One of the distinguishing features of mathematics is the exceptional level of consensus among mathematicians. However, an analysis of what mathematicians agree on, how they achieve this agreement, and the relevant historical conditions is lacking. This paper is a programmatic intervention providing a preliminary analysis and outlining a research program in this direction.First, I review the process of ‘negotiation’ that yields agreement about the validity of proofs. This process most often does generate consensus, however, it may give rise to another (...) kind of disagreement: whether the original and new proof are effectively the same, leading to potential disagreement about the validity of the original proof.Second, I historicize the phenomenon of consensus. I show that in earlier European mathematics and other mathematical cultures, consensus about the validity of arguments was substantially weaker or conceived differently than it is today. This means that contemporary consensus about the validity of mathematical proofs should be explained by historical changes in mathematical practice.Finally, I conjecture what brought about the contemporary form of mathematical consensus. Since a sharp rise in consensus occurs around the turn of the 20th century, it makes sense to explain this consensus by the concurrent formalization of mathematics. However, this explanation has a major flaw: it explains a really existing phenomenon (consensus) by something that hardly ever happens (writing proofs in formal languages). I will therefore explain the ways in which formalization does enter mathematical practice so as to account for contemporary forms of mathematical consensus. (shrink)

This paper studies Paul Cohen’s philosophy of mathematics and mathematical practice as expressed in his writing on set-theoretic consistency proofs using his method of forcing. Since Cohen did not consider himself a philosopher and was somewhat reluctant about philosophy, the analysis uses semiotic and literary textual methodologies rather than mainstream philosophical ones. Specifically, I follow some ideas of Lévi-Strauss’s structural semiotics and some literary narratological methodologies. I show how Cohen’s reflections and rhetoric attempt to bridge what he experiences as an (...) uncomfortable tension between reality and the formal by means of his notion of intuition. (shrink)

Self-regulation refers to the self's ability to control its own thoughts, emotions, and actions. Through self-regulation, we consciously control how much we eat, whether we give in to impulse, task performance, obsessive thoughts, and even the extent to which we allow ourselves recognition of our emotions. This work provides a synthesis and overview of recent and long-standing research findings of what is known of the successes and failures of self-regulation. People the world over suffer from the inability to control their (...) finances, their weight, their emotions, their craving for drugs, their sexual impulses, and more. The United States in particular is regarded by some observers as a society addicted to addiction. Therapy and support groups have proliferated not only for alcoholics and drug abusers but for all kinds of impulse control, from gambling to eating chocolate. Common to all of these disorders is a failure of self-regulation, otherwise known as "self-control." The consequences of these self-control problems go beyond individuals to affect family members and society at large. In Losing Control, the authors provide a single reference source with comprehensive information on general patterns of self-regulation failure across contexts, research findings on specific self-control disorders, and commentary on the clinical and social aspects of self-regulation failure. Self-control is discussed in relation to what the "self" is, and the cognitive, motivational, and emotional factors that impinge on one's ability to control one's "self." Discusses the importance of the concept of self-regulation to general issues of autonomy and identity Encompasses self-control of thoughts, feelings, and actions Contains a special section on the control of impulses and appetites First book to integrate recent research into a broad overview of the area. (shrink)

Ancient prayers exist in a rich variety of often unexamined forms, and so they require a comprehensive study. This volume includes diverse scholars, who reveal the wondrous breadth of prayerful religious traditions from the first to the fifteenth centuries.

First Published in 2001. Routledge is an imprint of Taylor & Francis, an informa company.

