Evolution, mathematics, and the evolution of mathematics -- Mathematics and the Greeks' view of the world -- Mathematics and the view of the world in early modern times -- Mathematics and the modern view of the world -- The mathematics of randomness -- The mathematics of human behavior -- computations and computers -- Is there really no doubt? -- The nature of research in mathematics -- Why is teaching and learning mathematics so hard?

In this stunning reappraisal of the celebrated case of Daniel Paul Schreber, Lothane takes the reader on a richly documented tour of all the ingredients that made Schreber's illness a unique psychiatric event. Building outward from a close examination of Schreber's troubled relationship to his two psychiatrists, Flechsig and Weber, Lothane elaborates the personal, familial, and cultural contexts of Schreber's illness. Incorporating extensive new archival and bibliographic research, and providing extensive accounts of the personalities and theories of Schreber's two psychiatrists, (...) Paul Flechsig and Guido Weber, Zvi Lothane offers a stunning reappraisal of the Schreber case that overturns virtually all previous opinion. Lothane examines both the man and his milieu in a way that allows the reader fresh access not only to the tragedy of Schreber's illness but also to his heroic, if doomed, attempts to come to terms with his condition through writing. In the process, he persuasively demonstrates that important issues of both psychiatric diagnosis and psychoanalytic interpretation have heretofore been compromised by a failure to pay sufficient attention to Schreber's interpersonal, cultural, and historical contexts. (shrink)

Intonational focus can be observed on parts of words that appear to lack intrinsic meaning, and triggers alternatives that are similar in form. In order to provide a unified treatment of focus above and below the word level (they do, after all, behave the same in most respects), I develop a theory of denotations for arbitrary word parts in which focused word parts denote their own sound and the unfocused parts are functions from sounds to word meanings. This allows focus (...) theories to generalize below the word level; any differences with focus above the word level are located in the semantics of word parts. The paper also explores phonological constraints on focus placement, and shows that the focusability of a word part depends solely on its prosodic status, not on any semantic factors. (shrink)

Quantificational arguments can take scope outside of temporal adjunct clauses, in an apparent violation of locality restrictions: the sentence few secretaries cried after each executive resigned allows the quantificational NP each executive to take scope above few secretaries. I show how this scope relation is the result of local operations: the adjunct clause is a temporal generalized quantifier which takes scope over the main clause (Pratt and Francez, Linguistic and Philosophy 24(2), 187–222. [2001]), and within the adjunct clause, the quantificational (...) argument takes scope above the implicit determiner which forms the temporal generalized quantifier. The paper explores various relations among quantificational arguments across clause boundaries, including temporal clauses that are modified internally by a temporal adverbial and temporal clauses with embedded sentential complements. (shrink)

Newton began his Principia with three Axiomata sive Leges Motus. We offer an interpretation of Newton’s dual label and investigate two tensions inherent in his account of laws. The first arises from the juxtaposition of Newton’s confidence in the certainty of his laws and his commitment to their variability and contingency. The second arises because Newton ascribes fundamental status both to the laws and to the bodies and forces they govern. We argue the first is resolvable, but the second is (...) not. However, the second tension shows that Newton conceives laws as formal causes of bodies and forces. This neo-Aristotelian conception goes missing in Kantian accounts of laws, as well as accounts that stress laws’ grounding in powers and capacities. (shrink)

Newton's Principia begins with eight formal definitions and a scholium, the so-called scholium on space and time. Despite a history of misinterpretation, scholars now largely agree that the purpose of the scholium is to establish and defend the de fi nitions of key concepts. There is no consensus, however, on how those definitions differ in kind from the Principia's formal definitions and why they are set-off in a scholium. The purpose of the present essay is to shed light on the (...) scholium by focusing on Newton's notion and use of de fi nition. The resulting view is developmental. I argue that when Newton first wrote the Principia, he viewed the scholium's definitions as items of “natural philosophy.” By the time of the third edition, however, he came to view their methodological status differently; he viewed them as belonging to the more qualified “manner of geometers.” I explicate the two methods of natural inquiry and draw out their implications for Newton's account of space. (shrink)

We examine the contrast between the “Newtonian style” and the Cartesian, hypothetico-deductive method in order to expand on George Smith's account of working hypotheses and theory-mediation. We stress the pivotal role of theory-mediation in turning experience into well-defined phenomena and introduce the complementary notions of conditional and independent evidence. Conditional evidence is evidence in favor of an hypothesis that is based on phenomena that would not be constituted as phenomena without the hypothesis in question. Direct evidence is evidence based on (...) phenomena that are independently available. We use the distinction to interrogate the role of mathematical representation as the most basic constitutive posit of the Newtonian style, as the working hypothesis that enables all further theory-mediation. Our primary examples are Newton's struggles with motion in fluids and his defense of the Laws of Motion. (shrink)

