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)

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

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)

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.

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)

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 report on some recent work centered on attempts to understand when one set is more random than another. We look at various methods of calibration by initial segment complexity, such as those introduced by Solovay [125], Downey, Hirschfeldt, and Nies [39], Downey, Hirschfeldt, and LaForte [36], and Downey [31]; as well as other methods such as lowness notions of Kučera and Terwijn [71], Terwijn and Zambella [133], Nies [101, 100], and Downey, Griffiths, and Reid [34]; higher level randomness notions (...) going back to the work of Kurtz [73], Kautz [61], and Solovay [125]; and other calibrations of randomness based on definitions along the lines of Schnorr [117].These notions have complex interrelationships, and connections to classical notions from computability theory such as relative computability and enumerability. Computability figures in obvious ways in definitions of effective randomness, but there are also applications of notions related to randomness in computability theory. For instance, an exciting by-product of the program we describe is a more-or-less naturalrequirement-freesolution to Post's Problem, much along the lines of the Dekker deficiency set. (shrink)

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 ...

The usual treatment of a dinner table utterance of ‘Can you pass the salt?’ is that it involves an indirect request to pass the salt as well as a direct question about the hearer’s ability to do so: an indirect speech act. These are held to involve two illocutionary forces and two illocutionary acts. Rod Bertolet has raised doubts about whether consideration of such examples warrants the postulation of indirect speech acts and illocutionary forces other than the literal ones. In (...) a recent article, Mary Kate McGowan, Shan Shan Tam, and Margaret Hall claim to show that these doubts are unfounded. The purpose of this paper is to show that they have not established this. (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.

Traditionally, Sociology has identified its subject matter as a distinct set - social phenomena - that can be taken as quite different and largely disconnected from potentially relevant disciplines such as Psychology, Economics or Planetary Ecology. Within Sociology and Human Ecology, Smith and Jenks argue that this position is no longer sustainable. Indeed, exhorting the reader to confront human ecology and its relation to the physical and biological environments, Smith and Jenks suggest that the development of understanding with (...) regards to the position occupied by the social requires, in turn, an extension of the component disciplines and methodologies of a 'new' human socio-ecology. Aiming to evoke critical change to the possibility, status and range of the social sciences whilst also offering essential grounding for inter-disciplinary engagement, Sociology and Human Ecology will appeal to postgraduate students and postdoctoral researchers interested in fields such as Social Theory, Socio-Biology and Ecological Economics. (shrink)

As a natural example of a 1-random real, Chaitin proposed the halting probability Ω of a universal prefix-free machine. We can relativize this example by considering a universal prefix-free oracle machine U. Let [Formula: see text] be the halting probability of UA; this gives a natural uniform way of producing an A-random real for every A ∈ 2ω. It is this operator which is our primary object of study. We can draw an analogy between the jump operator from computability theory (...) and this Omega operator. But unlike the jump, which is invariant under the choice of an effective enumeration of the partial computable functions, [Formula: see text] can be vastly different for different choices of U. Even for a fixed U, there are oracles A =* B such that [Formula: see text] and [Formula: see text] are 1-random relative to each other. We prove this and many other interesting properties of Omega operators. We investigate these operators from the perspective of analysis, computability theory, and of course, algorithmic randomness. (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)

Explains why the debate initiated by Stephen Lloyd Smith’s plea to jettison the so-called ‘Standard Account of Method’ ––the conventional wisdom of how research philosophy and methodology ought to be taught to management students––is of the utmost importance to the teaching of management studies in British universities. Identifies a fully-developed presentation of the SAM framework in a well-considered and widely-used textbook––‘Research Methods for Managers’ by John Gill and Phil Johnson––and demonstrates that the book’s argument is both logically and scholarly defective. (...) Identifies the SAM as a form of dogmatic rationalism; one that is oblivious to the possibility of applying deductive inference in the service of a critical rationalism. Outlines the logical role of deductive testing in empirical research and demonstrates that there need be no great divide between nomothetic and ideographic research problems once appropriate distinctions are drawn between different forms of explanation. Nonetheless, questions the relevance of these research problems to the concerns of practising managers by highlighting the contrast, as made by philosophers, between social science and social technology. Concludes that the continued presentation and defence of the SAM, as the conventional wisdom of how research philosophy and methodology ought to be taught to management students, is thoroughly lamentable. (shrink)

Despite the evidence showing the promise of HIV treatment as prevention (TasP) in reducing HIV incidence, a variety of ethical questions surrounding the implementation and “scaling up” of TasP have been articulated by a variety of stakeholders including scientists, community activists and government officials. Given the high profile and potential promise of TasP in combatting the global HIV epidemic, an explicit and transparent research priority-setting process is critical to inform ongoing ethical discussions pertaining to TasP.

