We study the complexity of proving the Pigeon Hole Principle in a monotone variant of the Gentzen Calculus, also known as Geometric Logic. We prove a size-depth trade-off upper bound for monotone proofs of the standard encoding of the PHP as a monotone sequent. At one extreme of the trade-off we get quasipolynomia -size monotone proofs, and at the other extreme we get subexponential-size bounded-depth monotone proofs. This result is a consequence of deriving the basic properties of certain monotone formulas (...) computing the Boolean threshold functions. We also consider the monotone sequent expressing the Clique-Coclique Principle defined by Bonet, Pitassi and Raz [9]. We show that monotone proofs for this sequent can be easily reduced to monotone proofs of the one-to-one and onto PHP, and so CLIQUE also has quasipolynomia -size monotone proofs. As a consequence of our results, Resolution, Cutting Planes with polynomially bounded coefficients, and Bounded-Depth Frege are exponentially separated from the monotone Gentzen Calculus. Finally, a simple simulation argument implies that these results extend to the Intuitionistic Gentzen Calculus. Our results partially answer some questions left open by P. Pudlák. (shrink)

Resumen: En este escrito defiendo la realización de seminarios de lectura como una experiencia educativa innovadora que permite una mejor comprensión de los textos. En el marco de la educación contra Auschwitz, se propone la lectura conjunta de Si esto es un hombre, obra testimonial de Primo Levi. Mediante este seminario, se busca promover en los estudiantes la deliberación activa, el diálogo, la transmisión de valores y la importancia de escuchar a las víctimas. Palabras clave: seminario de lectura, Primo Levi, (...) Auschwitz, testimonio. English title: Educating against Auschwitz with a reading groupAbstract: In this paper, I argue that reading groups can involve innovative teaching experiences which allow for a better understanding of books. Within the framework of education against Auschwitz, I propose the group reading of If this is a man—a testimonial book by Primo Levi. The aim is to promote in our students active deliberation, dialogue, transmission of values, and the importance of listening to the victims. Keywords: reading group, Primo Levi, Auschwitz, testimony. (shrink)

La categorización del discurso radiofónico está determinada por los modelos estructurales sobre los que se articula el primer capítulo de la historia del broadcast, que concluye, finalizada la Segunda Guerra Mundial, con la irrupción de la televisión y la inmediata reestructuración del sistema mediático. Las estrategias de legitimación de la programación radiofónica, del vínculo pragmático que aspira a crear este nuevo dominio cultural, son esenciales en la evaluación del mapa disciplinar en el que se inscribe la fundamentación de la teoría (...) de la radio. En la formulación de las distintas propuestas teóricas y metodológicas son determinantes las políticas de regulación, los modelos de negocio de la economía radiofónica y la función política y cultural reconocida a la radio. La investigación «administrativa» norteamericana construyó un modelo de análisis cuantitativo de aquel prodigioso broadcast esencial para el desarrollo de la audimetría mediática analógica y habilitó los primeros procedimientos para un análisis del like/dislike capital en el ámbito televisivo, primero, y, después, en el de las plataformas audiovisuales digitales y las redes sociales. El análisis cuantitativo sigue contando hoy, necesariamente, con los procedimientos tradicionales de la audimetría analógica, mientras prosigue la irresistible ascensión de la radio digital, que convierte en su ámbito aquella incierta medición en automático registro online. Los interrogantes suscitados por el análisis cualitativo desarrollado en tiempos aciagos, en Europa y en Estados Unidos, se mantienen vivos. El proceso de digitalización del broadcast, concluido en el caso de la televisión e inconcluso en el de la radio, la extensión del podcast y la multiplicación de los dispositivos de transmisión obligan a retomar una controversia que se dispone a cumplir un siglo. (shrink)

A defence of the idea that there are sui generis duties of love: duties, that is, that we owe to people in virtue of standing in loving relationships with them. I contrast this non‐reductionist position with the widespread reductionist view that our duties to those we love all derive from more generic moral principles. The paper mounts a cumulative argument in favour of the non‐reductionist position, adducing a variety of considerations that together speak strongly in favour of adopting it. The (...) concluding section connects this debate with larger issues in moral theory concerning the general idea of obligation. (shrink)

We argue that thoughts are structures of concepts, and that concepts should be individuated by their origins, rather than in terms of their semantic or epistemic properties. Many features of cognition turn on the vehicles of content, thoughts, rather than on the nature of the contents they express. Originalism makes concepts available to explain, with no threat of circularity, puzzling cases concerning thought. In this paper, we mention Hesperus/Phosphorus puzzles, the Evans-Perry example of the ship seen through different windows, and (...) Mates cases, and we believe that there are many additional applications. (shrink)

