The prime number theorem, established by Hadamard and de la Vallée Poussin independently in 1896, asserts that the density of primes in the positive integers is asymptotic to 1/ln x. Whereas their proofs made serious use of the methods of complex analysis, elementary proofs were provided by Selberg and Erdos in 1948. We describe a formally verified version of Selberg's proof, obtained using the Isabelle proof assistant.

In Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicative conditionals, most notably the proposals by de Finetti and Reichenbach on the one hand, and by Cooper and Cantwell on the other. Here we provide the proof theory for the resulting logics DF/TT and CC/TT, using tableau calculi and sequent calculi, and proving soundness and completeness results. Then we turn to the algebraic semantics, where both logics have substantive limitations: DF/TT allows for (...) algebraic completeness, but not for the construction of a canonical model, while CC/TT fails the construction of a Lindenbaum-Tarski algebra. With these results in mind, we draw up the balance and sketch future research projects. (shrink)

What is unique and essential about theatre? What separates it from other arts? Do we need 'theatre' in some fundamental way? The art of theatre, as Paul Woodruff says in this elegant and unique book, is as necessary-and as powerful-as language itself. Defining theatre broadly, including sporting events and social rituals, he treats traditional theatre as only one possibility in an art that-at its most powerful-can change lives and bring a divine presence to earth. The Necessity of Theater analyzes (...) the unique power of theatre by separating it into the twin arts of watching and being watched, practiced together in harmony by watchers and the watched. Whereas performers practice the art of being watched-making their actions worth watching, and paying attention to action, choice, plot, character, mimesis, and the sacredness of performance space-audiences practice the art of watching: paying close attention. A good audience is emotionally engaged as spectators; their engagement takes a form of empathy that can lead to a special kind of human wisdom. As Plato implied, theatre cannot teach us transcendent truths, but it can teach us about ourselves. Characteristically thoughtful, probing, and original, Paul Woodruff makes the case for theatre as a unique form of expression connected to our most human insticts. The Necessity of Theater should appeal to anyone seriously interested or involved in theatre or performance more broadly. (shrink)

There are basic questions concerning truth that have been perennial throughout the history of philosophy from the Ancient Greeks onwards: Is 'true' a ...

This review of ethical implications of the professionalisation of sport argues that conventional sports ethics, which in the spirit of amateurism emphasise concepts of fair play, are increasingly inappropriate in professional sport. The formalist position, that fair play requires playing within the rules, is explored as are notions of playing to the rules, gamesmanship and cheating. It is argued that ethical problems in elite sport increase as a result of external factors including the celebrity of sportspeople, a tarnished image of (...) some administrators, influences of external stakeholders , and the expectations of fans. Hence a worryingly negative picture of declining ethical standards in the face of internal and external pressures emerges, with little prospect of sports reforming from within, despite that appearing to be in a sport's best interests. (shrink)

In the United States, amid the fractious politics of attempting to achieve something close to universal access to basic health care, two impressions are likely to feed skepticism about the status of a right to universal access: the moral principles that underlie any right to universal access may seem incredibly "ideal," not well rooted in the society's actual fabric, and the necessary practical and political attempts to limit the scope of universally accessible care to make its achievement realistic may seem (...) marked less by moral rhyme and reason than by the pull of conflicting interests. I try to directly dispel the first of these impressions and to obliquely question the second. The immense political barriers to .. (shrink)

