Die Frage, wie sich Aussagen uber Fahigkeiten von Personen zu Aussagen uber Moglichkeiten von Zustanden in der Welt verhalten, ist fur unser menschliches Selbstverstandnis zentral. Der vorliegende Band versammelt unter dieser Frage durchweg Originalbeitrage in historisch-systematischer Absicht; sie behandeln die Geschichte der Metaphysik und Ontologie von Parmenides bis Heidegger.INHALT: VORWORT - Klaus Jacobi: Das Konnen und die Moglichkeiten. Potentialitat und Possibilitat - Mischa von Perger: Moglichkeit, Parmenideisch - Ulrich Nortmann: 'Das Saatkorn ist dem Vermogen nach eine Pflanze'. Uber ontologische und (...) logische Aspekte Aristotelischer Moglichkeitssatze - Sang-Jin Kang: Anselm und die modallogische Betrachtung der gottlichen Notwendigkeit - Michael Astroh: Petrus Abaelardus on Modalities de re and de dicto - Christopher Martin: Peter Abaelard on Modality. Some Possibilities and Some Puzzles - Allan Back: Avicenna and Averroes: Modality and Theology - Seung-Chan (Elias) Park: Die Differenz von personlicher und unpersonlicher Moglichkeit bei Thomas von Aquin - Charles Lohr: 'Art' and Possibility: The Rule Concerning Possibility in the Ars lulliana - Peter King: Duns Scotus on Possibilities, Powers, and the Possible - Matthias Kaufmann: Gottes Allmacht und die Wahrheit modaler Satze. Potentialitat und Possibilitat bei Wilhelm von Ockham - Simo Knuuttila: On the History of Theory of Modality as Alternativeness - Stephan Meier-Oeser: Potentia versus Possibilitas? Posse! Zur cusanischen Konzeption der Moglichkeit - Dominik Perler: Cartesische Moglichkeiten - Hans Poser: Leibniz'sche Handlungsmodi zwischen Ontologie und Deontologie - Wilhelm Metz: Der transzendentale Moglichkeitsbegriff bei Kant und Fichte - Rainer Marten: Heidegger: Die eigenste eigentliche Moglichkeit - Tilman Borsche: Moglichkeiten des Seins, Moglichkeiten des Denkens - Thomas Buchheim: Zwischen Antinomie und Kompatibilitat: Versuch uber die naturliche Einbettung unserer Handlungsfreiheit - Kuno Lorenz: Dynamis und Energeia. Zur Aktualitat eines begrifflichen Werkzeugs von Aristoteles. (shrink)

Though many well-known German philosophers have devoted considerable attention to music and its aesthetics, surprisingly few of their writings on the subject have been translated into English. Stefan Lorenz Sorgner, a philosopher, and Oliver Fürbeth, a musicologist, here fill this important gap for musical scholars and students alike with this compelling guide to the musical discourse of ten of the most important German philosophers, from Kant to Adorno. _Music in German Philosophy_ includes contributions from a renowned group of ten (...) scholars, including some of today’s most prominent German thinkers, all of whom are specialists in the writers they treat. Each chapter consists of a short biographical sketch of the philosopher concerned, a summary of his writings on aesthetics, and finally a detailed exploration of his thoughts on music. The book is prefaced by the editors’ original introduction, presenting music philosophy in Germany before and after Kant, as well as a new introduction and foreword to this English-language addition, which places contemplations on music by these German philosophers within a broader intellectual climate. (shrink)

