Es werden vier verbreitete Verwendungsweisen des Wortes ‘Argument’ beschrieben, an Beispielen erläutert und dann schrittweise expliziert. Die wichtigsten Explikata sind: ‘eine Satzfolge x ist ein deskriptives Argument in Standardform’, ‘ein deskriptives Argument x in Standardform ist bei der subjektiven Wahrscheinlichkeitsverteilung p stark (bzw. schwach)’, ‘ein Aussagesatz x ist bei der subjektiven Wahrscheinlichkeitsverteilung p ein Argument für (bzw. gegen) einen Aussagesatz y’, ‘ein geordneter Tripel x von deskriptiven Argumenten in Standardform, von Argumentebenen und von Argumentsträngen ist eine deskriptive Argumenthierarchie in Standardform’, (...) ‘eine deskriptive Argumenthierarchie x in Standardform ist gültig (bzw. ungültig; stichhaltig; konsistent; inkonsistent; sichtlich zirkelhaft; stark (bzw. schwach) bei der subjektiven Wahrscheinlichkeitsverteilung p)’. (shrink)

This article presents a comparative theory of subjective argument strength simple enough for application. Using the axioms and corollaries of the theory, anyone with an elementary knowledge of logic and probability theory can produce an at least minimally rational ranking of any set of arguments according to their subjective strength, provided that the arguments in question are descriptive ones in standard form. The basic idea is that the strength of argument A as seen by person x is a function of (...) three factors: x's degree of belief in the premisses of A; x's degree of belief in the conclusion of A under the assumption that all premisses of A are true; and x's belief in the conclusion of A under the assumption that not all premisses of A are true. (shrink)

Karl Popper discovered in 1938 that the unconditional probability of a conditional of the form ‘If A, then B’ normally exceeds the conditional probability of B given A, provided that ‘If A, then B’ is taken to mean the same as ‘Not (A and not B)’. So it was clear (but presumably only to him at that time) that the conditional probability of B given A cannot be reduced to the unconditional probability of the material conditional ‘If A, then B’. (...) I describe how this insight was developed in Popper’s writings and I add to this historical study a logical one, in which I compare laws of excess in Kolmogorov probability theory with laws of excess in Popper probability theory. (shrink)

I set up two axiomatic theories of inductive support within the framework of Kolmogorovian probability theory. I call these theories ‘Popperian theories of inductive support’ because I think that their specific axioms express the core meaning of the word ‘inductive support’ as used by Popper (and, presumably, by many others, including some inductivists). As is to be expected from Popperian theories of inductive support, the main theorem of each of them is an anti-induction theorem, the stronger one of them saying, (...) in fact, that the relation of inductive support is identical with the empty relation. It seems to me that an axiomatic treatment of the idea(s) of inductive support within orthodox probability theory could be worthwhile for at least three reasons. Firstly, an axiomatic treatment demands from the builder of a theory of inductive support to state clearly in the form of specific axioms what he means by ‘inductive support’. Perhaps the discussion of the new anti-induction proofs of Karl Popper and David Miller would have been more fruitful if they had given an explicit definition of what inductive support is or should be. Secondly, an axiomatic treatment of the idea(s) of inductive support within Kolmogorovian probability theory might be accommodating to those philosophers who do not completely trust Popperian probability theory for having theorems which orthodox Kolmogorovian probability theory lacks; a transparent derivation of anti-induction theorems within a Kolmogorovian frame might bring additional persuasive power to the original anti-induction proofs of Popper and Miller, developed within the framework of Popperian probability theory. Thirdly, one of the main advantages of the axiomatic method is that it facilitates criticism of its products: the axiomatic theories. On the one hand, it is much easier than usual to check whether those statements which have been distinguished as theorems really are theorems of the theory under examination. On the other hand, after we have convinced ourselves that these statements are indeed theorems, we can take a critical look at the axioms—especially if we have a negative attitude towards one of the theorems. Since anti-induction theorems are not popular at all, the adequacy of some of the axioms they are derived from will certainly be doubted. If doubt should lead to a search for alternative axioms, sheer negative attitudes might develop into constructive criticism and even lead to new discoveries. -/- I proceed as follows. In section 1, I start with a small but sufficiently strong axiomatic theory of deductive dependence, closely following Popper and Miller (1987). In section 2, I extend that starting theory to an elementary Kolmogorovian theory of unconditional probability, which I extend, in section 3, to an elementary Kolmogorovian theory of conditional probability, which in its turn gets extended, in section 4, to a standard theory of probabilistic dependence, which also gets extended, in section 5, to a standard theory of probabilistic support, the main theorem of which will be a theorem about the incompatibility of probabilistic support and deductive independence. In section 6, I extend the theory of probabilistic support to a weak Popperian theory of inductive support, which I extend, in section 7, to a strong Popperian theory of inductive support. In section 8, I reconsider Popper's anti-inductivist theses in the light of the anti-induction theorems. I conclude the paper with a short discussion of possible objections to our anti-induction theorems, paying special attention to the topic of deductive relevance, which has so far been neglected in the discussion of the anti-induction proofs of Popper and Miller. (shrink)