A semantics with plural entitles and plural times accounts for cumulative relations between plural arguments and temporal expressions. The semantics equips nominal, verbal and sentential meanings with temporal context variables and treats temporal modifiers as temporal generalized quantifiers; cumulative conjunction, however, takes place at types lower than generalized quantifiers. The mediation of temporal context variables allows cumulative relations to percolate between an argument in a main clause and one in a temporal clause, in apparent violation of locality restrictions. Plural times (...) form a semilattice structure imposed on the set of intervals; no interaction is observed between this and the internal temporal structure of intervals. (shrink)

The paradigmatic bases, which sustain traditional western psychological interpretative efforts, need not be just a footnote to Plato. In this paper we introduce the Talmudic interpretative perspective, which we use to point at some weaknesses we identify in contemporary research imaginings. While the empiricist approach may be traced to Plato and the interpretative and the critical approaches may be traced to Heraclitus, we argue that the Talmudic approach is a differentiated and unique perspective that, because of its non-epistemic nature, its (...) dialogical character, and its recognition of two intermingled levels of interpretation, can make an important contribution to new ways of thinking about understanding and meaning in research. (shrink)

All families are political, each in its own way. Nevertheless, the diversity of family politics has not negated, by and large, patriarchal influence on the Political Family. This Article introduces the Political Family as a key concept in a scholarly and activist movement in family law studies which I identify as Critical Family Law. In Part I a reminder is offered that “alternative families” have existed since the dawn of history. However, I argue that despite constant changes in the configuration (...) of the family, for the most part all family forms have adhered to patriarchy. Part II offers a brief overview of some of the central themes in contemporary critical study of family law. I show how dichotomies such as private/public and intervention/autonomy have lain at the basis of the definition of the family since antiquity, constantly shifting the very meaning of the family across time, cultures and legal traditions, but rarely challenging its patriarchal ideology. Such challenges necessitate a critical look at the language of rights and obligations within the family, in acknowledgment that this very discourse is already saturated with ideology and biased preconceptions. Under the umbrella of “Critical Family Law,” I explore the potential for promoting such a shift, discussing articles in this issue. In memory of Paula Ettelbrick, 1955-2011. (shrink)

We argue that a conflict between two conceptions of “quantity of matter” employed in a corollary to proposition 6 of Book III of the Principia illustrates a deeper conflict between Newton’s view of the nature of extended bodies and the concept of mass appropriate for the theoretical framework of the Principia. We trace Newton’s failure to recognize the conflict to the fact that he allowed for the justification of natural philosophical claims by two types of a posteriori, empiricist methodologies. Newton's (...) thoughts on these methodologies demonstrate that his natural philosophy continued to develop after the publication of the first edition of Principia and that De Grav should be understood as an early, and not necessarily representative, text. (shrink)

The introduction considers the state of scholarship on empiricism as a philosophical and historical category, particularly as it pertains to experimental philosophy. It concludes that empiricism properly understood is a rich category encompassing epistemic, semantic, methodological, experimental, and moral elements. Its richness makes it a suitable lens through which to account for actual historical complexity. The introduction relates the category to the work of Sir Isaac Newton, who influenced all of empiricism’s elements.

Teaching Newtonian physics involves the replacement of students’ ideas about physical situations with precise concepts appropriate for mathematical applications. This paper focuses on the concepts of ‘matter’ and ‘mass’. We suggest that students, like some pre-Newtonian scientists we examine, use these terms in a way that conflicts with their Newtonian meaning. Specifically, ‘matter’ and ‘mass’ indicate to them the sorts of things that are tangible, bulky, and take up space. In Newtonian mechanics, however, the terms are defined by Newton’s Second (...) Law: ‘mass’ is simply a measure of the acceleration generated by an impressed force. We examine the relationship between these conceptions as it was discussed by Newton and his editor, Roger Cotes, when analyzing a series of pendulum experiments. We suggest that these experiments, as well as more sophisticated computer simulations, can be used in the classroom to sufficiently differentiate the colloquial and precise meaning of these terms. (shrink)

I embark on the writing of this short note not as an expert in ethics or a seasoned war analyst but rather as an involved observer nudged into the spotlight by a colleague’s overestimation of my insight into the Israel–Hamas conflict. I approach this task with scepticism yet hoping to morph it into a form of therapy. My own therapy, a means to break the shackles of silence that have gripped not only myself but, I suspect, many others in Israel.

