From ancient times to the present, the discovery and presentation of new proofs of previously established theorems has been a salient feature of mathematical practice. Why? What purposes are served by such endeavors? And how do mathematicians judge whether two proofs of the same theorem are essentially different? Consideration of such questions illuminates the roles that proofs play in the validation and communication of mathematical knowledge and raises issues that have yet to be resolved by mathematical logicians. The Appendix, in (...) which several proofs of the Fundamental Theorem of Arithmetic are compared, provides a miniature case study. (shrink)

Die von Karl Menger und seinen Mitarbeitern (darunter Kurt Gödel) herausgegebenen "Ergebnisse eines Mathematischen Kolloquiums" zählen zu den wichtigsten Quellenwerken der Wissenschafts- und Geistesgeschichte der Zwischenkriegszeit, mit bahnbrechenden Beiträgen von Menger, Gödel, Tarski, Wald, John von Neumann und vielen anderen. In diesem Band liegt der Inhalt erstmals gesammelt vor. Der Nobelpreisträger Gerard Debreu schrieb die Einleitung, die Kommentare wurden vom Logiker und Gödel-Biographen John Dawson jr., dem Topologen Ryszard Engelking und dem Wirtschaftstheoretiker Werner Hildenbrand verfasst. Außerdem enthält (...) der Band einen biographischen Aufsatz über Karl Menger sowie einen von Menger verfassten Überblick über die wichtigsten topologischen und geometrischen Arbeiten des Kolloquiums. (shrink)

This article provides an English translation of a historic discussion on the foundations of mathematics, during which Kurt GÖdel first announced his incompleteness theorem to the mathematical world. The text of the discussion is preceded by brief background remarks and commentary.

As initially envisioned, Gödel's Collected Works were to include transcriptions of material from his mathematical workbooks. In the end that material, as well as some other manuscript items from Gödel's Nachlass, had to be left out. This note describes some of the unpublished items in the Nachlass that are likely to attract the notice of scholars and surveys the extent of shorthand transcription efforts undertaken hitherto. Some examples of sources outside Gödel's Nachlass that may be of interest to Gödel scholars (...) are also indicated. (shrink)

Though regarded today as one of the most important results in logic, the compactness theorem was largely ignored until nearly two decades after its discovery. This paper describes the vicissitudes of its evolution and transformation during the period 1930-1970, with special attention to the roles of Kurt Gödel, A. I. Maltsev, Leon Henkin, Abraham Robinson, and Alfred Tarski.

The symposium »Does the Concept of ›Truth‹ Have Value in the Pursuit of Cross-Cultural Philosophy?« hones on a methodological question which has deep implications on doing philosophy cross-culturally. Drawing on early Confucian writers, the anchor, Henry Rosemont, Jr., attempts to explain why he is skeptical of pat, affirmative answers to this question. His co-symposiasts James Maffie, John Maraldo, and Sonam Thakchoe follow his trail in working out multi-faceted views on truth from Mexican, Japanese Confucian, and Tibetan Buddhist perspectives respectively. (...) As these positions substantiate, the aforementioned non-Anglo-European traditions seem to draw on an integrated view of thinking, feeling, and living a human life. For their practitioners, truth is less of a correspondence with a given external reality. In fact, it enables human beings to strike the right path in living good, social lives. (shrink)

Despite recent advances in HIV prevention and treatment, high HIV incidence persists among people who inject drugs. Difficult legal and political environments and lack of services for PWID likely contribute to high HIV incidence. Some advocates question whether any HIV prevention research is ethically justified in settings where healthcare system fails to provide basic services to PWID and where implementation of research findings is fraught with political barriers. Ethical challenges in research with PWID include concern about whether research evidence will (...) be translated into practice; concerns that research might exacerbate background risks; and ethical challenges regarding the standard of HIV prevention in research. While these questions arise in other research settings, for research with PWID, these questions are especially controversial. This paper analyses four ethical questions in determining whether research could be ethically acceptable: Can researchers ensure that research does not add to the burden of social harms and poor health experienced by PWID? Should research be conducted in settings where it is uncertain whether research findings will be translated into practice? When best practices in prevention and care are not locally available, what standard of care and prevention is ethically appropriate? Does the conduct of research in settings with oppressive policies constitute complicity? We outline specific criteria to address these four ethical challenges. We also urge researchers to join the call to action for policy change to provide proven safe and effective HIV prevention and harm reduction interventions for PWID around the world. (shrink)

Despite recent advances in HIV prevention and treatment, high HIV incidence persists among people who inject drugs. Difficult legal and political environments and lack of services for PWID likely contribute to high HIV incidence. Some advocates question whether any HIV prevention research is ethically justified in settings where healthcare system fails to provide basic services to PWID and where implementation of research findings is fraught with political barriers. Ethical challenges in research with PWID include concern about whether research evidence will (...) be translated into practice; concerns that research might exacerbate background risks; and ethical challenges regarding the standard of HIV prevention in research. While these questions arise in other research settings, for research with PWID, these questions are especially controversial. This paper analyses four ethical questions in determining whether research could be ethically acceptable: Can researchers ensure that research does not add to the burden of social harms and poor health experienced by PWID? Should research be conducted in settings where it is uncertain whether research findings will be translated into practice? When best practices in prevention and care are not locally available, what standard of care and prevention is ethically appropriate? Does the conduct of research in settings with oppressive policies constitute complicity? We outline specific criteria to address these four ethical challenges. We also urge researchers to join the call to action for policy change to provide proven safe and effective HIV prevention and harm reduction interventions for PWID around the world. (shrink)

According to several commentators, Kurt Godel's incompleteness discoveries were assimilated promptly and almost without objection by his contemporaries - - a circumstance remarkable enough to call for explanation. Careful examination reveals, however, that there were doubters and critics, as well as defenders and rival claimants to priority. In particular, the reactions of Carnap, Bernays, Zermelo, Post, Finsler, and Russell, among others, are considered in detail. Documentary sources include unpublished correspondence from Godel's Nachlass.

