Constructive Type Theory and the Dialogical Approach to Meaning

In its origins Dialogical logic constituted one part of a new movement called the Erlangen School or Erlangen Constructivism. Its goal was to provide a new start to a general theory of language and of science. According to the Erlangen-School, language is not just a fact that we discover, but a human cultural accomplishment whose construction reason can and should control. The resulting project of intentionally constructing a scientific language was called the Orthosprache-project. Unfortunately, the Orthosprache-project was not further developed and seemed to fade away. It is possible that one of the reasons for this fading away is that the link between dialogical logic and Orthosprache was not sufficiently developed - in particular, the new theory of meaning to be found in dialogical logic seemed to be cut off from both the project of establishing the basis for scientific language and also from a general theory of meaning. We would like to contribute to clarifying one possible way in which a general dialogical theory of meaning could be linked to dialogical logic. The idea behind the proposal is to make use of constructive type theory in which logical inferences are preceded by the description of a fully interpreted language. The latter, we think, provides the means for a new start not only for the project of Orthosprache, but also for a general dialogical theory of meaning

Dialogue in Peirce, Lotman, and Bakhtin: A comparative study

Th e notion of dialogue is foundational for both Juri Lotman and Mikhail Bakhtin. It is also central in Charles S. Peirce’s semeiotics and logic. While there are several scholarly comparisons of Bakhtin’s and Lotman’s dialogisms, these have yet to be compared with Peirce’s semeiotic dialogues. Th is article takes tentative steps toward a comparative study of dialogue in Peirce, Lotman, and Bakhtin. Peirce’s understanding of dialogue is explicated, and compared with both Lotman’s as well as Bakhtin’s conceptions. Lotman saw dialogue as the basic meaning-making mechanism in the semio sphere. Th e benefi ts and shortcomings of reconceptualizing the semiosphere on the basis of Peircean and Bakhtinian dialogues are weighed. Th e aim is to explore methodological alternatives in semiotics, not to challenge Lotman’s initial model. It is claimed that the semiosphere qua model operating with Bakhtinian dialogues is narrower in scope than Lotman’s original conception, while the semiosphere qua model operating with Peircean dialogues appears to be broader in scope. It is concluded that the choice between alternative dialogical foundations must be informed by attentiveness to their diff erences, and should be motivated by the researcher’s goals and theoretical commitments

Formale Dialogspieltheorien

Das Feld der Dialoganalyse umfaßt sehr unterschiedliche theoretische und methodische Ansätze, von der hermeneutischen Erschließung eines bestimmten Einzeldialogs über die quantitative Analyse bestimmter Typen von Dialogverläufen und die systematische Analyse der Grundstrukturen von Dialogformen bis hin zur formalen Theorie eines bestimmten Fragments einer Dialogform. Diese unterschiedlichen Ansätze können miteinander durchaus verträglich sein, insofern als sie unterschiedliche Aspekte des dialogischen Redens zum Gegenstand haben oder unterschiedliche Reichweite beanspruchen. Die in den bisherigen Artikeln dieses Handbuchs behandelten dialoganalytischen Ansätze erheben alle den Anspruch auf Systematizität der Analyse, sind aber keine formalen Theorien im strengen Sinne. Das heißt allerdings nicht, daß sie nicht formalisierbar sind, wie etwa die Formalisierung der Sprechakttheorie in Searle/ Vanderveken (1985) und die formale Beschreibungssprache für Handlungen in Heringer (1974) zeigen

Paul Lorenzen -- Mathematician and Logician

This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen’s systematical ideas in today’s debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen’s work on lattice-groups and divisibility theory, and modern set theory and Lorenzen’s critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen’s consistency proof and Hilbert’s larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz

Proof Search in Multi-Agent Dialogues for Modal Logic

In computer science, and also in philosophy, modal logics play an important role in various areas. They can be used to model knowledge structures among software-agents, behaviour of computer systems, or ontologies. They also provide mathematical tools to perform reasoning in these models, e.g., to extract common knowledge of agents, check whether security-relevant problems might occur when running a program, or to detect contradictions in a set of terminological definitions. Intuitionistic or constructive propositional logic can be considered as a special kind of modal logic. Constructive modal logics, as a combination of intuitionistic propositional logic and classical modal logics, describe a family of modal systems which are, compared to the classical variant, more restrictive concerning the validity of formulas. To prove validity of a statement formalized in such a logic, various reasoning procedures (also called calculi) have been investigated. There are especially many variants of sequent and tableau systems which can be used easily to find proofs by applying given syntactical rules one after another. Sometimes there are different possibilities to find a proof for the same formula within the same calculus. It also happens that a bad choice of non-invertible rule applications at the wrong time makes it impossible to finish the proof successfully, although the formula is provable. For this reason, a normalization of deductions in a calculus is desired. This restricts the possibilities to apply rules arbitrarily and emphasizes the situations in which significant, non-invertible rule applications are necessary. Such a normalization is enforced in so-called focused sequent systems. Another attempt to find a normalized calculus leads to dialogical logic, a game-theoretic reasoning technique. Usually, two players, one proponent and one opponent, argue about an assertion, expressed as a formula and stated by the proponent at the beginning of the play. The kinds of arguments, namely attacks and defences, are bound to special game rules. These are designed in such a way that the proponent has a winning strategy in the game if and only if his initial statement is a valid formula. The dialogical approach is very flexible as the game rules can be adjusted easily. Sets of rules exist to perform reasoning in many different kinds of logic, however proving soundness and completeness of dialogical calculi is complex and, if at all, often only considered very roughly in the literature. The standard two-player dialogues do not have much potential to enforce normalization like focus sequent systems. However, it turns out that introducing further proponent-players who fight against one opponent in a round-based setting leads to a normalization as described above. The flexibility of two-player games is largely preserved in multi-proponent dialogues. Other ordinary sequent systems can easily be transferred into the dialectic setting to achieve a normalization. Further, the round-based scheduling induces a method to parallelize the reasoning process. Modifying the game rules makes it possible to construct new intermediate or even more restrictive logics. In this work, dialogical systems with multiple proponents are presented for intuitionistic propositional logic and modal logics S4 and CS4. Starting with the former one, it is shown that the normalization can be transferred easily to both the latter systems. Informal game rules are introduced and, to make them concrete and unambiguous, translated into the dialogical sequent-style calculi DiaSeqI, DiaSeqS4, and DiaSeqCS4. An extra system for intuitionistic logic, which guarantees termination in proof searches, even if the target formula is not valid, is also provided. Soundness and completeness of all these presented dialogical sequent calculi is proven formally, by showing that it is always possible to translate derivations in the game-oriented approach into another sound and complete sequent system and vice versa. Thereby, a new (ordinary) multi-conclusion sequent calculus for CS4 is introduced for which adequateness is shown, too. The multi-proponent dialogical systems of this work are compared to different sequent calculi and other dialogical attempts found in literature. A comprehensive survey of such approaches is also part of this thesis