: Although Galileo's struggle to mathematize the study of nature is well known and oft discussed, less discussed is the form this struggle takes in relation to Galileo's first new science, the science of the second day of the Discorsi. This essay argues that Galileo's first science ought to be understood as the science of matter—not, as it is usually understood, the science of the strength of materials. This understanding sheds light on the convoluted structure of the Discorsi's first day. (...) It suggests that the day's meandering discussions of the continuum, infinity, the vacuum, and condensation and rarefaction establish that a formal treatment of the "eternal and necessary" properties of matter is possible; i.e., that matter as such can be considered mathematically. This would have been a necessary, and indeed revolutionary, preliminary to the mathematical science of the second day because matter itself was thought in the Aristotelian tradition to be responsible for the departure of natural bodies from the unchanging and thus mathematizable character of abstract objects. In addition, the first day establishes that when considered physically, these properties account for matter's force of cohesion and resistance to fracture. This essay closes by showing that this dual style of reasoning accords with the conceptual structure of mixed mathematics. (shrink)

This paper addresses the phenomenon of judicial greatness by developing a general concept of greatness and applying it to law. Under the view offered in the paper, greatness is connected to theoretical or methodological diversification. When applied to adjudication, this means that great judges are revered because they successfully make a prima facie case for their novel adjudicative methods. This is not a judicial duty but rather a voluntary project. However, once a judge succeeds in making such a prima facie (...) case, he is exempt from other judicial duties. This thesis challenges many theories of judicial duty, which do not allow normative room for supererogatory actions in law. The paper demonstrates these claims by discussing two paradigmatic great judges – Chief Justice Marshall and Justice Holmes. (shrink)

The effect of upper bounds on message delivery times in a computer network upon the dynamics of knowledge gain is investigated. Recent work has identified centipedes and brooms—causal structures that combine message chains with time bound information—as necessary conditions for knowledge gain and common knowledge gain, respectively. This paper shows that, under the full-information protocol, these structures are both necessary and sufficient for such epistemic gain. We then apply this analysis to gain insights into the relation between “everyone knows” and (...) common knowledge. We prove a tight threshold on the depth k, beyond which Ek G (everyone in G knows nested to depth k) collapses into CG (common knowledge), when this knowledge concerns the occurrence of a spontaneous event. The threshold depends on the size of the group G of agents, as well as the time that has elapsed since the event of interest occurred. The existence of such a threshold is not guaranteed for all protocols, which is demonstrated here by presenting a counterexample in which no such threshold exists. (shrink)

The creation of a "market for virtue" and social responsibility is dependent on the flow of information from the corporation to the responsible agents. To achieve a free flow of information, excessive, missing and unreliable information must be avoided. More generally, a market for virtue should make it possible to create the appropriate means to signal true commitments and enable informed agents to know how to effectively use their limited resources for deploying market power that rewards and sanctions the corporations (...) that deserve such responses. The underlying assumption of this query is that if corporations in fact compete among themselves in the dimension of social responsibility, then some corporations will identify ways of demonstrating credibility of both efforts and results. The purpose of publishing codes of conduct and annual Corporate Social Responsibility reports would be to improve the level of information that is needed for the market for virtue to function. In order to assess the existence of a competitive market for virtue, the Article analyzes the codes and associated documents of sixteen multinational companies in three industries — textile, petrochemical and automobile. The Article finds some differences between labor and environmental norms, both within each of the sectors, as well as between sectors. However, the major finding casts doubt on the very assumption that labor and environmental norms are shaped by a market for virtue. Contrarily, the Article sheds new light on alternative reasons for developing social norms in corporations and rethinks the purpose of CSR reports. (shrink)

I argue that Isaac Newton's De Gravitatione should not be considered an authoritative expression of his thought about the metaphysics of space and its relation to physical inquiry. I establish the following narrative: In De Gravitatione (circa 1668–84), Newton claimed he had direct experimental evidence for the work's central thesis: that space had "its own manner of existing" as an affection or emanative effect. In the 1710s, however, through the prodding of Roger Cotes and G. W. Leibniz, he came to (...) see that this evidence relied on assumptions that his own Principia rendered unjustifiable. Consequently, he (i) revised the conclusions he explicitly drew from the experimental evidence, (ii) rejected the idea that his spatial metaphysics was grounded in experimental evidence, and (iii) reassessed the epistemic status of key concepts in his metaphysics and natural philosophy. The narrative I explore shows not only that De Gravitatione did not constitute the metaphysical backdrop of the Principia as Newton ultimately understood it, but that it was the Principia itself that ultimately lead to the demise of key elements of De Gravitatione. I explore the implications of this narrative for Andrew Janiak's and Howards Stein's interpretations of Newton's metaphysics. (shrink)

