English summary: Does pastoral care require ethical competence in order to fulfil its task properly? And, conversely, to what extent does ethical reflection require feedback from pastoral experience in order to remain true to life and of practical relevance? Wilfried Sturm examines the way hospital pastors deal with ethical challenges and conflict situations in neonatal clinics and enquires into the insights that can be gained from them for the relationship of pastoral care and ethics. German description: Braucht Seelsorge (...) ethische Kompetenz, um ihrem Auftrag gerecht zu werden? Inwiefern bedarf umgekehrt die ethische Reflexion der Ruckkopplung an seelsorgerliche Erfahrung, um lebensnah und praxisrelevant zu bleiben? Wilfried Sturm untersucht den Umgang von Klinikseelsorgerinnen und -seelsorgern mit ethischen Herausforderungen und Konfliktsituationen in der Fruh- und Neugeborenenmedizin und fragt, welche Einsichten sich daraus fur das Verhaltnis von Seelsorge und Ethik gewinnen lassen. (shrink)

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)

This paper explains Kant’s views on the theory of matter as developed in the Dynamics chapter of his Metaphysical Foundations, and elaborates their background in the chemistry of the period. Kant’s general approach to matter theory unites Newtonian and Leibnizian motifs, and entails an intricate internal structure for matter involving a multiple overlap of material shells of different density. Kant’s chemical views derive from Stahlian chemistry and involve a noncorpuscularian account of chemical combination and a nonoperational conception of chemical elements.

This essay reconsiders Kant's denial of scientific status to the discipline of empirical psychology, which have often been viewed as quite problematic. In the preface to the Metaphysical Foundations of Natural Science, Kant denies that psychology can be natural science proper. I argue that Kant's impossibility claim is based on a very specific conception of science that he did not put forward elsewhere, and that is restricted to *natural* sciences in any case. Also, Kant's critical remarks are directed merely against (...) a particular conception of psychology, namely one going back to Baumgarten and adopted by many psychologists in the eighteenth century, according to which introspection is the sole means of gathering empirical evidence about the mind. Although this particular conception of psychology precludes it from being natural science proper, it is possible that other conceptions of psychology could allow it to be scientific. Also, for Kant the study of the mind should not be introspection-based. He himself developed a "pragmatic anthropology", which he viewed as a significant factor in our knowledge of the world. (shrink)

Wilfred Sieg. Mechanical Procedures and Mathematical Experience.

This book explores Kant's philosophy of the human sciences, their status, their relations and prospects. Contrary to widespread belief, he is not dogmatic about the question of whether these disciplines are proper sciences. Instead, this depends on whether we can rationally adjust assumptions about the methods, goals, and subject matter of these disciplines - and this has to be done alongside of ongoing research. Kant applies these ideas especially in lectures on "pragmatic antropology" given from 1772-1796. In doing so, he (...) refines his conception of anthropology and clarifies its relation to physiology, psychology, history, and ethics. He also discusses then leading approaches in the human sciences, from Wollfian psychology over Bonnet's attempt to explain the mind in terms of the brain up to Hume's naturalism and Herder's historicism. Only against the background of these arguments can we understand and assess Kant's view of the human being as a social and rational being, capable of creating its own laws of conduct. He moreover argues that and why we can view ourselves as free agents even from an empirical point of view. This is quite a fresh perspective on the human sciences, their goals, potentials and limits - and fresh not only in the 18th century. (shrink)

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifteenth publication in the Lecture Notes in Logic series, collects papers presented at the symposium 'Reflections on the Foundations of Mathematics' held in celebration of Solomon Feferman's 70th birthday (The 'Feferfest') at Stanford University, California in 1988. (...) Feferman has shaped the field of foundational research for nearly half a century. These papers reflect his broad interests as well as his approach to foundational research, which emphasizes the solution of mathematical and philosophical problems. There are four sections, covering proof theoretic analysis, logic and computation, applicative and self-applicative theories, and philosophy of modern mathematical and logic thought. (shrink)

The realm of non-rational influence, which includes nudging, is home to many other morally interesting phenomena. In this paper, I introduce the term bumping, to discuss the category of unintentional non-rational influence. Bumping happens constantly, wherever people make choices in environments where they are affected by other people. For instance, doctors will often bump their patients as patients make choices about what treatments to pursue. In some cases, these bumps will systematically tend to make patients’ decisions worse. Put another way: (...) doctors will sometimes harm their patients by bumping them in systematic ways. I use the case of medical overuse, the provision of medical services where the likely harm outweighs the likely benefit to the patient, as a touchstone for arguing that doctors who systematically bump their patients towards harm can be blameworthy for their unwitting influence. (shrink)

