For many centuries, a predominant view of meaning was that the meaning of a word is some kind of chunk of mind-stuff (“idea”) glued to the word and animating it. However, while the traditional view was that we must first understand meaning, which enables us to understand language and hence our linguistic practices, a new approach to semantics that has emerged in the second half of the twentieth century, and which I see as marking the future of meaning, suggests that (...) it is our linguistic practices on which we must concentrate from the beginning. In this paper I suggest a specific understanding of these practices, yielding the conclusion that meanings are reasonably seen as creatures of our activity of setting up certain systems of rules, thus opening up new kinds of virtual spaces which we can “enter”. Meaning is what emerges within the intricately orchestrated space that we have somehow managed to bring into being by means of accepting the rules which are in charge of our language games, especially the game of giving and asking for reasons. (shrink)

The question how to turn the principles implicitly governing the concept of truth into an explicit definition of the concept hence coalesced with the question how to get a finite grip on the infinity of T-sentences. Tarski's famous and ingenious move was to introduce a new concept, satisfaction, which could be, on the one hand, recursively defined, and which, on the other hand, straightforwardly yielded an explication of truth. A surprising 'by-product' of Tarski's effort to bring truth under control was (...) the breathtaking finding that truth is in a precisely defined sense ineffable, that no non trivial language can contain a truth-predicate which would be adequate for the very 4 language. This implied that truth proved itself to be strangely 'language-dependent': we can have a concept of truth-in-L for any language L, but we cannot have a concept of truth applicable to every language. In a sense, this means, as Quine put it, that truth belongs to "transcendental metaphysics", and Tarski's 'scientific' investigations seem to lead us back towards a surprising proximity of some more traditional philosophical views on truth. 3. TARSKI'S THEORY AS A PARADIGM So far Tarski himself. Subsequent philosophers then had to find out what his considerations of the concept of truth really mean and what are their consequences; and this now seems to be an almost interminable task. (shrink)

What is a minimal proof-theoretical foundation of logic? Two different ways to answer this question may appear to offer themselves: reduce the whole of logic either to the relation of inference, or else to the property of incompatibility. The first way would involve defining logical operators in terms of the algebraic properties of the relation of inference—with conjunction $$\hbox {A}\wedge \hbox {B}$$ A ∧ B as the infimum of A and B, negation $$\lnot \hbox {A}$$ ¬ A as the minimal (...) incompatible of A, etc. The second way involves introducing logical operators in terms of the relation of incompatibility, such that X is incompatible with $$\{\lnot \hbox {A}\}$$ { ¬ A } iff every Y incompatible with X is incompatible with {A}; and X is incompatible with $$\{\hbox {A}\!\wedge \!\hbox {B}\}$$ { A ∧ B } iff X is incompatible with {A,B}; etc. Whereas the first route leads us naturally to intuitionistic logic, the second leads us to classical logic. The aim of this paper is threefold: to investigate the relationship of the two approaches within a very general framework, to discuss the viability of erecting logic on such austere foundations, and to find out whether choosing one of the ways we are inevitably led to a specific logical system. (shrink)

Carnap’s search for a criterion of empirical significance is usually considered a failure. I argue that the results from two out of his three different approaches are at the very least problematic, but that one approach led to success. Carnap’s criterion of translatability into logical syntax is too vague to allow for definite results. His criteria for terms—introducibility by chains of reduction sentences and his criterion from “The Methodological Character of Theoretical Concepts”—are almost trivial and have no clear relation to (...) the empirical significance of sentences. However, his criteria for sentences—translatability, verifiability, falsifiability, confirmability—are usable, and under the assumptions needed for the Carnap sentence approach, verifiability, falsifiability, and translatability become equivalent. As a result of the Carnap sentence approach, metaphysics is rendered analytic. (shrink)

Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.

Hans Reichenbach’s position in the debate over scientific realism is remarkable. On the one hand, he endorsed the programmatic premises of logical empiricism; on the other, he explicitly employed a realist approach to conceptions such as reference, causality, and inference to the best explanation. How could that work out? It will be shown in the present paper that in Reichenbach’s view scientific realism is not, as frequently assumed, opposed to logical empiricism but rather to logical positivism. A distinction without a (...) difference? Not at all, at least for Reichenbach. As is well known, his particular—probabilistic—variant of logical empiricism was intended to circumvent what he considered the shortcomings of the Vienna Circle’s verificationist approach to the language of science. In Experience and Prediction, Reichenbach became most explicit in this regard. However, I shall argue that his position remained notoriously unstable in the end. It oscillated between a full-fledged scientific realist reading and an eminently pragmatist reading. Nevertheless, Reichenbach’s contribution proved instrumental in preparing subsequent efforts at reconciling logical empiricism and scientific realism. (shrink)