: Sabır, hayatın zorlukları karşısında daha sakin davranma ve problemlerle mantıksal bir biçimde başa çıkabilmeyi sağlayan önemli bir erdemdir. Din ise içerdiği ritüeller ve öğretiler yoluyla insana pozitif duygular kazandırmakta ve sabır davranışını geliştirmektedir. Dini kaynaklarda sıkıntılar karşısında sabretme birçok yerde geçmektedir. Bu sebeple çalışmamız çağımızın en önemli problemlerinden biri olan şiddete ve kızgınlığa karşı koruyucu gücü bulunan sabrın gelişiminde dinin etkisini koyması açısından önem taşımaktadır. Bu çalışmanın amacı üniversite öğrencilerinde dindarlık ile sabır ilişkisini tespit etmektir. Çalışmanın örneklemi Nevşehir Hacı (...) Bektaş Veli Üniversitesi İlahiyat fakültesinde öğrenim görmekte olan toplam 230 gönüllü öğrenciden oluşmaktadır. Çalışmada veri toplama araçları olarak Kişisel Bilgi Formu, Dini Yönelim Ölçeği ve Sabır Ölçeği kullanılmıştır. Anketler yüz yüze gerçekleştirilmiş ve anketleri cevaplama süresi 15-20 dakika sürmüştür. Uygulama yapmadan önce çalışmaya katılanlara verilerin gizli kalacağı söylenmiştir. Araştırmada ulaşılan verilerin analizinde SPSS (v23) yazılımı tercih edilmiştir. Bu çalışmada öncelikli olarak cinsiyet, yaş, sosyo-ekonomik durum, baba eğitim düzeyi ve anne eğitim düzeyi değişkenlerine bakılmış ve ardından da sabır ve dindarlığın demografik değişkenler ile korelasyonu üzerinde durulmuştur. Son olarak da dindarlıkla sabır arasındaki ilişki belirlenmiştir. Yapılmış olan analizlerde korelasyon, t-testi, tek yönlü ANOVA ve Pearson korelasyon testleri uygulanmış ve önemli bulgular çalışmada sunulmuştur. Yapılan araştırmadan özetle şu bilgiler elde edilmiştir: Kadınların dini yönelim düzeyi ile erkeklerin dini yönelim düzeyleri arasında istatiksel olarak anlamlı bir fark bulunamamıştır. Yine kadınların sabır puanları ile erkeklerin sabır puanları arasında anlamlı bir fark tespit edilememiştir. Örneklem yaş değişkeni açısından ele alındığında ise 18-19 yaş arasında olanların hem sorgulama dini yönelim hem de dini yönelim puanları 22 yaş üstü olanlara göre daha düşük çıkmış ve bu durum anlamlı bir fark oluşturmuştur. Sosyo-ekonomik durum düzeyinde ise hem dini yönelim puanları hem de sabır ve alt boyut puanları açısından anlamlı bir fark bulunamamıştır. Baba eğitim durumu değişkenine göre katılımcıların hem dini yönelim hem de sabır puanları arasında anlamlı bir ilişki tespit edilememiştir. Anne eğitim durumu değişkenine göre kişilerarası sabır alt boyut puanı ve sabır puanı bakımından istatistiksel olarak anlamlı bir fark bulunmaktadır. Buna göre; annesi ilköğretim mezunu olanların kişilerarası sabır alt boyut puanı ve sabır puanı, annesi ortaöğretim mezunu olanlara göre daha yüksek bulunmuştur. Bu veriler ışığında araştırmamızın literatüre katkı sağlayacağı düşünülmüştür. (shrink)

R.G. Collingwood defined historical knowledge as essentially ‘scientific’, and saw the historian's task as the ‘re-enactment of past thoughts’. The author argues the need to go beyond Collingwood, first by demonstrating the authenticity of available evidence, and secondly, using Namier as an example, by considering methodology as well as epistemology, and the need to relate past thoughts to their present context. The ‘law of the consumption of time’ encourages historians to focus on landmark events, theories and generalisations, thus breaking from (...) Collingwood's emphasis on fidelity to past ideas and interpreting the past from the concepts of the present. This conflict can only be reconciled by the study of historiography. (shrink)

In this article, which is the first of two to examine the ideas of R. S. Peters on moral education, consideration is given to his justificatory arguments found in Ethics and Education. Here he employs presupposition arguments to show to what anyone engaging in moral discourse is committed. The result is a group of procedural principles which are recommended to be employed in moral education. This article is an attempt to examine the presupposition arguments Peters employs, to comment on the (...) procedural principles he believes are presupposed, and to consider the strength of the presupposition argument. My conclusion is that Peters's arguments fail to establish the conclusion he arrives at, and that any gains from the form of argument he uses are hollow. (shrink)

R. S. Peters on Education and Ethics reissues seven titles from Peters' life's work. Taking an interdisciplinary approach, the books are concerned with the philosophy of education and ethics. Topics include moral education and learning, authority and responsibility, psychology and ethical development and ideas on motivation amongst others. The books discuss more traditional theories and philosophical thinkers as well as exploring later ideas in a way which makes the subjects they discuss still relevant today.

