Euclidean geometry, as presented by Euclid, consists of straightedge-and-compass constructions and rigorous reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. This involves finding “uniform” constructions where normally a case distinction is used. For example, in finding a perpendicular to line L through point p, one usually uses two different constructions, “erecting” a perpendicular when p is on L, and “dropping” a perpendicular when p is not on L, but in (...) constructive geometry, it must be done without a case distinction. Classically, the models of Euclidean geometry are planes over Euclidean fields. We prove a similar theorem for constructive Euclidean geometry, by showing how to define addition and multiplication without a case distinction about the sign of the arguments. With intuitionistic logic, there are two possible definitions of Euclidean fields, which turn out to correspond to different versions of the parallel postulate.We consider three versions of Euclid’s parallel postulate. The two most important are Euclid’s own formulation in his Postulate 5, which says that under certain conditions two lines meet, and Playfair’s axiom, which says there cannot be two distinct parallels to line L through the same point p. These differ in that Euclid 5 makes an existence assertion, while Playfair’s axiom does not. The third variant, which we call the strong parallel postulate, isolates the existence assertion from the geometry: it amounts to Playfair’s axiom plus the principle that two distinct lines that are not parallel do intersect. The first main result of this paper is that Euclid 5 suffices to define coordinates, addition, multiplication, and square roots geometrically.We completely settle the questions about implications between the three versions of the parallel postulate. The strong parallel postulate easily implies Euclid 5, and Euclid 5 also implies the strong parallel postulate, as a corollary of coordinatization and definability of arithmetic. We show that Playfair does not imply Euclid 5, and we also give some other independence results. Our independence proofs are given without discussing the exact choice of the other axioms of geometry; all we need is that one can interpret the geometric axioms in Euclidean field theory. The independence proofs use Kripke models of Euclidean field theories based on carefully constructed rings of real-valued functions. “Field elements” in these models are real-valued functions. (shrink)

This article answers two questions (posed in the literature), each concerning the guaranteed existence of proofs free of double negation. A proof is free of double negation if none of its deduced steps contains a term of the formn(n(t)) for some term t, where n denotes negation. The first question asks for conditions on the hypotheses that, if satisfied, guarantee the existence of a double-negation-free proof when the conclusion is free of double negation. The second question asks about the existence (...) of an axiom system for classical propositional calculus whose use, for theorems with a conclusion free of double negation, guarantees the existence of a double-negation-free proof. After giving conditions that answer the first question, we answer the second question by focusing on the Lukasiewicz three-axiom system. We then extend our studies to infinite-valued sentential calculus and to intuitionistic logic and generalize the notion of being double-negation free. The double-negation proofs of interest rely exclusively on the inference rule condensed detachment, a rule that combines modus ponens with an appropriately general rule of substitution. The automated reasoning program Otter played an indispensable role in this study. (shrink)

We use Herbrand’s theorem to give a new proof that Euclid’s parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions to give a short, simple, and intuitively appealing proof.

In this multiple case study, the authors compare the instruction of two high school civics teachers during the 2012 Presidential Election. Both were highly-qualified practitioners who worked in schools with one-to-one laptop initiatives, creating an environment in which access to digital technology ceased to be an issue. Although both teachers regularly used technology in their classrooms, the authors describe stark differences in the complexity and authenticity of their instruction, which the authors attribute to the teachers’ technological pedagogical content knowledge (TPCK). (...) The authors conclude by discussing implications for better understanding TPCK within civics instruction, specifically in classrooms with one-to-one laptop access. (shrink)

Under the assumption that all "rules" are recursive (ECT) the statement $\operatorname{Cont}(N^N,N)$ that all functions from N N to N are continuous becomes equivalent to a statement KLS in the language of arithmetic about "effective operations". Our main result is that KLS is underivable in intuitionistic Zermelo-Fraenkel set theory + ECT. Similar results apply for functions from R to R and from 2 N to N. Such results were known for weaker theories, e.g. HA and HAS. We extend not only (...) the theorem but the method, fp-realizability, to intuitionistic ZF. (shrink)

In this paper I outline the PAIR account of joint attention as a perceptual-practical, affectively charged intentional relation. I argue that to explain joint attention we need to leave the received understanding of propositions and propositional attitudes and the picture of content connected to it behind and embrace the notions of subject mode and position mode content. I also explore the relation between joint attention and communication.

