This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. -/- The chapters of which this book is composed discuss the (...) subject from a rich variety of angles, including the history of logic, the proper interpretation of logical validity, natural deduction rules, the notions of harmony and of synonymy, the structure of proofs, the logical status of equality, intentional phenomena, and the proof theory of second-order arithmetic. All chapters relate directly to questions that have driven Schroeder-Heister's own research agenda and to which he has made seminal contributions. The extensive autobiographical chapter not only provides a fascinating overview of Schroeder-Heister's career and the evolution of his academic interests but also constitutes a contribution to the recent history of logic in its own right, painting an intriguing picture of the philosophical, logical, and mathematical institutional landscape in Germany and elsewhere since the early 1970s. The papers collected in this book are illuminatingly put into a unified perspective by Schroeder-Heister's comments at the end of the book. Both graduate students and established researchers in the field will find this book an excellent resource for future work in proof-theoretic semantics and related areas. (shrink)

Typically, if I understand a sentence, then it expresses a proposition that I entertain. Nonsensical sentences don’t express propositions, but there are contexts in which we talk about understanding nonsensical sentences. For example, we accept various kinds of semantically defective sentences in fiction, philosophy, and everyday life. Furthermore, it is a standard assumption that if a sentence is nonsensical, then it makes no sense to say that it implies anything or is implied by other sentences. Semantically uninterpreted sentences don’t have (...) logical characteristics. Hence, the riddle of understanding nonsense arises. We seem to use nonsensical sentences in reasoning, thinking, judging, and drawing conclusions, but they convey no propositions, which are the vehicles of their semantic properties. In this article, I propose the pretence theory of understanding nonsense to explain the riddle of understanding nonsense, and discuss alternative frameworks that are insufficient to solve it. -/- . (shrink)

The use of the symbol ∨for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead and (...) Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of ∨ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed. (shrink)

The austere view of nonsense says that the source of nonsense is not a violation of the rules of logical syntax, but nonsense is always due to a lack of meaning in one of the components of a sentence. In other words, the necessary and sufficient condition for nonsensicality is that no meaning has been assigned to a constituent in a sentence. The austere conception is the key ingredient of the resolute reading of Tractatus Logico-Philosophicus that presents a therapeutical interpretation (...) of the work, and rejects a possibility of conveying some ineffable truths by means of nonsensical sentences. In this paper, I defend the austere view against the most important objections. Firstly, I discuss textual sources for ascribing to Wittgenstein the austere view that have not been sufficiently thoroughly discussed yet. Next, I indicate that the apparent occurrence of words out of the context of a sentence on lists of verbs and in definitions is not in conflict with the version of the context principle recommended by austere theorists, since this argument does not sufficiently take into account the distinction between sign and symbol. Furthermore, I argue that the austere conception and the principle of compositionality are jointly tenable, for the former view does not exclude the existence of syntactic and semantic rules, but only shows that they are recognizable conditionally. Finally, I indicate that the austere view of nonsense should be seen as a viable option by a contemporary theorist of nonsense, for it helps us to avoid making controversial assumptions about the nature of meaning and content. (shrink)

I challenge Alexander Bird’s contention that the divergence between Kuhn’s views and recent philosophy of science is a matter of Kuhn having taken a wrong turn. Bird is right to remind us of Kuhn’s naturalistic tendencies, but these are not clearly an asset, rather than a liability. Kuhn was right to steer clear of extreme referential conceptions of meaning, since these court an unacceptable semantic scepticism. Although he eschewed the concepts of truth and knowledge as philosophers of science have tended (...) to understand them, this doesn’t mean that, as Bird claims, Kuhn was a sceptic about scientific knowledge. Bird’s claim that recent philosophical naturalism represents a rejection of positivism far more thorough than Kuhn’s is problematic since, from a different perspective, this kind of naturalism can be seen to have inherited some equally important positivistic themes. Finally, it’s not clear that Kuhn should have endorsed a computational approach to the philosophy of science, such as connectionism, since such approaches may be more behaviouristic, and thus unacceptably positivistic, than the original cognitive revolution promised.Author Keywords: Kuhn; Positivism; Verificationism; Truth; Naturalism; Connectionism. (shrink)

The essential role of language in rational cognition is analysed. The approach is functional: only the results of the connection between language, reality, and thinking are considered. Scientific language is analysed as an extension and improvement of everyday language. The analysis gives a uniform view of language and rational cognition. The consequences for the nature of ontology, truth, logic, thinking, scientific theories, and mathematics are derived.