The paper examines the interrelationship between mathematics and logic, arguing that a central characteristic of each has an essential role within the other. The first part is a reconstruction of and elaboration on Paul Bernays’ argument, that mathematics and logic are based on different directions of abstraction from content, and that mathematics, at its core it is a study of formal structures. The notion of a study of structure is clarified by the examples of Hilbert’s work on the axiomatization of (...) geometry and Hilbert et al.’s formalist proof theory. It is further argued that the structural aspect of logic puts it under the purview of the mathematical, analogously to how the deductive nature of mathematics puts it under the purview of logic. This is then linked, in the second part, to certain aspects of Gödel’s critique of Carnap’s conventionalism, that ‘mere syntax’ cannot capture the full content of mathematics, which is revealed to be closely related to the characteristic of mathematics argued for by Bernays. Finally, this is connected with Gödel’s latter-day views about two kinds of formality, intensional and extensional, and the relationship between them. (shrink)

I argue that Quine’s early critique of Carnap’s conventionalism is in serious tension with the holism of "Two Dogmas of Empiricism", since his critique of convention- alism makes a compelling case for a privileged status either for logic, or for some other principle by means of which to derive consequences. Based on this, I call for a modification of Quinean holism, on grounds internal to Quine’s views. The result motivates a rehabilitation of Carnap’s notion of framework principles, and a rethinking (...) of logic as a kind of relativised a priori. (shrink)

We shift attention from the development of model theory for demarcated languages to the development of this theory for fragments of a language. Although it is often assumed that model theory for demarcated languages is not compatible with a universalist conception of logic, no one has denied that model theory for fragments of a language can be compatible with that conception. It thus seems unwarranted to ignore the universalist tradition in the search for the origins and development of model theory. (...) This point is illustrated by Carnap’s early semantics and model theory, which he developed within a type theoretical framework and which stand out both for their universalistic treatment and for certain idiosyncratic technicalities by which the construction is supported. One special property is that individuals are context relative in Carnap’s system. This leads to a model theory in which the model domains are more flexible than has been suggested in the literature. (shrink)

G. Schiemer has recently ascribed to Carnap the so-called domains-as-fields conception of models, which he subsequently used to defend Carnap’s treatment of extremal axioms against J. Hintikka’s criticism that the number of tuples in a relation, and not the domain of discourse, is optimised in Carnap’s treatment. We will argue by a careful textual analysis, however, that this domains-as-fields conception cannot be applied to Carnap’s early semantics, because it includes a notion of submodel and subrelation that is not only absent (...) from Carnap’s work at that time, but even contradicts it. As a consequence, Schiemer’s defense of Carnap’s extremal axioms against Hintikka’s criticism fails. We will reconcile Carnap’s treatment of extremal axioms and Hintikka’s observation by taking into account the practice of axiomatics in the early twentieth century. If one realises that, in Carnap’s time, a predicate for the domain of discourse was often introduced in the formal theory, and that Carnap defined such predicates from the basic relations of an axiom system, the apparent disagreement between optimising relations and optimising domains disappears. (shrink)

Keywords: climate change, integrated assessment, knowledge integration, transdisciplinary research, vulnerability, vulnerability assessment. This thesis explores how transdisciplinary knowledge integration can be facilitated in the context of integrated assessments and vulnerability assessments of climate change. Even though knowledge integration is fundamental in such transdisciplinary assessments, the actual process of integrating knowledge is rarely addressed explicitly and methodically. Here, knowledge integration is conceptualised into the subsequent phases of the elaboration of a shared language and the design of a methodology. Three devices for (...) facilitating knowledge integration are put forward: 1. semantic ascent or the shift from speaking in a language to speaking in a meta-language about the former, 2. formalisation or the translation of statements made in ordinary or technical language into a formal language, and 3. knowledge integration methods, which are methods that provide a meta-language for speaking about the knowledge to be integrated and organise the process of integration. Four cases of knowledge integration are presented. First, the general problem of methodology design is addressed and a graphical framework for representing methodologies is presented. Second, the problem of developing a shared language for speaking about vulnerability to climate change is addressed. A formal mathematical framework of vulnerability and related concepts is presented. Third, a special case of methodology design, the integration of computer models in the context of modular integrated assessment modelling is addressed. A modular approach developed in the PIAM project is presented. Fourth, the integration of computer models, this time in the context of a global assessment of coastal vulnerability to sea-level rise, is addressed. A knowledge integration method, which was developed and applied in the DINAS-COAST project, is presented. These cases show that semantic ascent is a useful device in those cases in which it is difficult to directly elaborate a shared language at the beginning of the assessment. Formalisation can contribute to the elaboration of a shared language in those cases in which concepts overlap non trivially in their meanings. More emphasis should be placed on the development and application of iterative knowledge integration methods as iteration is crucial in order to benefit from the mutual learning during the course of the assessment. (shrink)

This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory. The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach (...) within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons, they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How. (shrink)

