In Plato on the Unity of the Virtues, Rod Jenks argues that while Plato makes several attempts to show how virtue is one, he deliberately fails to secure this because he thinks the way in which the virtues are both one and many is finally ineffable.

The author focuses on Plato's reliance on images as a way of communicating abstract doctrinal points to his audience.

This work is an introduction to logic, covering what is most commonly taught in the first term of a two-term sequence in logic at four-year colleges and universities. It is designed for use by community college students who plan to transfer credits to four-year institutions. The material covered seeks to maintain logic's place in philosophical thought systems, and avoids political examples in order to appeal to reason and study rather than ill-conceived jokes that often offend students' varying policitcal beliefs. This (...) work concludes with studies in proof constructions and rules and provides explanations of various grading decisions commonly made in logic courses, a unique feature helpful to students and teachers alike. (shrink)

Moral expertise in the Laches -- The Laches -- Socratic ignorance and socratic wisdom -- Vituperation -- Virtue and craft -- Expertise in the Charmides -- Ironies -- The definitions -- Quietness -- Modesty -- Doing or making one's own -- Doing, not making, one's own -- Doing good things -- Knowing oneself -- Knowledge of itself and all other knowledges -- Good, evil, and temperance -- Expertise in republic -- Preliminaries -- Republic viii -- The text -- Mathematical indeterminacy (...) -- Metaphysical necessity -- Justice "writ large" -- The most formidable question -- Preliminaries -- The context of the argument -- The most formidable argument itself -- The image -- Not knowing the things we know -- Attending to words -- Larger issues -- The third man argument. (shrink)

In the first chapter of The Contribution of Socratic Method and Plato’s Theory of Truth to Plato Scholarship, Rod Jenks argues that since Socrates and Plato take the Socratic elenchus to establish truths and the Socratic elenchus can only establish consistency, Socrates and Plato must be committed to a coherence theory of truth. Jenks denies any explicit recognition of such a commitment in Plato’s early dialogues. The claim is rather that “early Socratic practice as recorded by Plato makes (...) sense only against the backdrop of the assumption of a coherence theory of truth”. It is, according to Jenks, Plato’s solution to “the problem of the elenchus.” In the middle and later dialogues, Jenks argues, Plato exposes the philosophical foundations of this assumption and addresses various problems associated with it, only to return to the Socratic elenchus—now supported by a philosophically grounded CTT—in the Philebus. (shrink)

This paper attempts to undermine Michael McKinsey’s Important objections to Kripke’s attempts to refute cluster versions of description theories of name reference. McKinsey argues that Kripke Ignores descriptions to which a clustser theorist might appeal In constructing his counterexamples, but that these same descriptions are what guide our intuitions In evaluating the examples. I argue that the descriptions McKinsey offers are question-begging, and thus of no help to a cluster theorist. In a second brief section, I offer an argument designed (...) to show that even If McKinsey*s descriptions were legitimate, the views Kripke endorses in "Naming and Necessity" would be supported rather than vitiated. (shrink)

Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.

In Part 1 the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, (...) time, processes, knowledge and belief, obligation and permission. Accessible, authoritative, and assured, Modal Logics and Philosophy requires no more background than the completion of a standard introductory logic course. It will be welcomed not only by students looking for a bridge between introductory logic texts and the high-level technical literature but as a guide to, and exploration of, work at the forefront of logic and philosophy. (shrink)

The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, "Modal Logics and Philosophy" (...) places its emphasis firmly on showing how useful modal logic can be as a tool for formal philosophical analysis. In part 1 of the book, the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, obligation and permission. (shrink)

Robert I. Soare, Automorphisms of the Lattice of Recursively Enumerable Sets. Part I: Maximal Sets.Manuel Lerman, Robert I. Soare, $d$-Simple Sets, Small Sets, and Degree Classes.Peter Cholak, Automorphisms of the Lattice of Recursively Enumerable Sets.Leo Harrington, Robert I. Soare, The $\Delta^0_3$-Automorphism Method and Noninvariant Classes of Degrees.

First Published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.

From the myths of the ancient world to the Middle Ages to Darwin and beyond, Preece captures the most telling and fascinating accounts of humankind's ...

Construed broadly as interpretation theory, hermeneutics could be understood to encompass all modes of interpretation (textual or otherwise), including any kind of literary criticism, from Aristotle's poetics to the New Criticism of the 1950s, as well as the French tradition of structuralism and even perhaps Derridean poststructural thought. Although Gadamer and Ricoeur both recognize the poetic work or, at least, lyric poetry, as belonging to a special class of literature, they do display somewhat different attitudes toward it. For Gadamer, one (...) of the hallmarks of the eminent text is its un‐translatability. That is, all literary works resist translation to one degree or another, but lyric poetry defies it altogether. In Part I of Truth and Method, Gadamer lays out the history of aesthetics and takes issue with the kind of “aesthetic consciousness” that takes the work of art as an object of study. (shrink)

