In this chapter we introduce concepts for analyzing proofs, and for analyzing undergraduate and beginning graduate mathematics students’ proving abilities. We discuss how coordination of these two analyses can be used to improve students’ ability to construct proofs. -/- For this purpose, we need a richer framework for keeping track of students’ progress than the everyday one used by mathematicians. We need to know more than that a particular student can, or cannot, prove theorems by induction or contradiction or can, (...) or cannot, prove certain theorems in beginning set theory or analysis. It is more useful to describe a student’s work in terms of a finer-grained framework that includes various smaller abilities that contribute to proving and that can be learned in differing ways and at differing periods of a student’s development. (shrink)

Unsurpassed as a text for upper-division and beginning graduate students, Raman Selden's classic text is the liveliest, most readable and most reliable guide to contemporary literary theory. Includes applications of theory, cross-referenced to Selden's companion volume, Practicing Theory and Reading Literature.

This is a general reading of Callimachus' work within the socio-political context of Ptolemaic Alexandria. "Alibis" refers to the constitutionally expatriate nature of the populace and culture established there, which in Callimachus gives rise to a poetics based on the principles of displacement and convergence. Close analysis of a wide variety of passages, drawn principally from the epigrams, Aetia, and Hymns, demonstrates how the "order of the alibi" informs all major aspects of the poet's work, from the lexical make-up of (...) his texts to their larger narrative and thematic structure. Certain poems in the corpus, such as the Lock of Berenice and the Hymn to Apollo, not only require detailed knowledge of Greek literature, history, and religious institutions, but also draw extensively on Egyptian mythography and cultural models, which do not so much replace the Hellenic matter as-characteristically-cohabit with it. In this respect, Callimachus served both as a key architect of the new, multi-ethnic culture that the Ptolemies institutionalized in Egypt and as its most penetrating critic. (shrink)

Every art…needs its own critical organisation, and poetics will form a part of aesthetics as soon as aesthetics becomes the unified criticism of all of the arts instead of whatever it is now.1.

Aksumite elites electively identified themselves as “black” in relation to the paler integument of other Mediterranean peoples. Prior to the fourth century CE, the proper noun Aithiopía referred to the area of northern Sudan. Aksum, however, deliberately appropriated the Greek term for its own geopolitical purposes, partly as a way to write itself both into the grand narratives of Graeco-Roman history, where “Ethiopians” recurrently figure as morally “blameless,” as well as—with their conversion to Christianity—into Old and New Testamental eschatologies that (...) consistently position “Ethiopians” as first in the sight of God. This process of self-definition—achieved under the formative gaze of Hellenic, Roman, and Levantine Others—ultimately allowed ‘Ityȯpyā to become a key, if nonetheless still liminal and rogue, player in the post-Constantinian politico-religious arena, in such a way that both economic and cultural capital accrued to the benefit of Aksum. (shrink)

A complete translation of Aristotle's classic that is both faithful and readable, along with an introduction that provides the modern reader with a means of understanding this seminal work and its impact on our culture. In this volume, Joe Sachs (translator of Aristotle's _Physics, Metaphysics,_ and the _Nicomachean Ethics _)also supplements his excellent translation with well-chosen notes and glossary of important terms. Focus Philosophical Library translations are close to and are non-interpretative of the original text, with the notes and a (...) glossary intending to provide the reader with some sense of the terms and the concepts as they were understood by Aristotle’s immediate audience. (shrink)

Nudging works through dispositions to decide with specific heuristics, and has three component parts. A nudge is a feature of an environment that enables such a disposition; a person is nudged when such a disposition is triggered; and a person performs a nudged action when such a disposition manifests in action. This analysis clarifies an autonomy-based worry about nudging as used in public policy or for private profit: that a person’s ability to reason well is undermined when she is nudged. (...) Reasoning well is a component of self-guidance, which is an aspect of autonomy and so something there is reason to promote, preserve, or respect. However, a person can reason well when she is nudged: Many of these heuristics are good rules to reason with, and she can be flexible with respect to them when she takes there to be a better way to reason. Along the way, this paper uncovers several design specifications for responsible nudging, and discusses open empirical questions. However, nudging’s being compatible with reasoning well crystallizes a distinct worry about manipulation: that nudge designers can rely on nudged people guiding themselves toward the designers’ own ends. Manipulation of this sort exploits one aspect of autonomy (namely, self-guidance) to undermine autonomy in other respects. (shrink)

Selected Logic Papers, long out of print and now reissued with eight additional essays, includes much of the author's important work on mathematical logic and ...