In September of 2002, without fanfare, Ivor Grattan-Guinness retired from the faculty of Middlesex University. His scholarly activity, however, has continued unabated, his time now no longer fetter...

This paper critiques the biological race realism of Quayshawn Spencer. Spencer's recent embrace of “radical race pluralism” (RRP) is welcome but incomplete, because it needs methods that distinguish different communicative contexts for how American English speakers use “race” and related terms. I offer a pragmatic approach to identifying such contexts that combines pragmatic argumentation theory, rhetorical polysemy, and a pragmatic approach to definition. One consequence of embracing RRP is that Spencer's theory of “OMB race talk” is unsupportable because it collapses (...) three distinct communicative contexts: genomic research, legal and regulatory governance, and ordinary talk. By so doing, OMB race talk blocks attempts to fight racism and violates ethical standards that should allow people the agency to define their own identities. (shrink)

The idea of God’s action in history was prominent in the Biblical theology of the past generation. This theology was generally opposed to philosophic explication of its doctrine of God, and consequently it is difficult to say just what it meant by divine action. In any case, that movement faded and, with it, talk of God’s acts.

The word “euthanasia” is hopelessly overloaded with emotional connotations. It means so many things to many different people. The implications of euthanasia associated with the Second World War have often rendered the term unsuitable for discussions of a rational manner. As far as I am concerned, what happened in Germany under Hitler had nothing to do with the classic meaning of a gentle and easy death but was rather simply a policy of mass murder.

What kind of persons could engage in political torture? Not only the morally impaired who lack empathy or compassion, or even the merely obedient, but also the righteous who struggle with conscience, and the realists who set morality aside.

We develop a modified system of standard logic, Augmented Standard Logic (ASL), and we employ ASL in an effort to show that, contrary to prevailing opinion, both Aristotle and Diodorus presented impressive arguments, having valid structures and highly plausible premisses, in their famous fatalism debate. We argue that ASL, which contains standard logic and a full system of modal and temporal logic emanating from a modicum of primitives, should not only enable one to appreciate the sophisticated philosophizing which characterized this (...) ancient debate, but should prove to be quite useful in application to contemporary issues. (shrink)

With this issue History and Philosophy of Logic begins its twenty-fifth year of publication. In the years since its founding, by virtue of its high standards and broad scope of coverage, it has bec...

Philosophical defenses of cognitive/evolutionary psychological accounts of racialism claim that classification based on phenotypical features of humans was common historically and is evidence for a species-typical, cognitive mechanism for essentializing. They conclude that social constructionist accounts of racialism must be supplemented by cognitive/evolutionary psychology. This article argues that phenotypical classifications were uncommon historically until such classifications were socially constructed. Moreover, some philosophers equivocate between two different meanings of “racial thinking.” The article concludes that social constructionist accounts are far more robust (...) than psychological accounts for the origins of racialism. (shrink)

In crafting our paper on addressing the ethical challenges in HIV prevention research with people who inject drugs,1 we had hoped to stimulate further discussion and deliberation about the topic. We are pleased that three commentaries on our paper have begun this process.2 3 4 The commentaries rightly bring up important issues relating to community engagement and problems in translating research into practice in the fraught environments in which PWID face multiple risks. These risks include acquisition of HIV as well (...) as criminalisation, stigma and lack of access to needed healthcare, prevention and social services. We take this opportunity to respond to the excellent points raised by the commentators. All of the commentaries support our emphasis on robust community engagement with PWID and other stakeholders in designing and conducting HIV prevention research, but urge us to go farther. Wolfe highlights the difficulty of even engaging with community members in oppressive settings, where authorities severely restrict civil liberties of PWID so that even discussing issues related to drug use and enforcement may place individuals at risk. To overcome such limitations, he appropriately suggests interviewing confidentially those who have previously been detained in closed settings as part of the community engagement process. Similarly, Wolfe observes that critical issues can be overlooked with a narrow focus on study procedures if contextual factors before, during or after a study are ignored. For example, he cites the risk of overdose for study participants who have been abstinent during a study and subsequently resume injecting when the study concludes. These kinds of risks may not be obvious …. (shrink)

In crafting our paper on addressing the ethical challenges in HIV prevention research with people who inject drugs, 1 we had hoped to stimulate further discussion and deliberation about the topic. We are pleased that three commentaries on our paper have begun this process. 2 3 4 The commentaries rightly bring up important issues relating to community engagement and problems in translating research into practice in the fraught environments in which PWID face multiple risks. These risks include acquisition of HIV (...) as well as criminalisation, stigma and lack of access to needed healthcare, prevention and social services. We take this opportunity to respond to the excellent points raised by the commentators. All of the commentaries support our emphasis on robust community engagement with PWID and other stakeholders in designing and conducting HIV prevention research, but urge us to go farther. Wolfe highlights the... (shrink)

A colleague’s personal recollections of Jean van Heijenoort’s contributions to the editing of volumes I–III of Gödel’s Collected Works and of his interactions with the other editors.