We show that the c.e. Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degrees are not an upper semilattice. We prove that if M is an r-maximal set, A is an arbitrary set and M≡Q1,NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M \equiv{}_ {Q_{1,N}}A}$$\end{document}, then M≤mA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M\leq{}_{m} A}$$\end{document}. Also, if M1 and M2 are r-maximal sets, A and B are major subsets of M1 and M2, respectively, and M1\A≡Q1,NM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus} A\equiv{}_{Q_{1,N}}M_{2}{\setminus} B}$$\end{document}, then M1\A≡mM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus}A\equiv{}_{m}M_{2}{\setminus} B}$$\end{document}. If M1 and M2 are r-maximal sets and M10,M11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0},\,M_{1}^{1}}$$\end{document} and M20,M21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{2}^{0},\,M_{2}^{1}}$$\end{document} are nontrivial splittings of M1 and M2, respectively, then M10≡Q1,NM20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{Q_{1,N}}M_{2}^{0}}$$\end{document} if and only if M10≡1M20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{1}M_{2}^{0}}$$\end{document}. From this result follows that if A and B are Friedberg splitting of an r-maximal set, then the Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degree of A contains only one c.e. 1-degree. (shrink)

Architect-scientist R. Buckminster Fuller talks about the discovery of the eternal pattern that is operative in the universe.

Peters's views on moral education are to be found in several books and articles written over a period of about 20 years. Two essential elements of his ideas are what he calls procedural principles and basic rules. This article is an attempt to consider his recommendations, particularly in terms of any practical assistance that can be derived from them for those interested in moral education. Close examination reveals some inconsistencies, vagueness and difficulties which suggest problems for his procedural approach and (...) raise the issue of whether alternative, more positive efforts should be reconsidered. (shrink)

A longish (12 page) discussion of Richard Sorabji's excellent book, with a further discussion of what it means for a theory of emotions to be a cognitive theory.

I had a strange dream, or half-waking vision, not long ago. I found myself at the top of a mountain in the mist, feeling very pleased with myself, not just for having climbed the mountain, but for having achieved my life's ambition, to find a way of answering moral questions rationally. But as I was preening myself on this achievement, the mist began to clear, and I saw that I was surrounded on the mountain top by the graves of all (...) those other philosophers, great and small, who had had the same ambition, and thought they had achieved it. And I have come to see, reflecting on my dream, that, ever since, the hard-working philosophical worms have been nibbling away at their systems and showing that the achievement was an illusion. True, their skeletons, indigestible to worms, remained, and were surprisingly similar to one another. But I was led to think again about what one can, and what one cannot, achieve in this direction. (shrink)

[R. M. Sainsbury] Evans argued that most ordinary proper names were Russellian: to suppose that they have no bearer is to suppose that they have no meaning. The first part of this paper addresses Evans's arguments, and finds them wanting. Evans also claimed that the logical form of some negative existential sentences involves 'really' (e.g. 'Hamlet didn't really exist'). One might be tempted by the view, even if one did not accept its Russellian motivation. However, I suggest that Evans gives (...) no adequate account of 'really', and I point to unclarities in Wiggins's similar, but distinct, attempt to use 'really' in the logical form of true negative existentials. /// [David Wiggins] Evans was not wrong (I maintain) to say that the senses of genuine proper names invoke and require objects. Names in fiction or hypothesis mimic such names. Pace Evans, Sainsbury and free logicians, proper names are scopeless. (Evans's 'Julius' is not a name.) Names create a presumption of existential generalization. In sentences such as 'Vulcan does not really exist', that presumption is bracketed. The sentence specifies by reference to story or report a concept identical with Vulcan and declares it be really uninstantiated. (The sentence, which partakes of play, is a kind of palimpsest.) It is explained why this second level view of 'exists' is to be preferred. (shrink)

On what grounds will the rational man become a Christian? It is often assumed by many, especially non-Christians, that he will become a Christian if and only if he judges that the evidence available to him shows that it is more likely than not that the Christian theological system is true, that, in mathematical terms, on the evidence available to him, the probability of its truth is greater than half. It is the purpose of this paper to investigate whether or (...) not this is a necessary and sufficient condition for the rational man to adopt Christianity. (shrink)

This is a first summary of the author's writing and publishing on the topic of fearism--and, Desh Subba's optimistic "philosophy of fearism.".

In this article we show that it is possible to completely classify the degrees of r.e. bases of r.e. vector spaces in terms of weak truth table degrees. The ideas extend to classify the degrees of complements and splittings. Several ramifications of the classification are discussed, together with an analysis of the structure of the degrees of pairs of r.e. summands of r.e. spaces.