`Folk Psychology' - our everyday talk of beliefs, desires and mental events - has long been compared with the technical language of `Cognitive Science'. Does folk psychology provide a correct account of the mental causes of our behaviour, or must our everyday terms ultimately be replaced by a language developed from computational models and neurobiology? This broad-ranging book addresses these questions, which lie at the heart of psychology and philosophy. Providing a critical overview of the key literature in the field, (...) including the seminal work of Fodor and Churchland, the author explores the classic `Frame Problem' and assesses the future prospects of cognitive science. The scope of the frame problem, touching on connec. (shrink)

_Selections_ seeks to provide an accurate and readable translation that will allow the reader to follow Aristotle's use of crucial technical terms and to grasp the details of his argument. Unlike anthologies that combine translations by many hands, this volume includes a fully integrated set of translations by a two-person team. The glossary--the most detailed in any edition--explains Aristotle's vocabulary and indicates the correspondences between Greek and English words. Brief notes supply alternative translations and elucidate difficult passages.

Some cognitive processes appear to have “phenomenal” properties that are directly revealed to the subject and not determined by physical properties. I suggest that the source of this appearance is the method by which our brain processes sensory information. The appearance is an illusion. Nonetheless, we are not mistaken when we judge that people sometimes fee lpain.

The _Physics_ is a foundational work of western philosophy, and the crucial one for understanding Aristotle's views on matter, form, essence, causation, movement, space, and time. This richly annotated, scrupulously accurate, and consistent translation makes it available to a contemporary English reader as no other does—in part because it fits together seamlessly with other closely associated works in the New Hackett Aristotle series, such as the _Metaphysics_, _De Anima_, and forthcoming _De Caelo_ and _On Coming to Be and Passing Away_. (...) Eventually the series will include all of Aristotle's works. Sequentially numbered endnotes provide the information most needed at each juncture, while a detailed Index of Terms indicates places where focused discussion of key notions occurs. An illuminating general Introduction describes the book that lies ahead, explaining what sort of work it is and what sorts of evidence it relies on. (shrink)

These seventeen lectures given in 1963 focus largely on Kant, 'a thinker in whose work the question of morality is most sharply contrasted with other spheres of existence'. After discussing a number of the Kantian categories of moral philosophy, Adorno considers other, seemingly more immediate general problems, such as the nature of moral norms, the good life, and the relation of relativism and nihilism. In the course of the lectures, Adorno addresses a wide range of topics, including: theory and practice, (...) ethics as bad conscience, the repressive character, the problem of freedom, dialectics in Kant and Hegel, the nature of reason, the moral law as a given, psychoanalysis, the element of the Absurd, freedom and law, the Protestant tradition of morality, Hamlet, self-determination, phenomenology, the concept of the will, the idea of humanity, The Wild Duck, and Nietzsche's critique of morality. (shrink)

Appearing in English for the first time, Schelling’s 1842 lectures develop the idea that many philosophical concepts are born of religious-mythological notions.

There are two alternative approaches to accommodating an agent-centered restriction against, say, φ-ing. One approach is to prohibit agents from ever φ-ing. For instance, there could be an absolute prohibition against breaking a promise. The other approach is to require agents both to adopt an end that can be achieved only by their not φ-ing and to give this end priority over that of minimizing overall instances of φ-ing. For instance, each agent could be required both to adopt the end (...) of minimizing their own promise-breakings and to give this end priority over that of minimizing promise-breakings overall. The former is what I’ll call the side-constraint approach, and the latter is what I’ll call the teleological approach. In this chapter, I argue that, when it comes to accommodating restrictions, we should (1) favor the teleological approach over the side-constraint approach, (2) favor an act-consequentialist approach over a non-consequentialist, teleological approach (such as Rossian pluralism), and (3) favor a Kantsequentialist approach over other act-consequentialist approaches, where Kantsequentialism is a version of act-consequentialism that holds that persons are ends-in-themselves who are inherently and unconditionally valuable and are, thus, owed our respect. (shrink)