In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it (...) is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. (shrink)

In his Complaint of Peace, the great sixteenth-century humanist Erasmus allows "Peace" to talk. Peace speaks as a plaintiff, protesting her shabby treatment at the hands of humankind and our ever-ready inclination to launch wars. Against this lure of warfare, Erasmus pits the higher task of peace-building, which can only succeed through the cultivation of justice and respect for all human life. First articulated in 1517, the complaint of peace has echoed through subsequent centuries and down to our age--an age (...) convulsed by world wars, holocausts, and ethnic cleansings. Distinguished political scientist Fred Dallmayr traces this complaint from the writings of Erasmus through the evolution of the "law of nations" to recent and contemporary co-plaintiffs in the West. He also highlights the role of non-Western thinkers and teachings in giving voice to "Peace." In addition to Erasmus, Dallmayr engages major thinkers such as Francisco de Vitoria, Hugo Grotius, Immanuel Kant, Hannah Arendt, Martin Heidegger, Mahatma Ghandi, the Dalai Lama, John Rawls, and Martha Nussbaum. This timely book urgently pleads for greater attentiveness to peace's complaint as an antidote to the prevailing culture of violence and the escalating danger of nuclear catastrophe. Dallmayr offers not only a compelling historical narrative, but powerful ethical and religious arguments vindicating the primacy of peace over violence and war. (shrink)

This paper developes a relational---as opposed to a functional---theory of types. The theory is based on Hilbert and Bernays' eta operator plus the identity symbol, from which Church's lambda and the other usual operators are then defined. The logic is intended for use in the semantics of natural language.

We present Logical Description Grammar (LDG), a model ofgrammar and the syntax-semantics interface based on descriptions inelementary logic. A description may simultaneously describe the syntacticstructure and the semantics of a natural language expression, i.e., thedescribing logic talks about the trees and about the truth-conditionsof the language described. Logical Description Grammars offer a naturalway of dealing with underspecification in natural language syntax andsemantics. If a logical description (up to isomorphism) has exactly onetree plus truth-conditions as a model, it completely specifies thatgrammatical (...) object. More common is the situation, corresponding tounderspecification, in which there is more than one model. A situation inwhich there are no models corresponds to an ungrammatical input. (shrink)

In 2000, Rüdiger Thiele [1] found in a notebook of David Hilbert, kept in Hilbert's Nachlass at the University of Göttingen, a small note concerning a 24th problem. As Hilbert wrote, he had considered including this problem in his famous problem list for the International Congress of Mathematicians in Paris in 1900.

In a recent paper we have defined an analytic tableau calculus PL_16 for a functionally complete extension of Shramko and Wansing's logic based on the trilattice SIXTEEN_3. This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logic---such as the relations |=_t, |=_f, and |=_i that each correspond to a lattice order in SIXTEEN_3; and |=, the intersection of |=_t and |=_f,. -/- It turns out that our method of characterising these semantic relations---as (...) intersections of auxiliary relations that can be captured with the help of a single calculus---lends itself well to proving interpolation. All entailment relations just mentioned have the interpolation property, not only when they are defined with respect to a functionally complete language, but also in a range of cases where less expressive languages are considered. For example, we will show that |=, when restricted to L_{tf}, the language originally considered by Shramko and Wansing, enjoys interpolation. This answers a question that was recently posed by M. Takano. (shrink)

This paper argues for the idea that in describing language we should follow Haskell Curry in distinguishing between the structure of an expression and its appearance or manifestation . It is explained how making this distinction obviates the need for directed types in type-theoretic grammars and a simple grammatical formalism is sketched in which representations at all levels are lambda terms. The lambda term representing the abstract structure of an expression is homomorphically translated to a lambda term representing its manifestation, (...) but also to a lambda term representing its semantics. (shrink)

Entlang zweier großer Entwicklungslinien werden, ausgehend von Descartes, dem Begründer der Transzendentalphilosophie, bis hin zum Ende des 19. Jahrhunderts, die bedeutendsten philosophischen Konzeptionen dargestellt: die an strenger epistemologischer Begründung orientierte Philosophie und lebensphilosophische Ansätze. Die entscheidende Leistung in erster Hinsicht vollzieht die Periode bis Kant mit der Überwindung der alten, ontologisch ausgerichteten Metaphysik und mit der Aufklärung; zugleich mit dieser Entwicklung werden ihre mannigfachen Zusammenhänge mit der lebensphilosophische...

