We prove that a variant of Robinson arithmetic $\mathsf{Q}$ with nontotal operations is interpretable in the theory of concatenation $\mathsf{TC}$ introduced by A. Grzegorczyk. Since $\mathsf{Q}$ is known to be interpretable in that nontotal variant, our result gives a positive answer to the problem whether $\mathsf{Q}$ is interpretable in $\mathsf{TC}$. An immediate consequence is essential undecidability of $\mathsf{TC}$.

A modal theory Z using the Guaspari witness comparison signs $\leq, is developed. The theory Z is similar to, but weaker than, the theory R of Guaspari and Solovay. Nevertheless, Z proves the independence of the Rosser fixed-point. A Kripke semantics for Z is presented and some arithmetical interpretations of Z are investigated. Then Z is enriched to ZI by adding a new modality sign for interpretability and by axioms expressing some facts about interpretability of theories. Two arithmetical interpretations of (...) ZI are presented. The proofs of the validity of the axioms of ZI in arithmetical interpretations use some strengthening of Solovay's result about interpretability in Godel-Bernays set theory. (shrink)

A Kripke-style semantics developed by de Jongh and Veltman is used to investigate relations between several extensions of interpretability logic, IL.

The decision problem for provability logic remains PSPACE-complete even if the number of propositional atoms is restricted to one.

We present an alternative, purely semantical and relatively simple, proof of the Statman's result that both intuitionistic propositional logic and its implicational fragment are PSPACE-complete.

Bilder gehören zu den ältesten Zeugnissen der menschlichen Kultur. Sie sind, soweit bekannt, wesentlich älter als jede Form des sprachlich vermittelten diskursiven Denkens. Bereits dieser historische Umstand markiert die Bilder als etwas Vortheoretisches. Philosophische Theorien über Bilder stützen von Beginn an diese geschichtliche Kontingenz. Die Bildtheorie verdankt Platon die bis in unsere Tage überaus wirksame Denkposition, dass sich Bilder primär an die Sinnlichkeit wenden und nicht an den Verstand. Eine alte Feindschaft - die zwischen Sprache und Bild, dem Diskursiven und (...) Nicht-Diskursiven oder dem Propositionalen und Nicht-Propositionalen - wurde im Laufe der Zeit von disparat bestehenden philosophischen Traditionen erhärtet. Die seit Anfang der 90er Jahre des 20. Jh. s immer intensiver betriebene Bildtheorie konzentriert sich ebenfalls auf das, was Bilder von der Sprache trennt. Im folgenden wird dagegen jener Aspekt hervorgehoben, den Bilder mit der Sprache gemeinsam haben. Bilder sind wie sprachliche Äußerungen in erster Linie äußerst flexible und vielseitig einsetzbare Werkzeuge. Die Frage nach ihrer Bedeutung gleicht der Frage nach ihrem Gebrauch durch die Menschen. (shrink)

The difference in formulation of the question of heredity on a different level of knowledge in Brno in the 1830s and after 1850 is discussed in this article. In order to solve the problem the most important source is forshown in the new philosophy of plant physiology and in physics. Mendel was pleased to have met excellent teachers of both these fields. This explanation is an example of Mirko Grmek's thesis: 'l'histoire des sciences est le laboratoire de l'épistomologie'.

Steve Fuller has argued that a scientific discovery will not be recognized unless it can be justified within the history of the relevant science. He cites Mendel's work on genetics, which was not recognized until thirty-five years after its publication, as an example. This essay argues that Mendel's work comes out of the tradition of work by both agricultural breeders and academics in nineteenth century Austria. Thus, Fuller is mistaken, and one must look elsewhere for the neglect of Mendel's work. (...) This essay also places Mendel's work within the philosophy of Jan Comenius, whose work was very likely known to Mendel.--------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- -----------------------------------------------. (shrink)