Preface to Volumes 1 and 2 Lorenz Krüger xv Introduction to Volume 1 Lorraine J. Daston 1 I Revolution 1 What Are Scientific Revolutions? Thomas S. Kuhn 7 2 Scientific Revolutions, Revolutions in Science, and a Probabilistic Revolution 1800-1930 I. Bernard Cohen 23 3 Was There a Probabilistic Revolution 1800-1930? Ian Hacking 45 II Concepts 4 The Slow Rise of Probabilism: Philosophical Arguments in the Nineteenth Century Lorenz Krüger 59 5 The Decline of the Laplacian Theory of Probability: (...) A Study of Stumpf, von Kries, and Meinong Andreas Kamlah 91 6 Fechner’s Indeterminism: From Freedom to Laws of Chance Michael Heidelberger 117 7 The Saint Petersburg Paradox 1713-1937 Gerard Jorland 157 8 Laplace and Thereafter: The Status of Probability Calculus in the Nineteenth Century Ivo Schneider 191 9 Emile Borel as a Probabilist Eberhard Knobloch 215 III Uncertainty 10 The Domestication of Risk: Mathematical Probability and Insurance 1650-1830 237 11 The Objectification of Observation: Measurement and Statistical Methods in the Nineteenth Century Zeno G. Swijtink 261 12 The Measurement of Uncertainty in Nineteenth-Century Social Science Stephen M. Stigler 287 IV Society 13 Rational Individuals versus Laws of Society: From Probability to Statistics Lorraine J. Daston 295 14 Decrire, Compter, Calculer: The Debate over Statistics during the Napoleonic Period Marie-Noelle Bourguet 305 15 Probability in Vital and Social Statistics: Quetelet, Farr, and the Bertillons Bernard-Pierre Lécuyer 317 16 Paupers and Numbers: The Statistical Argument for Social Reform in Britain during the Period of Industrialization Karl H. Metz 337 17 Lawless Society: Social Science and the Reinterpretation of Statistics in Germany, 1850-1880 Theodore M. Porter 351 18 Prussian Numbers 1860-1882 Ian Hacking 377 19 How Do Sums Count? On the Cultural Origins of Statistical Causality M. Norton Wise 395. (shrink)

I PSYCHOLOGY 5 The Probabilistic Revolution in Psychology--an Overview Gerd Gigerenzer 7 1 Probabilistic Thinking and the Fight against Subjectivity Gerd Gigerenzer 11 2 Statistical Method and the Historical Development of Research Practice in American Psychology Kurt Danziger 35 3 Survival of the Fittest Probabilist: Brunswik, Thurstone, and the Two Disciplines of Psychology Gerd Gigerenzer 49 4 A Perspective for Viewing the Integration of Probability Theory in Psychology David J. Murray 73 II SOCIOLOGY 101 5 The Two Empirical Roots of (...) Social Theory and the Probability Revolution Anthony Oberschall 103 III ECONOMICS 133 The Probabilistic Revolution in Economics--an Overview Mary S. Morgan 135 6 Why Was There No Probabilistic Revolution in Economic Thought? Claude Mènard 139 7 The Rise of Macroeconomic Calculations in Economic Statistics Robert A. Horváth 147 8 Statistics without Probability and Haavelmo’s Revolution in Econometrics Mary S. Morgan 171 IV PHYSIOLOGY 199 9 Experimental Physiology and Statistical Inference: The Therapeutic Trial in Nineteenth-Century Germany William Coleman 201 V EVOLUTIONARY BIOLOGY 227 The Probabilistic Revolution in Evolutionary Biology--an Overview John H. Beatty 229 10 Natural Selection as a Causal, Empirical, and Probabilistic Theory M. J. S. Hodge 233 11 Dobzhansky and Drift: Facts, Values, and Chance in Evolutionary Biology John H. Beatty 271 12 Random Genetic Drift, R. A. Fisher, and the Oxford School of Ecological Genetics John R. G. Turner 313 13 On the Prior Probability of the Existence of Life Bernd-Olaf Küppers 355 VI PHYSICS 371 The Probabilistic Revolution in Physics--an Overview Lorenz Krüger 373 14 Probabilistic Physics the Classical Way Jan von Plato 379 15 Max Born and the Reality of Quantum Probabilities Nancy Cartwright 409 16 Philosophical Problems of Quantum Theory: The Response of American Physicists Nancy Cartwright. (shrink)

Mit dem vorliegenden Werk schliesst Lorenz B. Puntel seine Seinstrilogie ab; die beiden vorherigen Bande sind unter dem Titel Struktur und Sein (2006) und Sein und Gott (2010) erschienen. Der neue Band fuhrt das in den anderen Banden nur inchoativ formulierte gesamtsystematische philosophische Programm aus. Lorenz B. Puntel betrachtet das Thema Sein und Nichts als das ursprungliche Thema der Philosophie und stellt daruber eine umfassende Theorie auf. Diese Theorie nennt er Seinstheorie; sie besteht aus den beiden Subtheorien: Ontologie (...) als Theorie (des Seins) der Seienden und Einailogie als Theorie des Seins selbst oder als solchen. Ausgangspunkt ist die von Heidegger eingefuhrte ontologische Differenz, die Unterscheidung von Sein und Seienden. In eingehenden, auf den einschlagigen Originaltexten der wichtigsten Philosophen basierenden Ausfuhrungen wird der Nachweis gefuhrt, dass der in der Philosophiegeschichte feststellbare Grundmangel in der haufigen totalen und in sehr wenigen Fallen partiellen Ignorierung der grossen Seinsfrage besteht; nirgends wird diese in adaquater Weise thematisiert. In Teil II arbeitet der Autor die Grundzuge sowohl der allgemeinen Ontologie als auch der Einailogie heraus. Zwei grundlegende Thesen werden bewiesen: die Moglichkeit des relativen Nichts, d. h. des Verschwindens aller Seienden auf der Basis ihrer Kontingenz, und die Unmoglichkeit des absoluten Nichts, d. h. des Verschwindens des Seins selbst auf der Basis seines notwendigen Status. Gezeigt wird schliesslich, dass dem Sein selbst eine geistige Verfasstheit innewohnt, die aus Intelligenz/Denken, Wille und Freiheit besteht, womit die Moglichkeit eroffnet wird, dass das notwendige geistig verfasste und damit freie Sein sich weiter offenbaren kann. Dem nachzugehen, setzt aber eine grundlegende methodische und thematische Zasur voraus. (shrink)

