The ontological argument fails because of an operator order switch between (1) “necessarily there is an perfect being” and (2) “there is a being which necessarily is perfect”. Here (1) is trivially true logically but (2) problematic. Since Kant's criticisms were directed at the notion of existence, not at the step from (1) to (2), they are misplaced. They are also wrong, because existence can be a predicate. Moreover, Kant did not anticipate Frege's claim that “is” is ambiguous between existence, (...) predication, identity, and class‐inclusion. To restore the ontological argument, an extra premise is needed to the effect that it is known who the existentially perfect being is. The question is raised whether Kant could have meant the failure of this extra premise by his thesis that existence is not a real predicate. (shrink)

The 2007 edition of the Amsterdam Colloquium is the Sixteenth in a series which started in 1976. Originally, the Amsterdam Colloquium was an initiative of the Department of Philosophy of the University of Amsterdam. Since 1984 the Colloquium is organized by the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam.

In my thesis, I aim to develop a systematic and philosophically coherent thesis of ultimate reality for Ibn Arabi. In this pursuit, I adopt the style of analytic philosophy, seeking to employ and utilise some of its methods and theories. The philosophical aspects of Ibn Arabi’s doctrine are in dire need of conceptual clarification and systematic analysis with a closer focus on argumentation. The analytic tradition will prove most helpful in this regard. In my thesis, I begin by tracing Ibn (...) Arabi’s related views and concepts as they are dispersed throughout his writings. I then clarify, sharpen and, in many cases, develop these views and concepts into fully constructed forms. Finally, I weave the developed concepts and views into a systematic thesis or set of sub-theses. Where necessary, I provide my own arguments and concepts to help substantiate and strengthen the structure of Ibn Arabi’s thesis. I propose that Ibn Arabi’s various, and sometimes apparently inconsistent, views are best presented in terms of three main concepts: the concept of ultimate reality as existence, which has long been known as Ibn Arabi’s thesis of the oneness of existence ; the concept of ultimate reality as the Divine Self ; and the concept of ultimate reality as God. The three concepts neither represent different ultimate realities nor different perspectives of the same ultimate reality. Instead, they represent the same ultimate reality but each one has its own unique scope and encompassment. The three concepts are aimed at encompassing Ibn Arabi’s various views and concepts of ultimate reality in a consistent and systematic manner. (shrink)

Kaplan (drawing on Montague and Prior, inter alia) made explicit the idea of world and time neutral propositions, which bear truth values only relative to world and time parameters. There was then a debate over the role of time. Temporalists sided with Kaplan in maintaining time neutral propositions with time relative truth values, while eternalists claimed that all propositions specify the needed time information and so bear the same truth value at all times. But there never was much of a (...) parallel debate over the role of worlds. Let contingentism be the view (parallel to temporalism) that sides with Kaplan in maintaining world neutral propositions with world relative truth values, and let necessitarianism be the view (parallel to eternalism) that propositions specify the needed world information and so bear the same truth value at all worlds. This is the story of how the debate between the contingentists and the necessitarians might begin. (shrink)

In the present paper we confront Martin- Löf’s analysis of the axiom of choice with J. Hintikka’s standing on this axiom. Hintikka claims that his game theoretical semantics for Independence Friendly Logic justifies Zermelo’s axiom of choice in a first-order way perfectly acceptable for the constructivists. In fact, Martin- Löf’s results lead to the following considerations:Hintikka preferred version of the axiom of choice is indeed acceptable for the constructivists and its meaning does not involve higher order logic.However, the version acceptable (...) for constructivists is based on an intensional take on functions. Extensionality is the heart of the classical understanding of Zermelo’s axiom and this is the real reason behind the constructivist rejection of it.More generally, dependence and independence features that motivate IF-Logic, can be formulated within the frame of constructive type theory without paying the price of a system that is neither axiomatizable nor has an underlying theory of inference – logic is about inference after all.We conclude pointing out that recent developments in dialogical logic show that the CTT approach to meaning in general and to the axiom of choice in particular is very natural to game theoretical approaches where metalogical features are explicitly displayed at the object language-level. Thus, in some way, this vindicates, albeit in quite of a different manner, Hintikka’s plea for the fruitfulness of game-theoretical semantics in the context of the foundations of mathematics. (shrink)

The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously — having to do, amongst other things, with different scientific mentalities in the two disciplines (section 1). Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the (...) key notion of a scientific theory in a logical perspective. First, various formal explications of this notion are reviewed (section 2), then their further logical theory is discussed (section 3). In the absence of grand inspiring programs like those of Klein in mathematics or Hilbert in metamathematics, this preparatory ground-work is the best one can do here. The paper ends on a philosophical note, discussing applicability and merits of the formal approach to the study of science (section 4). (shrink)

It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke’s new theory of reference are (...) adequately modeled within IIF. Finally, I compare the logic IIF to David Lewis' counterpart theory, drawing some morals concerning the interrelation between metaphysical and semantic issues in possible-world semantics. (shrink)

The dynamic nature ofGame-Theoretical Semantics is emphasized. The role of strategic meaning in accounting for linguistic competence is examined. The semantics of epistemic possibility is shown to involve a dynamic ingredient. Update semantics has been designed to capture it. The paper focuses on the interplay betweenlogical and linguistic competences indiscourse understanding.