In paragraph 21 of his "Logic of Scientific Discovery", Karl Popper characterizes with the help of two seemingly synonymous definitions the falsifiability of a theory as a logical relation between the theory itself and its basic statements. It is shown that his definitions do not agree with each other, and this result is applied to the problem of the falsifiability of contradictions, to the difference between falsifiable and empirical statements and to the demarcation criterion.

Bolzano hat seine Wahrscheinlichkeitslehre in 15 Punkten im § 14 des zweiten Teils seiner Religionswissenschaft sowie in 20 Punkten im § 161 des zweiten Bandes seiner Wissenschaftslehre niedergelegt. (Ich verweise auf die Religionswissenschaft mit 'RW II', auf die Wissenschaftslehre mit 'WL II'.) In der RW II (vgl. p. 37) ist seine Wahrscheinlichkeitslehre eingebettet in seine Ausführungen "Über die Natur der historischen Erkenntniß, besonders in Hinsicht auf Wunder", und die Lehrsätze, die er dort zusammenstellt, dienen dem ausdrücklichen Zweck, mit mathematischem Rüstzeug (...) Lehrmeinungen entgegentreten zu können, gemäß denen Wundererzählungen keine Glaubwürdigkeit zukommen könne. In der WL II (vgl. p. 171) führt Bolzano im großen und ganzen dieselben Lehrsätze an wie in der RW II, entwickelt nun aber die Wahrscheinlichkeitslehre innerhalb seiner Lehre von den Sätzen an sich. Dabei orientiert er sich zwar durchaus an den Lehrsätzen in den damaligen "Schriften über die Wahrscheinlichkeitsrechnung" (vg. WL II, p. 190), korrigiert aber dort, wo es ihm nötig erscheint (vgl. WL II, pp. 187–191), und leistet so im Grunde eine Reformulierung des elementaren Teils der Wahrscheinlichkeitslehre seiner Zeit innerhalb seiner logischen Theorie von den Sätzen an sich. — Ich bezwecke hier keine historische Studie über Bolzanos Wahrscheinlichkeitslehre, obwohl es von Interesse sein mag, herauszuschälen, worin Bolzano mit welchen Wahrscheinlichkeitstheoretikern seiner Zeit übereinstimmt, und worin nicht, insbesondere welche Schwächen von Bolzanos Wahrscheinlichkeitslehre Schwächen aller damaligen Wahrscheinlichkeitslehren waren. Eine wichtige systematische Studie über Bolzanos Wahrscheinlichkeitslehre bestünde — wie von Berg (1962, pp. 148-149) ansatzweise begonnen — in einer exakten Rekonstruktion seiner Wahrscheinlichkeitslehre innerhalb eines konsistenten logischen Systems der Sätze an sich. Ich werde im folgenden etwas bei weitem Bescheideneres, doch möglicherweise durchaus Fruchtbares versuchen, nämlich die Lehrsätze von Bolzanos Wahrscheinlichkeitslehre in die Sprache einer heutigen Wahrscheinlichkeitstheorie zu übersetzen und die übersetzten Lehrsätze dort herzuleiten, soweit dies möglich ist. Man könnte dann in einem zweiten Schritt, der hier nicht mehr unternommen wird, untersuchen, inwieweit jene Thesen, die den Herleitungstest überstanden haben, jenen Zweck erfüllen, den Bolzano ihnen ursprünglich zugedacht hat: als mathematisches Rüstzeug für seine Argumentationen gegen die Auffassung zu dienen, Wundererzählungen könnten nicht glaubwürdig sein. (shrink)