Erwin Panofsky explicitly states that the first half of the opening chapter of Studies in Iconology—his landmark American publication of 1939—contains ‘the revised content of a methodological article published by the writer in 1932’, which is now translated for the first time in this issue of Critical Inquiry.1 That article, published in the philosophical journal Logos, is among his most important works. First, it marks the apogee of his series of philosophically reflective essays on how to do art history,2 that (...) reach back, via a couple of major pieces on Alois Riegl, to the 1915 essay on Heinrich Wölfflin.3 Under the influence of his colleague at Hamburg Ernst Cassirer, the principal interpreter of Kant in the 1920s, Panofsky from 1915 on exhibits in his work ever more Kantian thinking and language.4 But Logos was not an art-historical review or one dedicated to aesthetics but a principal mainstream journal of the philosophy of culture. So ‘On the Problem of Describing and Interpreting Works of the Visual Arts’ has a good claim to be the culmination of Panofsky's philosophical thinking in his German period under the Weimar Republic. · 1. Erwin Panofsky, Studies in Iconology: Humanistic Themes in the Art of the Renaissance , p. xv; hereafter abbreviated SI. See Panofsky, ‘Zum Problem der Beschreibung und Inhaltsdeutung von Werken der bildenden Kunst’, Logos 21 : 103–19; trans. Jaś Elsner and Katharina Lorenz under the title ‘On the Problem of Describing and Interpreting Works of the Visual Arts’, Critical Inquiry 38 : 467–82; hereafter abbreviated ‘P’.· 2. See the discussion in Carlo Ginzburg, ‘From Aby Warburg to E. H. Gombrich: A Problem of Method’, Myths, Emblems, Clues, trans. John and Anne C. Tedeschi , pp. 17–59, esp. pp. 36–41.· 3. See Panofsky, ‘Das Problem des Stils in der bildenden Kunst’, Deutschsprachige Aufsätze, ed. Karen Michels and Martin Warnke, 2 vols. , 2:1009–18; ‘Der Begriff des Kunstwollens’,Deutschsprachige Aufsätze, 2:1019–34, trans. Kenneth J. Northcott and Joel Snyder under the title ‘The Concept of Artistic Volition’, Critical Inquiry 8 : 17–33; and ‘Über das Verhältnis der Kunstgeschichte zur Kunsttheorie: Ein Beitrag zu der Erörterung über die Möglichkeit kunstwissenschaftlicher Grundbegriffe’, Deutschsprachige Aufsätze, 2: 1035–63, trans. Lorenz and Elsner under the title ‘On the Relationship of Art History and Art Theory: Towards the Possibility of a Fundamental System of Concepts for a Science of Art’, Critical Inquiry 35 : 43–71.· 4. On neo-Kantianism in pre-Nazi Germany, see Michael Friedman, A Parting of the Ways: Carnap, Cassirer, and Heidegger , pp. 25–37; Éric Dufour and T. Z. R. Créteil, ‘Le Statue du singulier: Kant et le néokantisme de l’École de Marbourg', Kantstudien 93 : 324–50; Edward Skidelsky, Ernst Cassirer: The Last Philosopher of Culture , pp. 22–51; and Peter E. Gordon, Continental Divide: Heidegger, Cassirer, Davos , pp. 52–86. Specifically on the Cassirerian Kantianism of Panofsky, see Michael Podro, The Critical Historians of Art , pp. 181–82; Michael Ann Holly, Panofsky and the Foundations of Art History , pp. 91–92, 147–52; Silvia Ferretti, Cassirer, Panofsky, and Warburg: Symbol, Art, and History, trans. Richard Pierce , pp. 174–77, 182–84; David Summers, ‘Meaning in the Visual Arts as a Humanistic Discipline’, in Meaning in the Visual Arts: Views from the Outside, ed. Irving Lavin , pp. 9–24; Mark A. Cheetham, Kant, Art, and Art History: Moments of Discipline , pp. 68–77; Paul Crowther, The Transhistorical Image: Philosophizing Art and Its History , pp. 70–73; Allister Neher, ‘“The Concept of Kunstwollen”, Neo-Kantianism, and Erwin Panofsky's Early Art Theoretical Essays', Word and Image 20 : 41–51; Georges Didi-Huberman,Confronting Images: Questioning the Ends of a Certain History of Art, trans. John Goodman , pp. 4–6, 90–138; and Lorenz and Elsner, ‘Translators’ Introduction', Critical Inquiry35 : 33–42, esp. pp. 38, 40–42. (shrink)