" Quel contraste! quel brusque passage! La hiérarchie, la dis¬cipline, l'ordre que l'autorité se charge d'assurer, les dogmes qui règlent fermement la vie : voilà ce qu'aimaient les hommes du dix-septième siècle. Les contraintes, l'autorité, les dogmes, voilà ce que détestent les hommes du dix-huitième siècle, leurs successeurs immédiats. Les premiers sont chrétiens, et les autres antichrétiens ; les premiers croient au droit divin, et les autres au droit naturel ; les premiers vivent à l'aise dans une société qui se (...) divise en classes inégales, les seconds ne rêvent qu'éga-lité. Certes, les fils chicanent volontiers les pères, s'imaginant qu'ils vont refaire un monde qui n'attendait qu'eux pour devenir meilleur : mais les remous qui agitent les générations successi¬ves ne suffisent pas à expliquer un changement si rapide et si décisif. La majorité des Français pensait comme Bossuet ; tout d'un coup, les Français pensent comme Voltaire : c'est une révolution.Pour savoir comment elle s'est opérée, nous nous sommes engagés dans des terres mal connues. On étudiait beaucoup le dix-septième siècle, autrefois ; on étudie beaucoup le dix-¬huitième siècle, aujourd'hui. A leurs confins s'étend une zone incertaine, malaisée, où l'on peut espérer encore découvertes et aventures. Nous l'avons parcourue, choisissant pour la borner deux dates non rigoureuses : d'une part, les environs de 1680, et d'autre part, 1715...". (shrink)

This paper demonstrates that a rationale for a circumscribed form of desire-based justification can be developed out of a contemporary Kantian account as a natural extension of that account. It maintains that certain of Christine Korsgaard's recent arguments establish only that desires must have certain features antithetical to instrumentalism in order to justify. Other arguments purport to establish the standard (stronger) result: that because desires do not have these features, they cannot justify. Her arguments for this strong result, it contends, (...) cannot be reconciled with central commitments in her epistemology and philosophy of mind. The consistent implementation of these commitments opens up a surprising space within what is still readily recognizable as a Kantian ethics--the space for desire-based justification. (shrink)

This books offers a naturalistic and critical theory of signs, minds, and meaning-in-the-world.

The majority of studies of post-communism – habitually grouped under the heading of 'transitology' – understand the transition ultimately as a political and cultural convergence of the ex-communist societies with Western Europe. Even those critical approaches that regard the post-communist transition as a relatively unique phenomenon (as in the approaches of path dependency and neo-classical sociology) tend to conflate normative prescriptions with empirical descriptions and to move within an overall framework of what Michael Kennedy has aptly called 'transition culture'. This (...) article argues instead that the transition's nature can only be fully grasped if a case-specific and historical-contextual approach is taken. In theoretical terms, a three-step movement to grasp diversity in Central and Eastern Europe is proposed: (1) the acknowledgement of the plurality of modernizing agency and its creativity; (2) the acknowledgement of multi-interpretability and difference as primary elements of modernity; and (3) a sensitivity to the resulting institutional variety in societal constellations. In substantive terms, it is argued that diversity is a distinctive mark of Europe that is bound to persist in an enlarged Europe, despite the spirit of assimilation in the accession process. (shrink)

Angelaki, Volume 16, Issue 4, Page 5-17, December 2011.

A God would have the wisdom, power and concern to do all that must be done to supplement man's activities in such a way that only good is done, and this everywhere. If we could count on his existence, concern and aid, we could be sure of getting the right help and to the right degree. Only a God is both powerful and wise enough to provide all the help that would be needed, and only a God is good and (...) wise enough to give it always at the right time and in the right way. He alone can guarantee the perfect production of whatever was distorted and left undone because of man's impotence, ignorance and folly. It is tempting therefore to claim that men always do, or that they always should look to a God for the aid they need if good is to be fully realized. (shrink)

When men interplay with nature, they constitute with it the distinctive public time of a human realm. And when, as members of that realm, they combine with the nature that still remains outside the human realm, they constitute with it the distinctive public time of objective history. The time of history is thus less delimited, less specialized, and more inclusive than the time of the human realm.

This doctrine is sound, I think, but not entirely adequate. If each thing is concerned with all the rest, no two things could have exactly the same object of concern. There will then be no reason why any two of them, contemporaries at any one moment, should be contemporaries at the next. Each will face a future distinct from that of any other, into which it will go in its own way and at its own pace. It was rightly remarked (...) in Reality that the different futures share a number of features, making it possible to deal with individuals as members of various classes. But since no individuals act in terms of those features, and since those features exert no controlling power, those features cannot keep contemporary beings in temporal accord. (shrink)