Zwischen 1987 und 1994 sandte ich 20 Briefe an Karl Popper. Die meisten betrafen Fragen bezüglich seiner Antiinduktionsbeweise und seiner Wahrscheinlichkeitstheorie, einige die organisatorische und inhaltliche Vorbereitung eines Fachgesprächs mit ihm in Kenly am 22. März 1989 (worauf hier nicht eingegangen werden soll), einige schließlich ganz oder in Teilen nicht-fachliche Angelegenheiten (die im vorliegenden Bericht ebenfalls unberücksichtigt bleiben). Von Karl Popper erhielt ich in diesem Zeitraum 10 Briefe. Der bedeutendste ist sein siebter, bestehend aus drei Teilen, geschrieben am 21., 22. (...) und 23. Oktober 1992, in dem er eine Vorform jener Definition der probabilistischen Unabhängigkeit entwickelte, die er 1994 im neuen Anhang *XX der 10. Auflage seiner Logik der Forschung (LdF) der wissenschaftstheoretischen Forschergemeinde vorstellte. Der berührendste ist sein letzter, geschrieben am 26. Juli 1994, in dem er trotz Erschöpfung mit Humor schildert, wie mühselig der Druck des Anhangs *XX verlaufen ist. Mein Bericht ist zugleich chronologisch und systematisch gegliedert: die ersten, vergleichsweise wenigen Briefe, großteils 1987 geschrieben, handeln von der Induktion; der große Rest, zeitlicher Schwerpunkt 1992, beschäftigt sich mit der Wahrscheinlichkeitstheorie. Das Kapitel 1 über Induktion ist in vier Abschnitte unterteilt: 1.1 Das Popper/Miller-Argument: eine Nachkonstruktion, 1.2 Karl Poppers Brief vom 25.8.1987: Deduktive Stützung, 1.3 Karl Poppers Brief vom 29.9.1987: Nochmals zur deduktiven Stützung, 1.4 Echt induktive Stützung und Schwächung: zwei eigene Beweise. Das Kapitel 2 über Wahrscheinlichkeit ist ebenfalls in vier Abschnitte unterteilt: 2.1 Ein Mangel an Überschußgesetzen in der Logic of Scientific Discovery, 2.2 Probabilistische Unabhängigkeit, 2.3 Wahrscheinlichkeitstheorie und Wahrscheinlichkeitssemantik, 2.4 Die neue Unabhängigkeitsdefinition im Anhang *XX der LdF. (shrink)

Paul Weingartner's classification of the sciences is analyzed in detail. There is a small mistake in the definition of the set of descriptive-normative sciences, which makes the classification incorrect, but which can easily be remedied.

This article presents a comparative theory of subjective argument strength simple enough for application. Using the axioms and corollaries of the theory, anyone with an elementary knowledge of logic and probability theory can produce an - at least minimally rational - ranking of any set of arguments according to their subjective strength, provided that the arguments in question are descriptive ones in standard form. The basic idea is that the strength of argument A as seen by person x is a (...) function of three values: x ’s degree of belief in the premisses of A; x ’s degree of belief in the conclusion of A under the assumption that all premisses of A are true; and x ’s belief in the conclusion of A under the assumption that not all premisses of A are true. (shrink)

We define the term ⌜\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ulcorner $$\end{document}a set T of sentential-logical formulae grounds a sentential-logical formula A from a syntactic point of view⌝\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\urcorner $$\end{document} in such a way that A is a syntactic sentential-logical consequence of T, and specific additional syntactic requirements regarding T and A are fulfilled. These additional requirements are developed strictly within the syntactics of sentential-logical languages, the three most important (...) being new, namely: to be atomically minimal, to be minimal in degree, and not to be conjunction-like. Our approach is independent of any specific sentential-logical calculus. (shrink)

The basic idea by means of which Popper and Miller proved the non-existence of inductive probabilistic support in 1983/1985/1987, is used to prove that inductive probabilistic countersupport does exist. So it seems that after falsification has won over verification on the deductive side of science, countersupport wins over support on the inductive side.

This is, to the best of my knowledge, the first published attempt at a rigorous logical formalization of a passage in Leibniz's Monadology. The method we followed was suggested by Johannes Czermak.

