It has recently been argued that some cases of naked statistical evidence license a high credence, but not an outright belief. If this is correct, there cannot be an unconditional bridge principle from credence to outright belief. We show that at least one prominent putative counterexample to such a bridge principle is based on a mistake, by demonstrating that the statistical evidence falls short not only of licensing rational belief, but also of justifying a high credence.

The paper investigates the prospects of Spohn’s ranking theory with respect to Goodman’s New Riddle of Induction. Based on a novel analysis of the riddle (Freitag [manuscript]), we show it to be an inductive extension of Hansson’s puzzle (Hansson 1992, 1999). As a consequence, a solution needs to take into account the dependence relations between evidential beliefs: “grue” is unprojectible because it depends on evidence whose projection is defeated. It will be suggested that this solution can be implemented into Spohn’s (...) ranking theory, but that ranking theory is unable to provide a proper explanation of the required conditional ranks. (shrink)

We investigate a construction schema for first-order logical systems, called “form logic”. Form logic allows us to overcome the dualistic commitment of predicate logic to individual constants and predicates. Dualism is replaced by a pluralism of terms of different “logical forms”. Individual form-logical systems are generated by the determination of a range of logical forms and of the formbased syntax rules for combining terms into formulas. We develop a generic syntax and semantics for such systems and provide a completeness proof (...) for them. To illustrate the idea of form logic, and the possibilities it facilitates, we discuss three particular systems, one of which is the form-logical reconstruction of standard first-order predicate logic. (shrink)

This collection includes twenty original philosophical essays in honour of Wolfgang Spohn. The contributions mirror the scope of Wolfgang Spohn’s work. They address topics from epistemology (e.g., the theory of ranking functions, belief revision, and the nature of knowledge and belief), philosophy of science (e.g., causation, induction, and laws of nature), the philosophy of language (e.g., the theory of meaning and the semantics of counterfactuals), and the philosophy of mind (e.g., intentionality and free will), as well as problems (...) of ontology, logic, the theory of practical rationality, and meta-philosophy. ― Contributors: Ansgar Beckermann, Wolfgang Benkewitz, Bernd Buldt, Ralf Busse, Christoph Fehige, Wolfgang Freitag, Gordian Haas, Volker Halbach, Franz Huber, Andreas Kemmerling, Manfred Kupffer, Hannes Leitgeb, Godehard Link, Arthur Merin, Thomas Müller, Julian Nida-Rümelin, Martine Nida-Rümelin, Hans Rott, Holger Sturm, Thomas Ede Zimmermann, Alexandra Zinke. (shrink)

Kant's theory of cognition centrally builds on his conception of self‐consciousness and the transcendental use of the phrase “I think”: the ability to add the phrase “I think” to a representation is a necessary condition of the ability to cognize objects. The paper argues that “I think”, rather than denoting the content of a predicative judgement, is typically an expression of the subject's thinking. It expresses a kind of self‐consciousness that, without assertively representing the subject itself, indicates that representational contents (...) are unified in a single consciousness of a single subject. Our aim is thus to develop and defend an expressivist interpretation of Kant's “I think”. (shrink)

One of the main controversies of the Logic Schools of the 12th century centered on the question: What follows from the impossible? In this paper arguments for two diametrically opposed positions are examined. The author of the ‘Avranches Text’ who probably belonged to the school of the Parvipontani defended the view that from an impossible proposition everything follows (‘Ex impossibili quodlibet’). In particular he developed a proof to show that by means of so-called ‘disjunctive syllogism’ any arbitrary proposition B can (...) be logically derived from a pair of contradictory propositions A and Not-A. The author of the Ars Meliduna instead argued that nothing follows from an impossible proposition (‘ex falso nihil sequitur’). This view is supported by various counterexamples which aimed to show that the admission of impossible premises would give rise to inconsistent conclusions. Upon closer analysis these inconsistencies do not, however, have the formal structure of a real contradiction like A and Not-A, but rather the structure of two rivalling conditionals like ‘If B then A’ and ‘If B then Not-A’. Hence these counterexamples rather have to be considered as refutations of the basic principles of ‘connexive logic’. (shrink)