Can an epistemic conception of truth and an endorsement of the excluded middle (together with other principles of classical logic abandoned by the intuitionists) cohabit in a plausible philosophical view? In PART I I describe the general problem concerning the relation between the epistemic conception of truth and the principle of excluded middle. In PART II I give a historical overview of different attitudes regarding the problem. In PART III I sketch a possible holistic solution.

Emphasis in historiography of science is naturally placed on the discoveries and inventions which scientists make and generally less on new methods of doing science, but sometimes the latter can he an important clue to help us understand the former. For example, while we all acknowledge how great the contributions of Maxwell, Boltzmann, Planck, and Einstein were to physics from roughly 1870 to 1920, we often overlook the significance of a methodological phrase which was popular during that same period, namely, (...) what in German was called “Bildtheorie” or in English “picture theory”. But even before we can properly study its significance we have to know what the theory was, but even this presents problems, since the meaning changed. In fact, this paper is an attempt not only to describe the history of that change from Maxwell to Wittgenstein but to study in particular how Boltzmann’s conception of Bildtheorie seems to have been at least partly incorporated into the approach of Ludwig Wittgenstein. (shrink)

Gliederung Übersicht zu den Ausgaben mit Quellen im Nachlass ... 2 „Titel“-Ausgaben ... 2 Helsinki-Ausgabe ... 3 Teil-Ausgaben ... 3 Wiener Ausgabe ... 4 Bergen Electronic Edition (CD-ROM) ... 4 Bergen Web-Ausgaben ... 4 1 Bibliographie der Sammelausgaben... 5 1.1 Nachlass-Faksimile ... 5 1.2 Bergen Nachlass-Textausgaben ... 5 1.3 Suhrkamp-Schriften ... 6 1.4 Suhrkamp-Werkausgabe ... 6 1.5 Intelex-Ressource ... 7 1.6 Wiener Ausgabe ... 7 1.7 Helsinki-Ausgabe ... 8 1.8 Sammelbände ... 8 1.9 Korrespondenz-Sammelausgaben ... 8 2 Bibliographie der Einzelausgaben... (...) 9 2.1 Veröffentlichungen mit Erstveröffentlichung zu Lebzeiten (außer Logisch- philosophische Abhandlung / Tractatus logico-philosophicus) ... 9 2.2 Veröffentlichungen mit Quellen in den Manuskripten 101– und Typoskripten 201–... 10 2.3 Veröffentlichungen mit Quellen in den Diktaten 301–... 20 2.4 Veröffentlichungen von Erinnerungen und Vorlesungs- und Gesprächsaufzeichnungen (Auswahl) ... 21 2.5 Veröffentlichungen von Korrespondenz (Auswahl) ... 25 3 Bibliographie der Veröffentlichungen von Waismanns „Wittgenstein-Arbeiten“ (Auswahl)... 29. (shrink)

Research into Kelsen’s conception of judicial justice seems at first sight contradictory to his own Pure Theory of Law. Upon closer consideration this prima facie contradiction turns out to be only an appearance due to the paradoxical effect that is produced by Kelsen’s pure theory of law itself. By revealing three paradoxical effects of Kelsen’s work in this article, I try to show that research into a Kelsenian representation of judicial justice is not only possible but also meaningful. The first (...) paradox originates from Kelsen’s formalised and value-free concept of law, which unexpectedly confronts the judge with his moral responsibility for the material valuation of the law. Secondly, a paradox arises from Kelsen’s rationalised notion of relative justice, which in fact forces the judge to be absolutely convinced of the moral rightness of his judgement. The third paradox is a result of Kelsen’s idea of objectivised ‘social peace’, by which the judge just realises the subjective and irrational demands of justice. From my analysis of these three seeming contradictions in Kelsen’s pure theory of law emerges an apparent Kelsenian representation of judicial justice. Starting from his pure theory of law it should be possible to conceive of a ‘pure’ form of administration of law, which would stipulate social peace as a condition for the ‘purity’ of a judicial judgement. I even imagine that Kelsen considered peace as a conditio tacita for the validity of the whole legal order, just as he regarded the basic norm as conditio per quam and effectivity as conditio sine qua non for the validity of the legal order. In any case, according to Kelsen’s conception of judicial justice, social peace proves to be the implicit or tacit condition for a ‘pure’ judgement. With that this ‘pacifying jurisprudence’ can be understood as a surprising paragon of a ‘pure’ administration of justice, on the understanding that peace is not a sufficient but an obvious condition for a just administration of law. That this should also apply mutatis mutandis for Kelsen’s concept of the legal order as a whole will be made subject of further research. (shrink)

All concepts, methods, and techniques of the philosophy of language arise from its conceptions of language. Conceptions of language have determined the character of the philosophy of language and the direction of its philosophical research. Various schools and currents within the philosophy of language differ from each other, mainly in the way they understand the referential character of the sign—that is, the relationship between the meaning of a word and its referential object.