Our report and bibliography concentrate on research in the philosophy of science carried out in Austria within the last 20 years. The term 'philosophy of science' is here to be understood in the broad sense of 'Wissenschaftstheorie', that is, syntactics, semantics and pragmatics of the natural sciences and of the humanities, including law. After a general introduction to the philosophy of science scene in Austria, we report about those institutions in Austria at which relevant research has been conducted, starting with (...) institutions in Graz and then continuing - in alphabetical order - with institutions in Innsbruck, Klagenfurt, Linz, Salzburg, and Wien. Our report is supplemented by a bibliography; please note that this contains only references to original publications which deal mainly with questions in the philosophy of science, hence no contributions to lexica, no reviews, no translations, no articles in mass media, no editorial and no unpublished works are cited. Finally, there is an appendix, Alphabetical List of Austrian Institutions at which Philosophy of Science is Conducted, to facilitate communication between you and Austrian philosophers in whose work you may become interested by reading this report. (shrink)

ENGLISH ABSTRACT: Basic statements play a central role in Popper's "The Logic of Scientific Discovery", since they permit a distinction between empirical and non-empirical theories. A theory is empirical iff it consists of falsifiable statements, and statements (of any kind) are falsifiable iff they are inconsistent with at least one basic statement. Popper obviously presupposes that basic statements are themselves empirical and hence falsifiable; at any rate, he claims several times that they are falsifiable. In this paper we prove that (...) no basic statement is falsifiable, if the term 'basic statement' is to be understood according to Popper's definitions of that term. More precisely, we prove not only that no Popperian basic statement in the narrow sense of the word is falsifiable, but also that no Popperian basic statement in the broader sense, and even in the broadest possible sense, is falsifiable. This leads to the paradoxical result that, according to Popper's definitions of 'basic statement', the basis of the empirical sciences is not itself empirical. Furthermore, we point out a similar paradox as regards Popper's falsifiability scheme for theories. We close with a look at possibilities for overcoming these paradoxes. DEUTSCHE ZUSAMMENFASSUNG: Basissätze spielen eine zentrale Rolle in Poppers Logik der Forschung, denn sie erlauben die Unterscheidung zwischen empirischen und nichtempirischen Theorien: Eine Theorie ist empirisch genau dann, wenn sie aus falsifizierbaren Aussagesätzen besteht, und Aussagesätze (beliebiger Art) sind falsifizierbar genau dann, wenn sie mindestens einem Basissatz widersprechen. Popper setzt offensichtlich voraus, dassŸ die Basissätze selbst empirisch und somit falsifizierbar sind. Jedenfalls behauptet er mehrmals ihre Falsifizierbarkeit. Wir beweisen in unserem Aufsatz, dassŸ die Basissätze nicht falsifizierbar sind, und wir beweisen dies nicht nur für Poppersche Basissätze im engeren Sinn, sondern auch für Poppersche Basissätze im weiteren Sinn und schlieߟlich für Poppersche Basissätze im weitesten, mit den Vorstellungen Poppers gerade noch verträglichen Sinn. Dies führt zu dem paradoxen Ergebnis, dass nach Poppers eigenen methodologischen Postulaten die Basis der empirischen Wissenschaften nicht selbst empirisch ist. Darüber hinaus entwickeln wir ein ähnliches Paradoxon bezüglich Poppers Falsifizierbarkeitsschema für Theorien. Zum AbschlussŸ unseres Aufsatzes betrachten wir einige Möglichkeiten, die von uns entdeckten Paradoxa zu überwinden. (shrink)

We define the term \a set T of sentential-logical formulae grounds a sentential-logical formula A from a syntactic point of view\ in such a way that A is a syntactic sentential-logical consequence of T, and specific additional syntactic requirements regarding T and A are fulfilled. These additional requirements are developed strictly within the syntactics of sentential-logical languages, the three most important being new, namely: to be atomically minimal, to be minimal in degree, and not to be conjunction-like. Our approach is (...) independent of any specific sentential-logical calculus. (shrink)

This volume comprises a selection of papers that were contributed to the 7th International Congress of Logic, Methodology and Philosophy of Science, which was held in Salzburg from the 11th - 16th July, 1983. There were 14 sections in this congress: 1. proof theory and foundations of mathematics 2. model theory and its applica ti on 3. recursion theory and theory of computation 4. axiomatic set theory 5. philosophical logic 6. general methodology of science 7. foundations of probability and induction (...) 8. foundations and philosophy of the physical sciences 9. foundati ons and phi 1 osophy of biology 10. foundations and philosophy of psychology foundations and philosophy 11. of the social sciences 12. foundati ons and philosophy of linguistics 13. history of logic, methodology and philosophy of science 14. fundamental principles of the ethics of science In each section, three or four invited addresses were given, which will be published in the Congress Proceedings (Ruth Barcan Marcus, Georg J. W. Dorn and Paul Weingartner, eds. : Logic, Metho dology and Philosophy of Science VII. Proceedings of the Seventh International Congress of Logic, Methodology and Philosophy of v PREFACE Science, Salzburg, 1983. - Amsterdam, New York, Oxford: North-Holland Publishing 'Company, 1985. ) Every section with the exception of section 14 also contained contributed papers. (shrink)

