Wilfred Sieg and Dirk Schlimm. Dedekind's Analysis of Number: Systems and Axioms.

Wilfred Sieg and Mark Ravaglia. David Hilbert and Paul Bernays, Grundlagen der Mathematik I and II: A Landmark.

Wilfred Sieg. Mechanical Procedures and Mathematical Experience.

Wilfred Sieg. Relative Consistency and Accesible Domains.

Wilfred Sieg and Rosella Lupiccini. Computing Machines: Entry for the Second Edition of the Encyclopedia of Philsophy.

Wilfred Sieg. Aspects of Mathematical Experience.

Wilfred Sieg and Clinton Field. Automated Search for Gödel's Proofs.

Wilfred Sieg. Intercalculation Calculi for Classical Logic.

Wilfred Sieg and John Byrnes. Generalizing Turing's Machine and Arguments.

Wilfred Sieg and John Byrnes. K-Graph Machines: Generalizing Turing's Machines and Arguments.

Wilfred Sieg. “Church's Thesis”, “Consistency”, “Formalization”, “Proof Theory”: Dictionary Entries.

Wilfred Sieg and Saverio Cittadini. Normal Natural Deduction Proof (In Non-Classical Logics.

Wilfred Sieg. Effectiveness and Provability.

Wilfred Sieg. Mechanisms and Search: Aspects of Proof Theory.

Wilfred Sieg and Stanley S. Wainer. Program Transformation and Proof Transformation.

Richard Scheines and Wilfred Sieg. Computer Environments for Proof Construction.

Daniele Mundici and Wilfred Sieg. Computability Theory.

The second volume of Charles Parsons’ selected papers, dedicated to Solomon Feferman, Wilfred Sieg, and William Tait, collects eleven mainly historical essays and reviews on philosophy and philosop...

Wilfred Cantwell Smith, maintained in this vastly important work that Westerners have misperceived religious life by making "religion" into one thing.

We establish by elementary proof-theoretic means the conservativeness of two subsystems of analysis over primitive recursive arithmetic. The one subsystem was introduced by Friedman [6], the other is a strengthened version of a theory of Minc [14]; each has been shown to be of considerable interest for both mathematical practice and metamathematical investigations. The foundational significance of such conservation results is clear: they provide a direct finitist justification of the part of mathematical practice formalizable in these subsystems. The results are (...) generalized to relate a hierarchy of subsystems, all contained in the theory of arithmetic properties, to a corresponding hierarchy of fragments of arithmetic. The proof theoretic tools employed there are used to re-establish in a uniform, elementary way relationships between various fragments of arithmetic due to Parsons, Paris and Kirby, and Friedman. (shrink)

A recent review of his work describes Wilfred Carr as 'one of the most brilliant philosophers now working in the rich British tradition of educational philosophy ... His work is rigorous, refreshing and original ... and examines a number of fundamental issues with clarity and penetration'. In For Education Wilfred Carr provides a comprehensive justification for reconstructing educational theory and research as a form of critical inquiry. In doing this, he confronts a number of important philosophical questions. What (...) is educational theory? What is an educational practice? How are theory and practice related? What is the role of values in educational research? Is a genuinely educational science possible? By appealing to developments in critical theory, the philosophy of science and the philosophy of the social sciences, Wilfred Carr provides answers to these questions which vindicate the idea of an educational science that is not 'on' or 'about' education but 'for education' - a science genuinely committed to promoting educational values and ideals. (shrink)

Wilfried Sieg. Formal Systems, Church Turing Thesis, and Gödel's Theorems: Three Contributions to The MIT Encyclopedias of Cognitive Science.

