The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly conceived. (...) The proof-theory of non-classical logics is a rapidly developing field, and even the generalizations of the ordinary notion of sequent listed in Chapter 1 can hardly be presented in great detail within a single volume. In addition to further investigating the various approaches toward generalized Gentzen systems, it is important to compare them and to discuss their relative advantages and disadvantages. An initial attempt at bringing together work on different kinds of proof systems for modal logics has been made in [188]. Another step in the same direction is [196]. Since Chapter 1 contains introductory considerations and, moreover, every remaining chapter begins with some surveying or summarizing remarks, in this preface I shall only emphasize a relation to philosophy that is important to me, register the sources of papers that have entered this book in some form or another, and acknowledge advice and support. (shrink)

In this paper, we shall consider the so-called cancellation view of negation and the inferential role of contradictions. We will discuss some of the problematic aspects of negation as cancellation, such as its original presentation by Richard and Valery Routley and its role in motivating connexive logic. Furthermore, we will show that the idea of inferential ineffectiveness of contradictions can be conceptually separated from the cancellation model of negation by developing a system we call qLPm, a combination of Graham Priest’s (...) minimally inconsistent Logic of Paradox with q-entailment as introduced by Grzegorz Malinowski. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Still I RiseLynnell Stephani LongYears ago I would not have had the courage to write my story. I was too ashamed to tell anyone my “secret.”I was born June 11, 1963 in Chicago. I found out thirty–seven years after my birth that I was born with severe hypospadias and a bifid scrotum. Surgery was performed at birth, leaving me with a micropenis. My labia were fused to form (...) a scrotum. After a couple of days in the hospital, my parents were able to take home their baby “boy.”Throughout my childhood I had urinary tract infections because of the surgery to move my [End Page 100] urethra from the base of the penis to the tip. For years I would get a burning sensation in the middle of the penis after urination. My endocrinologist at the time concluded that I had an infection of some type, but it was never explained to me where it originated.My mother raised me with my seven siblings on the south side of Chicago. Aside from me jumping rope with the girls, playing with dolls, and sitting when I peed, I had a pretty normal childhood. From an early age, I knew I was different. I was effeminate, and was often called “faggot” by everyone in the neighborhood, including my own brothers. I always liked hanging out with girls. In fact, I believed that I was a girl until my mother, a minister, beat it out of me. Literally.At the age of nine, I was first admitted to a teaching hospital. It was there that I was treated for growth hormone deficiency, hypothyroidism, panhypopituitarism, hypoadrenalism, and hypogonadism. At age 14, while other boys in high school were beginning to become young men, my voice got higher and I started growing breasts. My endocrinologist diagnosed me with gynecomastia and started me on testosterone injections to stop the breast growth, and to help with the masculinization process. To me these changes confirmed what I believed all along: I was indeed female.I took male hormone injections for five years. My endocrinologist convinced me that I could be a “normal” male if I took male hormones; I didn’t want to be male, I wanted to be female. But no one asked me what I wanted. Besides, the testosterone was making me sick. I wouldn’t be diagnosed with PAIS (Partial Androgen Insensitivity Syndrome) until a number of years later. I still remember trips to the hospital like they happened yesterday. There were multiple IVs, MRI’s, CAT scans, and photos taken of me. I still have flashbacks of standing in front of the graph board, naked, while strangers walked in and out of the room.There was no one I could talk to about this. I was never allowed to tell my friends why I was hospitalized numerous times a year. In the black community you don’t talk about family secrets. And that’s what I was, a secret. I would go to school between the hospitalizations and pretend everything was okay. I hated my life. I hated being different. I would get teased in school, but I managed to survive it.One day on a routine office visit—I had to be around 16 at that time—my endocrinologist told me that I was infertile, and could never have kids. He didn’t offer any psychotherapy, just smiled and said “I’ll see you in three months”. I went home that afternoon and attempted suicide for the first time.I was hospitalized every summer, for weeks at a time, for testing. My endocrinologist and his parade of residents awakened me every morning in the hospital. They stood by my bed, peeking under my gown, and talking about me like I was not present. I discontinued my visits to the hospital, and all medications, at the age of twenty–four. I just wanted to be normal, but I knew I wasn’t.The next ten years of my life were full of drinking and getting high, trying to forget that I was different. I did have girlfriends in that time, and I even got married. I was convinced that a... (shrink)

Heinrich Rickert (1863-1936) war einer der bedeutendsten deutschen Philosophen vor dem Zweiten Weltkrieg und gilt neben Wilhelm Windelband als einer der Hauptvertreter der südwestdeutschen Schule des Neukantianismus. Seine auch heute noch anregende Philosophie hatte großen, interdisziplinären wie internationalen Einfluss. Die philologisch-kritische Ausgabe macht die Schriften endlich wieder verfügbar.