This book about philosophical and methodological problems in psychoanalytic theory is surely one of the best pieces of literature on this subject of recent vintage. The author, a psychiatrist on the faculty of Harvard Medical School, displays considerable logical skill and philosophical sophistication, in addition to the expected familiarity with the psychoanalytic literature. The major purport of the book is a logical and philosophical defense of the claim that psychoanalytic explanations of human behavior--if constructed with proper and adequate regard for (...) relevant clinical data--are methodologically sound and genuinely scientific. One useful and novel feature of Sherwood's argument is the particular type of illustrative case material which he employs: instead of mustering various bits and instances of behavior from large numbers and varieties of cases, Sherwood considers the psychiatric explanation actually given by Freud in one of his recorded clinical case histories--the famous "Karl Lorenz" or "rat man" case. Sherwood devotes two chapters to a detailed description of this case, and an analysis of the logic of Freud's explanations of the behavior presented therein. From the point of view of logical and methodological considerations, there is an obvious advantage in such an approach, for it enables the critic to avoid leveling charges against the theory which might originate simply from extracting portions of explanatory material from their proper context. Sherwood also includes a chapter of criticism of what he calls "the thesis of the separate domain"--the view that there are fundamental differences in the logic of explanations of human behavior, cognition, and other phenomena involving reasons and intentions on the one hand, and other forms of explanation characteristic of the physical sciences, on the other. Philosophically, this is the most mature chapter of the book, and will be of interest to philosophers of mind, as well as philosophers of science, particularly for its criticism of the views of R. S. Peters. Unfortunately, however, Sherwood's argument is not unmarred by serious flaws and deficiencies. These include a highly psychologistic analysis of the logic and structure of explanation whose subsequent use repeatedly involves the author in context-of-discovery vs. context-of-justification confusions. Moreover, an apparent lapse into a non-Humean account of causality in the second section of the fifth chapter leads Sherwood to an unfortunate petitio principii on the issue of causes vs. reasons. Sherwood's critical discussion of the classical "covering-law" model of scientific explanation in the penultimate chapter exhibits numerous failures to come to grips with the essential aspects of the Braithwaite-Hempel-Oppenheim theory. Finally, an important sin of omission: Sherwood completely ignores the highly germane and decisive issues raised by authors such as Nagel and Arthur Pap, who charge the theoretical concepts of psychoanalysis with lack of cognitive and empirical significance. In sum, this is a flawed but eminently worthwhile book in the philosophy of behavioral science.--H. P. K. (shrink)

Summary In the first part of this contribution, the three probably most influential conceptions of evolutionary epistemology are surveyed, as they were put forward by Konrad Lorenz, Gerhard Vollmer, and Rupert Riedl, respectively. It is demonstrated that, as far as the essentials are concerned, these conceptions largely correspond with each other as well as with a further conception advanced by Karl Popper from the point of view of Critical Rationalism. It can be clearly shown, moreover, that fundamentals of the (...) latter conception can be traced back to Popper's earliest publications (e. g., to hisLogik der Forschung [The Logic of Scientific Discovery]). By means of an examination of the language used by these authors, it is tried to elucidate the fact that, for the reasons of lacking consideration of the lingual/non-lingual distinction and of faults and inadequacies in consequence of this lack alone, the proposed conceptions can be rejected as being at least highly defective. (shrink)

Duality in Logic and Language [draft--do not cite this article] Duality phenomena occur in nearly all mathematically formalized disciplines, such as algebra, geometry, logic and natural language semantics. However, many of these disciplines use the term ‘duality’ in vastly different senses, and while some of these senses are intimately connected to each other, others seem to be entirely … Continue reading Duality in Logic and Language →.