Collected here for the first time is a history of images of Oman, one of the most developed and stable countries in the Arab world and among the earliest adherents to Islam. A sultanate, the country sits along the east coast of the Arabian Peninsula. From early days of world trade through the port of Muscat to contemporary engagement with international diplomacy and the West, Oman has always evoked beauty and mystery in equal measure. This art-house quality volume reveals an (...) intimate picture of the country as its contours emerged over the last 80 years in the eyes of the West, as captured in images by English explorer Wilfred Thesiger in the 1940s and ‘50s, British Army major Charles Butt in the 1960s, and award-winning American documentary photographer Edward Grazda in the first decade of this new century. (shrink)

Dedekind’s structuralism is a crucial source for the structuralism of mathematical practice—with its focus on abstract concepts like groups and fields. It plays an equally central role for the structuralism of philosophical analysis—with its focus on particular mathematical objects like natural and real numbers. Tensions between these structuralisms are palpable in Dedekind’s work, but are resolved in his essay Was sind und was sollen die Zahlen? In a radical shift, Dedekind extends his mathematical approach to “the” natural numbers. He creates (...) the abstract concept of a simply infinite system, proves the existence of a “model”, insists on the stepwise derivation of theorems, and defines structure-preserving mappings between different systems that fall under the abstract concept. Crucial parts of these considerations were added, however, only to the penultimate manuscript, for example, the very concept of a simply infinite system. The methodological consequences of this radical shift are elucidated by an analysis of Dedekind’s metamathematics. Our analysis provides a deeper understanding of the essay and, in addition, illuminates its impact on the evolution of the axiomatic method and of “semantics” before Tarski. This understanding allows us to make connections to contemporary issues in the philosophy of mathematics and science. (shrink)

Wilfred Carr; What is an Educational Practice?, Journal of Philosophy of Education, Volume 21, Issue 2, 30 May 2006, Pages 163–175, https://doi.org/10.1111/j.14.

The phenomenon of consumption has increasingly drawn attention from economists. While the ‘sole purpose of production is consumption’, as Adam Smith has claimed, economists have up to recently generally ignored the topic. This book brings together a range of different perspectives on the topic of consumption that will finally shed the necessary light on a largely neglected theme, such as Why is the consumption of symbolic goods different than that of goods that are not constitutive of individuals’ identity? How does (...) the consumption of symbolic goods affect social processes and economic phenomena? Will taking consumption seriously impact economics itself? The book discusses these issues theoretically, and, through analyses of such cases as food, religion, fashion, empirically as well. It also discusses the possible role in the future of consumption. This book was previously published as a special issue of _Review of Social Economy_. (shrink)

In the European Union, the General Data Protection Regulation (GDPR) provides comprehensive rules for the processing of personal data. In addition, the EU lawmaker intends to adopt specific rules to protect confidentiality of communications, in a separate ePrivacy Regulation. Some have argued that there is no need for such additional rules for communications confidentiality. This Article discusses the protection of the right to confidentiality of communications in Europe. We look at the right’s origins to assess the rationale for protecting it. (...) We also analyze how the right is currently protected under the European Convention on Human Rights and under EU law. We show that at its core the right to communications confidentiality protects three individual and collective values: privacy, freedom of expression, and trust in communication services. The right aims to ensure that individuals and organizations can safely entrust communication to service providers. Initially, the right protected only postal letters, but it has gradually developed into a strong safeguard for the protection of confidentiality of communications, regardless of the technology used. Hence, the right does not merely serve individual privacy interests, but also other more collective interests that are crucial for the functioning of our information society. We conclude that separate EU rules to protect communications confidentiality, next to the GDPR, are justified and necessary. (shrink)

African philosophy has for long been rejected on the basis that it is not known, or has not been written down. Behind this view is the idealist presumption that for something to exist, it must first be perceived. However, for something to be perceived, it must first exist. African Philosophy: Critical Dimensions examines what constitutes African philosophy in terms of its meaning, foundation, sources, methodology, characteristics, and relevance. The book analyses traditional African philosophy from the political, social, ethical, epistemological and (...) metaphysical angles. The book further critically discusses modern African political philosophy, modern African social philosophy, modern African economic philosophy, and modern African philosophy of religion. It ends with the identification of the different conclusions that were derived from the study and general recommendations, some specifically for researchers and writers, especially in the area of African philosophy. Wilfred Lajul joins other authentic voices examining African Philosophy. (shrink)

