant factors in the constitution of dialogue. “Pluralogic” is the evading of true dialogue, which is intense and exclusive, by conducting simultaneously multiple superficial conversations. Pluralogic enables to escape the internal turmoil and conscience’s call for critiquing that (...) are part and parcel of true dialogue. To examine the two dialogisms, I use Martin Buber’s thought, which Goldschmidt sees himself as continuing, as a case in point as well as a resource to further unpack Goldschmidt’s thought. In the course of the paper, I criticize what I call “Human Resource Office Morality,” the celebration of mere diversity at the expense of true contradiction. (shrink)

This paper corrects a pervasive mistake in readings of Buber’s iconic trope, “I-Thou” (Ich-Du; hereafter, I-You). The mistake lies in considering it synonymous to the principal concept of his dialogical thought, “relation” (Beziehung). A detailed reading of relevant passages in Buber’s I and Thou (hereafter, IAT) reveals their difference: While both “relation” and “I-You” refer to the same reality—to the dialogic moment—they do so with a different focus and scope: “Relation” refers to the dialogic moment in its bilateral entirety. However, (...) “primary word I-You” (hereafter, PWIY)—the phrase in which the I-You trope in fact appears in IAT—focuses on the active share of only one of the two interlocutors in the dialogic moment. While PWIY does refer to the dialogical moment (which is indeed bilateral), it denotes only a partial aspect of the dialogical moment. It focuses exclusively on my active turning toward you and defocuses your concurrent turning toward me (which, no doubt, is present as well). This mistake, I show, is due to interpreters’ enthusiastic endorsement of Buber’s later phrase, the “I-You relation,” which is indeed synonymous with “relation.” It is then easy to read back the “I-You relation” into the earlier, more focused concept of PWIY. Furthermore, this enthusiasm has blinded readers from realizing that, following IAT, Buber in fact abandoned the I-You trope and used it only reluctantly, mainly when addressing his interpreters who used it themselves, or when discussing IAT where it indeed appeared. (shrink)

The global economic crisis makes closer collaboration between economics and other social sciences even more urgent. One major cause of divergence has been the attitudes of the parties towards the ‘market’. Yet, the market economy, in all its diversity, is one of the immutable facts of modern life. Understanding the causes of its survival will improve the dialogue. Another interesting puzzle is the lack of credible alternatives to it despite the depth of the crisis. The experience of the economists in (...) constructing models of society based on the behaviour of individuals composing it can be valuable for other social sciences. We apply the framework developed by ‘institutional economics’ to gain insights into the relations between Islam, capitalism and democracy. The article finishes with some observations on Turkey and draws lessons for other Muslim societies. (shrink)