In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type (...) of logical diagrams, viz. duality diagrams. At a more fundamental level, we present a unifying perspective which sheds new light on the connections between new and existing metalogical diagrams, as well as between object- and metalogical diagrams. Overall, the paper studies two types of logical diagrams and four kinds of metalogical decorations. (shrink)

Die vorliegende Arbeit hat den Leibnizschen metaphysischen Optimismus und einige der weniger bekannten Stationen und Zuge der Rezeption der "Essais de Theodicee" und des Theorems von der besten Welt im deutschen 18. Jahrhundert zum Gegenstand. Sie erhebt nicht den Anspruch, eine auch nur annahernd vollstandige Darstellung des Verlaufes der Debatte um die "beste Welt" zu geben. Angesichts der Fulle der zeitgenossischen Einlassungen und Ausserungen zum Thema war eine Auswahl bestimmter Rezeptionsmomente vorzunehmen. Auf die Prozesse der Verwandlung einer strikt metaphysischen Theodizee (...) hin zu einem populareren, dafur aber auch anfechtbareren Optimismus will diese Arbeit ebenso hinweisen wie auf den Umstand, dass nicht erst die Kantische Schrift "Uber das Misslingen aller philosophischen Versuche in der Theodizee" von 1791 die (philosophische) Problematik der Lehre von der besten Welt dingfest macht. (shrink)

The aim of this paper is to initiate a systematic exploration of the model theory of epistemic plausibility models (EPMs). There are two subtly different definitions in the literature: one by van Benthem and one by Baltag and Smets. Because van Benthem's notion is the most general, most of the paper is dedicated to this notion. We focus on the notion of bisimulation, and show that the most natural generalization of bisimulation to van Benthem-type EPMs fails. We then introduce parametrized (...) bisimulations, and prove various bisimulationimplies- equivalence theorems, a Hennessy-Milner theorem, and several (un)definability results. We discuss the problems arising from the fact that these bisimulations are syntax-dependent (and thus not fully structural), and we present and compare two different ways of coping with this issue: adding a modality to the language, and putting extra constraints on the models. We argue that the most successful solution involves restricting to uniform and locally connected (van Benthem-type) EPMs: for this subclass the intuitively most natural notion of bisimulation and the technically sound notion coincide. Such EPMs turn out to correspond exactly with Baltag/Smets-type EPMs, which can be interpreted as constituting a methodological argument, favoring Baltag and Smets's definition of EPM over that of van Benthem. (shrink)

This paper studies the Lockean thesis from the perspective of contemporary epistemic logic. The Lockean thesis states that belief can be defined as ‘sufficiently high degree of belief’. Its main problem is that it gives rise to a notion of belief which is not closed under conjunction. This problem is typical for classical epistemic logic: it is single-agent and static. I argue that from the perspective of contemporary epistemic logic, the Lockean thesis fares much better. I briefly mention that it (...) can successfully be extended from single-agent to multi-agent settings. More importantly, I show that accepting the Lockean thesis (and a more sophisticated version for conditional beliefs) leads to a significant and unexpected unification in the dynamic behavior of (conditional) belief and high (conditional) probability with respect to public announcements. This constitutes a methodological argument in favor of the Lockean thesis. Furthermore, if one accepts Baltag’s Erlangen program for epistemology, this technical observation has even stronger philosophical implications: because belief and high probability display the same dynamic behavior, it is plausible that they are indeed one and the same epistemic notion. (shrink)

This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then (...) the strong analogy between Buridan's octagons starts to break down. These differences in Boolean structure can already be discerned within the octagons themselves; on a more abstract level, they lead to these two octagons having different degrees of Boolean complexity (i.e. Boolean closures of different sizes). These results are obtained by means of bitstring analysis, which is one of the key tools from contemporary logical geometry. Finally, I argue that this historical investigation is directly relevant for the theoretical framework of logical geometry, and discuss how it helps us to address certain open questions in this framework. (shrink)

In the recent debate on future contingents and the nature of the future, authors such as G. A. Boyd, W. L. Craig, and E. Hess have made use of various logical notions, such as the Aristotelian relations of contradiction and contrariety, and the ‘open future square of opposition.’ My aim in this paper is not to enter into this philosophical debate itself, but rather to highlight, at a more abstract methodological level, the important role that Aristotelian diagrams can play in (...) organizing and clarifying the debate. After providing a brief survey of the specific ways in which Boyd and Hess make use of Aristotelian relations and diagrams in the debate on the nature of the future, I argue that the position of open theism is best represented by means of a hexagon of opposition. Next, I show that on the classical theist account, this hexagon of opposition ‘collapses’ into a single pair of contradictory statements. This collapse from a hexagon into a pair has several aspects, which can all be seen as different manifestations of a single underlying change. (shrink)