This paper proceeds through four stages. First, it provides an account of the origins and evolution of the concept of educational theory. Second, it uses this historical narrative to show how what we now call 'educational theory' is deeply rooted in the foundationalist discourse of late nineteenth and early twentieth century modernity. Third, it outlines and defends a postfoundationalist critique of the foundationalist epistemological assumptions on which our understanding of educational theory has been erected. Finally, it argues that the only (...) conclusion to draw from this postfoundationalist critique is that educational theory has run its course and should now be brought to a dignified end. (shrink)

Hilbert's finitist program was not created at the beginning of the twenties solely to counteract Brouwer's intuitionism, but rather emerged out of broad philosophical reflections on the foundations of mathematics and out of detailed logical work; that is evident from notes of lecture courses that were given by Hilbert and prepared in collaboration with Bernays during the period from 1917 to 1922. These notes reveal a dialectic progression from a critical logicism through a radical constructivism toward finitism; the progression has (...) to be seen against the background of the stunning presentation of mathematical logic in the lectures given during the winter term 1917/18. In this paper, I sketch the connection of Hilbert's considerations to issues in the foundations of mathematics during the second half of the 19th century, describe the work that laid the basis of modern mathematical logic, and analyze the first steps in the new subject of proof theory. A revision of the standard view of Hilbert's and Bernays's contributions to the foundational discussion in our century has long been overdue. It is almost scandalous that their carefully worked out notes have not been used yet to understand more accurately the evolution of modern logic in general and of Hilbert's Program in particular. One conclusion will be obvious: the dogmatic formalist Hilbert is a figment of historical (de)construction! Indeed, the study and analysis of these lectures reveal a depth of mathematical-logical achievement and of philosophical reflection that is remarkable. In the course of my presentation many questions are raised and many more can be explored; thus, I hope this paper will stimulate interest for new historical and systematic work. (shrink)

Natural Formalization proposes a concrete way of expanding proof theory from the meta-mathematical investigation of formal theories to an examination of “the concept of the specifically mathematical proof.” Formal proofs play a role for this examination in as much as they reflect the essential structure and systematic construction of mathematical proofs. We emphasize three crucial features of our formal inference mechanism: (1) the underlying logical calculus is built for reasoning with gaps and for providing strategic directions, (2) the mathematical frame (...) is a definitional extension of Zermelo–Fraenkel set theory and has a hierarchically organized structure of concepts and operations, and (3) the construction of formal proofs is deeply connected to the frame through rules for definitions and lemmas. To bring these general ideas to life, we examine, as a case study, proofs of the Cantor–Bernstein Theorem that do not appeal to the principle of choice. A thorough analysis of the multitude of “different” informal proofs seems to reduce them to exactly one. The natural formalization confirms that there is one proof, but that it comes in two variants due to Dedekind and Zermelo, respectively. In this way it enhances the conceptual understanding of the represented informal proofs. The formal, computational work is carried out with the proof search system AProS that serves as a proof assistant and implements the above inference mechanism; it can be fully inspected at (see link below). (shrink)

The man or woman of faith living in today's pluralist world must have a theology that will do justice to his or her own faith, and also to the neighbours' - and to the differences between them. Similarly, humanists must have a theory that does justice to their own vision and also to the fact that for most of their fellows on earth the proper way of being human has been one or another of various `religious' ways. Any interpretation of (...) human history, both past and present, must take into serious account the self-consciousness of each major part, as well as the diversity and the dynamic of the whole. This exciting book, first published in 1981 and now also available in paperback, is perhaps our world's first serious endeavour towards a theology in global perspective. Here is a wrestling with the demands of an authentic theology of the comparative history of religion. (shrink)

This volume provides a thought-provoking critique the main, existing school of environmental ethics and seeks to build a more coherent and rigorous philosophical basis for future environmental policy.

Although there are many theories of justice, one crucial feature of those that are most widely accepted is that they lay down principles that determine the allocation of rights and obligations in society. They do not eliminate conflicts of interest between different groups but, by specifying such principles, they are designed to enable conflicting interests to be resolved in a peaceful and harmonious manner. But insofar as future generations cannot be said to have any rights, their interests cannot be protected (...) within the framework of any theory of intergenerational justice. This chapter discusses the general relationship between ‘rights’ and ‘justice’, and the obstacles to any theory of intergenerational justice. (shrink)

Another widely suggested principle governing our obligations to future generations is ‘sustainable development’. The first part of this chapter argues that the mainstream interpretations of the concept of sustainable development are open to serious objections on ethical grounds. The chapter also shows that even if intergenerational egalitarianism were a viable objective there is nothing intergenerationally egalitarian about sustainable development.