When we read, we do not fixate on each word! How does that work? By deep theory those sorts of decisions must be the result of complex decisions involving the specific “word,” the linguistic context in which it appears, and visual information. But is reading really all that difficult? After all, simple heuristics models of reading seem to do sort of okay by only considering the additive effects of word and context. Entropy measures do well at predicting word “skipping” and (...) suggest that “word frequency” may play the dominant role in the “decision” to skip or not skip! (shrink)

Despite its internal divisions and the uncertainty surrounding many of its foundations, there is a growing consensus that the on‐going search for an alternative model of the mind finds a minimal theoretical identity in the pursuit of an anti‐Cartesian conception of mental phenomena. Nevertheless, this anti‐Cartesianism remains more or less explicitly committed to the neo‐Brentanian idea that intentionality is an essential feature of the mental—an idea that has prevailed since the advent of modern cognitive science in the 1950s. An issue (...) of compatibility is thereby raised, as neo‐Brentanism arguably sides with cognitive Cartesianism. The main goal of the paper is to put into full light one specific aspect of this largely unperceived problem of compatibility by arguing that the neo‐Brentanian property of intentionality is an essentially representational one that runs counter to the salient anti‐representationalism of anti‐Cartesianism. And, that this representational essence confronts the search for alternative models of the mind of an anti‐Cartesian kind with the following theoretical issue: To what extent is it possible to devise a non‐Brentanian property of intentionality, particularly one that is fully dissociated from the property of representation? This issue is shown to be much deeper and more difficult than it looks once the nature of representation is properly apprehended; it seems to be still waiting for an answer in the current search for an alternative model of the mind, if only because it has not yet be set in fully adequate terms. (shrink)

Islamic building codes require mosques to face Mecca. The further Islam spreads, the more apt are believers to fall into a quandary. X faces Y only when the front of X is closer to Y than any other side of X. So the front of the mosque should be oriented along a shortest path to Mecca. Which way is that? Does the path to Mecca tunnel through the earth? Or does the path follow the surface of the earth?

Can the early Yogācāra be said to present a systematic theory of meaning? The paper argues that Sthiramati’s bhāṣya on Vasubandhu’s Triṃśikā, in which he argues that all language-use is metaphorical, indeed amounts to such a theory, both because of the text’s engagement with the wider Indian philosophical conversation about reference and meaning and by virtue of the questions it addresses and its motivations. Through a translation and analysis of key sections of Sthiramati’s commentary I present the main features of (...) this theory of meaning and discuss the ways in which it is distinct from Vasubandhu’s ideas. I demonstrate how this theory of meaning enabled Sthiramati to present a unique understanding of discourse that distinguishes between varying levels of truth within the conventional realm. This understanding sat well with the Yogācāra soteriological and theoretical needs, and most importantly, enabled him to establish the meaningfulness of the school’s own metaphysical discourse. Securing this meaningfulness was especially important to Sthiramati in meeting the challenge posed by the radical conventionalism of the Madhyamaka, and his response as I interpret it suggests that one of the main disputes between the early Yogācāra with the Mādhyamika, at least as reflected in the Triṃśikā-bhāṣya, in fact turns on linguistic rather than ontological issues. (shrink)

The decades before and after the turn of the twentieth century, like those surrounding the turn of the twenty-first, are often understood as periods of globalization. The two periods share key features that characterize the global as a motif, including high mobility of goods, services, people, ideas and, perhaps most centrally, capital. An important distinguishing feature between the periods is the monetary regime: the gold standard for the turn of the twentieth century; managed flexibility for the turn of the twenty-first. (...) This paper examines the legal infrastructure of these two monetary regimes in order to illuminate two distinct yet related issues. The first is the connection between the form of rulemaking and the means of isolating monetary policy decisions from political influence. The second is the role of the monetary regime in mediating value. Both the gold standard and the managed flexibility regime aim to shield money from partisan intervention, but they do so in different ways; attention to the legal framework sheds light on how these differing regimes pursue the goal of insulating money from politics. (shrink)

The computational hypothesis was formulated with due concern for limits and is consistent with imposed intelligibility doctrines. Theories are products of scientific work that impose human classifications and formalisms on nature. The claim that “cognitive agents are dynamical systems” is untenable. Dynamical formalisms imposed on a natural system, given an approximate fit, serve as an explanatory framework and render a represented system predictable and intelligible.