Efforts to bring science into early 19th century breeding practices in Central Europe, organised from Brno, the Hapsburg city in which Mendel would later turn breeding experiments into a body of timeless theory, are here considered as a significant prelude to the great discovery. During those years prior to Mendel's arrival in Brno, enlightened breeders were seeking ways to regulate the process of heredity, which they viewed as a force to be controlled. Many were specialising in sheep breeding for the (...) benefit of the local wool industry while others were showing an interest in commercial plants, especially fruit trees and vines, and later cereals. Breeders explained their problems in regulating heredity in terms of climatic influences disruption due to crossing sports or saltations. Practical experience led them to the concepts of 'inheritance capacity' and the 'mutual elective affinity' of parents. The former was seen to differ among individuals and also among traits; the latter was proposed as a means of adding strength to heredity. The breeders came to recognise that traits might be hidden and yet transmitted as a 'potential' to future generations. They also grew to understand that heredity would be strengthened when a quality was 'fixed' within a lineage by 'pure blood relations.' Continued selection of the desired quality might then lead to 'a higher perfection.' But the ultimate 'physiological' question about breeding, 'what is inherited and how?,' found no answer. Major figures in this development included Abbot Napp, the one who asked this question and who was due to receive Mendel into the monastery in 1843, and Professor Diebl whose lectures on agriculture and natural science at the Brno Philosophical Institute Mendel would attend in 1846. Here we analyse their progress in theorizing about breeding up until about 1840. In discussing this development, we refer to certain international contacts, especially with respect to information transfer and scientific education, within the wider context of the late Enlightenment. (shrink)

Each closed (i.e. variable free) formula of interpretability logic is equivalent in ILF to a closed formula of the provability logic G, thus to a Boolean combination of formulas of the form n.

[Publisher's description:] When can we be morally responsible for our behavior? Is it fair to blame people for actions that are determined by heredity and environment? Can we be responsible for the actions of relatives or members of our community? In this provocative book, Tamler Sommers concludes that there are no objectively correct answers to these questions. Drawing on research in anthropology, psychology, and a host of other disciplines, Sommers argues that cross-cultural variation raises serious problems for theories that propose (...) universally applicable conditions for moral responsibility. He then develops a new way of thinking about responsibility that takes cultural diversity into account. -/- Relative Justice is a novel and accessible contribution to the ancient debate over free will and moral responsibility. Sommers provides a thorough examination of the methodology employed by contemporary philosophers in the debate and a challenge to Western assumptions about individual autonomy and its connection to moral desert. (shrink)

We study Fermat's last theorem and Catalan's conjecture in the context of weak arithmetics with exponentiation. We deal with expansions of models of arithmetical theories (in the language ) by a binary (partial or total) function e intended as an exponential. We provide a general construction of such expansions and prove that it is universal for the class of all exponentials e which satisfy a certain natural set of axioms. We construct a model and a substructure with e total and (...) (Presburger arithmetic) such that in both and Fermat's last theorem for e is violated by cofinally many exponents n and (in all coordinates) cofinally many pairwise linearly independent triples. On the other hand, under the assumption of ABC conjecture (in the standard model), we show that Catalan's conjecture for e is provable in (even in a weaker theory) and thus holds in and. Finally, we also show that Fermat's last theorem for e is provable (again, under the assumption of ABC in ) in “coprimality for e”. (shrink)

Axiomatization of Gödel-Dummett predicate logics S2G, S3G, and PG, where PG is the weakest logic in which all prenex operations are sound, and the relationships of these logics to logics known from the literature are discussed. Examples of non-prenexable formulas are given for those logics where some prenex operation is not available. Inter-expressibility of quantifiers is explored for each of the considered logics.

The persisting controversial interpretation of constant hybrids and of the term Entwicklungsgeschichte, mentioned by Mendel in the Pisum paper, is elucidated in the context of his experiments with other plant species and of the growth of knowledge in scientific animal and plant breeding in Moravia.

Die Philosophie wurde von so unterschiedlichen Philosophen wie Wolff und Russell als Moglichkeitswissenschaft bezeichnet. Doch erwiesen sich die modalen Konzepte von Moglichkeit und Notwendigkeit als sperrig und vieldeutig, und ihr Verhaltnis zum Wirklichkeitsbegriff bleibt problematisch. Die vorliegende Sammlung beleuchtet die Metaphysik und Logik von Moglichkeit und Wirklichkeit aufs Neue und betrachtet sie aus unterschiedlichsten Perspektiven jenseits der Dichotomie von analytischer und kontinentaler Philosophie. Die Philosophiegeschichte (von der griechischen Antike bis zu David Lewis) kommt ebenso zu Wort wie die Semantik moglicher (...) Welten; Logik, Mathematik und Computerwissenschaft ebenso wie Literatur und Neue Medien; Formen des wissenschaftlichen ebenso wie des fiktionalen Diskurses. Philosophy has been called the science of the possible by philosophers as diverse as Christian Wolff and Bertrand Russell. The modal concepts of possibility and necessity, however, have proved to be ambiguous and recalcitrant to analysis, and their relation to the concept of reality have remained problematic up to the present day. Transcending the worn-out dichotomy between analytic and continental philosophy, this collection of papers takes a fresh look at the metaphysics and logic of possibility and reality, and illuminates them from a great variety of perspectives. Topics include the history of philosophy (from Greek antiquity to David Lewis) as well as the semantics of possible worlds; logic, mathematics and computer science as well as literature and the new media; forms of scientific as well as fictional discourse.". (shrink)