We study for each computably bounded $\Pi ^0_1$ class P the set of degrees of c.e. paths in P. We show, amongst other results, that for every c.e. degree a there is a perfect $\Pi ^0_1$ class where all c.e. members have degree a. We also show that every $\Pi ^0_1$ set of c.e. indices is realized in some perfect $\Pi ^0_1$ class, and classify the sets of c.e. degrees which can be realized in some $\Pi ^0_1$ class as exactly (...) those with a computable representation. (shrink)

Philosophical arguments stemming from the public health ethics arena suggest that public health interventions ought to be subject to normative inquiry that considers relational values, including concepts such as solidarity, reciprocity and health equity. As yet, however, the extent to which ‘public’ values influence the ‘autonomous’ decisions of the public remains largely unexplored. Drawing on interviews with 50 men in Vancouver, Canada, this study employs a critical discourse analysis to examine participants’ decisions and motivations to voluntarily access HIV testing and/or (...) to accept a routine HIV test offer. Within a sub-set of interviews, a transactional discourse emerged in which the decision to test features an arrangement of ‘giving and receiving’. Discourses related to notions of solidarity emphasize considerations of justice and positions testing as a ‘public’ act. Lastly, ‘individualistic’ discourses focused on individual-level considerations, with less concern for the broader public ‘good’. These findings underscore how normative dimensions pertaining to men’s decisions to test are dialectically interrelated with the broader social and structural influences on individual and collective health-related behaviour, thereby suggesting a need to advance an explicit empirical-normative research agenda related to population and public health intervention research. (shrink)

We describe punctual categoricity in several natural classes, including binary relational structures and mono-unary functional structures. We prove that every punctually categorical structure in a finite unary language is${\text {PA}}(0')$-categorical, and we show that this upper bound is tight. We also construct an example of a punctually categorical structure whose degree of categoricity is$0''$. We also prove that, with a bit of work, the latter result can be pushed beyond$\Delta ^1_1$, thus showing that punctually categorical structures can possess arbitrarily complex (...) automorphism orbits.As a consequence, it follows that binary relational structures and unary structures are not universal with respect to primitive recursive interpretations; equivalently, in these classes every rich enough interpretation technique must necessarily involve unbounded existential quantification or infinite disjunction. In contrast, it is well-known that both classes are universal for Turing computability. (shrink)

A problem is a multivalued function from a set of instances to a set of solutions. We consider only instances and solutions coded by sets of integers. A problem admits preservation of some computability-theoretic weakness property if every computable instance of the problem admits a solution relative to which the property holds. For example, cone avoidance is the ability, given a noncomputable set A and a computable instance of a problem ${\mathsf {P}}$, to find a solution relative to which A (...) is still noncomputable.In this article, we compare relativized versions of computability-theoretic notions of preservation which have been studied in reverse mathematics, and prove that the ones which were not already separated by natural statements in the literature actually coincide. In particular, we prove that it is equivalent to admit avoidance of one cone, of $\omega $ cones, of one hyperimmunity or of one non- $\Sigma ^{0}_1$ definition. We also prove that the hierarchies of preservation of hyperimmunity and non- $\Sigma ^{0}_1$ definitions coincide. On the other hand, none of these notions coincide in a nonrelativized setting. (shrink)

Věda a vědecká práce jsou dle obecně přijatého axiomu považovány za něco, co generuje vědecké objevy, a tím pozitivně posouvá lidskou civilizaci směrem dopředu. Vědeckým objevům v určitých oblastech však vytváří bariéry základní vlastnost široké skupiny jevů - neměřitelnost. Zejména ve společenských vědách je neměřitelnost jevu spojena s absencí tzv. tvrdých dat, která omezuje okruh metod, jež by mohly být aplikovány v cestě za vědeckým objevem. Existuje však metoda, která si klade za cíl eliminovat tento deficit a s jejíž pomocí (...) lze, pří dodržování zásad správného použití, kvantifikovat proměnné, které se zdají být na první pohled neměřitelné. Tato metoda se nazývá škálování. Text příspěvku pojednává o přístupu filozofie a metodologie vědy k neměřitelným faktorům a jejich potenciální kvantifikaci pomocí jednorozměrné šalovací metody nazvané Likertovo škálování. Stať paperu se věnuje popisu této metody, analýze jejích kladů a záporů a detailnímu návodu na její aplikaci. V závěru je zodpovězena otázka, zda má pro vědce smysl věnovat čas studiu nových metod (např. právě škálování), když toto pro vědce vzdělaného v určitém oboru generuje velmi vysoké náklady obětované příležitosti? Studium nových metod smysl rozhodně má, neboť obětovaná příležitost je dle výkladu středního proudu v ekonomii označována jako "druhá nejlepší varianta" za podmínky dokonalé informovanosti o dostupných alternativách. Bez uspokojivé znalosti studovaných nových metod však nemůžeme označit doposud aplikovanou metodu za nejvhodnější - to je hlavní argument podporující studium nových metod. (shrink)

A step-by-step guide to develop your idea from the first spark to the finished product, with charming illustrations recalling the whimsy and imagination of childhood.