Brouwer's positions about existence (reality) and truth are examined in the light of ninety years of scientific progress. Relevant results in proof theory, recursion theory, set theory, relativity, and quantum mechanics are used to cast light on the following philosophical questions: What is real, and how do we know it? What does it mean to say a thing exists? Can things exist that we can't know about? Can things exist that we don't know how to find? What does it mean (...) to say something is true? How can we know whether something is true? Can things be true that we can't ever know to be true? (shrink)

The pain -- I thought church would be different -- The pain goes so deep -- Where does all this pain come from? -- Nobody sees me -- I feel beat up in church -- I live in shame all the time -- I feel used -- I can't forgive -- The hope -- Will I ever get past the pain? -- Why do I feel so unsafe in church? -- I can't keep up with all the rules -- What's (...) wrong with these people? -- I just need to be perfect -- The church doesn't seem to care -- How do I find a good church? -- Hope beyond the pain -- Demonic lies and doctrines -- Learning to live in the kingdom of light. (shrink)

Morals from Motives develops a virtue ethics inspired more by Hume and Hutcheson's moral sentimentalism than by recently-influential Aristotelianism. It argues that a reconfigured and expanded "morality of caring" can offer a general account of right and wrong action as well as social justice. Expanding the frontiers of ethics, it goes on to show how a motive-based "pure" virtue theory can also help us to understand the nature of human well-being and practical reason.

The American Journal of Bioethics, Volume 12, Issue 7, Page 27-30, July 2012.

Western Australia has recently assumed an unaccustomed centrality in the minds of Australian policymakers. The recent resource boom briefly propelled WA to the forefront of national economic affairs. While this proved a relatively short-lived prominence, the emergence of WA at the centre of a putative ‘Indo-Pacific’ region promises to give it a more enduring strategic significance. This paper details how geopolitical and geoeconomic forces have shaped WA’s developmental history, and why they are likely to do so in the future as (...) well. (shrink)

This book fills a gap in studies of meaning by providing detailed case studies of attested corpus data on the meanings of words and phrases.

Theories of discourse bring to realism new ideas about how knowledge develops and how representations of reality are influenced. We gain an understanding of the conceptual aspect of social life and the processes by which meaning is produced. This collection reflects the growing interest realist critics have shown towards forms of discourse theory and deconstruction. The diverse range of contributions address such issues as the work of Derrida and deconstruction, discourse theory, Eurocentrism and poststructuralism. What unites all of the contributions (...) is a sense that it is essential to provide a realist alternative to the hitherto dominance of social constructionism, hermeneutics and postmodernism, over many of the issues discussed. By developing a realist perspective the different authors attempt to embed discourse within the structured nature of the reality of the world. Realism can situate language, discourse and ideology within context specific, or 'causally efficacious' circumstances. Realism can help to uncover issues of power, representation, and subjectivity and how discursive and other social practices produce real effects. This can help us understand the manner in which social structures are reproduced through various forms of ideology and discourse. And by knowing this, we can start to address questions concerning human emancipation and how the world is to be transformed. (shrink)

One of the more striking, surprising, and optimism-inducing features of the contemporary international system has been the decline of interstate war. The key question for students of international relations and comparative politics is how this happy state of affairs came about. In short, was this a universal phenomenon or did some regions play a more important and pioneering role in bringing about peaceful change? As part of the roundtable “International Institutions and Peaceful Change,” this essay suggests that Western Europe generally (...) and the European Union in particular played pivotal roles in transforming the international system and the behavior of policymakers. This helped to create the material and ideational conditions in which other parts of the world could replicate this experience, making war less likely and peaceful change more feasible. This argument is developed by comparing the experiences of the EU and the Association of Southeast Asian Nations and their respective institutional offshoots. The essay uses this comparative historical analysis to assess both regions’ capacity to cope with new security challenges, particularly the declining confidence in institutionalized cooperation. (shrink)

The definitive work on the philosophical nature and impact of the theories of Charles Darwin, written by a well-known authority on the history and philosophy of Darwinism. Broadly explores the theories of Charles Darwin and Darwin studies Incorporates much information about modern Biology Offers a comprehensive discussion of Darwinism and Christianity – including Creationism – by one of the leading authorities in the field Written in clear, concise, user-friendly language supplemented with quality illustrations Examines the status of evolutionary theory as (...) a genuine theory and its implications for philosophy, epistemology and ethics Provides a strong understanding of the philosophical nature and impact of Darwin's thought Holds wide appeal for general audiences outside the world of academic philosophy Strongly supports Darwinism and fully explores modern naturalistic explanations of religion. (shrink)

Michael Quante focuses on what Hegel has to say about such central concepts as action, person and will, and then brings these views to bear on contemporary debates in analytic philosophy. This book enables professional analytic philosophers and their students to understand the significance of Hegel's philosophy to contemporary theory of action. As such, it will contribute to the ever-increasing erosion of the barrier between the continental and analytic approaches to philosophy.