I aim to alleviate the pessimism with which some philosophers regard the 'objective attitude', thereby removing a particular obstacle which P.F. Strawson and others have placed in the way of more widespread scepticism about moral responsibility. First, I describe what I consider the objective attitude to be, and then address concerns about this raised by Susan Wolf. Next, I argue that aspects of certain attitudes commonly thought to be opposed to the objective attitude are in fact compatible with it. Finally, (...) I examine the prospects of someone who wishes to adopt the objective attitude permanently. In response to philosophers who claim that this would be psychologically impossible, I argue that our commitment to attitudes that presuppose moral responsibility can soften and fade, often without our noticing it. (shrink)

Reviewers of this book have praised Christina Hoff Sommer's well-reasoned argument against many feminists' reliance on misleading, politically motivated 'facts' about how women are victimised.

Relational egalitarianism, the view that social equality is fundamentally about equal relationships, has a problem addressing intergenerational justice. Specifically, how can we have any relationship, egalitarian or otherwise, with people that we do not overlap with temporally? I argue that the problem is even greater than that since we do not overlap in many other relevant ways, and are not in relationships with most of our temporal peers either. If relational equality relies on actual relationships, it cannot succeed as an (...) account of justice. However, we stand in certain social relations to one another, less direct than relationships, that might connect us, in an egalitarian fashion, to many more people than the ones with whom we have relationships. If this account, or one like it, cannot succeed, however, we may have to give up on relational egalitarianism altogether. (shrink)

Jenseits von Gut und Böse ist ein Werk, mit dem Nietzsche einen neuen Ton fand, um so die „Philosophie der Zukunft“ zu initiieren. Es untergräbt gewohnte Gewissheiten in fundamentalphilosophischer, religiöser, moralischer und politischer Hinsicht. Zugleich verspricht es, die Perspektiven, das Leben der Leser grundlegend zu verändern. Signalbegriffe wie „Wille zur Macht“ und „Sklaven-Moral“ dürfen nicht als feste Lehren missverstanden werden.

An Invitation to Formal Reasoning introduces the discipline of formal logic by means of a powerful new system formulated by Fred Sommers. This system, term logic, is different in a number of ways from the standard system employed in modern logic; most striking is its greater simplicity and naturalness. Based on a radically different theory of logical syntax than the one Frege used when initiating modern mathematical logic in the 19th Century, term logic borrows insights from Aristotle's syllogistic, Scholastic logicians, (...) Leibniz, and the 19th century British algebraists. Term logic takes its syntax directly from natural language, construing statements as combinations of pairs of terms, where complex terms are taken to have the same syntax as statements. Whereas standard logic requires extensive 'translation' from natural language to symbolic language, term logic requires only 'transcription' into the symbolic language. Its naturalness is the result of its ability to stay close to the forms of sentences usually found in every day discourse. Written by the founders of the term logic approach, An Invitation to Formal Reasoning is a unique introduction and exploration of this new system, offering numerous exercises and examples throughout the text. Summarising the standard system of mathematical logic to set term logic in context, and showing how the two systems compare, this book presents an alternative approach to standard modern logic for those studying formal logic, philosophy of language or computer theory. Fred Sommers is Professor Emeritus, Brandeis University, USA; George Englebretsen is Professor of Philosophy, Bishop's University, Canada. (shrink)

This paper develops a sympathetic critique of recent experimental work on free will and moral responsibility. Section 1 offers a brief defense of the relevance of experimental philosophy to the free will debate. Section 2 reviews a series of articles in the experimental literature that probe intuitions about the "compatibility question"—whether we can be free and morally responsible if determinism is true. Section 3 argues that these studies have produced valuable insights on the factors that influence our judgments on the (...) compatibility question, but that their general approach suffers from significant practical and philosophical difficulties. Section 4 reviews experimental work addressing other aspects of the free will/moral responsibility debate, and section 5 concludes with a discussion of avenues for further research. (shrink)

