Directional deep brain stimulation contacts provide greater spatial flexibility for therapy than traditional ring-shaped electrodes, but little is known about longitudinal changes of impedance and orientation. We measured monopolar and bipolar impedance of DBS contacts in 31 patients who underwent unilateral subthalamic nucleus deep brain stimulation as part of a randomized study. At different follow-up visits, patients were assigned new stimulation configurations and impedance was measured. Additionally, we measured the orientation of the directional lead during surgery, immediately after surgery, and (...) 1 year later. Here we contrast impedances in directional versus ring contacts with respect to local anatomy, active stimulation contact, and over time. Directional contacts display larger impedances than ring contacts. Impedances generally increase slightly over the first year of therapy, save for a transient decrease immediately post-surgery under general anesthesia during pulse generator placement. Local impedances decrease at active stimulation sites, and contacts in closest proximity to internal capsule display higher impedances than other anatomic sites. DBS leads rotate slightly in the immediate postoperative period but otherwise remain stable over the following year. These data provide useful information for setting clinical stimulation parameters over time. (shrink)

The main aim of this work is to evaluate whether Boolos’ semantics for second-order languages is model-theoretically equivalent to standard model-theoretic semantics. Such an equivalence result is, actually, directly proved in the “Appendix”. I argue that Boolos’ intent in developing such a semantics is not to avoid set-theoretic notions in favor of pluralities. It is, rather, to prevent that predicates, in the sense of functions, refer to classes of classes. Boolos’ formal semantics differs from a semantics of (...) pluralities for Boolos’ plural reading of second-order quantifiers, for the notion of plurality is much more general, not only of that set, but also of class. In fact, by showing that a plurality is equivalent to sub-sets of a power set, the notion of plurality comes to suffer a loss of generality. Despite of this equivalence result, I maintain that Boolos’ formal semantics does not committ second-order languages to second-order entities, contrary to standard semantics. Further, such an equivalence result provides a rationale for many criticisms to Boolos’ formal semantics, in particular those by Resnik and Parsons against its alleged ontological innocence and on its Platonistic presupposition. The key set-theoretic notion involved in the equivalence proof is that of many-valued function. But, first, I will provide a clarification of the philosophical context and theoretical grounds of the genesis of Boolos’ formal semantics. (shrink)

Razón, poesía, historia.--La cuestión del estoicismo español.--El querer.

Dibujar el pensamiento de Seneca es dibujar su figura viva, trazar el esquema de su persona. Seneca es un mediador que para alzarse sobre nosotros necesita de nuestra necesidad, pues solo apoyado en nuestra indigencia tiene sentido. Maria Zambrano lleva a cabo un lucido estudio de la figura y significacion del pensador cordobes y presenta una seleccion de sus escritos.

Two thoughts about the concept of number are incompatible: that any zero or more things have a (cardinal) number, and that any zero or more things have a number (if and) only if they are the members of some one set. It is Russell's paradox that shows the thoughts incompatible: the sets that are not members of themselves cannot be the members of any one set. The thought that any (zero or more) things have a number is Frege's; the thought (...) that things have a number only if they are the members of a set may be Cantor's and is in any case a commonplace of the usual contemporary presentations of the set theory that originated with Cantor and has become ZFC. In recent years a number of authors have examined Frege's accounts of arithmetic with a view to extracting an interesting subtheory from Frege's formal system, whose inconsistency, as is well known, was demonstrated by Russell. These accounts are contained in Frege's formal treatise Grundgesetze der Arithmetik and his earlier exoteric book Die Grundlagen der Arithmetik. We may describe the two central results of the recent re-evaluation of his work in the following way: Let Frege arithmetic be the result of adjoining to full axiomatic second-order logic a suitable formalization of the statement that the Fs and the Gs have the same number if and only if the F sand the Gs are equinumerous. (shrink)

This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency. Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos (...) does is to show how the concepts, techniques, and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self-referential' sentences constructed in their proof. The book explores the effects of reinterpreting the notions of necessity and possibility to mean provability and consistency. (shrink)

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a (...) simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual. (shrink)

This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; ...