Die Hypothese meines Beitrags ist, dass Interpretationen fiktionaler Romane zum Teil rationale Erklärungen der emotionalen Zustände fiktiver Romanfiguren sein sollten. Der Hintergrund dieser Hypothese ist zum einen die generelle Definition von Interpretationen als rationalen Erklärungen und zum anderen die neue Theorie der affektiven Intentionalität von Gefühlen (eine Variante der kognitiven Gefühlstheorie). Diese Theorie unterscheidet mehrere Komponenten von Gefühlen und weist nach, dass eine überwiegend rationale Vernetzung dieser Komponenten eine notwendige Bedingung für ihre Interpretation ist (Abschnitt 1). Dieser methodische Zugriff lässt (...) sich an geeigneten Romanen testen und verifizieren, beispielsweise an Flauberts 'Madame Bovary' – einer fiktionalen Geschichte, die sich als eine einzige komplexe und verkettete rationale Erklärung der suizidalen Verzweiflung Emmas deuten lässt. Das bedeutet allerdings nicht, dass eine solche rationale Erklärung die Interpretation fiktionaler Romane ausschöpft. Vielmehr lassen sich fünf verschiedene, ineinandergreifende Stufen von Romaninterpretationen unterscheiden (Abschnitt 2). Gerade wenn Literaturinterpretationen eine komplexe Form annehmen, wird das bekannte Paradox virulent, dass wir uns bemüßigt fühlen, komplexe Interpretationen der Emotionen und Handlungen von Figuren zu liefern, die nicht existieren. In neueren Arbeiten zeichnet sich eine primär psychologische Lösung dieses Paradoxes ab. Zu dieser Lösung gehört der Befund, dass das Bemühen um rationale Erklärungen fiktiver Figuren unsere Fähigkeit, reale Personen in unserem sozialen Umfeld, aber auch in fremden Kulturen angemessen zu interpretieren, in erstaunlichem Ausmaß fördert. (shrink)

What is an image? An image, it might be said, is a kind of amity between the medium and the model it assumes. The purpose of this relationship is to reproduce the model and to become similar to it. Such a definition invites – perhaps in a purely playful way – some preliminary considerations.

The intervention of the divine in human history, more precisely the transition from fiction to incarnation that is peculiar to the origins of Christianity, marks a turning-point in our understanding of the genealogical principle. With a Son of Man who is also Son of God and his Mother's Father, there is no paternity and, more generally, no genealogy that is not reversible. To this questioning of elementary kinship structures we should add the contesting of the hitherto accepted distribution of genders (...) and sexes. The superimposition of the Holy Family and the Trinity created an uncertain sex whose effect is to uncouple sex from its functions, in particular procreation. Hence a circulation and instability of sex. It is from this viewpoint that we should see the notion of an androgynous Christ and the Church Fathers' thinking on the resurrected body. (shrink)

The respectably legitimate offspring of an age-old affair between writing and picture-making, the calligramme — that is, “a poem in which the typographical layout creates a picture, generally related to the ‘subject’ of the text” (Dictionnaire des littératures, Larousse) — is often seen as an esoteric minority art of dubious reputation. Starting from an exclusively Western approach to the history of the calligramme, my aim is to demonstrate that this artform may in fact represent something more than simply (here I (...) deliberately use a metaphor from the far east, as a counterargument to my theme) the “Kyogen of the No theatre” — i.e., more than a lightweight interlude between more literary, aesthetic, even metaphysical preoccupations — more elevated, more serious, or, in general terms, more extended. Apart from the play and the pleasure of an approach that is creative in terms of letters and language, it contains serious elements related to the actual exercise of writing in our media civilization. (shrink)

We define classes Φnof formulae of first-order arithmetic with the following properties:(i) Everyφϵ Φnis classically equivalent to a Πn-formula (n≠ 1, Φ1:= Σ1).(ii)(iii)IΠnandiΦn(i.e., Heyting arithmetic with induction schema restricted to Φn-formulae) prove the same Π2-formulae.We further generalize a result by Visser and Wehmeier. namely that prenex induction within intuitionistic arithmetic is rather weak: After closing Φnboth under existential and universal quantification (we call these classes Θn) the corresponding theoriesiΘnstill prove the same Π2-formulae. In a second part we consideriΔ0plus collection-principles. We (...) show that both the provably recursive functions and the provably total functions ofare polynomially bounded. Furthermore we show that the contrapositive of the collection-schema gives rise to instances of the law of excluded middle and hence. (shrink)

This article discusses the history of the concepts of potential infinity and actual infinity in the context of Christian theology, mathematical thinking and metaphysical reasoning. It shows that the structure of Ancient Greek rationality could not go beyond the concept of potential infinity, which is highlighted in Aristotle's metaphysics. The limitations of the metaphysical mind of ancient Greece were overcome through Christian theology and its concept of the infinite God, as formulated in Gregory of Nyssa's theology. That is how the (...) concept of actual infinity emerged. However, Gregory of Nyssa's understanding of human rationality went still further. He said that access to the infinity of God was to be found only in an asymptotic ascension, as expressed in apophatic theology, and this view endangered the rationality of theology. Deeply influenced by the apophatic tradition, Nicholas of Cusa avoided this danger by showing that infinity could be accessed by symbolic representation and asymptotic mathematical reasoning. Thus, he made an immense contribution in making infinity rationally accessible. This endeavor was finally realized by Georg Cantor. This rational accessibility revealed discernible structures of infinity, such as the continuum hypothesis, and the cardinal numbers. However, the probable logical inconsistency of Georg Cantor's all-encompassing Absolute Infinity points to an intuitive understanding of infinity that goes beyond its rational structures – as in apophatic theology. (shrink)

Wissenschaft ist nach Aristoteles eine spezielle Form des Wissens, das seinerseits ein bestimmter mentaler Zustand, aber auch als Wissensgehalt der Gegenstand oder Inhalt epistemischer Zustände ist. Erkenntnistheoretische Priorität hat jedoch Wissen als Gehalt: Ob eine Person im Zustand des Wissens ist, hängt davon ab, ob ihr ein Wissensgehalt in bestimmter Form präsent ist.