The paper reconstructs three main stages in the development of Carnap’s approach to language in the years 1931 – 1947. It starts with Carnap’s approach to metalogic in his Viennese Zirkelprotokolle and his Logische Syntax der Sprache from the point of view of one-level approach to the relation between metalanguage and its object-language. It then analyzes Tarski’s turn to semantics in his paper presented at the Paris conference in September 1935, as well as the implications of his view for Carnap’s (...) approach to semantics from 1935 until 1943. Finally, it analyzes Church’s rediscovery of Frege and its impact on Carnap’s shift to the extension/intension distinction in his semantics in the years 1943 – 1947. (shrink)

In the early Analytic Philosophy, the concept of a pseudosentence was used as a polemical device. To try and formalize a sentence without success was a means to ›debunk‹ it as a pseudosentence. The classical example is Heidegger’s dictum of the nothing which noths. But, according to Carnap, not only did Carnap not understand what Heidegger said, but also Heidegger himself must have misunderstood his own utterances! Does Carnap's diagnosis remain intact if one admits the possibility of a misunderstanding and (...) misconstrual on Carnap’s side, too? Should not Carnap's concept of formalization be substituted by that of logico-hermeneutical reconstruction in order to obviate any such infelicities? In everyday communication, we very rarely ever feel the need to undertake a significant effort to understand each other. This attitude is at odds with Friedrich Schleiermacher’s view that misunderstandings are ubiquitous and that one has to actively invest into the establishment of correct understandings. Therefore, one should ask: Are there good reasons to reject the view that we misunderstand ourselves all the time? Or: Is there any worth in the view that misunderstandings are prevalent? The answers developed in this paper are generalized so that they apply to philosophical contexts and a maxim of escalating formalization is formulated. The debate about peer disagreement is adduced as an illustration of philosophical practices that evade the maxim and thus stagnate cognitively. (shrink)

The method of explication has been somewhat of a hot topic in the last 10 years. Despite the multifaceted research that has been directed at the issue, one may perceive a lack of step-by-step procedural or structural accounts of explication. This paper aims at providing a structural account of the method of explication in continuation of the works of Geo Siegwart. It is enhanced with a detailed terminology for the assessment and comparison of explications. The aim is to provide means (...) to talk about explications including their criticisms and their interrelations. There is hope that this treatment will be able to serve as a foundation to a step-by-step guide to be established for explicators. At least it should help to frame and mediate explicative disputes. In closing the enterprise will be considered an explication of ‘explication’, though consecutive explications improving on this one are undoubtedly conceivable. (shrink)

The relationship between Carnap’s Logical Syntax of Language and Wittgenstein’s Tractatus Logico-Philosophicus has been interpreted in several ways during past decades. One of the interpretations has gained keen advocates among Carnap scholars. It was originally provoked by what Caranp said in LSL, and it consists of two parts. First, it indicates that in TLP the possibility of speaking about the logical form of a language within the same language had been foresworn by Wittgenstein, but Carnap proved him wrong by producing (...) a book written exactly in the manner which had been proscribed by Wittgenstein. This is the debate about the possibility of speaking about logical form. Second, Wittgenstein’s dogmatism with regard to the existence of a unique correct grammar at the foundation of the language has been contrasted with Carnap’s open-mindedness in conceiving a boundless ocean of possibilities for constructing logical systems. Interestingly enough, Wittgenstein rambled with rage in reaction to Carnap’s view about the LSL-TLP relationship. But unlike Carnap’s view, which led to a dominant interpretation of the relationship, Wittgenstein’s testimony about the case has been strangely ignored in the history of analytic philosophy. In this paper, I try to make an inquiry about the grounds for Wittgenstein’s dissatisfaction with the Carnapian reading of the LSL-TLP relationship. I will show that Wittgenstein was not totally unfair in his judgment, and that some salient aspects of LSL could be best understood in the light, or rather the gloom, of TLP, and bear a significant resemblance to it. This, however, does not need to diminish the logical and historical significance of LSL. (shrink)

The failed criterion of logical truth proposed by Carnap in the Logical Syntax of Language was based on the determinateness of all logical and mathematical statements. It is related to a conception which is independent of the specifics of the system of the Syntax, hints of which occur elsewhere in Carnap’s writings, and those of others. What is essential is the idea that the logical terms are invariant under reinterpretation of the empirical terms, and are therefore semantically determinate. A certain (...) objection to Carnap’s version of the invariance conception has been repeated several times in the literature. It is based on Gödel incompleteness, which is puzzling, since Carnap’s Syntax is otherwise quite careful to take account of Gödel. We show here that, in fact, the objection is invalid and is based on a confusion about determinacy. Sorting this out is worthwhile not only for the purpose of better understanding Carnap’s thinking in the Syntax, though. The invariance conception is also related to recent work in the philosophy of logic regarding “logicality”—the characterization of logical concepts—following a proposal of Tarski’s. It is even connected to some very recent developments in the foundations of mathematics. (shrink)