Empirismo e semantica: da Rudolf Carnap all'epistemologia contemporanea

Empiricism and Semantics: From Rudolf Carnap to Contemporary Epistemology In recent years analytic philosophy has developed a deeper interest in the historiographical reconstruction of its roots. This interest is testified by many publications, which have appeared since the 90’s, about the life and thought of classical authors of analytic tradition, like Frege, Russell, Wittgenstein, Carnap and Tarski. In my doctoral thesis I take up this line, focusing on two famous works of Rudolf Carnap: Der logische Aufbau der Welt, published in 1928, and Logische Syntax der Sprache, published in 1934. The main reference points of my historical and philosophical research are Jorge Alberto Coffa and Michael Friedman: I try to imitate their style of combining the analysis of technical aspects of logic and philosophy of language with broader considerations about conceptual trends and theoretical contexts. In the first chapter I present Carnap’s attempt in 1928 to build a symbolic system that formalizes scientific concepts. With this technique of formalization Carnap aims for the reduction of science to subjective experiences. The Aufbau can be seen as a programmatic manifesto of a verificationist theory of meaning, belonging to the empiricist tradition – as Quine indicated in his famous critic. Nevertheless, in the book there are strong influences of the Neokantian school, which link Carnap’s thought to 19th century transcendental philosophy. In the chapter, I highlight the points of the Aufbau in which a “transcendental scheme” can be identified; particularly, the concept of structure, that plays an important role in Carnap’s arguments, shows a kinship with the Kantian tradition. In addition, I emphasize the problematic status of solipsism in the carnapian system. The second chapter begins with a summary of the Protocol Sentence Debate among the members of the Vienna Circle in the early 30’s. Discussing the function of protocol sentences in the epistemology of logical empiricism, one has to deal with the task of explaining the syntactical relation that the authors had in mind, when they were disputing the foundation of theoretical sentences through the protocols. With regard to this subject, I start to analyze Logische Syntax der Sprache, whose main goal is to define the concept of consequence, a syntactical/semantic relation broader than that determined by the usual rules of derivation in axiomatic systems. Coping with this problem, Carnap develops some technical devices that are pretty close to Tarski’s definition of truth. The chapter finishes with a brief survey of the significance of tarskian semantics for contemporary philosophy of science. The third chapter consists of the synthetic exposition of an original approach to the problems of formalization and semantics, developed in the 60’s and 70’s by Paul Lorenzen and his scholars. The Erlangen School of epistemological constructivism is here considered because it doesn’t assume the standard opposition between syntax and semantics, the conceptual cornerstone of Carnap’s and Tarski’s analysis of scientific theories. Lorenzen’s approach emphasizes the instrumental and operational elements of the scientific practice; at the same time, he advocates a conception of language in which pragmatics plays a prominent role, encompassing the syntactical and the semantic dimensio

Beyond Logic. Proceedings of the Conference held in Cerisy-la-Salle, 22-27 May 2017

The project "Beyond Logic" is devoted to what hypothetical reasoning is all about when we go beyond the realm of "pure" logic into the world where logic is applied. As such extralogical areas we have chosen philosophy of science as an application within philosophy, informatics as an application within the formal sciences, and law as an application within the field of social interaction. The aim of the conference was to allow philosophers, logicians and computer scientists to present their work in connection with these three areas. The conference took place 22-27 May, 2017 in Cerisy-la-Salle at the Centre Culturel International de Cerisy. The proceedings collect abstracts, slides and papers of the presentations given, as well as a contribution from a speaker who was unable to attend

Toward Truthlikeness in Historiography

Truthlikeness in historiography would allow us to be optimistic fallible realists about historiography – to hold that historical knowledge is about the past, true albeit fallible, and can increase over time. In this paper, three desiderata for a concept of truthlikeness in historiography will be outlined. One of the main challenges for truthlikeness is historiographic skepticism which holds that historiography is indistinguishable from fiction and cannot therefore furnish us with true knowledge about the past. Such skepticism rests on the postmodern challenge, which will be criticized on the grounds that it rests on an implausible theory of meaning. It will be shown that Peirce’s semeiotic and pragmatist theory of truth, interpreted dialogically or game-theoretically, provides a suitable framework within which to pursue the project of defining a concept of truthlikeness for historiography. Finally, directions for possible future research into truthlikeness in historiography, including ways of defining a measure of truthlikeness, will be considered