Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...) She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics. (shrink)

My aim in this paper is to propose what seems to me a distinctive approach to set theoretic methodology. By ‘methodology’ I mean the study of the actual methods used by practitioners, the study of how these methods might be justified or reformed or extended. So, for example, when the intuitionist's philosophical analysis recommends a wholesale revision of the methods of proof used in classical mathematics, this is a piece of reformist methodology. In contrast with the intuitionist, I will focus (...) more narrowly on the methods of contemporary set theory, and, more importantly, I will certainly recommend no sweeping reforms. Rather, I begin from the assumption that the methodologist's job is to account for set theory as it is practiced, not as some philosophy would have it be. This credo lies at the very heart of the so-called ‘naturalism’ to be described here.A philosopher looking at set theoretic practice from the outside, so to speak, might notice any number of interesting methodological questions, beginning with the intuitionist's ‘why use classical logic?’, but this sort of question is not a live issue for most practicing set theorists. One central question on which the philosopher's and the practitioner's interests converge is this: what is the status of independent statements like the continuum hypothesis (CH)? A number of large questions arise in its wake: what criteria should guide the search for new axioms? For that matter, what reasons support our adoption of the old axioms? (shrink)

Penelope Maddy has defended a modified version of mathematical platonism that involves the perception of some sets. Frederick Suppe has developed a conclusive reasons account of empirical knowledge that, when applied to the sets of interest to Maddy, yields that we have knowledge of these sets. Thus, Benacerraf's challenge to the platonist to account for mathematical knowledge has been met, at least in part. Moreover, it is argued that the modalities involved in Suppe's conclusive reasons account of knowledge can be (...) handled without recourse to either laws of nature or possible worlds, and that this approach is preferable. (shrink)

In September 1933, Ludwig Miller, Nazi party member and newly elected Reich Bishop, stood before his fellow German Protestants at the infamous Wittenberg synod. He looked out over the delegates, many of whom had actually arrived wearing the brown shirts of the Nazi SA. "The political church struggle is over," he announced. "The struggle for the soul of the people now begins." For the Soul of the People portrays the dramatic struggle between Nazism and the Confessing Church. When storm troopers (...) started showing up at church services and the Nazis began issuing orders to the German Protestant Church, this group of outraged Christians sought to establish a church untainted by Nazi ideology. As the conflict progressed, Confessing Church members were spied on and harassed by the Gestapo. Martin Niemoller, one of the Church's most outspoken leaders, was sent to Dachau. Dietrich Bonhoeffer, one of its seminal figures, was executed in April 1945 for his involvement in the plot to kill Hitler. For this remarkable book, Victoria Barnett interviewed more than sixty Germans who were active in the Confessing Church, asking them to reflect on their personal experiences under Hitler and how they see themselves, morally and politically, today. She quotes liberally from their frank, unvarnished testimony, using rich historical and archival material to frame their stories. What emerges is no simple allegory of good triumphing over evil, as Barnett discovers that the Church's resistance was neither unqualified nor unanimous. For the Soul of the People portrays a church divided between those who compromised with Nazism and those who eventually tried to overthrow it. Church's strengths and weaknesses, particularly - despite the courageous efforts of a few - its general failure to help the Jews. Throughout, the voices of Germans who lived through the Nazi reign of terror - voices of grief and shame, of defensiveness and regret, of concern and hope for the future - reflect the honesty and courage of people who all their lives will wrestle with the past. The Confessing Church had a powerful legacy in postwar Germany, right up to the collapse of the Berlin Wall in 1989. Confessing Christians were actively involved in the postwar debates about guilt, rearmament, reunification, the political role of the church, and East-West relations. Many of those Barnett interviewed have played prominent roles in that debate, including such influential figures as a mayor of West Berlin, a member of Adenauer's cabinet, and a bishop of the East German church. Barnett's book studies the Confessing Church's influence in East and West Germany after 1945. (shrink)

Any system based on axioms is incomplete because the axioms cannot be proven from the system, just believed. But one system can be less-incomplete than other. Neutrosophy is less-incomplete than many other systems because it contains them. But this does not mean that it is finished, and it can always be improved. The comments presented here are an attempt to make Neutrosophy even less-incomplete. I argue that less-incomplete ideas are more useful, since we cannot perceive truth or falsity or indeterminacy (...) independently of a context, and are therefore relative. Absolute being and relative being are defined. Also the "silly theorem problem" is posed, and its partial solution described. The issues arising from the incompleteness of our contexts are presented. We also note the relativity and dependance of logic to a context. We propose "metacontextuality" as a paradigm for containing as many contexts as we can, in order to be less-incomplete and discuss some possible consequences. (shrink)

Bazzocchi disposes the text of the Tractatus in a user-friendly manner, exactly as Wittgenstein's decimals advise. This discloses the logical form of the book by distinct reading units, linked into a fashioned hierarchical tree. The text becomes much clearer and every reader can enjoy, finally, its formal and literary qualities.

A semiotic theory of systems derived from language would have the purpose of classifying all the systems of linguistic expression: philosophy, ideology, myth, poetry, art, as much as the dream, lapsus, and free association in a pluridimensional matrix that will interact with many diversified fields. In each one of these discourses it is necessary to consider a plurality of questions, the essence of which will only be comprehensible by the totality; it will be necessary to ask, in the first place, (...) what will be the purpose of this language, what function does it fulfill and for which reason has it been constructed. The concept of World vision (WV) is introduced and its relation with Generalized Collective Conscience (GCC) and Particularized Collective Conscience. Culture implies a particular WV. Culture creates GCC. The semantic field is a structure that formalizes the units of a certain culture constituting a portion of the vision of the Reality that owns this culture. An ecological case is explained. (shrink)