In lieu of an abstract, here is a brief excerpt of the content:Farting for Dollars:A Note on Agyrrhios in Aristophanes Wealth 176Wilfred E. MajorEarly in aristophanes wealth,1 Khremylos and his slave, Karion, are trying to persuade the blind god of Wealth that he is the mightiest of all divinities. Men sacrifice to Zeus but for wealth. All professions exist for the pursuit of wealth. The mighty King of Persia grooms himself because of it. Karion next focuses on Athens in particular:(171)Doesn't (...) the Assembly meet because of it (wealth)?Karion follows with examples of money supporting military efforts and then returns to the formula:(174)Won't Pamphilos suffer because of it?Scholia explain that Pamphilos had a reputation, at least in comedy, for demagoguery and embezzlement. Around this time, he was facing a trial. Karion's next example is more enigmatic:(176)Doesn't Agyrrhios fart because of it?Precisely why Agyrrhios should fart on account of wealth has eluded critics and commentators. While modern scholars have long recognized that the scholia to this line contain no reliable information, interpretations still rely on the scholiasts' best guesses. Comparison with other comic [End Page 549] references to farting, however, and to Agyrrhios and his philoi, suggest that farting here refers not directly to his excessive wealth, as is generally supposed, but to his activity as a corrupt orator.Agyrrhios (PA 179, PAA 107660) is known for several key events in his political career, including his role in instituting pay for attending the Ekklesia and his generalship of 389.2 His skill in tax farming made him wealthy, but his financial dealings also landed him in prison for a time (Dem. 24.135). Why he should be associated with the troubles of wealth is clear enough, but not why he should fart on its account. The scholiasts clearly had no more context for the line than we possess now. Older scholia offer two categories of explanations for Agyrrhios' incontinence. It may have resulted from Agyrrhios' extravagant living, perhaps from the overeating characteristic of the rich. On the other hand, it may refer to Agyrrhios' sexual perversions.3 Later scholia expand on the latter explanation, probably by comparing this line with the reference to Agyrrhios' sexuality at Ecc. 102.4 In no case, however, do the scholiasts seem to operate on information unavailable to us. Indeed, modern scholars have rightly dismissed the scholia altogether but have tended to fall back on the older scholia's suggestion of farting as a mark of extravagant living.5 Confidence in this interpretation erodes in the face of comparisons with other instances of farting in Greek comedy.This explanation can appear logical enough, and it is often assumed that the reference thus fits an established typology of the overstuffed rich man farting from excess, but, in fact, there is no parallel in ancient Greek comedy for farting in this context. Forms and variations on occupy a wide semantic range in Greek comedy, but some groups and trends can be usefully demarcated. For example, the similarity [End Page 550] in sound of snoring and farting means sleeping people fart (an equation explicit at Kn. 115 and implied at Cl. 9). Farting can come as a surprise substitute in a mock religious ritual (as part of an oath at Wa. 394; as a good omen in place of a sneeze at Kn. 639). Although religious fear leads Strepsiades to fart at Cl. 293, more properly covers semantic ranges associated with fear.6 The frightening bogey Lamia, however, is associated with (Ecc. 78, 1177). Collapse from physical pain can also result in farting (Fr. 10 and 1097). Farting can accompany idleness and boredom (Ach. 30; Ecc. 464). More often, however, someone farts as part of a triumphal celebration, which may include aggressively farting on or at one's opponent (Wa. 1305; Pc. 335, 547; We. 618; Cratinus fr. 6.3; Epicrates fr. 10.29; Sosipater fr. 1.12). Isolated jokes specific to context also occur (a joke about conditions for rowers at Fr. 1074; a homely example of physics at Cl. 392; a feed for a joke about physicians at We. 699). All of these instances showcase a lower class, rustic, or foolish individual farting... (shrink)