Many believe that we have a duty not to discriminate when we act in certain ‘public’ capacities, for example when it is our job to select among various candidates for a job. In contrast, they deny that we have duties of a similar kind in our private lives, for example in our romantic lives. In this paper, we challenge this well‐entrenched asymmetry. We do so primarily by canvassing and rebutting central arguments to the effect that acting discriminatorily, for example when (...) we date, is something we have a right to, including arguments from: (1) freedom of association, (2) legitimate self‐interest, (3) power and (4) love versus duties. In this way, we challenge a common permissive view regarding private discrimination. (shrink)

English summary: The idea of a negative dialectics encapsulates the critical theory of Theodor W. Adorno in its entirety. In a critical engagement with Hegel's philosophy, Adorno develops a dialectic that is no longer tied to the idealistic concept of a speculative identity of subject and object, yet nevertheless aims at a concept of the absolute. So far neither the scope nor the argumentative consistency of this model of dialectics has been taken into account. Marc Nicolas Sommer reconstructs negative (...) dialectics through its engagement with Hegelian dialectics and defends its central claim: that negative dialectics liberates dialectics from its idealistic shackles and in doing so develops a viable concept of the absolute after Auschwitz. German description: Die kritische Theorie Theodor W. Adornos findet ihre vollstandige Artikulation im Konzept einer negativen Dialektik. In kritischer Auseinandersetzung mit der hegelschen Philosophie entwickelt Adorno die Idee einer Dialektik, die nicht mehr an das idealistische Konzept einer spekulativen Identitat von Subjekt und Objekt gebunden ist, deren gedankliche Bewegung dennoch auf einen Begriff des Absoluten ausgerichtet ist. Konzeptueller Anspruch, begrifflicher Umfang und argumentative Konsistenz dieses zweiten grossen Modells dialektischen Denkens sind bis heute nicht geklart.Marc Nicolas Sommer rekonstruiert negative Dialektik aus der Auseinandersetzung mit Hegel und verteidigt ihren Anspruch, den eigentlichen Gehalt der hegelschen Dialektik von seinen idealistischen Schlacken befreit zu haben und aus dieser Denkbewegung einen nach Auschwitz tragfahigen Begriff des Absoluten zu entwickeln. (shrink)

1. Philosophers tend to talk of belief as a ‘propositional attitude.’ As Fodor says:" The standard story about believing is that it's a two place relation, viz., a relation between a person and a proposition. My story is that believing is never an unmediated relation between a person and a proposition. In particular nobody grasps a proposition except insofar as he is appropriately related to some vehicle that expresses the proposition. " Fodor's story – that belief is a three-place relation (...) between a person, a proposition and a vehicle – is hardly non-standard; by assigning to propositions an essential place in acts of belief, he too is a ‘propositionalist’. My own view is that believing is primarily a relation between a believer and the world . While a great many human beliefs are propositional, many, perhaps most, are mondial and propositionless. As for animals who lack language, it may be that all their beliefs are mondial. In the present article, I show that distinguishing these two very different kinds of belief – de mundo as well as de dicto – enables one to explain phenomena of doxastic dissonance that standard propositionalist accounts cannot adequately explain .The next two sections, §1.1 and §1.2, are about ‘the world’ that is the doxastic object in the primary belief relation, providing needed background for the thesis that mondial belief is more primitive and basic than propositional belief.1.1. The world does not contain itself. Things in the world are …. (shrink)

The relative strengths of first-order theories axiomatized by transfinite induction, for ordinals less-than 0, and formulas restricted in quantifier complexity, is determined. This is done, in part, by describing the provably recursive functions of such theories. Upper bounds for the provably recursive functions are obtained using model-theoretic techniques. A variety of additional results that come as an application of such techniques are mentioned.

When Nietzsche published his pamphlet The Case of Wagner in 1888 he succeeded in catching the attention of the reading public after many years of neglect. His radical critique of Wagner is viewed as influential in reception history. The Twilight of the Idols captures the essence of Nietzsche's late philosophy. The work shows Nietzsche at the high point of his creative powers and provides a vivid example of experimental philosophy in practice.