This paper studies Aumann’s agreeing to disagree theorem from the perspective of dynamic epistemic logic. This was first done by Dégremont and Roy (J Phil Log 41:735–764, 2012) in the qualitative framework of plausibility models. The current paper uses a probabilistic framework, and thus stays closer to Aumann’s original formulation. The paper first introduces enriched probabilistic Kripke frames and models, and various ways of updating them. This framework is then used to prove several agreement theorems, which are natural formalizations of (...) Aumann’s original result. Furthermore, a sound and complete axiomatization of a dynamic agreement logic is provided, in which one of these agreement theorems can be derived syntactically. These technical results are used to show the importance of explicitly representing the dynamics behind the agreement theorem, and lead to a clarification of some conceptual issues surrounding the agreement theorem, in particular concerning the role of common knowledge. The formalization of the agreement theorem thus constitutes a concrete example of the so-called dynamic turn in logic. (shrink)

This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their (...) interplay turn out to be far more complicated. In particular, the paper describes an elegant and natural interaction between bitstrings and logic-sensitivity, which makes perfect sense when bitstrings are viewed as purely combinatorial entities. However, when we view bitstrings as semantically meaningful entities (which is actually the standard perspective, cf. the term ‘bitstring semantics’!), this interaction does not seem to have a full and equally natural counterpart. The paper describes some attempts to address this situation, but all of them are ultimately found wanting. For now, it thus remains an open problem to capture this interaction between bitstrings and logic-sensitivity from a semantic (rather than merely a combinatorial) perspective. (shrink)

This article describes a specific pedagogical context for an advanced logic course and presents a strategy that might facilitate students’ transition from the object-theoretical to the metatheoretical perspective on logic. The pedagogical context consists of philosophy students who in general have had little training in logic, except for a thorough introduction to syllogistics. The teaching strategy tries to exploit this knowledge of syllogistics, by emphasizing the analogies between ideas from metalogic and ideas from syllogistics, such as existential import, the distinction (...) between contradictories and contraries, and the square of opposition. This strategy helps to improve students’ understanding of metalogic, because it allows the students to integrate these new ideas with their previously acquired knowledge of syllogistics. (shrink)

The Sure-Thing Principle famously appears in Savage’s axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. In particular, we show that each of P2 and P3 is equivalent to a dominance condition; (...) that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage’s and the Anscombe- Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage’s axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance. (shrink)

In logic, Aristotelian diagrams are almost always assumed to be closed under negation, and are thus highly symmetric in nature. In linguistics, by contrast, these diagrams are used to study lexicalization, which is notoriously not closed under negation, thus yielding more asymmetric diagrams. This paper studies the interplay between logical symmetry and linguistic asymmetry in Aristotelian diagrams. I discuss two major symmetric Aristotelian diagrams, viz. the square and the hexagon of opposition, and show how linguistic considerations yield various asymmetric versions (...) of these diagrams. I then discuss a pentagon of opposition, which occupies an uneasy position between the square and the hexagon. Although this pentagon belongs neither to the symmetric realm of logic nor to the asymmetric realm of linguistics, it occurs several times in the literature. The oldest known occurrence can be found in the cosmological work of the 14th-century author Nicole Oresme. (shrink)

Burgess-Jackson has recently suggested that the debate between theism and atheism can be represented by means of a classical square of opposition. However, in light of the important role that the position of agnosticism plays in Burgess-Jackson’s analysis, it is quite surprising that this position is not represented in the proposed square of opposition. I therefore argue that the square of opposition should be extended to a slightly larger, more complex Aristotelian diagram, viz., a hexagon of opposition. Since this hexagon (...) does represent the position of agnosticism, it arguably yields a more helpful representation of the theism/atheism debate. It would be naïve to presume that Aristotelian diagrams can, by themselves, lead to a comprehensive solution of debates as intricate as that between theism and atheism. Nevertheless, this paper aims to show that these diagrams — especially if they are chosen carefully — have an important methodological role to play, by systematically organizing and clarifying the debate. (shrink)