With this issue George Annas contributes his last At Law to the Hastings Center Report. Since the column was inaugurated in 1976 as Law and the Life Sciences, George has charted the course of biomedical ethics in the courts, challenging readers to come to grips with an emerging body of law in provocative analyses of critical decisions. As he retires from this column we wish him well, and look forward to his continued contributions to our pages. In bidding farewell to (...) one friend we are nonetheless pleased to welcome another as Alexander Morgan Capron, Henry W. Bruce University Professor of Law and Medicine at the University of Southern California and codirector of the Pacific Center for Health Policy and Ethics, joins the Report in the September‐October issue as a regular contributor to this column. Prof. Capron, formerly executive director of The President's Commission for the Study of Ethical Problems in Medicine and Biomedical and Behavioral Research, is a distinguished scholar and writer well known to our readers. We welcome the opportunity to share his insights on issues before courts and legislatures nationwide. (shrink)

The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of truth. This opens a (...) new way of thinking---thinking in terms of degrees rather than absolutes. For example, it leads to the definition of a new kind of sets, referred to as fuzzy sets, in which membership is a matter of degree. The book examines the genesis and development of fuzzy logic. It surveys the prehistory of fuzzy logic and inspects circumstances that eventually lead to the emergence of fuzzy logic. The book explores in detail the development of propositional, predicate, and other calculi that admit degrees of truth, which are known as fuzzy logic in the narrow sense. Fuzzy logic in the broad sense, whose primary aim is to utilize degrees of truth for emulating common-sense human reasoning in natural language, is scrutinized as well. The book also examines principles for developing mathematics based on fuzzy logic and provides overviews of areas in which this has been done most effectively. It also presents a detailed survey of established and prospective applications of fuzzy logic in various areas of human affairs, and provides an assessment of the significance of fuzzy logic as a new paradigm. (shrink)

Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

This thesis attempts to show that Georg Lukacs' Marxist theory of realism is best understood, not as a self sufficient body of theory, but in the context of his pre- Marxist theory of literature and his,role in the Communist movement, A comparison of the theory expounded in "Die Seele and die Fonaen" and "Die Theorie des Romans" with the main positions of "Geschichte und Kiassenbewusstsein" reveals that it was remarkably easy for Lukacs to accommodate his literary theory within the (...) newly-acquired philosophy. An examination of Lukacs' career shows that his move to Marxism was motivated by a search for the practical instrument to implement the ideal which was the mainspring behind both his own life and, in his theory, all great literature, namely, the classical ideal of harmony. The resulting change in emphasis from aesthetics to political action led, in the thirties, to the attempt to synthesize both in a cultural campaign. Political pressure, combined with the genuine belief that the excesses of Stalinism were the acceptable price of resistance to the overriding threat of fascism, resulted in the employment of a rigid determinism, deplored ill others, which was incompatible with the core of his understanding of literary realism. The creation of realism was, however, for both the pre- Marxist and the Marxist Lukacs, ultimately inexplicable in materialist terms. (shrink)

This work examines the complex relationship between two influential modern thinkers, G.W.F. Hegel and Ernst Troeltsch, one of Hegel's interpreters and a figure who has not received the attention he deserves.

An outgrowth of Ryle’s three week visit at Rice in the spring of 1972, this collection of critical essays bears some resemblance to the collection edited by Oscar P. Wood and George Pitcher in the Anchor series. The principle differences are: 1) the range of topics treated here and the detail of treatment is considerably less extensive than in the Wood collection, and 2) this volume contains two new essays by Ryle himself: "Thinking and Self-Teaching" and "Thinking and Saying." Four (...) papers by members of the philosophy staff at Rice form a group. Each of them discusses Ryle’s contribution to a problem in which the author is interested, carefully delineating Ryle’s analysis and treatment of the problem. Generally Ryle is regarded as having said some important things about the topic, having said some things which are questionable, and having at least advanced the topic in an important way. Subjects dealt with in roughly this fashion are "Reference and Existence" by Lyle Angene, "Sensations, Feelings, and Expression" by Richard J. Sclafani, "Dispositions and Hypotheticals" by Robert W. Burch, and "Why Virtue Cannot be Taught" by Thomas McElvain. As surveys of Ryle’s position and as assessments of his views, the essays are consistently good. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.