The effects of utterances such as cue phrases, keep-turn markers, and grounding signals cannot be characterized as changes to a shared record of the propositions under discussed: the simplest (and arguably most natural) way of characterizing the meaning of these utterances is in terms of a theory in which the conversational score is seen as a record of the discourse situation, or at least of the speech acts that have been performed. The problem then becomes to explain how discourse entities (...) are accessible. We consider three hypotheses about the dynamics of a speech act-based theory of the conversational score, and argue that they could be implemented with relatively minor modifications to the technical tools already introduced in theories such as Compositional DRT. (shrink)

ArgumentIn the decade between 1983 and 1993, Herbert Mehrtens in West Berlin and I in East Berlin communicated closely about our parallel work on mathematics under the National Socialist (NS) regime. For a short period (1988–89), we worked on a joint book on this topic. We agreed that the book should be based primarily on empirical historical material, using a theoretical approach largely guided by Mehrtens’ work on social systems in mathematics (Mehrtens1981, 1987a). However, parallel work for his habilitation thesis (...) on modernity in mathematics increasingly captivated Mehrtens’ interests. This, together with ongoing resistance among older mathematicians and the insecurities of our individual careers during times of considerable political change, particularly in East Germany, led to the failure of our joint project.This paper aims at reconstructing—mostly by drawing on correspondence—parts of the dialogue between Mehrtens and me at the time. Our dialogue was influenced by our different upbringing and socialization in the two parts of Germany, and by different, though complementary, views about the combination of empirical and theoretical approaches to the historiography of mathematics.In the epilogue, I describe how my later work in the decades from the 1990s on the history of mathematics profited much from Mehrtens’ early theoretical and empirical work but was less influenced by his book on modernity. That later work of mine was, however, mostly done at a time when Mehrtens had largely left the field and considered himself increasingly as a “cultural scientist” (Kulturwissenschaftler). (shrink)

This volume comprises original articles by leading authors – from philosophy as well as sociology – in the debate around relativism in the sociology of (scientific) knowledge. Its aim has been to bring together several threads from the relevant disciplines and to cover the discussion from historical and systematic points of view. Among the contributors are Maria Baghramian, Barry Barnes, Martin Endreß, Hubert Knoblauch, Richard Schantz and Harvey Siegel.

The major part of our beliefs and our knowledge of the world is based on, or grounded in, sensory experience. But, how is it that we can have perceptual beliefs that things are thus and so, and, moreover, be justified in having them? What conditions must experience satisfy to rationally warrant, and not merely to cause, our beliefs? Against the currently very popular contention that experience itself already has to be propositionally and conceptually structured, I will rehabilitate the claim that (...) there is given element in experience which is independent of thought and which is possessed of a distinctive nonpropositional and nonconceptual content. Further, I will argue that this given element is indeed fit to play a significant evidential role in the justification of our beliefs about the world. (shrink)

Auf der Arbeitstagung der Deutschen Gesellschaft fur Soziologie im Oktober 1961 hielten Karl R. Popper und Theodor W. Adorno Referate zur -Logik der Sozialwissenschaften-. Dies leitete den -Positivismusstreit- in der deutschen Soziologie ein, an dem sich prominent vor allem Jurgen Habermas auf Seiten der Kritischen Theorie der Frankfurter Schule und Hans Albert auf Seiten des Kritischen Rationalismus beteiligten. Der daraus entstandene Sammelband, der 1969 kurz vor dem Tod Adornos erschien, wurde im deutschen Sprachraum viel gelesen und diskutiert. Das -Adorno-Jahr- 2003 (...) und das -Popper-Jahr- 2004 gaben Anlass, sich mit den Fragen erneut auseinander zu setzen, die der Positivismusstreit aufgeworfen hat, und sie aus heutiger Sicht neu zu beleuchten. Dies wurde in den Referaten eines Symposiums der Karl Popper Foundation Klagenfurt unternommen. Dieser Sammelband beinhaltet die uberarbeiteten Referate dieses Symposiums. In ihnen werden die methodologische, die politische und die soziologische Dimension der damaligen Auseinandersetzungen mit heute dominierenden Themen und Positionen konfrontiert, was bisher in der einschlagigen wissenschaftlichen Diskussion nicht erfolgt ist.". (shrink)

This paper shows how the dynamic interpretation of natural language introduced in work by Hans Kamp and Irene Heim can be modeled in classical type logic. This provides a synthesis between Richard Montague's theory of natural language semantics and the work by Kamp and Heim.

We explore the different meanings of “quantum uncertainty” contained in Heisenberg’s seminal paper from 1927, and also some of the precise definitions that were developed later. We recount the controversy about “Anschaulichkeit”, visualizability of the theory, which Heisenberg claims to resolve. Moreover, we consider Heisenberg’s programme of operational analysis of concepts, in which he sees himself as following Einstein. Heisenberg’s work is marked by the tensions between semiclassical arguments and the emerging modern quantum theory, between intuition and rigour, and between (...) shaky arguments and overarching claims. Nevertheless, the main message can be taken into the new quantum theory, and can be brought into the form of general theorems. They come in two kinds, not distinguished by Heisenberg. These are, on one hand, constraints on preparations, like the usual textbook uncertainty relation, and, on the other, constraints on joint measurability, including trade-offs between accuracy and disturbance. (shrink)

In this paper it is shown how the DRT (Discourse Representation Theory) treatment of temporal anaphora can be formalized within a version of Montague Semantics that is based on classical type logic.

Original papers by leading international authors address the most important problem in the philosophy of language, the question of how to assess the prospects of developing a tenable theory of meaning, given the influential sceptical attacks mounted against the concept of meaning by Willard Van Quine and Saul Kripke and their adherents in particular. Thus the texts attempt to answer the fundamental questions of whether there are meanings, and, if there are, of what they are and of the form a (...) serious philosophical theory of meaning should take.". (shrink)