In this paper, we consider certain cardinals in ZF (set theory without AC, the axiom of choice). In ZFC (set theory with AC), given any cardinals C and D, either C ≤ D or D ≤ C. However, in ZF this is no longer so. For a given infinite set A consider $\operatorname{seq}^{1 - 1}(A)$ , the set of all sequences of A without repetition. We compare $|\operatorname{seq}^{1 - 1}(A)|$ , the cardinality of this set, to |P(A)|, the cardinality of (...) the power set of A. What is provable about these two cardinals in ZF? The main result of this paper is that $ZF \vdash \forall A(|\operatorname{seq}^{1 - 1}(A)| \neq|\mathscr{P}(\mathscr{A})|)$ , and we show that this is the best possible result. Furthermore, it is provable in ZF that if B is an infinite set, then $|\operatorname{fin}(B)| <|\mathscr{P}(B)|$ even though the existence for some infinite set B* of a function f from $\operatorname{fin}(B^\ast)$ onto P(B*) is consistent with ZF. (shrink)

Several authors have recently studied Aristotelian diagrams for various metatheoretical notions from logic, such as tautology, satisfiability, and the Aristotelian relations themselves. However, all these metalogical Aristotelian diagrams focus on the semantic (model-theoretical) perspective on logical consequence, thus ignoring the complementary, and equally important, syntactic (proof-theoretical) perspective. In this paper, I propose an explanation for this discrepancy, by arguing that the metalogical square of opposition for semantic consequence exhibits a natural analogy to the well-known square of opposition for the categorical (...) statements from syllogistics, but that this analogy breaks down once we move from semantic to syntactic consequence. I then show that despite this difficulty, one can indeed construct metalogical Aristotelian diagrams from a syntactic perspective, which have their own, equally elegant characterization in terms of the categorical statements. Finally, I construct several metalogical Aristotelian diagrams that incorporate both semantic and syntactic consequence (and their interaction), and study how they are influenced by the underlying logical system’s soundness and/or completeness. All of this provides further support for the methodological/heuristic perspective on Aristotelian diagrams, which holds that the main use of these diagrams lies in facilitating analogies and comparisons between prima facie unrelated domains of investigation. (shrink)

For a set M, let \\) denote the set of all finite sequences which can be formed with elements of M, and let \ denote the set of all 2-element subsets of M. Furthermore, for a set A, let Open image in new window denote the cardinality of A. It will be shown that the following statement is consistent with Zermelo–Fraenkel Set Theory \: There exists a set M such that Open image in new window and no function Open image (...) in new window is finite-to-one. (shrink)

In order to elucidate his logical analysis of modal quantified propositions (e.g. ‘all men are necessarily mortal’), the 14th century philosopher John Buridan constructed a modal octagon of oppositions. In the present paper we study this modal octagon from the perspective of contemporary logical geometry. We argue that the modal octagon contains precisely six squares of opposition as subdiagrams, and classify these squares based on their logical properties. On a more abstract level, we show that Buridan’s modal octagon precisely captures (...) the interaction between two classical squares of opposition, viz. one for the quantifiers and one for the modalities. Finally, we argue that several aspects of our contemporary formal analyses were already hinted at by Buridan himself. (shrink)

If we assume the axiom of choice, then every two cardinal numbers are comparable, In the absence of the axiom of choice, this is no longer so. For a few cardinalities related to an arbitrary infinite set, we will give all the possible relationships between them, where possible means that the relationship is consistent with the axioms of set theory. Further we investigate the relationships between some other cardinal numbers in specific permutation models and give some results provable without using (...) the axiom of choice. (shrink)

For \(n\in \omega \), the weak choice principle \(\textrm{RC}_n\) is defined as follows: _For every infinite set_ _X_ _there is an infinite subset_ \(Y\subseteq X\) _with a choice function on_ \([Y]^n:=\{z\subseteq Y:|z|=n\}\). The choice principle \(\textrm{C}_n^-\) states the following: _For every infinite family of_ _n_-_element sets, there is an infinite subfamily_ \({\mathcal {G}}\subseteq {\mathcal {F}}\) _with a choice function._ The choice principles \(\textrm{LOC}_n^-\) and \(\textrm{WOC}_n^-\) are the same as \(\textrm{C}_n^-\), but we assume that the family \({\mathcal {F}}\) is linearly orderable (...) (for \(\textrm{LOC}_n^-\) ) or well-orderable (for \(\textrm{WOC}_n^-\) ). In the first part of this paper, for \(m,n\in \omega \) we will give a full characterization of when the implication \(\textrm{RC}_m\Rightarrow \textrm{WOC}_n^-\) holds in \({\textsf {ZF}}\). We will prove the independence results by using suitable Fraenkel-Mostowski permutation models. In the second part, we will show some generalizations. In particular, we will show that \(\textrm{RC}_5\Rightarrow \textrm{LOC}_5^-\) and that \(\textrm{RC}_6\Rightarrow \textrm{C}_3^-\), answering two open questions from Halbeisen and Tachtsis (Arch Math Logik 59(5):583–606, 2020). Furthermore, we will show that \(\textrm{RC}_6\Rightarrow \textrm{C}_9^-\) and that \(\textrm{RC}_7\Rightarrow \textrm{LOC}_7^-\). (shrink)