It is a remarkable fact that Hilbert's programmatic papers from the 1920s still shape, almost exclusively, the standard contemporary perspective of his views concerning (the foundations of) mathematics; even his own, quite different work on the foundations of geometry and arithmetic from the late 1890s is often understood from that vantage point. My essay pursues one main goal, namely, to contrast Hilbert's formal axiomatic method from the early 1920s with his existential axiomatic approach from the 1890s. Such a contrast illuminates (...) the circuitous beginnings of the finitist consistency program and connects the complex emergence of existential axiomatics with transformations in mathematics and philosophy during the 19th century; the sheer complexity and methodological difficulties of the latter development are partially reflected in the well known, but not well understood correspondence between Frege and Hilbert. Taking seriously the goal of formalizing mathematics in an effective logical framework leads also to contemporary tasks, not just historical and systematic insights; those are briefly described as “one direction” for fascinating work. (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)

David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations.

This essay aims to sharpen debates on the pros and cons of historical epistemology, which is now understood as a novel approach to the study of knowledge, by comparing it with the history of epistemology as traditionally pursued by philosophers. The many versions of both approaches are not always easily discernable. Yet, a reasoned comparison of certain versions can and should be made. In the first section of this article, I argue that the most interesting difference involves neither the subject (...) matter nor goal, but the methods used by the two approaches. In the second section, I ask which of the two approaches or methods is more promising given that both historical epistemologists and historians of epistemology claim to contribute to epistemology simpliciter. Using traditional problems concerning the epistemic role of perception, I argue that the historical epistemologies of Wartofsky and Daston and Galison fail to show that studying practices of perception is philosophically significant. Standard methods from the history of epistemology are more promising, as I show by means of reconstructing arguments in a debate about the relation between perception and judgment in psychological research on the famous moon illusion. (shrink)

Alonzo Church's mathematical work on computability and undecidability is well-known indeed, and we seem to have an excellent understanding of the context in which it arose. The approach Church took to the underlying conceptual issues, by contrast, is less well understood. Why, for example, was "Church's Thesis" put forward publicly only in April 1935, when it had been formulated already in February/March 1934? Why did Church choose to formulate it then in terms of Gödel's general recursiveness, not his own λ (...) -definability as he had done in 1934? A number of letters were exchanged between Church and Paul Bernays during the period from December 1934 to August 1937; they throw light on critical developments in Princeton during that period and reveal novel aspects of Church's distinctive contribution to the analysis of the informal notion of effective calculability. In particular, they allow me to give informed, though still tentative answers to the questions I raised; the character of my answers is reflected by an alternative title for this paper, Why Church needed Gödel's recursiveness for his Thesis. In Section 5, I contrast Church's analysis with that of Alan Turing and explore, in the very last section, an analogy with Dedekind's investigation of continuity. (shrink)

With the tertiary education mantra of creativity, critical thinking and innovation in mind, we consider the critical-creativity of error. Taking the university to model social orthography, or ‘correct writing’, according to the norms of disciplines, we consider the role of error in the classroom. Looked at another way, error questions the norms governing norms and the instability of disciplinary grounds. Beyond correction, error involves a mis-taking, or taking another way. Tracing the origin of error we are able to reconstruct the (...) social world in terms of which it is conceivable for a mistake of any kind to have been made. The university, we find, withholds worlds which are not new but are sources of creativity, and constitutes a pluriversity or poly-versity. (shrink)

Wilfried Sieg. Calculations by Man and Machine: Conceptual Analysis.

Herbrand's Theorem, in the form of $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\exists } $$ -inversion lemmata for finitary and infinitary sequent calculi, is the crucial tool for the determination of the provably total function(al)s of a variety of theories. The theories are (second order extensions of) fragments of classical arithmetic; the classes of provably total functions include the elements of the Polynomial Hierarchy, the Grzegorczyk Hierarchy, and the extended Grzegorczyk Hierarchy $\mathfrak{E}^\alpha $ , α < ε0. A subsidiary aim of the paper is to show (...) that the proof theoretic methods used here are distinguished by technical elegance, conceptual clarity, and wide-ranging applicability. (shrink)

There is a tension between the idea of popular sovereignty and our understanding that basic constitutional rights and liberties have a normative authority which is independent from the results of democratic decision‐making procedures. On the one hand there is the claim that the content of political justice, at least as far as the basic liberties are concerned, is to be fixed solely by substantive moral and political argument, while on the other there is the claim that it is the people (...) who determine the specific scheme of basic liberties that they live under. The apparent tension between the two claims can be resolved by introducing, firstly, a distinction between the concept of justice and the concept of legitimacy and, secondly, between proto‐rights and constitutional rights. Unlike constitutional rights, proto‐rights are moral, not legal, rights, and they are less specific than constitutional rights: one set of proto‐rights allows for various schemes of legal constitutional rights. Proto‐rights are part of the principles of justice and can be established only by substantive argument while constitutional rights have to be established by the procedures of democratic legitimization, and, therefore, they are a result of the exercise of popular sovereignty. The correlated distinctions between justice and legitimacy, and between proto‐rights and constitutional rights, allow us to specify the scope of the two claims and, hence, to affirm both simultaneously. The philosophical and legal relevance of the distinctions made is elucidated by a brief discussion of the constitutional rights of freedom of speech in the US and Germany. (shrink)

Wilfried Sieg and John Byrnes. AnModel for Parallel Computation: Gandy's Thesis.