Was ist eine gute Weltanschauung? Die Aufsätze behandeln einige der großen Themen der westlichen Philosophie unter neuen Gesichtspunkten, wie z. B. das Apeiron des Anaximander, das Leib-Seele-Problem bei Descartes und Wittgensteins Begriff der Sprache und Lebensform. Sie beleuchten aber auch Seitenwege wie z. B. einen Ausflug Schopenhauers, ein „Plagiat" Nietzsches und einige der Aphorismen Ludwig Hohls.

In other works, I’ve proposed a solution to the semantic paradoxes which, at the technical level, basically relies on failure of contraction. I’ve also suggested that, at the philosophical level, contraction fails because of the instability of certain states of affairs. In this paper, I try to make good on that suggestion.

Epistemology is a conceptual template for how we think about the world, and the study of how we come to know the world around us. The world does not dictate unequivocally how to interpret it. This article will explore this position on the fluidity of epistemic constructs through two prominent philosophical perspectives, those being derived from the works of Ludwig Wittgenstein and Michael Foucault, respectively. These insights will be used to more deeply unfold the current situation for Aboriginal students within (...) dominant approaches to mathematics curriculum in Australia, and the subsequent approaches to the inclusion of Aboriginal knowledge and epistemologies. It is suggested that the epistemic constructs most valued and thus credited as conveyors of ‘truth’, and therefore positioned as powerful forms of knowledge within dominant curriculum and education policy, are those derived from Western, Eurocentric origins. This privileging of particular epistemological constructs over others is reinforced unconsciously through the articulation of educational goals deemed most appropriate, or ‘socially just’, for the Aboriginal student population. The place of Aboriginal knowledge within such constructs is therefore reflective of broader ideation around the role of education within society and its failure to challenge existing structures of power and injustice. (shrink)

"The ineffable" in Wittgenstein's Tractatus Logico-Philosophicus is an essential term that has various interpretations. It could be divided into two types, namely, positive and negative, or real and fake. The negative or fake type can be clarified by logical analysis, while the positive or real type can be understood only through philosophical critique. Both the positive and negative types consist of infinity or absoluteness, but the infinity is subject to distinctions in meaning and logic. "������������������" ������������������������������������������ «������������������������������» ������������������������������������������������������������������������������ ������, ������������������������������������������, (...) ������������������������������������������������, ������������������������������������������������. ������������������������������������������ ������������������������������������������������������������������������, ������������������������������������������������������������������������������������������������������������������������������������ ������. ������������������������������������������������������������������������������������������������������������, ������������������������������������������������������������������������������������ ������������������������. (shrink)

“The ineffable” in Wittgenstein’s Tractatus Logico-Philosophicus is an essential term that has various interpretations. It could be divided into two types, namely, positive and negative, or real and fake. The negative or fake type can be clarified by logical analysis, while the positive or real type can be understood only through philosophical critique. Both the positive and negative types consist of infinity or absoluteness, but the infinity is subject to distinctions in meaning and logic.

The physiologist and neo-Kantian philosopher Johannes von Kries (1853-1928) wrote one of the most philosophically important works on the foundation of probability after P.S. Laplace and before the First World War, his Principien der Wohrscheinlich-keitsrechnung (1886, repr. 1927). In this book, von Kries developed a highly original interpretation of probability, which maintains it to be both logical and objectively physical. After presenting his approach I shall pursue the influence it had on Ludwig Wittgenstein and Friedrich Waismann. It seems that von (...) Kries's approach had more potential than recognized in his time and that putting Waismann's and Wittgenstein's early work in a von Kries perspective is able to shed light on the notion of an elementary proposition. (shrink)

This article is about the history of logic in Australia. Douglas Gasking (1911?1994) undertook to translate the logical terminology of John Anderson (1893?1962) into that of Ludwig Wittgenstein's (1921) Tractatus. At the time Gilbert Ryle (1900?1976), and more recently David Armstrong, recommended the result to students; but it is reasonable to have misgivings about Gasking as a guide to either Anderson or Wittgenstein. The historical interest of the debate Gasking initiated is that it yielded surprisingly little information about Anderson's traditional (...) (syllogistic or Aristotelian) logic and its relation to classical (first-order predicate or Russellian) logic, the ostensible topic; but the materials now exist to interpret Anderson's logic in classical logic, possibly as an algebra of classes. This would be of little interest to contemporary logicians, but it might shed some light on Anderson's philosophy. (shrink)