For an integer \, Ramsey Choice\ is the weak choice principle “every infinite setxhas an infinite subset y such that\ has a choice function”, and \ is the weak choice principle “every infinite family of n-element sets has an infinite subfamily with a choice function”. In 1995, Montenegro showed that for \, \. However, the question of whether or not \ for \ is still open. In general, for distinct \, not even the status of “\” or “\” is known. (...) In this paper, we provide partial answers to the above open problems and among other results, we establish the following:1.For every integer \, if \ is true for all integers i with \, then \ is true for all integers i with \.2.If \ are any integers such that for some prime p we have \ and \, then in \: \ and \.3.For \, \\\ implies \, and \ implies neither \ nor \ in \.4.For every integer \, \ implies “every infinite linearly orderable family of k-element sets has a partial Kinna–Wagner selection function” and the latter implication is not reversible in \ ). In particular, \ strictly implies “every infinite linearly orderable family of 3-element sets has a partial choice function”.5.The Chain-AntiChain Principle implies neither \ nor \ in \, for every integer \. (shrink)

Excerpt from Die Kunst der Rechtsanwendung: Zugleich ein Beitrag zur Methodenlehre der Geisteswissenschaften Eine hnliche Definition der Philosophie geben Wundt ("system der Philosophie, S. 21) und Friedrich Paulsen, ("einleitung in die Philo sophie, S. W hrend Riehl ("philosophie der Gegenwart, S. 23) die Phi1030phie mit der Erkenntnistheorie indentif'rziert. Wesentlich enger fa t auch Windelband die Philosophie, indem er sie als die kritische Wissenschaft von den allgemeing ltigen Werten definiert, S. 1-irrtumer geworden. Daher unterscheidet sich die Philosophie im weiteren Sinne weder (...) im Objekt noch in der Methode von den positiven Einzelwissenschaften, vielmehr kann man alle Theorie als philosophisch bezeichnen, welche nicht im blo en empiristischen Kleinkram befangen bleibt, sondern sich der Einheit und des Zusammenhangs alles Wissens bewu t ist.1) Gew hnlich werden die theoretischen Disziplinen in Natur und Geisteswissenschaften eingeteilt. Hiernach haben die letz teren es mit der Erforschung des Seelenlebens zu tun, w hrend die ersteren die r umlichen Objekte betrachten. Neuerdings ist von Windelband in seiner Rede ber Geschichte und Natur wissenschaft und von Rickert in seinem Vortrag ber "kultur wissen schaft und Naturwissenschaft ein abweichender Ge sichtspunkt zur Klassifikation benutzt worden. Die genannten Autoren unterscheiden die sogenannten Gesetzeswissenschaften, denen es ausschlie lich um die Auffindung m glichst exakter Regeln zu tun ist, von den historischen Wissenschaften, denen die Schilderung des Einmaligen und Einzigartigen am Herzen liegt. Die Hervorhebung dieses Moments ist zweifellos sehr verdienstlich und fruchtbringend. Man darf aber nicht uber sehen, da sich diese Einteilung mit der alteren in "natur und Geisteswissenschaften kreuzt, denn es gibt sowohl nomotheti sche Geisteswissenschaften, wie vor allem die exakte Psycho logie als N aturwissenschaften, die auch idiographisch vorgehen, wie die Astronomie, wenn sie Mondgebirge und Sonnenflecken schildert, oder die Geologie, oder die Biologie, die von der Ent wicklung der Erde und ihrer Organismen berichten. Daher ist es verwirrend, wenn Rickert (s. 46) diejenigen Wissenschaften, deren Inhalt sich auf ein Besonderes und Individuelles bezieht, als Kulturwissenschaften bezeichnet, denn es ist nicht notwendig, da die idiographisch verfahrenden Disziplinen Werte oder Kulturbestrebungen als Objekte ins Auge fassen. Freilich mu die Darstellung des Individuellen und Einmaligen einen Wert besitzen, denn sonst w rde sich niemand mit ihnen besch ftigen. Aber das gleiche gilt von den nomothetischen Wissenschaften. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)