On June 4, 1925, Hilbert delivered an address to the Westphalian Mathematical Society in Miinster; that was, as a quick calculation will convince you, almost exactly sixty years ago. The address was published in 1926 under the title Über dasUnendlicheand is perhaps Hilbert's most comprehensive presentation of his ideas concerning the finitist justification of classical mathematics and the role his proof theory was to play in it. But what has become of the ambitious program for securing all of mathematics, once (...) and for all? What of proof theory, the very subject Hilbert invented to carry out his program? The Hilbertian ambition reached out too far: in its original form, the program was refuted by Gödel's Incompleteness Theorems. And even allowing more than finitist means in metamathematics, the Hilbertian expectations for proof theory have not been realized: a constructive consistency proof for second-order arithmetic is still out of reach. Nevertheless, remarkable progress has been made. Two separate, but complementary directions of research have led to surprising insights: classical analysis can be formally developed in conservative extensions of elementary number theory; relative consistency proofs can be given by constructive means for impredicative parts of second order arithmetic. The mathematical and metamathematical developments have been accompanied by sustained philosophical reflections on the foundations of mathematics. This indicates briefly the main themes of the contributions to the symposium; in my introductory remarks I want to give a very schematic perspective, that is partly historical and partly systematic. (shrink)

Wilfred Sieg. Relative Consistency and Accesible Domains.

Wilfried Sieg. Calculations by Man and Machine: Mathematical Presentation.

In his classic paper On Computable Numbers Turing analyzed what can be done by a human computor in a routine, “mechanical” way. He argued that mechanical op-erations obey locality conditions and are carried out on configurations satisfying boundedness conditions. Processes meeting these restrictive conditions can be shown to be computable by a Turing machine. Turing viewed memory limitations of computors as the ultimate reason for the restrictive conditions. In contrast, Gandy analyzed in his paper Church’s Thesis and Principles for Mechanisms (...) what can be done by “discrete deterministic mechanical devices” and appealed to physical considerations to motivate restrictive principles. These devices include, crucially, ones that carry out parallel processes, e.g., cellular automata. Following Turing’s methodological ways and guided by Conway’s “Game of Life” as a paradigm, Gandy formulated four restrictive principles and proved that devices satisfying them are computationally equivalent to Turing machines. (shrink)

Thema der vorliegenden Arbeit ist der dialektische Gehalt der wichtigsten bildungstheoretischen Abhandlungen des padagogischen Theoretikers Josef Derbolav. Ergebnis der zum grossten Teil immanent durchgefuhrten Analyse ist der Aufweis, dass Derbolav die dialektische Fassung didaktischer, anthropologischer und handlungstheoretischer Prinzipien aufgrund metaphysischer Denkstrukturen nicht oder nur teilweise gelingt. Inwieweit einige dieser Prinzipien dialektisches Potential enthalten konnten, zeigt der Verfasser anhand der Entwicklung eines eigenen, an der hermeneutischen Philosophie orientierten dialektischen Standpunktes.".

In this paper we deal with the logic which is the infinitary extension of propositional modal logic that has conjunctions and disjunctions only for countable sets of formulas. After introducing some basic concepts and tools from modal logic, we modify Makkai's generalization of the notion of consistency property to make it fit for modal purposes. Using this construction as a universal instrument, we prove, among other things, interpolation for as well as preservation results for universal, existential, and positive -formulas.

tomus I. Physica generalis. (2 v) -- tomus II. Physica specialis. (2 v.).

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)

Standard models for model predicate logic consist of a Kripke frame whose worlds come equipped with relational structures. Both modal and two-sorted predicate logic are natural languages for speaking about such models. In this paper we compare their expressivity. We determine a fragment of the two-sorted language for which the modal language is expressively complete on S5-models. Decidable criteria for modal definability are presented.

The Carnegie Mellon Proof Tutor project was motivated by pedagogical concerns: we wanted to use a "mechanical" (i.e. computerized) tutor for teaching students..

In this article we give a unifying approach to the theory of fundamental sequences and their related Hardy hierarchies of number-theoretic functions and we show the equivalence of the new approach with the classical one.

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