Aristoteles hat seine Lehrschriften sicherlich sowohl als Vorlesungsmanuskripte für seine Schüler als auch für ein abstraktes Publikum und für die Nachwelt geschrieben. Denn wir finden sowohl Bezugnahmen auf seine Hörer als auch Bemerkungen, die einzelne seiner Thesen selbstbewusst im positiven Sinne mit der Leistung der Vorgänger vergleichen und in einen historischen Zusammenhang stellen, was nur sinnvoll ist, wenn der Vergleich von außen nachvollzogen warden konnte. Wieweit einzelne Schriften zu seinen Lebzeiten in Umlauf kamen, ist unbekannt.

Rudolf Carnap was born on May 18, 1891, and Hans Reichenbach on September 26 in the same year. They are two of the greatest philosophers of this century, and they are eminent representatives of what is perhaps the most powerful contemporary philosophical movement. Moreover, they founded the journal Erkenntnis. This is ample reason for presenting, on behalf of Erkenntnis, a collection of essays in honor of them and their philosophical work. I am less sure, however, whether it is a good (...) time for resuming their philosophical impact; their work still is rather part than historical basis of the present philosophical melting-pot. Their basic philosophical theses have currently, it may seem, not so high a standing, but their impact can be seen in numerous detailed issues; they have opened or pushed forward lively fields of research which are still very actively pursued not only within philosophy, but also in many neighboring disciplines. Whatever the present balance of opinions about their philosophical ideas, there is something even more basic in their philosophy than their tenets which is as fresh, as stimulating, as exemplary as ever. I have in mind their way of philosophizing, their conception of how to do philosophy. It is always a good time for reinforcing that conception; and if this volume would manage to do so, it would fully serve its purpose. (shrink)

The subject of this paper is a characterization of the $\Sigma_1$ -definable set functions of Kripke-Platek set theory with infinity and a uniform version of axiom of choice: $KP\omega+(uniform\;AC)$ . This class of functions is shown to coincide with the collection of set functionals of type 1 primitive recursive in a given choice functional and $x\mapsto\omega$ . This goal is achieved by a Gödel Dialectica-style functional interpretation of $KP\omega+(uniform\;AC)$ and a computability proof for the involved functionals.

The core idea of the ontological proof is to show that the concept of existence is somehow contained in the concept of God, and that therefore God’s existence can be logically derived—without any further assumptions about the external world—from the very idea, or definition, of God. Now, G.W. Leibniz has argued repeatedly that the traditional versions of the ontological proof are not fully conclusive, because they rest on the tacit assumption that the concept of God is possible, i.e. free from (...) contradiction. A complete proof will rather have to consist of two parts. First, a proof of premiseGod is possible. Second, a demonstration of the “remarkable proposition”If God is possible, then God exists. The present contribution investigates an interesting paper in which Leibniz tries to prove proposition. It will be argued that the underlying idea of God as a necessary being has to be interpreted with the help of a distinguished predicate letter ‘E’ as follows:\\). Proposition which Leibniz considered as “the best fruit of the entire logic” can then be formalized as follows:\) \rightarrow \, E)\). At first sight, Leibniz’s proof appears to be formally correct; but a closer examination reveals an ambiguity in his use of the modal notions. According to, the possibility of the necessary being has to be understood in the sense of something which possibly exists. However, in other places of his proof, Leibniz interprets the assumption that the necessary being is impossible in the diverging sense of something which involves a contradiction. Furthermore, Leibniz believes that an »impossible thing«, y, is such that contradictory propositions like \\) and \\) might both be true of y. It will be argued that the latter assumption is incompatible with Leibniz’s general views about logic and that the crucial proof is better reinterpreted as dealing with the necessity, possibility, and impossibility of concepts rather than of objects. In this case, the counterpart of turns out to be a theorem of Leibniz’s second order logic of concepts; but in order to obtain a full demonstration of the existence of God, the counterpart of, i.e. the self-consistency of the concept of a necessary being, remains to be proven. (shrink)

Analogical reasoning addresses the question how evidence from various phenomena can be combined and made relevant for theory development and prediction. In the first part of my contribution, I review some influential accounts of analogical reasoning, both historical and contemporary, focusing in particular on Keynes, Carnap, Hesse, and more recently Bartha. In the second part, I sketch a general framework. To this purpose, a distinction between a predictive and a conceptual type of analogical reasoning is introduced. I then take up (...) a common intuition according to which analogical inferences hold if the differences between source and target concern only irrelevant circumstances. I attempt to make this idea more precise by addressing possible objections and in particular by specifying a notion of causal irrelevance based on difference making in homogeneous contexts. (shrink)