George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work (...) on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume. (shrink)

This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book has become a classic because of its accessibility to students without a mathematical background, and because it covers not simply the staple topics of an intermediate logic course such as Godel's Incompleteness Theorems, (...) but also a large number of optional topics from Turing's theory of computability to Ramsey's theorem. John Burgess has now enhanced the book by adding a selection of problems at the end of each chapter, and by reorganising and rewriting chapters to make them more independent of each other and thus to increase the range of options available to instructors as to what to cover and what to defer. (shrink)

The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate in modal logic that has (...) persisted for at least thirty years between the followers of C. I. Lewis and W. V. O. Quine. The author employs semantic methods developed by Saul Kripke in his analysis of modal logical systems. The book will be of interest to advanced undergraduate and graduate students in logic, mathematics and philosophy, as well as to specialists in those fields. (shrink)

Hilary Putnam is one of the world’s leading philosophers. His highly original and often provocative ideas have set the agenda for a variety of debates in philosophy of science, philosophy of mind and philosophy of language. His now famous philosophical thought experiments, such as the ‘Twin earth’ and ‘the brains in the vat’ have become part of the established canon in philosophy and cognitive science. _Reading Putnam_ is an outstanding overview and assessment of Hilary Putnam’s work by a team of (...) international contributors, and includes replies by Putnam himself. Divided into clear sections, it contains chapters on key aspects of Putnam’s large body of writing, including: Scientific realism and the changes that Putnam’s thought has undergone on this topic analyticity and ontology, including the important interconnections between the views of Putnam and Quine Putnam’s arguments concerning externalist views of meaning and reference, questions of conceptual relativity, and his preoccupation with ethics through a denial of the fact–value dichotomy Putnam’s developing views on perception. Offering an excellent survey of Putnam’s work, _Reading Putnam_ is essential for those studying philosophy of mind, philosophy of language, and philosophy of science, as well as for anyone interested in contemporary philosophy. (shrink)

George Boolos; IX*—Saving Frege from Contradiction, Proceedings of the Aristotelian Society, Volume 87, Issue 1, 1 June 1987, Pages 137–152, https://doi.org/10.

In this festschrift for the eminent philosopher Hilary Putnam, a team of distinguished philosophers write on a broad range of topics and thus reflect the remarkably fertile and provocative research of Putnam himself. The volume is not merely a celebration of a man, but also a report on the state of philosophy in a number of significant areas. The essays fall naturally into three groups: a central core on the theme of conventionality and content in the philosophy of mind, language, (...) and science, and two smaller sections on the relationship of ethics and language, and on the philosophy of logic and aesthetics. (shrink)

Positive reappraisal strategies have been found to reduce negative affect following the recall of negative personal events. This study examined the restorative effect of two mood-repair instructions (self-compassion vs benefit-focused reappraisal) and a control condition with no instructions following a negative Mood Induction Procedure by using the guided recall of a negative autobiographical event. A total of 112 university students participated in the online study (81% women, Mage: 21.0 years). Immediately following the negative memory recall, participants were randomised to each (...) condition [(self-compassion: n = 36, benefit-focused: n = 39) or a control condition (n = 37)]. Repeated measures ANOVAs 3 (Repair condition) × 3 (Time of mood assessment: pre-recall, post-recall, post-regulation) showed that, as expected, negative mood (sadness, shame, and guilt) worsened significantly after the guided recall in all groups (p <.001). After the mood-repair intervention, participants in the self-compassion and benefit-focused conditions showed a significant reduction in negative mood (p <.019), while such improvement was not observed in the control group. Self-compassion and benefit-focused reappraisal functioned similarly as mood repair strategies after experiencing negative affect induced by the recall of negative personal memories. Implications in the context of autobiographical memory biases are discussed. (shrink)

In this festschrift for the eminent philosopher Hilary Putnam, a team of distinguished philosophers write on a broad range of topics and thus reflect the remarkably fertile and provocative research of Putnam himself. The volume is not merely a celebration of a man, but also a report on the state of philosophy in a number of significant areas. The essays fall naturally into three groups: a central core on the theme of conventionality and content in the philosophy of mind, language, (...) and science, and two smaller sections on the relationship of ethics and language, and on the philosophy of logic and aesthetics.In this festschrift for the eminent philosopher Hilary Putnam, a team of distinguished philosophers write on a broad range of topics and thus reflect the remarkably fertile and provocative research of Putnam himself. The volume is not merely a celebration of a man, but also a report on the state of philosophy in a number of significant areas. The essays fall naturally into three groups: a central core on the theme of conventionality and content in the philosophy of mind, language, and science, and two smaller sections on the relationship of ethics and language, and on the philosophy of logic and aesthetics. (shrink)

George Boolos; IX*—Saving Frege from Contradiction, Proceedings of the Aristotelian Society, Volume 87, Issue 1, 1 June 1987, Pages 137–152, https://doi.org/10.

A close look at Frege's proof in "Foundations of Arithmetic" that every number has a successor. The examination reveals a surprising gap in the proof, one that Frege would later fill in "Basic Laws of Arithmetic".