Ever since Saul Kripke and others developed a semantic interpretation for modal logic, 'possible worlds' has been a much debated issue in contemporary metaphysics. To propose the idea of a possible world that differs in some way from our actual world - for example a world where the grass is red or where no people exist - can help us to analyse and understand a wide range of philosophical concepts, such as counterfactuals, properties, modality, and of course, the notions of (...) possibility and necessity. This book examines the ways in which possible worlds have been used as a framework for considering problems in logic and argument analysis. The book begins with a non-technical introduction to the basic ideas of modal logic in terms of Kripke's possible worlds and then moves on to a discussion of 'possible for' and 'possible that'. The central chapters examine questions of meaning, epistemic possibility, temporal logic, metaphysics, and impossibility. Girle also investigates how the idea of a possible world can be put to use in different areas of philosophy, the problems it may raise, and the benefits that can be gained. (shrink)

Ever since Saul Kripke and others developed a semantic interpretation for modal logic, 'possible worlds' has been a much debated issue in contemporary metaphysics. To propose the idea of a possible world that differs in some way from our actual world - for example a world where the grass is red or where no people exist - can help us to analyse and understand a wide range of philosophical concepts, such as counterfactuals, properties, modality, and of course, the notions of (...) possibility and necessity. This book examines the ways in which possible worlds have been used as a framework for considering problems in logic and argument analysis. The book begins with a non-technical introduction to the basic ideas of modal logic in terms of Kripke's possible worlds and then moves on to a discussion of 'possible for' and 'possible that'. The central chapters examine questions of meaning, epistemic possibility, temporal logic, metaphysics, and impossibility. Girle also investigates how the idea of a possible world can be put to use in different areas of philosophy, the problems it may raise, and the benefits that can be gained. (shrink)

We argue that the Soros account of reflexivity does not provide a clear-cut distinction between a social science such as economics and the physical sciences. It is pointed out that the participants who attempt to learn from refutations of conjectures in the Soros world are likely to be haunted by the Duhem–Quine problem of conjointness of hypotheses and unfocused refutation. On a more constructive note, we argue that models of inductive learning, in which participants form conjectures on the basis of (...) strictly limited information sets, can capture the basic thrust of the Soros position. The conjectures are in motion, as the participants attempt to avoid those that are systematically wrong, and there is something vague and uncertain about what can be learned from experience and refutations. The only notion of market efficiency in this world is one contingent on the strictly limited and varied information sets in play. Finally we present a mathematical model and numerical simulations that help justify the causal relationship between reflexivity and far-from-equilibrium dynamics postulated by Soros. (shrink)

In their book, Darwinism Evolving: Systems Dynamics and the Genealogy of Natural Selection, Depew and Weber (1995) argued for the need to address the relationship between self-organization and natural selection in evolutionary theory, and focused on seven “visions” for doing so. Recently, Batten et al. (2008) in a paper in this journal, entitled “Visions of evolution: self-organization proposes what natural selection disposes,” picked up the issue with the work of Depew and Weber as a starting point. While the efforts of (...) both sets of authors are to be commended, there are substantive errors in both the presentations of my work and of my work with colleagues (one of the “visions” discussed) that undermine theirs. My purpose here is to correct the errors in question, thereby removing the undermining effects and in so doing reassert the position my colleagues and I first advanced more than two decades ago, and that I still stand by and argue for today. The central points are as follows: (1) Self-organization or spontaneous ordering is a process of selection; (2) this selection process is governed by a “physical selection principle”; (3) this principle is the law of maximum entropy production; and (4) natural selection is a special case where the components are replicating. (shrink)

We construct a $\Delta^0_2$ degree which fails to be computably enumerable in any computably enumerable set strictly below $\emptyset'$.

We classify the asymptotic densities of the sets according to their level in the Ershov hierarchy. In particular, it is shown that for, a real is the density of an n‐c.e. set if and only if it is a difference of left‐ reals. Further, we show that the densities of the ω‐c.e. sets coincide with the densities of the sets, and there are ω‐c.e. sets whose density is not the density of an n‐c.e. set for any.

In their book, Darwinism Evolving: Systems Dynamics and the Genealogy of Natural Selection, Depew and Weber argued for the need to address the relationship between self-organization and natural selection in evolutionary theory, and focused on seven “visions” for doing so. Recently, Batten et al. in a paper in this journal, entitled “Visions of evolution: self-organization proposes what natural selection disposes,” picked up the issue with the work of Depew and Weber as a starting point. While the efforts of both sets (...) of authors are to be commended, there are substantive errors in both the presentations of my work and of my work with colleagues that undermine theirs. My purpose here is to correct the errors in question, thereby removing the undermining effects and in so doing reassert the position my colleagues and I first advanced more than two decades ago, and that I still stand by and argue for today. The central points are as follows: Self-organization or spontaneous ordering is a process of selection; this selection process is governed by a “physical selection principle”; this principle is the law of maximum entropy production; and natural selection is a special case where the components are replicating. (shrink)