Excerpt from Die Prinzipien der Mechanik in Neuem Zusammenhange Dargestellt Wahl eines Berufs entschliefsen mufste, wahlte er den des Ingenieurs. Es scheint, dafs die auch in spateren Jahren als ein charakteristischer Grundzug seines Wesens hervor tretende Bescheidenheit ihn an seiner Begabung fur theore tische Wissenschaft zweifeln liefs, und dafs er sich bei der Beschaftigung mit seinen geliebten mechanischen Arbeiten des Erfolges sicherer fuhlte, weil er deren Tragweite schon damals ausreichend verstand. Vielleicht hat ihn auch die in seiner Vaterstadt herrschende, mehr (...) dem Praktischen zugeneigte Sinnesweise beeinflufst. Ubrigens beobachtet man nicht selten diese Art zaghafter Bescheidenheit gerade bei jungen Leuten von hervorragenden Anlagen. Sie haben wohl eine deutliche Vorstellung von den Schwierigkeiten, die vor der Erreichung des ihnen vorschwebenden hohen Zieles zu uberwinden sind, und mussen ihre Krafte erst praktisch erprobt haben, ehe sie das zu ihrem schweren Werke notige Selbstvertrauen ge winnen. Aber auch in ihrer spateren Entwickelung pflegen reich veranlagte Naturen um so unzufriedener mit ihren eigenen Werken zu sein je hoher ihre Fahigkeiten und ihre Ideale reichen. Die Begabtesten erreichen offenbar nur des halb das Hochste, weil sie am empfindlichsten gegen jede Un vollkommenheit sind, und am unermudlichsten an deren Beseitigung arbeiten. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Heinrich Rickert (1863-1936) was One of the leading neo-Kantian philosophers in Germany and a crucial figure in the discussions of the foundations of the social sciences in the first quarter of the twentieth century. His views were extremely influential, most significantly on Max Weber. The Limits of Concept Formation in Natural Science is Rickert's most important work, and it is here translated into English for the first time. It presents his systematic theory of knowledge and philosophy of science, and (...) deals particularly with historical knowledge and the problem of demarcating the natural from the human sciences. The theory Rickert develops is carefully argued and of great intrinsic interest. It departs from both positivism and neo-Hegelian idealism and is worked out by contrast to the views of others, particularly Dilthey and the early phenomenologists. (shrink)

In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with (...) multiple sequent arrows satisfying some specific conditions, which we will lay out in this paper. We will unfold our ideas with the help of a case study in logical tetralateralism and present an extension of Almukdad and Nelson’s propositional constructive four-valued logic by unary operations of meaningfulness and nonsensicality. We will argue that in sequent calculi with multiple sequent arrows it is possible to maintain certain features that are desirable if we assume an understanding of the meaning of connectives in the spirit of proof-theoretic semantics. The use of multiple sequent arrows will be justified by the presence of congruentiality-breaking unary connectives. (shrink)

A version of strong negation is introduced into Categorial Grammar. The resulting syntactic calculi turn out to be systems of connexive logic.

Justification stit logic is a logic for reasoning about proving as a certain kind of activity, namely seeing to it that a proof is publicly available. It merges the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. In this paper, after recalling its language and basic semantical definitions, various ramifications and refinements of justification stit logic are presented and discussed: imposing natural restrictions upon the class of models under consideration, making (...) use of modalities that assert the existence of a proof, introducing a variant of justification stit logic based on a semantics introduced by M. Fitting, and adding variable-binding operators and extending the set of proof polynomials. (shrink)

Graham Priest takes the relation of identity to be non-transitive. In this paper, we are going to discuss several consequences of identity as a non-transitive relation. We will consider the Henkin-style completeness proof for classical first-order logic with a non-transitive “identity” predicate, Leibniz-identity in Priest’s second-order minimal logic of paradox, and the question whether or not identity of individuals should be defined as Leibniz-identity.