Sooner or later, every paradox is accused of equivocation. Usually sooner. For equivocation is a simple, well understood fallacy. People first try to explain a mystery in terms of what is familiar. If postulating a simple ambiguity fails, more subtle ambiguities will be postulated. Those who persist with this diagnosis elaborate the charge of equivocation into an esoteric form.

This paper explores the semiotic status of algebraic variables. To do that we build on a structuralist and post-structuralist train of thought going from Mauss and L vi-Strauss to Baudrillard and Derrida. We import these authors' semiotic thinking from the register of indigenous concepts (such as mana), and apply it to the register of algebra via a concrete case study of generating functions. The purpose of this experiment is to provide a philosophical language that can explore the openness of mathematical (...) signs to reinterpretation, and bridge some barriers between philosophy of mathematics and critical approaches to knowledge. (shrink)

We introduce a hitherto overlooked phenomenon in the cognitive and psycholinguistic study of metaphors that we termed imposed metaphoricity. We propose that a metaphorical reading can be imposed on a given expression regardless of its semantic content. We suggest that there is a class of constructions that impose metaphorical interpretation. We present findings from three experiments and from corpus-based analyses that support our proposal. Experiments 1–2 compared interpretations of expressions that can have both a literal and a metaphorical meaning when (...) embedded in a standard metaphorical form and in a form that imposes metaphoricity. In Experiment 3 we examine reaction time to such forms in an attempt to identify interference of form with early metaphorical processing. Two corpus-based analyses characterize the use of these two metaphorical constructions in natural language. We discuss the independence of metaphoricity from semantics, as demonstrated by forms that impose metaphorical interpretations. (shrink)

Editor's Preface Roy Wood Sellars's contributions to philosophy have been epochal. The originator and persistent elaborator of critical realism, ...

SummaryThis article surveys recent scholarship on the early history of British geology. It finds that many of the developments called for a decade ago by Dr Eyles and Dr Rappaport have not yet been realized. However, there has been progress in the broader understanding of geological ideas in their historical context, and a start has been made on the social history of the science. Some suggestions are offered as to a field of problems for the future, and a selective bibliography (...) of secondary materials, thematically arranged, is appended. (shrink)

We are printing, by kind permission of the Law Commission, two sections of the report of the Law Commission on injuries to unborn children. This report was the result of a request to the Law Commission by the Lord Chancellor at the time (Lord Hailsham of Saint Marylebone) to advise on `what the nature and extent of civil liability for antenatal injury should be'. The Law Commission followed its usual practice in such circumstances of consulting various bodies and obtaining expert (...) advice on the subject and then embodying the results in a working paper (Working Paper No. 47 - injuries to unborn children) published on 19 January 1973, which preceded their report (Cmnd 5709). Meanwhile a Royal Commission is considering much wider issues of civil liability for injury (including antenatal injury) but the terms of reference for the Law Commission were much narrower and confined to the position of children injured before birth. In the section relating to the present law the report makes it clear that it is probable that liability under the common law already exists. The Scottish Law Commission has also issued a report (Cmnd 5371). They were given different terms of reference and came to somewhat different conclusions. We are printing from this long report the paragraphs discussing the medical background and the summary of recommendations. As will be evident on reading the paragraphs on the medical background to injuries to the unborn child, events are moving very rapidly, particularly in the study of congenital defects and the effects of drugs but the problems of proof present great difficulty. Other causes of injury to the unborn child are better known to the general public: for example, those following the illness, infection and disease of the mother during pregnancy, injury caused in attempted termination of pregnancy and the risks resulting from the mother's condition. The summary of the recommendations sets out very clearly the legal position of the unborn child, as the Law Commission sees it, arising from injury before birth, the final conclusion being that `legislation is desirable'. These extracts from the report, apart from their intrinsic interest, lead on to the paper by Mr Kennedy and Dr Edwards in which they set out their criticisms of it, and provide quick references to the original document. (shrink)