The guiding inspiration of this book is the attraction and distance that mark the relation between anthropology and philosophy. This theme is explored through encounters between individual anthropologists and particular regions of philosophy. Several of the most basic concepts of the discipline—including notions of ethics, politics, temporality, self and other, and the nature of human life—are products of a dialogue, both implicit and explicit, between anthropology and philosophy. These philosophical undercurrents in anthropology also speak to the question of what it (...) is to experience our being in a world marked by radical difference and otherness. In The Ground Between, twelve leading anthropologists offer intimate reflections on the influence of particular philosophers on their way of seeing the world, and on what ethnography has taught them about philosophy. Ethnographies of the mundane and the everyday raise fundamental issues that the contributors grapple with in both their lives and their thinking. With directness and honesty, they relate particular philosophers to matters such as how to respond to the suffering of the other, how concepts arise in the give and take of everyday life, and how to be attuned to the world through the senses. Their essays challenge the idea that philosophy is solely the province of professional philosophers, and suggest that certain modalities of being in the world might be construed as ways of doing philosophy. Contributors. João Biehl, Steven C. Caton, Vincent Crapanzano, Veena Das, Didier Fassin, Michael M. J. Fischer, Ghassan Hage, Clara Han, Michael Jackson, Arthur Kleinman, Michael Puett, Bhrigupati Singh. (shrink)

Divided into four parts, this treatise begins with well-known criticisms of nonreligious ethics and then develops an atheistic metaethics. In Part 2, Martin criticizes the Christian foundation of ethics, specifically the ’divine command theory’ and the idea of imitating the life of Jesus as the basis of Christian morality. Part 3 demonstrates that life can be meaningful in the absence of religious belief. Part 4 criticizes the theistic point of view in general terms as well as the specific Christian doctrines (...) of the atonement, salvation, and the resurrection. (publisher, edited). (shrink)

The Oxford Handbook of Metaphysics offers the most authoritative and compelling guide to this diverse and fertile field of philosophy. Twenty-four of the world's most distinguished specialists provide brand-new essays about 'what there is': what kinds of things there are, and what relations hold among entities falling under various categories. They give the latest word on such topics as identity, modality, time, causation, persons and minds, freedom, and vagueness. The Handbook's unrivaled breadth and depth make it the definitive reference work (...) for students and academics across the philosophical spectrum. (shrink)

This thought provoking book uncovers a crisis in the political imagination, a wide-spread failure to provide the passionate sense of community "in which our need for belonging can be met." Seeking the answers to fundamental questions, Michael Ignatieff writes vividly both about ideas and about the people who tried to live by them—from Augustine to Bosch, from Rosseau to Simone Weil. Incisive and moving, The Needs of Strangers returns philosophy to its proper place, as a guide to the art (...) of being human. (shrink)

We ordinarily suppose that there is a difference between having and failing to exercise a rational capacity on the one hand, and lacking a rational capacity altogether on the other. This is crucial for our allocations of responsibility. Someone who has but fails to exercise a capacity is responsible for their failure to exercise their capacity, whereas someone who lacks a capacity altogether is not. However, as Gary Watson pointed out in his seminal essay ’Skepticism about Weakness of Will’, the (...) idea of an unexercised capacity is much more difficult to make sense of than it initially appears. The aim of ’Rational Capacities’ is to provide the needed explication of this idea. (shrink)

Eldred offers a remedy to the consequences of ancient Greek misconceptions of time that are also entrenched in today’s mathematized physics. Here time is spatialized as the one-dimensionally linear ‘arrow of time’ for the sake of predicting and controlling movement. But such spatialized time distorts the phenomenon of time itself. An alternative, hermeneutic-phenomenological path begins with a pre-spatial concept of time that is genuinely three-dimensional. This paves the way for recasting who we are as humans in belonging, first of all, (...) to the free openness of 3D-temporality. This belonging enables temporally 3D-vision of the psyche that empowers us to see movement at all and reconcile its inherent contradictoriness. We are then also able to conceive ourselves no longer merely as internally cogitating, self-conscious subjects, but as engaged existentially in temporally 3D-interplay, mutually estimating and esteeming who we are. This unpredictable interplay is constrained, however, by being played out in the sociating medium of thingified value, the accumulative movement of thingified value having gained the upper hand in dictating our life-movements as well as our interplay with the earth. (shrink)

Der private, sehr gefahrdete Bucherbestand Friedrich Nietzsches gilt als ein besonders interessantes Beispiel einer Schriftstellerbibliothek des 19. Jahrhunderts.