In this paper, Graham Priest’s understanding of dialetheism, the view that there exist true contradictions, is discussed, and various kinds of metaphysical dialetheism are distinguished between. An alternative to dialetheism is presented, namely a thesis called ‘dimathematism’. It is pointed out that dimathematism enables one to escape a slippery slope argument for dialetheism that has been put forward by Priest. Moreover, dimathematism is presented as a thesis that is helpful in rejecting the claim that logic is a normative discipline.

The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is (...) derived that all truths are, in fact, known. Nevertheless, the solution offered is in the spirit of the constructivist attitude usually maintained by defenders of the anti-realist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete. (shrink)

This book is the culmination of Heinrich Meier's acclaimed analyses of the controversial thought of Carl Schmitt. Meier identifies the core of Schmitt's thought as political theology--that is, political theorizing that claims to have its ultimate ground in the revelation of a mysterious or supra-rational God. This radical, but half-hidden, theological foundation unifies the whole of Schmitt's often difficult and complex oeuvre, cutting through the intentional deceptions and unintentional obfuscations that have eluded previous commentators. Relating this religious dimension to (...) Schmitt's support for National Socialism and his continuing anti-Semitism, Meier compels the reader to come to terms with the irreconcilable differences between political theology and political philosophy. His book will give pause to those who have tended to gloss over the troubling aspects of some of Schmitt's ideas. With editions in German, French, Italian, and now English, Meier's two books on Schmitt have dramatically reoriented the international debate about Carl Schmitt and his significance for twentieth-century political thought. "Standing far above the rest . . . is Heinrich Meier's new study, Die Lehre Carl Schmitts , which covers all of Schmitt's writings. . . . Meier's work has forced everyone to take a second look at the assumptions underlying Schmitt's better-known writings and reconsider some that have been ignored."--Mark Lilla, reviewing the German edition in The New York Review of Books. (shrink)

It is widely accepted that there is a clear sense in which the first-order paraconsistent constructive logic with strong negation of Almukdad and Nelson, QN4, is more constructive than intuitionistic first-order logic, QInt. While QInt and QN4 both possess the disjunction property and the existence property as characteristics of constructiveness (or constructivity), QInt lacks certain features of constructiveness enjoyed by QN4, namely the constructible falsity property and the dual of the existence property. This paper deals with the constructiveness of the (...) contra-classical, connexive, paraconsistent, and contradictory non-trivial first-order logic QC, which is a connexive variant of QN4. It is shown that there is a sense in which QC is even more constructive than QN4. The argument focuses on a problem that is mirror-inverted to Raymond Smullyan’s drinker paradox, namely the invalidity of what will be called the drinker truism and its dual in QN4 (and QInt), and on a version of the Brouwer-Heyting-Kolmogorov interpretation of the logical operations that treats proofs and disproofs on a par. The validity of the drinker truism and its dual together with the greater constructiveness of QC in comparison to QN4 may serve as further motivation for the study of connexive logics and suggests that constructive logic is connexive and contradictory (the latter understood as being negation inconsistent). (shrink)

En el artículo se hace la presentación de las ideas que san Agustín destaca sobre la Virgen María en sus sermones de Navidad. Se hace en primer lugar una presentación de dichos sermones, para posteriormente abordar el tema de los dos nacimientos de Cristo, que es usado para explicar las dos naturalezas en Cristo (divina y humana). Se destacan asimismo los sermones navideños en los que san Agustín señala el paralelismo entre la Virgen María y la Iglesia, ya ambas son (...) vírgenes y madres. Como un tema central de los sermones de Navidad de san Agustín, el artículo destaca la virginidad perpetua de María. Finalmente se ofrecen unas conclusiones en las que se pone de manifiesto que los sermones de Navidad de san Agustín que tratan sobre la Virgen María son parte de su “teología predicada”. Así como sus grandes tratados desarrollan la Mariología, sus sermones son la popularización de dicho pensamiento mariano. (shrink)