Newton’s Regulae philosophandi—the rules for reasoning in natural philosophy—are maxims of causal reasoning and induction. This essay reviews their significance for Newton’s method of inquiry, as well as their application to particular propositions within the Principia. Two main claims emerge. First, the rules are not only interrelated, they defend various facets of the same core idea: that nature is simple and orderly by divine decree, and that, consequently, human beings can be justified in inferring universal causes from limited phenomena, if (...) only fallibly. Second, the rules make substantive ontological assumptions on which Newton’s argument in the Principia relies. (shrink)

Abstract:This essay presents and discusses how James Rennel (1742–1830), a royal cartographer in eighteenth-century Bengal and father of British Modern Geography, presented and discussed the biblical concept of "exile" as a "practice" for the benefit of the empire. Following Rennell's readings in Biblical and Classical texts, this essay shows how Rennell intervened in contemporary European debates about Jews and trade.

What is sovereignty? Often taken for granted or seen as the ideology of European states vying for supremacy and conquest, the concept of sovereignty remains underexamined both in the history of its practices and in its aesthetic and intellectual underpinnings. Using global intellectual history as a bridge between approaches, periods, and areas, The Scaffolding of Sovereignty deploys a comparative and theoretically rich conception of sovereignty to reconsider the different schemes on which it has been based or renewed, the public stages (...) on which it is erected or destroyed, and the images and ideas on which it rests. The essays in The Scaffolding of Sovereignty reveal that sovereignty has always been supported, complemented, and enforced by a complex aesthetic and intellectual scaffolding. This collection takes a multidisciplinary approach to investigating the concept on a global scale, ranging from an account of a Manchu emperor building a mosque to a discussion of the continuing power of Lenin’s corpse, from an analysis of the death of kings in classical Greek tragedy to an exploration of the imagery of “the people” in the Age of Revolutions. Across seventeen chapters that closely study specific historical regimes and conflicts, the book’s contributors examine intersections of authority, power, theatricality, science and medicine, jurisdiction, rulership, human rights, scholarship, religious and popular ideas, and international legal thought that support or undermine different instances of sovereign power and its representations. (shrink)

Scientists are once again worried about ideologically driven bad science. We explain that this problem results from the conjunction of two worthy values that make science susceptible to recurrence of such situations. The solution is to acknowledge the social, political, economic, and ideological frameworks in which science is embedded.

Accounts of Hobbes’s ‘system’ of sciences oscillate between two extremes. On one extreme, the system is portrayed as wholly axiomtic-deductive, with statecraft being deduced in an unbroken chain from the principles of logic and first philosophy. On the other, it is portrayed as rife with conceptual cracks and fissures, with Hobbes’s statements about its deductive structure amounting to mere window-dressing. This paper argues that a middle way is found by conceiving of Hobbes’s _Elements of Philosophy_ on the model of a (...) mixed-mathematical science, not the model provided by Euclid’s _Elements of Geometry_. I suggest that Hobbes is a test case for understanding early-modern system-construction more generally, as inspired by the structure of the applied mathematical sciences. This approach has the additional virtue of bolstering, in a novel way, the thesis that the transformation of philosophy in the long seventeenth century was heavily indebted to mathematics, a thesis that has increasingly come under attack in recent years. (shrink)

I have been teaching qualitative research in education at The Hebrew University of Jerusalem for some years now. I have a sense that dealing with the issues of research methodology is of importance if we do indeed consider anthropology and qualitative methods to have something to contribute to improve the world in which we live. I write this rather short note out of a commitment to empirical research in the social sciences, emphasizing that which is observed and experienced, and recognizing (...) the complexity of studying that which is human. I reflect on my experience as a learner looking for ways to understand educational practice through methods able to capture its complexity. I then reflect on my experience as a teacher of anthropology and education, and consider the problems I encounter when trying to share my trade with my students. I hint at the potential connection between the political organizations within which we evolve and the paradigmtic perspectives which seem to become an obstacle in overcoming traditional empirical perspectives in the social sciences in general and in education in particular. Last, I consider multiple literacies as tools which might help us realize the problems mentioned and emphasize that these do not belong only in the world outside but also inside our immediate academic settings. (shrink)