The last posthumous manuscripts from 1888 bear witness to an enormous stylistic and intellectual radicalization. The Antichrist purports to be a total "reevaluation of all values." In Ecce homo, Nietzsche explores the genealogy of his own thinking, opening up new dimensions of self-reflection. Nietzsche contra Wagner sums up the many years of Nietzsche's continuing critique of Wagner, while the Dionysian Dithyrambs seek to breathe new life into lyric poetry.

In the advertising discourse of human genetic database projects, of genetic ancestry tracing companies, and in popular books on anthropological genetics, what I refer to as the anthropological gene and genome appear as documents of human history, by far surpassing the written record and oral history in scope and accuracy as archives of our past. How did macromolecules become "documents of human evolutionary history"? Historically, molecular anthropology, a term introduced by Emile Zuckerkandl in 1962 to characterize the study of primate (...) phylogeny and human evolution on the molecular level, asserted its claim to the privilege of interpretation regarding hominoid, hominid, and human phylogeny and evolution vis-à-vis other historical sciences such as evolutionary biology, physical anthropology, and paleoanthropology. This process will be discussed on the basis of three key conferences on primate classification and evolution that brought together exponents of the respective fields and that were held in approximately ten-years intervals between the early 1960s and the 1980s. I show how the anthropological gene and genome gained their status as the most fundamental, clean, and direct records of historical information, and how the prioritizing of these epistemic objects was part of a complex involving the objectivity of numbers, logic, and mathematics, the objectivity of machines and instruments, and the objectivity seen to reside in the epistemic objects themselves. (shrink)

Largely unacknowledged by historians of the human sciences, late-19th-century psychical researchers were actively involved in the making of fledgling academic psychology. Moreover, with few exceptions historians have failed to discuss the wider implications of the fact that the founder of academic psychology in America, William James, considered himself a psychical researcher and sought to integrate the scientific study of mediumship, telepathy and other controversial topics into the nascent discipline. Analysing the celebrated exposure of the medium Eusapia Palladino by German-born Harvard (...) psychologist Hugo Münsterberg as a representative example, this article discusses strategies employed by psychologists in the United States to expel psychical research from the agenda of scientific psychology. It is argued that the traditional historiography of psychical research, dominated by accounts deeply averse to its very subject matter, has been part of an ongoing form of ‘boundary-work’ to bolster the scientific status of psychology. (shrink)

Retributive emotions and behavior are thought to be adaptive for their role in improving social coordination. However, since retaliation is generally not in the short-term interests of the individual, rational self-interest erodes the motivational link between retributive emotions and the accompanying adaptive behavior. I argue that two different sets of norms have emerged to reinforce this link: (1) norms about honor and (2) norms about moral responsibility and desert. I observe that the primary difference between these types of retribution motivators (...) lies in where the normative focus is placed after an offense. In the first form of retribution, the normative focus is on the offended party. In the second, it is on the offender. Next, I show how each class of norms is well tailored to the particular features of the environment in which these forms of retributive behavior emerge. Finally, I consider some philosophical implications of these observations. I suggest that my account, if correct, would pose tough challenges for contemporary philosophical theories of moral responsibility and punishment. (shrink)

The Zhuangzi is one of the richest early Chinese sources for exploring conceptualizations of the visceral human form. Zhuangzi presents the human frame as a corpus of flesh, organs, limbs, and bone; he dissects it before the reader's eyes, turning it inside out and joyfully displaying its fragmented joints, sundered limbs, and beautifully monstrous mutations. This body is a site of immolation and fragmentation that ultimately evokes a larger wholeness and completeness. Drawing and quartering the body, Zhuangzi paradoxically frees it (...) from ordinary mortality. -/- Sommer explores the fields of meaning of different terms for the human body found in the Zhuangzi: the body might appear there as a gong body 躬, a sanctimonious ritualized body; as a shen body 身, a site of familial and social personhood; or as a ti body 體, a complex, multilayered corpus of multiple parts, each of which is consubstantial with the whole. Most commonly, however, the body in the Zhuangzi is the xing 形, an elemental or structural form. Zhuangzi enlivens and develops the xing form in ways that are not seen in other early Chinese texts. He mutilates and mutates it such that boundaries between form and formlessness disappear, and the physical frame becomes incorporated into a larger common body that includes all of life and death. (shrink)