This paper presents a novel proof-theoretic account of dialogue coherence. It focuses on an abstract class of cooperative information-oriented dialogues and describes how their structure can be accounted for in terms of a multi-agent hybrid inference system that combines natural deduction with information transfer and observation. We show how certain dialogue structures arise out of the interplay between the inferential roles of logical connectives (i.e., sentence semantics), a rule for transferring information between agents, and a rule for information flow between (...) agents and their environment. The order of explanation is opposite in direction to that adopted in game-theoretic semantics, where sentence semantics (or a notion of valid inference) is derived from winning dialogue strategies. That approach and the current one may, however, be reconcilable, since we focus on cooperative dialogue, whereas the game-theoretic tradition concentrates on adversarial dialogue. (shrink)

A variant of the standard deductive tableau system is introduced, and interrogative rules are added, resulting in a so-called interrogative tableau system. A game-theoretical account of entailment is sketched, and the deductive tableau system is interpreted in these terms. Finally, it is shown how to extend this account of entailment into an account of interrogative entailment, thereby providing a semantics for the interrogative tableau system.

In this paper I shall attempt to compare the dialogue approach originally advocated by Lorenz and Lorenzen and the game-theoretical approach of Hintikka with each other. I shall not try to present any survey of either one of the approaches and will assume that the reader is familiar with the basic ideas of these theories.The original works of Lorenzen and Lorenz have been reprinted in their while Stegmüller contains a survey (in English) of the basic ideas and results. Works in (...) this tradition which apply the approach to quantum logic include Denecke, Mittelstaedt Mittelstaedt and Stachow, Stachow. The reader will also find van Dunn, Krabbe, Lorenz and Stachow to be relevant.The literature on Hintikka’s game-theoretical semantics as applied both to different formal languages (including infinitary languages and intensional logic) and to natural language is rapidly growing. As for the latter, the reader is referred to papers by Hintikka, Carlson and myself reprinted in Saarinen, to Carlson and ter Meulen, and to Saarinen. (shrink)

This paper presents a novel proof-theoretic account of dialogue coherence. It focuses on an abstract class of cooperative information-oriented dialogues and describes how their structure can be accounted for in terms of a multi-agent hybrid inference system that combines natural deduction with information transfer and observation. We show how certain dialogue structures arise out of the interplay between the inferential roles of logical connectives (i.e., sentence semantics), a rule for transferring information between agents, and a rule for information flow between (...) agents and their environment. The order of explanation is opposite in direction to that adopted in game-theoretic semantics, where sentence semantics (or a notion of valid inference) is derived from winning dialogue strategies. That approach and the current one may, however, be reconcilable, since we focus on cooperative dialogue, whereas the game-theoretic tradition concentrates on adversarial dialogue. (shrink)

Without violating the spirit of Game-Theoretical semantics, its results can be re-worked in Martin-Löf''s Constructive Type Theory by interpreting games as types of Myself''s winning strategies. The philosophical ideas behind Game-Theoretical Semantics in fact highly recommend restricting strategies to effective ones, which is the only controversial step in our interpretation. What is gained, then, is a direct connection between linguistic semantics and computer programming.

This essay contains material which will hopefully be of interest not only to philosophers, but also to those social scientists whose research concerns the analysis of communication, verbal or non-verbal. Although most of the topics taken up here are central to issues in the philosophy of language, they are, in my opinion, indistinguishable from topics in descriptive social psychology. The essay aims to provide a conceptual framework within which various key aspects of communication can be described, and it presents a (...) formal language, using techniques from modern modal logic, in which such descriptions can themselves be formulated. It is my hope that this framework, or parts of it, might also turn out to be of value in future empirical work. There are, therefore, essentially two sides to this essay: the development of a framework of concepts, and the construction of a formal language rich enough to express the elements of which that framework is composed. The first of these two takes its point of departure in the statement quoted from Lewis (1972) on the page preceding this introduction. The distinction drawn there by Lewis is accepted as a working hypothesis, and in one sense this essay may be seen as an attempt to explore some of the consequences of that hypothesis. (shrink)

Im ersten Teil unseres Aufsatzes charakterisieren wir den Beitrag der ‘modernen’ Wissenschaftstheorie zur Methodologie des Textverstehens; im zweiten Teil diskutieren wir exemplarisch zwei Konzeptionen der ‘neueren’ Hermeneutik. Ziel dieser kritischen Untersuchungen ist eine Förderung des Dialogs zwischen Wissenschaftstheorie, Hermeneutik und Literaturwissenschaft.

The “dynamic turn” in semantic theory of natural language, which has been taking place roughly during the last decade, has resulted into seeing the meaning of a sentence as a “context-change-potential”, as a function which maps the set of possible contexts on itself. The development of theories of this kind has been stimulated especially by the effort to semantically cope with the anaphoric items of natural language . The most significant species of dynamic semantic theories are represented by Kamp´s “discourse (...) representations theory” and Groenendijk and Stokhof´s “dynamic logic”. The former sees sentences as means of building and rebuilding “discourse representations structures”; the latter, which tries to be an expressly logical objects to “discourse markers” into the same set. The paper presents basic principles of theories of both of these kinds and indicates how they can help us analyse natural language locutions involving anaphora. (shrink)